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APL-UW High-FrequencyOcean Environmental Acoustic Models

Handbook

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ELECTEJUN 0 8 1995

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APL-UW High-FrequencyOcean Environmental Acoustic Models

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DESTRUCTION NOTICE: - For classified documents follow Technicalthe procedures in DoD 5220.22-M, Industrial Security Manual, ReportSection 11-19 or DoD 5200.1-R, Information Security Program APL-UW TR 9407Regulation, Chapter IX. For unclassified, limited documents,destroy by any method that will prevent disclosure of contentsor reconstruction of the document. AEAS 9501

October 1994

Applied Physics Laboratory University of Washington1013 NE 40th Street Seattle, Washington 98105-6698

Contract N00039-9 1 -C-0072

ACKNOWLEDGMENTS

This report was sponsored by the Advanced Environmental Acoustic Support Pro-

gram of the Office of Naval Research, Code 322TE, with technical management by Barry

Blumenthal. Funding was provided through the APL-UW omnibus contract with the

Space and Naval Warfare System Command, N00039-91-C-0072.

UNIVERSITY OF WASHINGTON ° APPLIED PHYSICS LABORATORY

ABSTRACT

This report updates several high-frequency acoustic models used in simulations and

system design by Navy torpedo and mine countermeasure programs. The models

presented augment and supersede those given previously in APL-UW technical note 7-79

(August 1979) and its successors, APL-UW technical reports 8407 and 8907. The report

addresses the interaction of high-frequency acoustic energy with the ocean's volume, sur-

face, bottom, and ice. It also addresses ambient noise generated by physical processes at

the ocean surface and by biological organisms. The results are given in a form that can be

exploited in simulations. The relevant fundamental experimental and theoretical

research by APL and others upon which these models are based is available in the refer-

ences.

i

TR 9407 iii

UNIVERSITY OF WASHINGTON APPLIED PHYSICS LABORATORY

TABLE OF CONTENTS

Page

IN TR O D U C TIO N ................................................................................................. 1

A. BACKGROUND AND HISTORY ............................................................ 1

B. GUIDE FOR QUICK ENGINEERING ASSESSMENTCALCULATIONS ....................................................................................... 2

C. IMPLEMENTATION SOFTWARE ........................................................ 6

I. VOLUME

A. SPEED OF SOUND IN SEAWATER ........................................................ I-1

1. Chen-Millero-Li Equation .................................................................. I-1

2. MacKenzie Equation ........................................................................... 1-2

3. C haracteristics ...................................................................................... 1-3

4 . C om parisons ......................................................................................... 1-3

B. ABSORPTION COEFFICIENT ................................................................. 1-5

C. BACKSCATTERING .................................................................................. 1-12

1. Introduction .......................................................................................... 1-12

2. D eep O pen O cean ................................................................................ 1-14

3. Shallow W aters .................................................................................... 1-17

4. Ice-C overed R egions ........................................................................... 1-21

5. Spectral Spreading ............................................................................... 1-21

R eferences ............................................................................................................ 1-23

H. SURFACE

Introduction ........................................................................................................... 111-1

A. WIND SPEED AND SEA STATE .............................................................. 11-2

B. BACKSCATTER ......................................................................................... 11-5

1. Scattering from Bubbles ...................................................................... 11-6

2. Scattering from Sea Surface Roughness ............................................ 11-7

a. Scattering from small-scale roughness .................. 11-7b. Scattering from facets ............................................................... 11-8c. Interpolation between the scy and aTf cross sections ............... 11-9

3. Total Surface Backscattering Strength ayr + Cyb ................................. 11-10

4. Model/Data Comparisons .................................................................... 11-10

iv TR 9407

UNIVERSITY OF WASHINGTON • APPLIED PHYSICS LABORATORY

5. Model Implementation Notes and Model Accuracy ......................... 11-15

a. Implementation .......................................................................... 11-15b . A ccuracy .................................................................................... 11-15

6. Spectral Spread .................................................................................... 11-16

C. FORWARD LOSS ....................................................................................... 11-19

1. Introduction .......................................................................................... 11- 19

2. Preliminary Discussion ........................................................................ 11-19

3. Effective Reflection Loss for Forward Scattering inReverberation Simulations .................................................................. 11-20

4. Absorption Due to Near-Surface Bubbles ......................................... 11-21

a. Depth-dependent formulation of the SBL model .................... 11-24b. Recommended version based on a linear sound speed

profi le ......................................................................................... 11-25

5. Model Usage Notes and Accuracy ..................................................... 11-26

a. Model usage notes ..................................................................... 11-26b. Model accuracy ......................................................................... 11-27

6. Coherent Reflection Loss .................................................................... 11-28

7. Time-Dependent Intensity and Frequency Coherence in ForwardScattering .............................................................................................. 11-29

a. Time-dependent intensity ......................................................... 11-29b. Frequency coherence ................................................................ 11-32

8. Frequency Spreading ........................................................................... 11-33

9. S tatistics ................................................................................................ 11-33

D. AMBIENT NOISE ....................................................................................... 11-34

1. Ambient Noise Multipath Expressions ............................................... 11-34

2. Simplified Expressions for Isovelocity, Deep Water Conditions ..... 11-39

3. Surface Radiation Pattern (N) ............................................................. 11-40

4. Noise Level at the Air/Sea Interface at Normal Incidence (A),W ind Effects ......................................................................................... 11-40

5. Noise Level at the Air/Sea Interface at Normal Incidence (A),Combined W ind and Rain Effects ....................................................... 11-42

6. Sum m ary ............................................................................................... 11-45

R eferences ............................................................................................................ 11-48

TR 9407 v

-UNIVERSITY OF WASHINGTON APPLIED PHYSICS LABORATORY

III. BIOLOGICAL HIGH-FREQUENCY AMBIENT NOISE

A . B A C K G R O U N D ......................................................................................... II-i1

B. GENERALIZED FREQUENCY DISTRIBUTION .................................. 111-1

C. GENERALIZED MARINE MAMMAL AMBIENT NOISE ................... 111-2

D. GENERALIZED SNAPPING SHRIMP LEVELS .................................... 111-3

E. OTHER INVERTEBRATE NOISE SOURCES ........................................ 111-8

R eferences ............................................................................................................ 111-10

B ibliography ......................................................................................................... 111-10

IV. BOTTOM

Introduction .......................................................................................................... IV -1

A. MODEL INPUT PARAMETERS .............................................................. IV-2

1. Comments on Geoacoustic Modeling ................................................. IV-3

2. Definition of Model Input Parameters ................................................ IV-4

3. Table for Model Parameters in Terms of Sediment Name ................ IV-5

4. Model Input Parameters Using Grain Size .................... IV-7

5. Model Input Parameters Using Geoacoustic Data ............................. IV-1 1

6. Refinement of Input Parameters Using B ackscattering Data ........... IV- 13

7. Use of Bottom Roughness Data .......................................................... IV-14

8. Limits on Model Parameters ............................................................... IV- 17

B . FO R W A R D LO SS ....................................................................................... IV -18

1. Statement of the Forward Loss Model ................................................ IV- 18

2. M odel A ccuracy ................................................................................... IV -19

3. N um erical Considerations ................................................................... IV -21

C . B A C K SC AT IER ......................................................................................... IV -21

1. Introduction .......................................................................................... IV -2 1

2. Equations for Bottom Backscattering Strength ................................. IV-22

a. Roughness scattering cross section, cr(O) .............................. IV-26Kirchhoff Approximation ....................................................... IV-27 IComposite Roughness Approximation .................................. IV-28Large-Roughness Scattering Cross Section ......................... IV-31Interpolation Between Approximations ............................... IV-32

b. Sediment volume scattering cross section, av(0) .......... IV-33

3. M odel A ccuracy................................................................................... IV -35

4. N um erical Considerations ................................................................... IV -36

vi TR 9407

UNIVERSITY OF WASHINGTON. APPLIED PHYSICS LABORATORY

D. BISTATIC SCATTERING .......................................................................... IV-37

1. M odel Inputs ........................................................................................ IV -38

2. Equations for Bottom Bistatic Scattering Strength ........................... IV-43

a. Definition of geometric parameters ......................................... IV-44b. Roughness scattering cross section .......................................... IV-45

Kirchhoff Approximation ....................................................... IV-45Perturbation Approximation ................................................. IV-46Interpolation Between Approximations ............................... IV-47

c. Sediment volume scattering cross section ............................... IV-47

3. M odel A ccuracy ................................................................................... IV -48

4. Numerical Considerations ................................................................... IV-49

R eferences .............................................................................................................. IV -50

V. ARCTIC

Introduction .......................................................................................................... . V -1

A. SOUND SPEED AND ATTENUATION ................................................... V-2

1. Vertical Sound Speed as a Function of Salinity and Temperature ... V-2

2. Average Longitudinal Sound Speed as a Function of Thicknessand Air/Ice Interface Temperature ...................................................... V-4

3. Attenuation as a Function of Temperature .................... V-6

B. SCATTERING AND FORWARD ENERGY LOSS FROMU N R ID G ED IC E ......................................................................................... V -6

1. Forw ard Scattering ............................................................................... V -6

a. E nergy loss ................................................................................. V -6b. Scattering coefficient ................................................................ V-8c. Time-dependent intensity after forward scattering ................. V-9

2. Near Normal Incidence ....................................................................... V-10

a. Unridged ice amplitude "reflection" coefficient ................... V-10b. Scattering from an ice block ................................................... V-11

3. Low Angle Backscatter ...................................................................... V-12

C . IC E K E E L S .................................................................................................. V -15

1. Formation of Ridges ........................................................................... V- 15

2. R idge Structure .................................................................................... V -15

3. K eel Statistics ....................................................................................... V -16

TR 9407 vii

UNIVERSITY OF WASHINGTON , APPLIED PHYSICS LABORATORY

D. ICE KEEL REFLECTIONS ....................................................................... V-18

1. Point-Like Nature ................................................................................ V-i8

2. Reflector Density ................................................................................. V-18

3. Response Pattern .................................................................................. V-20

4. Frequency Dependence ....................................................................... V-20

5. M odeling of Ice Keels ......................................................................... V-22

References ............................................................................................................ V-26

viii TR 9407

Introduction


A. BACKGROUND AND HISTORY

This report is a revision of APL-UW TR 8907 and provides an up-to-date record of

the environmental acoustic models used in simulation studies at the Applied Physics

Laboratory, University of Washington. The report addresses the interaction of sound

with the ocean's volume, surface, bottom, and ice and discusses ambient noise generated

by processes at the ocean surface and by biological organisms.

The document is divided into five sections:

Volume (sound speed, attenuation, backscattering),

Surface (sea state, backscatter, forward loss, ambient noise),

Biological Ambient Noise (general frequency distributions, noise levels of snap-

ping shrimp, other invertebrate noise sources),

Bottom (model inputs, forward loss, backscatter, bistatic scatter),

Arctic (sound speed and attenuation [in ice], scattering and energy loss from

unridged ice, ice keels, ice keel reflections).

As an aid to the users of previous versions of this document, a synopsis of changes found

in each section is given below.

Volume: The order of preference for sound-speed models has changed. Argu-

ments for the order are given; however, several models are still listed as possibilities, and

the final decision is left to the user. The backscatter model gives more detailed regional

recommendations.

Surface: The backscatter model has undergone significant revision, including

notational changes. The general form now consists of two terms: Ob, or the scattering

due to bubbles, and (r, or the scattering due to interface roughness. Both of these terms

are estimated by submodels which have also been revised. The forward loss model has

been revised to include a wind-speed dependent threshold for wave breaking and

TR 9407 1


subsequent production of bubbles, and different wind-speed and frequency dependencies.

This model assumes isovelocity conditions in the upper 10 m of water. An alternate ver-

sion is also available for general sound-speed profiles and accommodates ray vertexing

near the surface. Minor changes have been made in the model for the time spread in for-

ward scattering. There have been changes in the coefficients in the ambient noise model

that depend on wind speed and rain rate. The model assumes the same form as the previ-

ous version, however, and therefore can be easily adapted.

Biological Ambient Noise: This is a completely new section. Its primary

emphasis is on the distribution, levels, and spectra of ambient noise caused by snapping

shrimp. This ambient noise source can dominate all others in some shallow water

environments.

Bottom: The forward loss and backscattering models are unchanged. The bistatic

model is new; however, many of the parameters used to drive the model are the same as

those for the forward loss and backscattering models. The bistatic model is capable of

treating all scattering geometries, including forward and backscattering. Thus, if desired,

the user can replace the forward loss and backscattering models by this one bistatic

scattering model. It is important to note that the results obtained using the bistatic model

in the forward and backward directions are consistent with the forward loss and back-

scattering models.

Arctic: New equations are given for sound speed and attenuation in ice. A for-

ward scattering model is given that uses the same high-frequency approximation used in

the "Surface" section. This allows calculation of the pulse elongation seen when an

acoustic signal is forward scattered off nonridged ice.

B. GUIDE FOR QUICK ENGINEERING ASSESSMENT

CALCULATIONS

This guide is intended to allow quick access to equations useful in preliminary assess-

ment calculations so that the engineer/scientist can perform overview calculations (e.g., the

sonar equation) without undue delay. In this guide, the reader is directed, by page number,

2 TR 9407


to specific equations and figures that can be used in such calculations. Some users may find

it useful to compile the appropriate pages in a quick reference document.

1. Volume

Speed of Sound in Water

Use the Mackenzie equation on page 1-3.

Absorption Coefficient in Water

Use Table 2 beginning on page 1-8. This table is for zero depth. It can be used to

100-m depth with negligible error. It gives attenuation values at temperatures and

salinities most often seen in the ocean.

Backscattering

Deep Ocean

Use values given in the first two paragraphs on page 1-16.

Shallow Water (less than 200 m deep)

Use values as described on page 1-19 in the first paragraph and in the following

paragraphs that continue on page 1-21.

Ice Covered Regions

Use value given on page 1-21.

2. Surface

Backscattering

For frequencies between 15 and 35 kHz, Figure 2a on page 11-11 gives useful backscat-

tering strengths as a function of angle for wind speeds from 3 to 15 m/s. Likewise, Fig-

ure 2b (page 11-11) can be used to determine backscattering from 50 to 70 kHz. As

indicated by Figure 1 on page 11-5, over 80% of oceanic winds fall within this 3 to

15 m/s wind-speed window. For other conditions, Eqs. 1-16 on pages 11-5 to 11-10

must be used.

TR 9407 3

UNIVERSITY OF WASHINGTON , APPLIED PHYSICS LABORATORY

Spectral Spread in Backscattering

Use Figure 9 on page II-18 to estimate the normalized spread (Eq. 19 on page II-16) as

a function of rms wave height. Wave height is related to wind speed by Eq. 22 on page

II-17. Figure 9 is for a grazing angle of 60' and an up/down wave direction. For other

conditions, use Eqs. 19-24 on pages 11-16 and 11-17.

Forward Loss

Use Eq. 27 on page 11-20 along with the definition of SBL(dB) in Eq. 28 on page 11-21

to calculate forward loss as a function of wind speed and grazing angle.

Time Dependence of Forward Scattered Energy

This is for cases where the pulse elongation seen in the forward scattered signal is

important (in addition to the forward loss). Use Eqs. 40-42 on pages 11-29 and 11-30.

Compare results with Figure 14 on page 11-32.

Frequency Spreading Associated with Forward Scattering

Use Eq. 43a on page 11-33.

Ambient Noise in Isovelocity Deep Water- Without Rain

Use curves of Figure 17a on page 11-43 that are associated with Eq. 53. That figure

shows the pressure received at an omnidirectional hydrophone as a function of fre-

quency for sea states 0 to 6. Use Table 2 on page 11-4 to relate wind speed to sea state.

Ambient Noise in Isovelocity Deep Water - With Rain

Use Figure 18a on page 11-46 to bound ambient noise levels for sea states between 0

and 5 and rain rates from 0 to 10 mm/hour.

Ambient Noise in Shallow Water

Unfortunately, simple Wenz-type curves do not suffice to obtain useful estimates in this

case. The equations of the Ambient Noise section will have to be coded in detail.

4 TR 9407


3. Biological Ambient Noise

Snapping shrimp are the principal source of biological ambient noise. Use text on page

111-7 to determine their associated noise spectrum level. Table I on page M11-2 gives signal

characteristics of some significant sources of high frequency biological ambient noise

(other than snapping shrimp).

I 4. Bottom

Forward Loss vs Grazing Angle

Use Figure 1 on page IV-19. Sediment descriptors on the figure come from Table 2 on

I page IV-6. The bulk grain size given in Table 2 is defined in Eq. 1 on page IV-7.

Backscattering Strength vs Grazing Angle

Use Table 3 on pages IV-23 to IV-25. Sediment descriptors given in Table 3 come from

Table 2 on page IV-6. The bulk grain size given in Table 2 is defined in Eq. 1 on pageIV-7.

5. Arctic

Sound Speed in Ice

Use Eqs. 1 and 2 on pages V-2 and V-3.

Attenuation in Ice

Use Eq. 4 on page V-6.

Forward Loss-Away from Normal Incidence

Use Figure 3 and the text on page V-7.

Forward Loss - Near Normal Incidence

Use Figure 5 on page V-11.

TR 9407 5


Time Dependence of Forward Scattered Energy

This is for cases where the pulse elongation seen in the forward scattered signal is

important (in addition to the forward loss). Use Eqs. 6 and 7 on page V-9. Refer to

Eqs. 40-42 on pages 11-29 and 11-30 for parameter definitions.

Low Angle Backscatter from Unridged Ice

Use Figure 7 and Eq. 10 on page V-14.

Average Target Strength of Ice Keels

Use Figure 11 on page V-22.

C. IMPLEMENTATION SOFTWARE

1. Introduction

Listed below are models from APL-UW TR 9407 that were selected for implementa-

tion in FORTRAN. Each model is implemented in a separate subroutine that is suitable for

inclusion into a larger simulation. For each model, a test driver that has two functions is

provided. The main function provides the user with the capability of making test runs and

examining the model results. The secondary function, in many cases, provides a table suit-

able for inclusion in a Generic Sonar Model (GSM) input file. The test drivers may also

provide a starting point for development of software to support other simulations. Names

of test drivers and outputs are provided below.

The software conforms to commonly accepted software engineering standards such

as those described in Software Engineering by Roger Pressman, McGraw-Hill, 1987. Com-

plete descriptions of software functions are provided in the subfunctions that implement the

acoustic models. Input arguments are checked to assure they are within acceptable inter-

vals. Where possible, the subroutines key variable names to the names used in the text of

APL-UW TR 9407 and link FORTRAN expressions with equations in the report's text.

This is intended to ease cross referencing between the text and the software.

The first argument in most functions is a logical variable, debug. If debug is true, vol-

umes of intermediate variables will be printed for debugging purposes and will allow the

6 TR 9407


user to determine the origin of model characteristics. In the drivers, test inputs for each

model are listed, along with the results of the model computation. This will allow the user

to compare results of his or her computations with ours to identify compiler and machine-

dependent problems.

Department of Defense (DoD) agencies and DoD contractors can receive further infor-

mation regarding this software by contacting Chris Eggen (206-543-9804) or Kevin Will-

iams (206-543-3949) at APL-UW, or by contacting the APL front desk (206-543-1300) to

page either Kevin or Chris. Alternatively, email may be sent to [email protected]

or [email protected]. A distribution of the software will be made after obtain-

ing verification of requester's status (preferably via a DoD contract number, if requester is

not a DoD agency) and a sponsor request. Requester must provide APL-UW with a blank

copy of the preferred means of data transfer. We are equipped to send data on a SUN car-

tridge tape, a 9-track tape, or an 8-mm tape. Agencies that are not DoD or DoD contractors

should coordinate requests for information and software through the Chief of Naval

Research, Code 322TE, Ballston Tower One, 800 North Quincy Street, Arlington, VA

22217-5660.

2. Software Descriptions

A description of software is provided for each model encoded. The function imple-

menting the model in this report is named and a description is provided, if necessary. This

is followed by specifications of the arguments, the returned quantity, and the subfunctions

(if any) used by the main model function. Finally, the test driver supplied to run the model

function is described.

Sound Speed

Function: ssp94.f

Arguments: depth = depth (m)

temp = temperature (degrees C)

sal = salinity (ppt)

Returns: Sound speed in m/s

TR 9407 7


Subfunctions: None

Driver: sspat94.f

Operation: Reads input file of depth, temperature, and salinity and computes

sound speed and attenuation vs depth. Alternatively, reads input file

of depth and sound speed, inverts sound speed to obtain temperature

and salinity, and computes attenuation vs depth. Output files are suit-

able for inclusion into GSM input files.

Inputs: line 1 Name of input file

line 2 Name of output sound speed file

line 3 Name of output attenuation file

line 4 Frequency (kHz), pH

line 5 Temperature units in input file

line 6 Depth and sound speed units in input file

line 7 Depth and sound speed units desired in output file

Other subroutines used by the driver:

fit Fits a regression line to loss (dB) vs grazing angle

gsmtab Writes a table to a file in standard GSM format

Attenuation

Function: attn94.f

Arguments: freq = signal frequency (kHz)

ph = ph measure of acid-base (0-14)

depth = depth (m)

temp = temperature (degrees C)

sal = salinity (ppt)

sonspd = sound speed (m/s) (inverted to obtain temperature and

salinity if these are 0)

Returns: Attenuation in dB/km

Subfunctions: None

8 TR 9407

_UNIVERSITY OF WASHINGTON* APPLIED PHYSICS LABORATORY

Driver: sspat94.f

This program serves as a driver for both sound speed and attenuation. See

description of driver for sound speed.

Surface Reflection Loss

There are three separate functions implementing this model.

Function: sbl94.f

This function implements the most direct form of the model, the equations of

which are derived assuming all loss is due to an attenuating layer of bubbles

and isovelocity propagation.

Arguments: debug = logical flag set to true if debug printouts desired

thetad = grazing angle (degrees)

ws = wind speed (m/s)

freq = signal frequency (kHz)

Returns: Surface reflection power loss

Subfunctions: None

Driver 1: tsloss.f

Operation: Computes surface reflection loss vs grazing angle at 0.1 degree

intervals below 1 degree and at 1.0 degree intervals between 1 and 90

degrees, and converts to dB. It then examines the results and retains

only sufficient vectors in the final matrix to support linear interpola-

tion. It outputs the matrix in a table suitable for GSM

Inputs: line 1 Wind speed in m/s and frequency in kHz

line 2 Name of output file

Other subroutines used by driver:



Driver 2: tslos2.f

Operation: Computes surface reflection loss vs wind speed from 0 m/s to 15 m/s

TR 9407 9

UNIVERSITY OF WASHINGTON - APPLIED PHYSICS LABORATORY

at 0.15 m/s intervals for a fixed grazing angle. Outputs the results in

an ascii file

Inputs: line 1 Wind speed in m/s and grazing angle in degrees


Function: batn94.f

This function computes bubble attenuation in the 10 m below the surface for a simu-

lation that can use such information to predict loss for rays that intersect or

come close to the surface. For an isovelocity sound speed profile, rays transiting

such a bubble attenuation layer and hitting the surface at a grazing angle of 0

would suffer a loss equal to that computed by the sb194.f


depth = depth below surface (m)



Returns: Attenuation (dB/m)

Subfunctions: None

Driver: tbatn.f

Operation: Computes bubble attenuation vs depth for the 10 m below the surface

at 0.5 m intervals. Outputs table vs depth in table suitable for GSM





Function: sbl94i.f

This function computes the loss for a ray transiting the bubble attenuation layer and

either vertexing or reflecting off the surface. It performs an integration of loss

over the ray path assuming a piecewise linear sound speed profile in the

upper 10 m of the water column. For a ray intersecting the surface, the results

10 TR 9407


can be interpreted as a surface reflection loss. For an isovelocity sound speed

profile, the results will be the same as the loss computed by sb194*f


depths = reference depth (m)

elevs = elevation angle at reference depth (degrees)



Returns: loss for ray transiting layer within 10 m of surface (dB)

Subfunctions:

Internal: integrnd Integrand for depth integral

erf Error function

External: dqags, dqagse, dqpsrt, dqk2l, dqelg, xerror, xerrwv, xerprt,

xerabt, xerctl, xgetua, xersav, fdump, j4save, s88fmt, dlmach,

ilmach: Performs double precision numerical integration

Driver 1: tslosi.f

Operation: Computes surface reflection loss vs grazing angle for a given sound

speed profile by calling sbl94i with depths = 0 and elevs = grazing

angle. As for sb194, it does this at 0.1 degree intervals below 1 degree

and at 1.0 degree intervals between 1 and 90 degrees, and converts to

dB. It then examines the results and retains only sufficient vectors in

the final matrix to support linear interpolation. It outputs the matrix in

a table suitable for GSM


line 2 Name of file containing sound speed profile (m m/s)





TR 9407 11


Driver 2: tslosj.f

Operation: Computes the loss for rays transiting the bubble attenuation

layer and either vertexing or reflecting off the surface using the

algorithm in sbl94i.f. Gets information defining series of rays

from the user and for each ray, writes the loss to standard output

and to an ascii file

Inputs: line 1 Wind speed in m/s and grazing angle in degrees

line 2 Name of file containing sound speed profile (m/s)


line 4-end Reference depth (m) and elevation at reference depth

(degrees)

Surface Scattering Strength

Function: srfs94.f





ierr = equals error code (if nonzero)

Returns: Surface scattering strength in dB

Subfunctions:

Internal: fcet94 Computes the scattering cross-section due to the large-

scale wave facets

sscr94 Computes scattering cross-section due to small-scale

roughness according to composite roughness theory

dB 15_of fc Computes the angle at which facet scattering falls to

15 dB below the maximum at 0 = 90'

bubl94 Computes the scattering cross-section due to bubbles

according to resonant bubble scattering theory

External: sb194 Called to compute attenuation of energy by the bubble field

on rays contributing to roughness scattering

12 TR 9407


Driver: tsscat.f

Operation: Computes surface scattering strength vs grazing angle at one degree

intervals and writes it in table suitable for GSM

Inputs: line 1 Wind speed in m/s

line 2 Frequency in kHz




Bottom Reflection Loss

Function: blos94.f



rho = density ratio at bottom interface (dimensionless)

nu = sound speed ratio at bottom interface (dimensionless)

delta = loss parameter of bottom (dimensionless)

Returns: Bottom reflection power loss

Subfunctions: None

Driver: tbscat.f

Operation: Develops physical bottom parameters from several types of bottom

inputs. Computes bottom reflection power loss vs grazing angle at 5.0

degree intervals and converts to dB. Increases resolution if reflection

loss changes by more than 0.5 dB between angles. Computes bottom

scattering strength vs grazing angle at 1.0 degree intervals. Outputs

both sets of results in single file as tables suitable for input to GSM

Inputs: line 1 Method of bottom characterization

line 2 For method 1, six bottom parameters

For method 2, bottom type from APL-UW TR 9407

For method 3, bulk grain size

For method 4, porosity of the upper few centimeters of the

bottom

TR 9407 13


For method 5, six bottom parameters that are known; then

next card includes miscellaneous information about the

bottom to compute parameters that are not known

For method 6, bulk mass ratio, bulk sound speed ratio, or

bulk porosity (i.e., values below the top few centimeters

of the bottom) where known

Next line Frequency (kHz) and sound speed in water at bottom (m/s)

Next line Name of output file


bnam2des Returns six bottom parameters for a given bottom type

gsiz2des Returns six bottom parameters for a given bulk grain size

por2des Returns six bottom parameters for a given porosity

rho2gsiz Returns bulk grain size for a given mass ratio

nu2gsiz Returns bulk grain size for a given sound speed ratio

des2des Inputs six bottom parameters and returns zeros if not

valid

alph2delt Returns loss parameter from attenuation in the surficial

sediment and from density ratio.

meas2relp Returns the relief bottom descriptors from measured

1-dimensional bottom characteristics

bulk2gsiz Returns bulk grain size from bulk mass ratio, bulk sound

speed ratio, or bulk porosity

rquadr Returns real roots for a quadratic polynomial with real

coefficients

rcubic Returns real roots for a cubic polynomial with real

coefficients


14 TR 9407


Bottom Backscattering Strength

Function: btms94.f




cs = sound speed in water at bottom (m/s)




w2 = spectral strength (cm 4)

gamma = spectral exponent (dimensionless)

sigma2 = volume parameter (dimensionless)

ierr = equals error code (if nonzero)

Returns: Bottom backscattering strength in dB

Subfunctions:

Internal: gammaf Computes the gamma function

erf Computes the error function

sigmpr Computes the bottom backscattering cross-section in the

small roughness perturbation approximation

sigmpv Computes sediment volume backscattering cross-section

External: None

Driver: tbscat.f

This program serves as the driver for both bottom reflection loss and bottom scatter-

ing strength. See the description of driver for bottom reflection loss.

Bottom Bistatic Scattering Strength

Function: bibs94.f


thetai = incident grazing angle (degrees)

thetas = scattered grazing angle (degrees)

TR 9407 15

-UNIVERSITY OF WASHINGTON - APPLIED PHYSICS LABORATORY

phis = scattered out-of-plane angle (degrees)


cs = sound speed in water at bottom (m/s)




w2 = spectral strength (cm 4)

gamma = spectral exponent (dimensionless)

w3 = sediment inhomogeneity spectral strength (cm 3)

gamma3 = sediment inhomogeneity spectrum exponent

(dimensionless)

mu = ratio of normalized compressibility to density fluctuations

(dimensionless)

Returns: Bottom bistatic scattering strength in dB

Subfunctions:

Internal: gammaf Computes the gamma functions

smbfrl Simple model for bottom forward reflection loss

External: None

Driver: tbbsct.f

Operation: Develops physical bottom parameters from several types of bottom

inputs. Computes bottom bistatic scattering strength for a given inci-

dent grazing angle vs a predefined set of scattered grazing out-of-plane

angles. Outputs results on standard output and in an ascii file.

Inputs: line 1 Frequency (kHz) and sound speed in water at bottom (m/s)

line 2 Method of bottom characterization

line 3 For method 1, eight bottom parameters

For method 2, bottom type from APL-UW TR 9407

For method 3, bulk grain size

For method 4, porosity of the upper few centimeters of the

bottom

16 TR 9407


For method 5, eight bottom parameters that are known.

Then next card includes miscellaneous information

about the bottom to compute those that are not known.

For method 6, bulk mass ratio, bulk sound speed ratio, or

bulk porosity (i.e., values below the top few centime-

ters of the bottom) where known

Next line Single or first, last, and increment in incident grazing

angles (degrees)

Next line Single or first, last, and increment in scattered grazing

angles (degrees)

Next line Single or first, last, and increment in scattered out-of-plane

angles (degrees)

Next line Name of output file


bnam2des Returns six bottom parameters for a given bottom type

gsiz2des Returns six bottom parameters for a given bulk grain size

por2des Returns six bottom parameters for a given porosity

rho2gsiz Returns bulk grain size for a given mass ratio

nu2gsiz Returns bulk grain size for a given sound speed ratio

des2des Inputs six bottom parameters and returns zeros if not

valid

alph2delt Returns loss parameter from attenuation in the surficial

sediments and from density ratio.

meas2relp Returns the relief bottom descriptors from measured

1-dimensional bottom characteristics

bulk2gsiz Returns bulk grain size from bulk mass ratio, bulk sound

speed ratio, or bulk porosity

mon2bist Returns three bistatic volume parameters given the six

monostatic bottom descriptors

TR 9407 17


rquadr Returns real roots for a quadratic polynomial with real

coefficients

rcubic Returns real roots for a cubic polynomial with real

coefficients


18 TR 9407

I. Volume


A. SPEED OF SOUND IN SEAWATER

The speed of sound in seawater can be measured directly with a velocimeter, but high

precision is possible only if sophisticated velocimeters, rather than expendable velocime-

ters, are used. Therefore, sound speed is customarily calculated using temperature, salinity,

and pressure (TS,P) data from a conductivity-temperature-depth (CTD) cast together with

an equation for sound speed. This technique is an accurate and economical means of deter-

mining a sound-speed profile.

There are many equations for calculating sound speed from temperature, salinity, and

pressure measurements? 1 " APL-UW recommends the Chen-Millero-Li equation6,1",'

because it is the most accurate and because it is valid over the broadest range of environ-

mental conditions. A simpler but less accurate equation is Mackenzie's nine-term equa-

tion.7

1. Chen-Millero-Li Equation

APL-UW recommends the Chen-Millero-Li equation6'1°,l(shown on the following

page) because the uncertainty in this equation is ±0.05 m/s and because it is valid for tem-

peratures from 0 to 40'C, salinities from 0 to 40%o (%o = ppt), and pressures from 0 to

1000 bars. Sound-speed equations are accurate only over the specified range of tempera-

ture, salinity, and pressure from which they were derived and should not be relied upon out-

side this range. The original Chen-Millero equation was recently modified to correct for

pressure-dependent biases of 0.6 m/s. 9,10 ,12 See Table 1 for conversion factors.

Table 1. Pressure conversions.

1 kg/cm 2 = 0.980665 bar

1 lb/in.2 = 0.0689476 bar

1 atm = 1.01325 bar

TR 9407 I-1

Chen-Millero-Li Equation, Refs. 6, 10, and 11

Ctp: Sound speed (m/s)

T :Temperature (°C), 0•_ T •40

S :Salinity (%c), 0• S •<40

P Pressure (bars), 0 _ P 5 1000

C, (T,P) Represents the sound speed of pure water, Ref. 11

C, ( T,P) Represents the correction to the original equation, Ref. 10

A(T,P) S ]B(T,P) S 3/2 Salinity-related terms, Ref. 6

D(P) S2 IC p = 1745.0954 for P = 1000 bars, T = 40'C, S = 40%o

Ctsp = Cw (T,P) - CC (T,P) + A(T,P) S + B(T,P) S3/2 + D(P) S 2

Cw (T,P) = 1402.388 + 5.03711 T - 5.80852x10-2 T2 + 3.3420xi10- T' - 1.4780x10-W T4 + 3.1464> 10-9 T5

+ (0.153563 + 6.8982x10-4 T- 8.1788x10-6 T' + 1.3621x10-W T3- 6.1185x10-'° T4) P

+ (3.1260x10-5- 1.7107x10-6 T + 2.5974x10-8 T -- 2.5335x10-I0 T3 + 1.0405x10-12 T4 )P2

+ (- 9.7729x10-9 + 3.8504x10-0° T- 2.3643x10-12 T 2) p3

C,(T,P) = (0.0029-2.19x10 -4T+ 1.4x105 T )P

+ (- 4.76x1W-6 + 3.47x10-7 T - 2.59x10-8 T 2) P2

+ 2.68x10-9 P 3

A(T,P) = 1.389- 1.262x10-2 T + 7.164x10- T + 2.006x 10- T3-3.21xl 0-T4

+ (9.4742x10-5- 1.2580x1 0-T- x6.4885x10-8 T + 1.0507.10-ST3-2.0122x10-WT4) P

+ (- 3.9064x10-7 + 9.1041x10-9 T - 1.6002x10-W T2 + 7.988x]0-12 T 3) p2

* (1.100.l0-l' + 6.649x10-12 T- 3.389x10-13 T') p 3

B(T,P) = - 1.922x10-2 -4.42x10-5 T + (7.3637x10-5 + 1.7945x10-7 T) P

D(P) = 1.727x10- 3 -7.9836x10-6 p

2. Mackenzie Equation

Mackenzie's equation7 is simpler but less accurate than the Chen-Millero-Li equation.

This equation is a function of temperature, salinity, and depth (instead of pressure). The

Mackenzie equation is valid for a range of temperatures from -2 to 30'C, salinities from 30

to 40%c, and depths to 8000 m. Within this more limited range of temperature, salinity, and

1-2 TR 9407

depth, the uncertainty of this equation is ±0.07 m/s, while the difference between the Mack-

enzie and Chen-Millero-Li equations is ±0.5 m/s over the entire validity range of the Chen-

Millero-Li equation. Pressure can be converted to depth by the approximation P x 0.99 =

D, where P is pressure in decibars (10 dbars = 1 bar) and D is depth in meters. Using this

approximation in the Mackenzie equation yields a sound-speed estimate that agrees with the

Chen-Millero-Li equation (over its entire range) to within ±0.5 mrs. (See Table 1 for con-

version factors).

Mackenzie Equation, Ref.7

C tsd : Sound speed (m/s)

T :Temperature (°C), -2_< T5 <30

S : Salinity (%c), 30 • S < 40

D :Depth (meters), 0:_ D • 8000

C tsd = 1448.96 + 4.591 T - 5.304x10-2 T2 + 2.374x10-4 T3

+ 1.340 (S-35) + 1.630x10-2 D + 1.675x10-7 D2

- 1.025x10-2 T( S-35 ) - 7.139x10 TD3

3. Characteristics

Sound speed increases with increasing temperature, salinity, or pressure. Figure 1

shows an example of corresponding temperature, salinity; and sound-speed profiles from

the Sargasso Sea. In general, an increase in temperature of IC at 10'C increases the sound

speed by 3.6 m/s, and an increase in salinity of 1%o increases the sound speed by 1.3 m/s.

4. Comparisons

Although 99.95% of the world's oceans have temperatures that range from -2 to 30'C,

salinities from 33 to 37%c, and pressures from 0 to =1000 bars,1 3 recent tactical interest in

littoral environments requires accurate estimates of sound speed in low-salinity conditions,

such as those occurring near river outlets. The Chen-Millero-Li equation, with a range that

extends to pure water, addresses the low-salinity regime. On the other hand, some regions

of tactical interest may require accurate estimates of sound speed in high-temperature/high-

salinity conditions. Unfortunately, none of the current sound-speed equations are reliable at

TR 9407 1-3


0

-0.5-

S-1.5

-2

-2.5

03O 10 20 35 36 37 1500 1520Temperature (°C) Salinity (o/o) Sound Speed (m/s)

Figure 1. Corresponding temperature, salinity, and sound speed profiles from a CTD castobtained in the Sargasso Sea. Sound speed increases toward the surface because ofincreasing temperature and toward the bottom because of increasing pressure.

temperatures greater than 40'C or salinities greater than 40%o. Although rare, such condi-

tions do occur, e.g., in portions of the Persian Gulf and the Mediterranean Sea, and, there-

fore, sound-speed equations may be inadequate in these regions.

Two equations in common use by the Navy are the Wilson equation] and the more

recent Del Grosso equation 5, also known as NRLII. The Chen-Millero-Li equation is supe-

rior to both these equations. The Del Grosso equation agrees with the Chen-Millero-Li

equation to within 0.15 m/s over the (TS,P) range of the original Del Grosso and Mader

measurements 14 (temperatures from 0 to 15'C, salinities from 33 to 38%o, and pressures

from 0 to =1000 bars), but, despite original claims,5 it is grossly in error for salinities less

than about 30%o (see Figure 2).

While the 1960 Wilson sound-speed equation is still in common use, researchers have

demonstrated several problems with this equation. First, there are a number of inconsisten-

cies in the data set used to derive the Wilson equation, some of which were caused by non-

uniform pressure dependence. 4,11, 12 Second, the Wilson equation has an overall bias on the

order of 0.5 n/s 4"1 and a pressure-dependent bias on the order of 0.6 m/s.'°,"2 For these rea-

sons APL-UW does not recommend the Wilson equation, although for many applications

the errors are inconsequential.

1-4 TR 9407


00-1000•-,,

0 0

-2000-0.

.. -0.5C)

(I, -1CD -5

-4000 \1 -10 rn/s

-5000 -20

\ -25 \.-2

\-30 T =100-6000 \\1

"0 10 20 30 40Salinity (oo)

Figure 2. The difference between the Chen-Millero-Li equation and the Del Grosso equation for109C temperature. Del Grosso's equation is not valid for low-salinity seawater underpressure. An accurate interpretation of this figure requires consideration of (T,S,P)values that actually occur in oceans (see Ref 2). Sound speed has not beenaccurately measured above a salinity of about 4 0%1. Contour units are metersisecond. Modified from Ref 12.

B. ABSORPTION COEFFICIENT

The sound absorption coefficient, ca, is computed using the Francois-Garrison

equation' 5 shown in Figure 3, in which the absorption coefficient is computed as the sum of

three contributions: boric acid, magnesium sulfate, and pure water. The absorption encoun-

tered in a particular area may vary by ±10% from the given equation, and such bounds

should be used when evaluating acoustic system performance.

The form of the Francois-Garrison equation uses relaxation theory and has been veri-

fied by laboratory measurements (e.g., Ref. 16). The constants for the equation, however,

TR 9407 1-5


TOTAL SOUND ABSORPTION IN SEAWATER

Total Boric MgSO4 Pure= Acid + MS4 + Water

Absorption Conti. Contrib. WotrContrib. Contrib.

A I PI f2 A2 P 2 2f-If2 2 + + A3P f dB kmf 2

2 2 33

for frequency f in kilohertz.

Boric Acid Contribution

A 8.86 x 10(0.78 pH - 5) dB km-I kHz-

cP1 =1

P = I

f = 2.8 (S/35) 0 "5 10(4- 1245/0) kHz,

where c is the sound speed (m/s), given approximately by

c = 1412+3.21T+l.19S+0.0167D,

T is the temperature ('C), 6 = 273+T, S is the salinity(•), and D is the depth (m).

MgSO4 Contribution

A = 21.44 - (1 +0.025T) dB km- kHz-I2c

P2 = I- 1.37x 10- 4D+6.2 x10-9 D2

2 = 8. 17x 10(8 -1990/6)

2 1 + 0.0018 (S - 35 kHz

Pure Water Contribution

For T - 20%C,

A3 = 4.937x 10-4-2.59 x10-5 T

+ 9.11x 10-7T2- 1.50x10- 8T3 dB km-I kHz-2

For T > 20%C,

A3 = 3. 964 x 10-4- 1.146 x 10-5 T

+ 1.45x10- 7T 2-6.5x10 10 T3 dB km"I kHz" 2 .

- 5 - 102P3 = -3.83 x 0 D +4.9 x 10 D

Figure 3. Francois-Garrison equation for sound absorption in seawater1 5

1-6 TR 9407

were selected to fit numerous and widely distributed oceanic measurements made by APL-

UW and others.

The boric acid contribution to the equation was determined from reported measure-

ments in several oceans with salinities of 34-41%, temperatures of -2' to 22°C, and depths

to 1500 m. The contribution may not be accurate below 200 Hz because of scattering and

bottom leakage losses. Above 20 kHz the boric acid contribution becomes insignificant.

The magnesium sulfate contribution was determined from field measurements for

salinities of 30-35%, temperatures of 2 to 22°C, and depths to 3500 m. The contribution

has been verified for frequencies up to 600 kHz.

The pure water contribution produces over 90% of the total absorption at frequencies

above 600 kHz. It was determined from laboratory measurements at temperatures from 0-

30'C and for pressures equivalent to depths to 10,000 m.

Table 2 provides absorption coefficient values (from Figure 3) for temperatures and

salinities most often encountered, for zero depth, and for a typical near-surface ocean pH of

8. For depths less than 100 m, the table can be used with negligible error. For waters with

extreme pH values (i.e., <7.7 or >8.2), using the table will produce appreciable discrepan-

cies below 10 kHz and discrepancies as high as 40% below 1 kHz. (See Refs. 17 and 18 for

the variation of pH with depth and geographic location.) Figure 4 gives guidelines for

ocean pH values estimated at the depth of the SOFAR channel axis. Lovett 17 took pH val-

ues from atlases edited by Gorshkov, 18 corrected for pressure, interpolated to the SOFAR

axis depth, and displayed contours of the boric acid absorption term (A), using

10(0.83pH - 6.0)A = 0.0237 x 1 0 . (1)

Here we have used Eq. 1 to back out the pressure-corrected pH values for the contours orig-

inally shown by Lovett.

The temperature dependence is illustrated in Figure 5 for several frequencies and for

typical ocean conditions (S = 35%o, D = 100 m). For other conditions, Table 2 or the equa-

tions in Figure 3 should be used.

TR 9407 1-7

___________-_UNIVERSITY OF WASHINGTON -APPLIED PHYSICS LABORATORY

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1-8 TR 9407

______________UNIVERSITY OF WASHINGTON APPLIED PHYSICS LABORATORY

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110 TR 9407

______________UNIVERSITY OF WASHINGTON -APPLIED PHYSICS LABORATORY

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TR 9407 1-i11

UNIVERSITY OF WASHINGTON APPLIED PHYSICS LABORATORY_ _ _ _

200- S = 35O/oo

D= 100 M

150-

500 kHz

too 300 kHzS50N

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a- 20-0

cc 50 kHz

ISI

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TEMPERATURE ("C)

Figure 5. Temperature dependence of the logarithmic absorption coefficient a.

C. BACKSCATTERING

1. Introduction

The energy backscattered from the ocean volume is determined primarily by the marine

biota in the water column, although important contributions may also be made by tempera-

ture inhomogeneities, bubbles, and particulate matter. In the frequency range defined as"high" (10-60 kHz), the backscatter through the water column is dominated by smaller fish,

both with and without resonant gas-filled swim bladders, and dense aggregations of zoop-

lankton. Volume backscatter is highly variable throughout the ocean, and there are signifi-

cant changes both in backscatter intensity and in depth distribution with changes in

geographical location, depth, season, frequency, and time of day. Prediction of these

1-12 TR 9407


changes is complicated by environmental factors that play a major role in the spatial distri-

bution and migration of fish and zooplankton; these factors include nutrient availability,

light level, temperature distribution, and bottom topography. All these factors create condi-

tions that attract biota to an area, but also influence the role predation will play in control-

ling the abundance and distribution of fish.

Because of the extensive dimensions of the ocean and our limited facilities to sample it,

our ability to predict volume backscatter in a particular region is limited, and all predictions

have a high variance associated with them. An extensive database and the acoustic survey

data supporting it (termed a databank) have been compiled by the U.S. Naval Oceano-

graphic Office (NAVOCEANO) as part of the Oceanographic and Atmospheric Master

Library (OAML). The database covers a frequency range of 2-50 kHz, four seasons, and

day and night conditions for most of the northern hemisphere, including the Arctic. The

data that support this database are based on extensive surveys at frequencies between 25

and 50 kHz in many important areas; these surveys were conducted by both NAVOCEANO

and marine research institutes of various nations. Because acoustic backscatter is highly

variable over space and time, operational measurements are always preferred. In their

absence, we recommend that, where available, the volume scattering data in the databank

be used for volume scattering predictions.

In the absence of data from a particular area of interest, we recommend using the

OAML database with the following caveat. Except for areas where there are data to support

the OAML volume scattering database, the predictions offered are uncertain. This is partic-

ularly true in shallow areas near continental shelves, especially areas of high upwelling or

of major fishing activity. As an alternative in these areas, we suggest the following regional

abstractions, based in part on a review of worldwide mesopelagic fish abundance,19 meso-

pelagics being the main volume backscatterers in deep ocean areas, and in part on a review

of worldwide fisheries catch and fish stock abundance data,2" primarily for shallow coastal

areas.

Significant advances are currently being made in explicitly linking fish and zoo-plank-

ton spatial distributions, both horizontally and vertically, to environmental factors that can

TR 9407 1-13


be measured more regularly and synoptically than the backscatter itself. However, it is pre-

mature to include this information in this report because the regional extent of this work is

so limited.

Japanese researchers21' 22 have successfully correlated pelagic fish production to sea

surface temperature in the North Central Pacific Ocean. Swartzman et al.23 found that the

horizontal distribution of Alaska pollock in the Bering Sea during summer was strongly

influenced by bottom depths and ocean fronts along the continental shelf break, while verti-

cal distribution also depended on the thermocline depth. Marchal et al. 24 found that the

depth of the scattering layer off the coast of West Africa at night was directly proportional to

the thermocline depth, with mesopelagics that migrated to the surface staying above the

thermocline. These studies suggest the eventual successful use of satellite and other

remotely sensed environmental data as a supplement to acoustic surveys for predicting

acoustic volume scattering.

2. Deep Open Ocean

Table 3 summarizes the volume backscattering in various regions of the Atlantic,

Pacific, Indian, and Arctic oceans (see Figure 6 for map). For each region, Table 3 gives a

column scattering strength (CSS) or its estimated range. In this document, CSS is defined

as the decibel equivalent to the backscattering cross section per unit volume integrated

through the water column, which itself is dimensionless. Also provided are commonly

observed scattering layers and additional comments on volume backscatter in a region,

where relevant. In open ocean areas and some coastal regions (e.g., the Arabian Sea), back-

scatter is dominated by mesopelagic fish in the Myctophidae and Gonostomatidae families.

These fish tend to aggregate in dense layers, often deep in the water column. The mesope-

lagic aggregates in intertropical and tropical waters can be distinguished from those in tem-

perate waters.25 The first group consists of mostly active swimmers that undergo diel (day

to night) vertical migration; the second group is more passive and does not undergo diel

migration. The lack of diel migration of the deep scattering layer(s) in temperate waters has

been observed frequently in acoustic surveys.26,27

1-14 TR 9407

UNIVERSITY OF WASHINGTON- APPLIED PHYSICS LABORATORY

Table 3. Volume backscatter regions of the world's oceans. Map ID numbers refer to regions ofsimilar backscattering shown in Figure 6. Geographically split regions (e.g., ]a and ib)are combined.

ColumnScattering

Map StrengthID Region (dB range) Scattering Layers Comments

1 North and South Atlantic (-43, -45) dB 0-100 m day and night

(> 45'N and > 45°S)

2 Central and Equatorial (-47, -50) dB 300-700 m day Lower backscatter nearerAtlantic (< 45°N and 0-100 m night equator< 45°S)

3 Coastal North and South (-43, -47) dB 0-50 m Higher dB range in upwelling

3' Atlantic (-37, -40) dB 0-100 m and mixing areas, e.g.,Namibian and N. African

day and night upwelling, George's bank

4 West Mediterranean (-40, -45) dB 0-50 m; 375-1000 m day

0-100 m; 400-500 m night

5 East Mediterranean -50 dB as in W. Med. Higher backscatter within200 m isobath

6 Mid-Pacific Ocean (-46, -50) dB 450-700 m day Higher backscatter nearer

0-50 m night equator

7 North Pacific (-44,-45) dB 200 or 400-600 m day.

0-50 m or 200 m and

800-1000 m night.

8 Pacific temperate coastal -45 dB 110-400 m day and night

9 Pacific coastal upwelling -38 dB 0-100 m; 400-700 m dayand night

10 Pacific southeast Asia rim -44 dB 0-200 m night

500-800 m day and night

11 Pacific subantarctic (-44,-45) dB 400-600 m day and night

12 Indian Ocean north rim (-37, -40) dB 0-50 m night World's highest mesopelagic

100-200 m; 250-300 m day fish production

13 Indian Ocean south rim -44 dB 150-350 m day

0-100 m night

14 Central Indian Ocean -54 dB 150-350 m day

0-100 m night

TR 9407 1-15


If the operating area is uncertain or a more generic input is desired, we suggest using a

nighttime profile with a strong scattering layer from the surface to 300-m depth and a back-

ground level that is 13 dB less. For a daytime profile assume a deep scattering layer

between 300 and 600 m and a background level that is 13 dB less. The volume scattering

strength within the scattering layer can be assumed to depend on the level of production in

the region. Suggested values (for 10-60 kHz) are:

Dense marine life (upwelling and mixing areas shown in Figure 7):

Sv = -66 dB re m-1

Intermediate marine life (most other temperate coastal areas):

SV = -74 dB re m-1

Sparse marine life (nonupwelling and mixing tropic areas):

Sv = -81 dB re m-1 .

An index of marine production, based on the Coastal Zone Color Scanner satellite

images for primary production, is given in Figure 7.

From the information provided in Table 3, we can calculate other parameters of inter-

est, including the volume scattering strength in the scattering layer (in decibels/meter) and

the cumulative scattering strength through the scattering layer (in decibels). To do this, we

must assume a relationship between the volume scattering strength of the scattering layer

and the scattering strength of the background volume. In the computations below, we

assume a background level 13 dB below the scattering layer level. Given the water column

volume scattering strength, CSS, the scattering layer volume scattering strength, Sv, is given

by

Sv = CSS- loiog[10- 3 (D-dv) +dl , (2)

where D is the water column depth in meters and dv is the thickness of the scattering layer

in meters. All logarithms are to the base 10. Similarly, CSS can be calculated from Sv,.

1-16 TR 9407


World Backscatter Regions (Deep Water)

aC

I3ditigusedbya b,•+ or ++ c.

3. Shallow..WatersAres ,o high pe i fh d y e

Figure 6 Deep-water backscattering regions in the Atlantic, Pacific, and Indian oceans.Numbered regions are defined in Table 3. Background map shows ocean bathymetry.

Depth ranges from yellow (shallow) through green and blue to purple (very deep).When regions defined in Table 3 are not contiguous the separate parts aredistinguished by a, b, or c.

3. Shallow Waters

Areas of high pelagic fish density exist along the continental shelves in many coastal

regions, but the distribution of such areas is determined by the environment, depending fre-

quently on wind-driven upwelling or other forms of nutrient mixing leading to high primary

and secondary production. Fisheries exist in these coastal regions for many pelagic species,

including sardine, anchovy, herring, pilchard, hake, menhaden, pollock, and cod. Volume

backscattering in these regions can be high near the surface but is extremely variable owing

to the schooling nature of these species. Also zooplankton abundance, especially euphausi-

ids, may be high enough in highly productive shallow areas to significantly affect volume

scattering.

TR 9407 1-17(following page is Mlank)


World Average Annual Primary Production

._ areas

Upwellingareas

Figure 7. World annual average ocean primary productivity obtained from Coastal Zone Color

Scanner satellite images. Major upwelling and front mixing areas are shown.Primary production ranges from orange (low) through yellow and green to blue(high).

In waters less than 200 m deep, volume scattering may be considered frequency inde-

pendent (at frequencies between 10 and 60 kHz). Volume scattering, to a first approxima-

tion, can be assumed to be uniform in depth. The following rule of thumb can be applied:

Dense marine life (upwelling and mixing areas in Figure 7):

Sv = -62 dB re rn-

Intermediate marine life (most other temperate coastal areas):

Sv = -72 dB re m-1

TR 9407 1- 19(following page is blank)


Sparse marine life (nonupwelling and mixing tropics areas):

Sv = -85 dB re m-1.

As marine life becomes more dense, there is a tendency, especially during the spring in

shallow temperate waters, to have a shallow scattering layer (0-20 m) composed largely of

zooplankters, which will have a higher backscatter than given above for frequencies

between 25 and 60 kHz.

4. Ice-Covered Regions

The Arctic Ocean and adjacent waters are ice covered for most of the year. Measure-

ments of volume scattering under the solid ice cap and in the marginal ice zone show nearly

constant backscatter from 100-600 m.2 8'2 9 Scattering at high frequencies (10-60 kHz) is

more variable in the top 100 m, with no day to night variation. Frequency independence

over the frequency range of interest is substantiated by available data. We suggest using an

average level of -75 dB re m-1 .

5. Spectral Spreading

Volume-induced spectral spreading is determined by volume scatterers whose speed

distribution in deep water is assumed to be Gaussian with a standard deviation of 0.13 m/s

(0.25 knot). Data available in the literature have not been completely analyzed to substanti-

ate this assumption, but it is reasonable for most conditions. Data taken on the shallow

water Quinault acoustic test range,30 however, show wider spectral widths because of scat-

tering from bubbles and marine organisms near the surface that undergo orbital motion

owing to large surface waves with long periods. Because these spectral widths are compa-

rable to those for the surface backscatter, it is recommended that the spectral widths for vol-

ume scattering near the surface be calculated using the spectral widths appropriate for the

surface backscatter (see Eq. 18 in Section II, this report) modified by a depth dependence

equal to e -,z, where K is the wave number corresponding to the peak of the surface-wave

spectrum, and z is the depth. In particular, the equation for the half-power spectral width is

TR 9407 1-21

-UNIVERSITY OF WASHINGTON • APPLIED PHYSICS LABORATORY

2.35(0.13U< 1 rn/s

Af 3 dB = 5 + -K35 0.13f 511/5 (3)I.f.e- + L235 1.f] U.5lm/s,

where K = (0.88)2 g U -2, 11 = Eq. 20 of Section II, g is the gravitational constant (m/s 2), U

is the wind speed (m/s),f is the frequency (kHz), and z is depth below the surface (m). Fig-

ure 8 shows results from Eq. 3 forf= 25 kHz, 0 (Eq. 23 of Section II) - 0, and several wind

speeds.

70

f =25 kHz

0 U=20 m/s =0 degrees

-e 50

C/)>• 40

• 30

20tU= m/s

10

U=l m/s10 20 30 40 50

Depth (m)

Figure 8. The half-power spectral width from Eq. 3 plotted for several wind speeds.

1-22 TR 9407


REFERENCES - Section I

1. W. D. Wilson, "Equation for the speed of sound in seawater," J. Acoust. Soc. Am., 32,1357, (1960).

2. C. C. Leroy, "Development of simple equations for accurate and more realistic calcula-tion of the speed of sound in seawater," J. Acoust. Soc. Am., 46, 216-226, (1969).

3. H. W. Frye and J. D. Pugh, "New equation for the speed of sound in seawater,"J.Acoust. Soc. Am., 50, 384-386, (1971).

4. E. R. Anderson, "Sound speed in seawater as a function of realistic temperature - salin-ity - pressure domains," Ocean Science Department, Naval Undersea Research Devel-opment Center, NAVUSEARANDCENTP 243, 1971.

5. V. A. Del Grosso, "New equation for the speed of sound in natural waters (with com-parisons to other equations),"J. Acoust. Soc. Am., 56, 1084-1091, (1974).

6. C. Chen and F. J. Millero, "Speed of sound in seawater at high pressures,"J. Acoust.Soc. Am., 62, 1129-1135, (1977).

7. K. V. Mackenzie, "Discussion of sea water sound-speed determinations," J. Acoust.Soc. Am., 70, 801-806, (1981).

8. J. L. Spiesberger and K. Metzger, "A new algorithm for sound speed in seawater," J.Acoust. Soc. Am., 89, 2677-2688, (1991).

9. J. L. Spiesberger, "Is Del Grosso's sound-speed algorithm correct?" J. Acoust. Soc.Am., 93, 2235-2237, (1993).

10. F. J. Millero and X. Li, "Comments on 'On equations for the speed of sound in seawa-ter'[J.Acoust. Soc. Am. 93. 255-275 (1993)]," J. Acoust. Soc. Am., 95, 2757-2759,(1994).

11. C. Chen and F. J. Millero, "Re-evalutation of Wilson's soundspeed measurements inpure water," J. Acoust. Soc. Am., 60, 1270-1273, (1976).

12. B. D. Dushaw, P. F. Worcester, B. D. Cornuelle, and B. M. Howe, "On equations forthe speed of sound in seawater," J. Acoust. Soc. Am., 93, 255-275, (1993).

13. W. D. Wilson, "Speed of sound in seawater as a function of temperature, pressure, andsalinity," J. Acoust. Soc. Am., 32, 641-644, (1960).

TR 9407 1- 23

-UNIVERSITY OF WASHINGTON* APPLIED PHYSICS LABORATORY

14. V. A. Del Grosso, and C. W. Mader, "Speed of sound in sea water samples," J. Acoust.Soc. Am., 52, 961-974, (1972).

15. R.E. Francois and G.R. Garrison, "Sound absorption based on ocean measurements.Part I: Pure water and magnesium sulfate contributions; Part II: Boric acid contribu-tion and equation for total absorption," J. Acoust. Soc. Am., 72, 896-907 and 1879-

1890 (1982).

16. F.H. Fisher and V.P. Simmons, "Sound absorption in sea water," J. Acoust. Soc. Am.,

62, 558-56 (1977).

17. J.R. Lovett, "Geographic variation of low-frequency sound absorption in the Atlantic,Indian, and Pacific oceans," J. Acoust. Soc. Am. 67, 338-340 (1980).

18. S.G. Gorshkov (Ed.), World Ocean Atlas, Atlantic and Indian Oceans, Vol. 2, 234-235,and World Ocean Atlas, Pacific Ocean, Vol. 1, 234-235 (Pergamon, 1974).

19. J. Gjesaeter and K. Kawaguchi, "A review of the world resources of mesopelagicfish," FAO Fisheries Technical Paper #193, FAO, Rome, Italy, 1980, 151 pp.

20. FAO Yearbook Fishery Statistics: Catches and Landings, 7, Food and AgriculturalOrganization, Rome, Italy, 1992.

21. H. Tameishi and I. Yamanaka, "Application of NOAA AVHRR data for fisheries ser-vice," Japan Fisheries Information Service Center Technical Bulletin, 1990, 29 pp.

22. I. Yamanaka, S. Ito, K. Niwa, R. Tanabe, Y. Yabuta and S. Chikunu, "The fisheriesforecasting system in Japan for coastal pelagic fish," FAO Fisheries Technical Paper301, FAO, Rome, 1988, 72 pp.

23. G.L. Swartzman,W. Stuetzle, K. Kulman, and M. Powojowski, "Relating the distribu-tion of pollock schools in the Bering Sea to environmental factors," ICES J. Mar Sci.,

51, 481-492, (1994).

24. E. Marchal, F. Gerlotto, and B. Stequert, "On the relationship between scatteringlayer, thermal structure and tuna abundance in the Eastern Atlantic equatorial currentsystem," Oceanol. Acta, 16(3), 261-272, (1993).

25. E.G. Barham, "Deep-sea fishes: Lethargy and vertical orientation," In Proceedings ofan International Symposium on Biological Sound-Scattering in the Ocean, G.B. Farqu-har, Rep. MC-005, Maury Center for Ocean Science, Washington, D.C., pp. 100-118,1971.

1-24 TR 9407

I_ UNIVERSITY OF WASHINGTON - APPLIED PHYSICS LABORATORY

26. G.L. Swartzman, R.T. Miyamoto, and J.S. Wigton, APP Volume Scattering Strength(VSS) Inputs for the Mediterranean Sea, Sargasso Sea, U.S. Pacific Coast, and Bering

Sea (U), APL-UW TR 9020, September 1991. (Confidential)

27. G.L. Swartzman, R.T. Miyamoto, J.S. Wigton, and R.K. Kerr. APP Volume ScatteringStrength (VSS) Inputs for the Gulf of Alaska, Barents Sea, Norwegian Sea, and NorthSea, APL-UW TR 9212, November 1992. (Confidential)

28. G. Maris and G.J. O'Brien, ICEX 1-86 Arctic Volume Scatter Strength (U), NUSCTM-87-1103, June 1987. (Secret).

29. T. Wen, R.P. Stein, F.W. Karig, R.T. Miyamoto, and W.J. Felton, Environmental Mea-surements in the Beaufort Sea, Spring 1987, APL-UW 1-87. February 1988.

30. S.O. McConnell, Simulation and Analysis of Acoustic Measurements Made in 1983 atthe Shallow Water Quinault Range (U), APL-UW TR 8909, April 1990. (Confidential)

TR 9407 1-25

II. Surface


Introduction

All models concerning ambient noise radiation and scattering from the sea surface,

and scattering and attenuation from near-surface bubbles, are contained in this section.

The models are applicable over the frequency interval 10-100 kHz, although we caution

that much of the data used in model development and verification lies within a narrower

frequency interval of 20-50 kHz. The exception to this is the ambient noise model

which predicts wind- and rain-generated ambient noise over the frequency interval

1-100 kHz. (Shipping and other noise sources are not considered; for biological noise,

see Section III.)

Most of the models in this section require frequency f in kilohertz and wind speed U

in meters/second (measured at a height of 10 m) as model inputs; other model inputs will

be introduced as necessary. Wind speed is used as a model input because it is the param-

eter most easily and reliably measured in operational and test areas, and it is the best

known environmental correlate to sea surface conditions and near-surface bubble con-

centration.

Included within Section II.A is a discussion of sea state, which can be used as a

single-parameter description of sea surface conditions combining both wind speed and

wave height. This section is included primarily to distinguish the three sea state codes

currently in use and to provide a conversion to wind speed and wave height when sea

state is the only environmental descriptor available. (The sea state parameter is not used

explicitly in any of the models given in this section.)

The effects of near-surface bubbles enter into nearly all of the models. At low to

moderate grazing angles, surface backscatter is dominated by returns from the near-

surface layer. At moderate to high angles, the bubble layer acts as an absorber. This

absorption (or, more precisely, extinction) effect is the reason for the loss of acoustic

energy. This loss is also an important element in the ambient noise model because noise

generated at the air/sea interface must propagate through the bubble layer to reach the

receiver (it is assumed that the receiver is below the bubble layer).

TR 9407 UI-1


A. WIND SPEED AND SEA STATE

The 10 m measurement height for wind speed is the standard reference height for

wind speed measurements at sea. In general, wind speed measurements made at heights

above 10 m will be greater than those made at 10 m, and measurements made at heights

below 10 m will be less. The exact change in wind speed with measurement height

depends on the stability of the air/sea interface, which is largely dependent on the air/sea

temperature difference AC. Knowing AC, one may use tables given in Smith1 to convert

measurements made at heights other than 10 m to the standard reference height. Note

that wind speed measurements taken at heights within the range 5-20 m differ from those

taken at the standard 10 m by less than 10%.

A far more important source of error in wind speed estimates is the averaging

period during which measurements were made. This period should be at least 20 min,

but no greater than 1 hour, for wind speed to correlate with sea surface conditions 2 and

near-surface bubble concentration. The averaging period should ideally be just prior to

the time of the acoustic measurements. Wind speed measurements taken over very short

averaging periods will introduce error into model predictions because such measure-

ments will be unduly influenced by gusts or quiescent periods and therefore will be less

correlated with sea surface conditions and bubble concentration.

The term sea state, with its long history in the field of naval oceanography, has

become a useful code for describing the surface conditions of the open ocean and is

widely used today. Unfortunately for scientific purposes, sea state is a loosely defined

quantity at best, with several definitions available. 3-7 A brief description of three of the

more commonly found definitions is given in Table 1. In addition to the problems associ-

ated with conflicting definitions, it is also apparent that these definitions are based on

fully developed wind-driven seas and do not encompass the full range of surface condi-

tions.

Three conditions can cause the general wind-speed/wave-height relationship to

deviate significantly from that for the fully developed sea: limited fetch, limited

11-2 TR 9407

_______________UNIVERSITY OF WASHINGTON - APPLIED PHYSICS LABORATORY

Ecz

r- 00 w'N

1111

C- ,

15N E

Ccz

2- 0 0 N ~

~~.)NI,6 C 00 C-4

en 1 1 T "1c m

m--)0 - NI N

m C-

511 1 11 S4

4 061c111

I C N

06 u C)

C1 V) E.

' n 'I V- 0 r- 00 Cr A 6 "c

TR 9407 11-

-UNIVERSITY OF WASHINGTON ° APPLIED PHYSICS LABORATORY

duration, and swell from distant sources. The first two generally result in wave heights

considerably less than those for a fully developed sea, whereas the third usually produces

larger wave heights for the same wind speed. All three can play a significant role in

modifying the general surface conditions described by the sea state.

Of the three sea state codes presented in Table 1, the WMO code is the one recom-

mended, for two reasons. First, it is the most widely used, both worldwide and in the

United States. Second, this code conforms more closely to the Pierson-Moskowitz 8 rela-

tionship between wave height and wind speed for fully developed seas. Table 2 summar-

izes the specific wind speeds and wave heights to use in accordance with the WMO sea

state code.

Wind speed is the key environmental correlate used as input for the acoustic models

that predict surface backscattering strength, surface forward loss, and ambient noise

level. The probability of encountering a given wind speed is plotted in Figure 1, which

shows that 80% of oceanic winds typically range between -3 and 11 m/s. The median

Table 2. Recommended wind speeds and wave heights for WMO sea states.

Significant rmsWMO Wind Speed,a Wave Height,a Wave Height,

Sea State kn (m/s) ft (m) ft (m)

0 1.5 (0.8) 0.0 (0.0) 0.0 (0.0)1 5.0 (2.6) 0.5 (0.15) 0.13 (0.04)2 8.5 (4.4) 1.5 (0.46) 0.38 (0.12)3 13.5 (6.9) 3.0 (0.91) 0.75 (0.23)4 19.0 (9.8) 6.0 (1.8) 1.5 (0.46)5 24.5 (12.6) 10.5 (3.2) 2.6 (0.79)6 37.5 (19.3) 16.5 (5.0) 4.1 (1.25)7 51.5 (26.5) 25.0 (7.6) 6.3 (1.9)8 59.5 (30.6) 37.5 (11.4) 9.4 (2.9)9 >64.0 (>32.9) >45.0 (>13.7) >11.3 (>3.4)

aMedian values of wind speed and wave height have been used in lieu of the ranges shown in Table 1.

11-4 TR 9407


SEA STATE

0 1 2 3 4 5 6100

S75

-J (

• 2s.co

0a 0 50(L

S25

00 5 10 15 20

WIND SPEED (m/s)

Figure ]. Examples of cumulative probability distribution of measured oceanic winds withcorresponding sea states for these latitudes.9 These data were obtained using theSeasat radar altimeter and averaged over the 3 months that Seasat was in operation(7July to 10 October 1978).

wind speed for the three cases shown ranges from 5 m/s to 9 m/s; winds corresponding to

sea state 0 or sea state 6 and beyond have a very low probability of occurrence. The

figure shows representative cumulative probability curves; wind probability data for

specific geographical locations and seasons can be found in marine climatic atlases.

B. BACKSCATTER

Sufficient experimental and theoretical work has been done in the past few years to

show that scattering from near-surface bubbles dominates at low to moderate grazing

angles and that scattering from the air/sea interface dominates at high grazing angles.

The resultant surface scattering strength (in decibels) is expressed as

S, = 101og[ar(y)+r( b(+)] , (1)

TR 9407 II-5


where

(b = dimensionless backscattering cross section per unit solid angle per unit

surface area due to volumetric bubble scattering

(y = dimensionless backscattering cross section per unit solid angle per unit

surface area due to sea surface roughness scattering.

The roughness contribution ar is divided into two components:

(f, due to large-scale wave facets based on specular point theory

CSu, due to small-scale roughness.

The term (Tb treats both scattering (reradiation) and absorption from bubbles in a con-

sistent manner. The components in cyr contain an additional factor that takes into account

bubble extinction (reradiation plus absorption) because the acoustic signal must traverse

the bubbly layer to reach the air/sea interface.

1. Scattering from Bubbles

Crowther, 10 and later McDaniel and Gorman, 1 developed the expression for the

backscattering cross section of a horizontally homogeneous layer of near-surface bub-

bles. The expression, recently modified by McDaniel 12 to include coherent addition of

two of the four paths involved, is

Ub __.2 p r 8 1 + 813e-2p -- e -4p 2ab=- 4r • [ 2f3 (2)

where

P3 = P3v/sinO (0 = grazing angle) (3)

and

5r = reradiation damping coefficient at resonance - 0.0136 (4)

11-6 TR 9407

UNIVERSITY OF WASHINGTON" APPLIED PHYSICS LABORATORY

The quantity P, is related to the depth-integrated bubble density of resonant sized bub-

bles. It has been estimated as a function of wind speed U (in meters/second) and fre-

quency Otin kilohertz) by inverting Eq. 2 to yield P., using the la..e Vc.K...dt...Ig .Uda.-

base described in Ref. 15. The result is

1.'= 1 .5 " ++04701 V L(f./2 5 )OF5. U < I n/s (5)

rV = 3.(U= 11 m/s)(U/l l)" L IŽ I m/,;

The remaining variable is the total damping coefficient (reradiation plus thermal) at reso-

nance 8, which is a function of frequency-

6 = 2.55 x 10-lf•'. (6)

Equation 6 is from McConnell and Dahl' 3 and represents a fit to measurements by

Devin.1

Note that the azimuthal scattering angle does not appear in Eq. 2; measurements to

date have not shown the scattering cro.A.S -'s .. a .... ,1j• ,,. ,•, a.l... .A,,, 4t i,,t

bubble densities. Eq. 2 reduces tos•ine 8" 7Sifl- 8= r

%* (7)

and the scattering cros section becoine.; independnmr ol •"u"b-le de-:.I.. (and w""id

speed). This saturation condition has been verified by several experiments."'- The low

bubble density limit when 1 < I is also of interest, in which case ,b bcomes

a =151 (8)

2. Scattering from Sea Surface Roughness

i. Scattering from small-scale roughness

Like o/b. a,, is based on data but guided by theory. in this case ornposiie roughnice'

theory developed by McDaniel and Gorman t' and McDaniel.l5 This theory is founded

A, Bragg scattering from surface ripples satisfying the condition LR X/2cosn whc r

TR 9407 11-7

ADR I 994;'

-UNIVERSITY OF WASH~INGTON - APPLIED PH4YSICS LABORATORY

LR is the ripple wavelength and ). the acoustic wavelength. These ripples ride upon the

lar-e-scale waves. and their composite describe,. the surface roughness. The main effect

of the laree-scale waves is to modulate the local grdzing angle 0. The l~arge-scale wa-%es

als:o shado~x portions of the wave profile, but this effect on backscattering strength is res,-

tricted to angles less than 5' wvhere bubble-1 cafer; m, ji. nrA-vn n Ac - rpriii thr-

Ra\ leigýh-Ricc formulation for the scattering- cross section can be applied. giving,

Ar, IAU) tan4 0, 0 585,ý (9)

0.. 0, 6> W5c

with an adjustahlc coefficient A fitted to data in the grazing anale inlter'al 30'-70'. The

interpolation formula described belnv. will take care of the sharp transition at 8F~.

The grazing angle dependence. tan 4 9 is supported by data reported by. Monti et a.1

and Waltzrnan and Thorsos.9 Thrse data (taken at 10-60 kH7) indicated no obvious

trend with frequency. According to the Rayleigh-Rice formulation, this frequency

independence is consistent with a tan 49 grazing! angle dependence because the twNo

deperndencies; are linkcd together by the shape of the wv-egtpwr~cta ~st

Wtk). The grazing angle and frequency dependencies imply that WVk) - k-. where k is

the -wavcnumber for surface roughness. The wind speed dependence of 0,. was found

from acoustic data by Waltzman and Thorsos 1 and McConnell.:" giving the coefficient

A as a function of wind speed:

A (U) = 1.3 x 10-5 V2 (10)

Note that since (7, is dimensionless, 1.3 x 10 5 must have implicit dimensions 5:/ny

h. Scattering from facets

The term art in the expression for the surface scattering, strength~ is applicable for the

near-specular scattering that occurs at steep grazing angles. Like ab and c;,,. the form of

the equation for Oj. 'Is guided by theorv. 21 but the dependence on enivironmental condi-tion,. is found in the acoustic dat~a. Fur very hig aznagl. e7 t'."" hcr

reduces to time high-frequency limit of th:ý Kirchhoff approximation and. assuming aGaussian. isotropic distribution (if surface slope.s. the ,cws!ering crkv,-' section I

11-8 TR 9407

I- UNIVERSITY OF WASHINGTON. APPLIED PHYSICS LABORATORY

4ns2 S 2

Iwhere y = 90 - 0 is the facet reflection angle and s. is the mean square s-.rface sdope.

The mean square surface slope is estimated using

sZ = 4.6 10-log,(2.1U') U _> I ris (12),

' = 0.0034 U < I m/s

I The origins of the subniodel for s2 and its comparison with data are discussed in Section

IT.R.2.c. The physical basis for this theory is that the ,tre,,,, ,-fimw n,. 'prti¢..l

I incidencc will come from properly oriented facets on the sea surface that specularly

reflect energy back to the receiver.

c. Interpolation between the cr, and at cross sections

I The surface roughness component a, to the total surface sci.teriny strength is found

b% interpolating between y,1 and (.,. using the interpolation function 22

f(.) - (13)

and first computing a,, such that

I Y, (0) = f (x)aj.{e + (I -f (xt 1,.x(6)

w\ith the argument of the interpolation function defined as

x - 0.524(0,-- 0) . (15)

I where angles 0 and 06 are expressed in degrees. Thi" transtion occur. M. "'^ "'"" OfO.. defined as the angle at which af is 15 dB below its peak value at 0 = 90". Finding Of

depends on the angular quantization (we use V" in the sample p!ots given nex!.. For an

arbitrary quantization, Of is defined as the sinallest angle 0 that satisfies

l0logI;,90-)/ao.A0) •__ 15 dB. The interpolation function provides for a smooth transi-

tion between the two cross sections, each of which is based on approx,,,,,•,,N .... v ies ,,,

TR 9407 11-9

A rN I oo A r:D

_______________UNIVERSITY OF WASHINGTON - APPLIED PHYSICS LABORATORY

%N ithin a certain range of grazing angles. Finally. cy, is computed from (T, by correcting

for the extinction loss due to penetration through thle ncar-surface bubb!elar.ivn

0'(0 = " () 10SK,01/0 .(16)

Tile equation for SilL (Surface bubble loss) is given in the next section (Eq. 291.

3. Total Surface Backscattering Strength a. .i-

Model predictions of total surface hack,ýcattering strength as a function of grazing

angle at frequencies of 25 Ukz and 60 kHz and wind speeds between 3 and 15 rn/s are

shown in Figures 2a and 2b. The m-odel is CIeANl milc more sei'31iv toWnd;u

when it is less than about 8 rn/s. The reason is that surface wave breaking shuts down

within this lower wind speed range. and therefore the production of near-surfacc bubbles

is much reduced.2>

4. Mtode VData Comparison.;

Representative modcl/data comparisons, are presented in this section. The data ori-

ginare from three experimfenits feprebenting buth deep water and shajikv: water condi-

tionh: FLIP77,'5 a 1977 deep ocean experiment conducted off the California coast:

NOREXS5.Y' a 198-5 shallow wairr exp.erimvit cunducted 4Onin wes of the -rix

and Danish coastline in waters 30mi deep-, SAXON-FPN3 4 a 1992 shallow %%ater

experiment conducted at thc NOREX85 site.

Figures 3-5 compare model predictions with FLIP77 data. In Figures 3 and 4. thle

model inputs for wind speed are the measured wind speed ± I iris. In Fi oure 3. for exam-

pie, the measured wind speed is 4.5 rn/s. and the model is run at 5.5 rn/s (dashed line) and

3.5 in/,, (solid line), Tn Figure 5. the wind speed is 12.8 rn/s and wind speed changes of

un/s mnake little difference in the rno,~ prediction.;. AgsLIIeihi-t L%~I e moeland the data is quite satisfactory.

Figures 6-8 compare model predictions with data from ifhe NORELX8S and

SAXON-FPN shallow water data sets. In Aligure 6. SAXON-FPN data taken at various

11-10 TR94107

AmnlnntArn ~-

IUNIVERSITY OF WASHINGTON * APPLIEO PI'i'SiCi. LABORATOi•¥

20

cr- 13,LL

I I

"6O 0 20 30 40 50 60 70 80 so

1 ~0

(b)

I '°4--

0-

1 10LAJ

O 1-0 20 3 0 4 0 5 0 so 7 0 B0 90

I ~GRAZING ANGLE (d"•)

Figure 2. Grazing OM gle depetuhencc of slvýace 6a'ksc'altering, strength at (it 25 k(Hz and (b,

60 ktf: .for isind speeds betivren 3 and 15 r/A. ripe numb, r (in eac'h curte indicate.s

the wind speed.I 9 7 I

Ii TR947 '" l

UNIVERSITY OF WASHINGTON• APPLED PHYS!CS LA2,FA'CrOY

10 , "-f-

/ -

E .20[

_ .33Lw I

I-

"O 10 20 30 40 50 60 70 8.2 90GRAZING ANGLE Wieg)

Figu e 3. Comparison ,f bacl.watrering nmodel u ith dara from FLIP77. Model inpus ate

f= 15 kW: and U = 3.5 n/s (solid linc) and 5.5 ti/s (dashed line;, representing a±1 nds spread about the imecoured wind .pteed of 4.5 n/s.

/--

I..

Z_ -0-,0 .40'-c

.50',

D 10 20 '?n 40 so 60 70 80 9cGRAZING ANGLE (deg

Figure 4. Comparison of back.catterin,, -nodel with data from FLIP77. Model inputs ireIf= 25 klil: an(d U = 4.1 ,./s tsolid line) and 6.1 Wms Idashed linei. represcsing a± I m/s spread about the measured i ind speed of !.I m4.

11-12 TR9407

I] UNIVERSITY OF WASH(NGTON APPLIED PHi¥SiCS LABOPATC;V

g.20

] ¶----- -- ________________

S-0-

.50-

0 0 2C 30 4 0 5 0 60 7 0 803 90] GRAZING ANGLE (deg)

Figure S. (Comparison of. backscattering , model with .data from FLIP77. M ,,,,,.; pit .are

Sf = 25LH: and U = 128, t/s.

~5~ 6 -6II ___0 ___. 10 2040 6• -2 o 0 7 o6e• ,

a:O Ce

SGRAZTNG ANGLE (Aeg6

[] ~Figure 6. Comnparison of back, cattering model with dataa from SAXON b"PN. Model inputsS~~are .f = 70 kHz and U = r n/. (dotted Iine). 4 mA" (.•olid line), and 7 nds (dashed

UU

inei. T6.e number beside each data poi rot iSX the winoe speed.

lITR9407 11-13

UNIVERSITY OF WASHINGTON -APPLIED PHYSICS LABORATORY I

10I

of0 -

-zIC -- '

ItIz 30- /

.5r.-C;40-*

.6.

C 10 2C 30 40 5o 60 70 8o 90GRAZING ANGLE Idc0)

Figure 7. Comnparison of backscattering mode! with data from SAXO.N FPV. Modtl inputs arcf = 70 kH: and U = 8 s/s *solid lineI. and 16 FVs5 (dashed linei. Cirde.' represettdatta takep, in the it itd speed interia! 12 < U 5 16 ,ri.: a.teri.•v- ripreepit data iakenii the wind 3pe~d wten'a! 8 < U < 12 12 s.

-0!

p I

50,Ii ,10 .... ....

GRAZING ANGLE (dog)

Figure 8. Cotipati.%on o fbaj~kscatteriing model w-iih data from :VOREX'R5. M-odel inpin. tire,f 8 kiltzand 1; = 17 i'J..

11-14 TR 940"1

mM

low wind speeds (noted in the figure) arc compared with model predictions for U = I m//,

(dotted line), 4 m/s (solid line), and 7 m/s (dashed line). In Figure 7. wind speed data

1beween 8 and 16 mns. also taken during SAXON-FPN, are shown grouped toge-thr. The

circles represert data taken at wsind speeds of 12-16 m/s: asterisks represent the interval

8-12 mA. The model results are for U = rn's (solid line) and U = 16 m/5 (dashed

line): the results for the two wind speeds are distinguishablc. but their difference is less

I than the overall spread of the data. Data from NOREX85 are shown in Figure 8.

1[ 5. Model Implementation Notes and Model Accuracy

a. Implementation

e Additional care must be taken to compute the backscattering strength at grazing

angles approaching 0' to avoid numerical problems. We recommend that the

j scattering streng:h values for grazing angles <0.5' be arbitrarily deCe,,1-mined by

linear extrapolation of the 'alues at 1' and 0.5-.

b. Accuracy

* For wind sp.eds greater than about 8 m/s, and at all grazing angles. a nominal esti-

mate of model uncertainty is ±4 dB: that is. most data will fall within this range of

the model.

9 For wind speeds less than about 8 m/s. model uncertainty necessarily increa-se.

Sbecause the precise threshold for wave breaking (and bubble productioni may vary.

Furthermore, in approximately half" the data runs we earnined that Nere taken in

the wind speed range 4 to 8 m/s, scattering strength in the grazing angle range

0 = 5 -20" decreased \0ith 0 more strongly than what the model predicts. The rea-

son for this remains unclear. However, \, ithin the wind speed range of 4 to 8 r/s.

I the air-sea interface is typically more sen-itive to small changes in wind speed.

Therefore, model predictions based on wind specd alone -re more difficult. An

TR 9407 11-15

UNIVERSITY OF WASHINGTON* APPLIED PHYSICS LABORATORY

Cstimate of mod,,el Uncertainty for kind speed less than 8 rn/s is +5 dR. We recome-

mend. however, that simulations be made using a -l mr/s wind speed spread aboutthe actual measured wind speed. This v.,-, th. ...... .-a :or., %A .... h ca I-C (AS II A.,.%: . uI,.:d"

as to the range of expected reverberation levels.

* The model ht,, been -ompared with data taken at frequencies between 12 and

70 kHz. and a frequency dependence in modce kccuracy h", not, b..n.. "b"- 0.

6. Spectral Spread

The power spectrum of a signal scattered from the sea surface at high frequencies

has, been found to have a Gaussian ,hape and a width principtlly dep-n.-,. "

height.15 The spectrum is expressed simply asP(f • = A e--y'/" , t17)

where A is the spectral amplitude (normalized to unity in this dicussionn1. f, is the spec-

tral shift, and Y is the standard deviation, which is related to the half-power spectral

width by

Af~js = 2.35; . (18)The spectral shift for a free-.sx irr'ir.n "- c "s 'e ... l...;; ... .... ....."'"- ." ";"""

Ir lllh I• IV.All++ lgl• .lllf %ýiU lJ,,l, lgld %%AmII mtl+S

associated with the vehicle's velocity. For a fixed sonar (e.g.. bottom-mounted) the shift

is typically determined by the radial component of the tidal current. In the following dis-

cussion. expressions are given for the normalized spectral width

T1f=Ajo (Hz)f(kHz)

and the spectral shift is ignored.

The expression for 7l can he factored as follow s:

1" = 2,35FI(f)F:(o,0)oj, (20)

I1-16 TR 9407

IUNIVERSITY OF WASHINGTON ° APPLIEO PI4YSICS LABOAATOAY

I v here a,. is associated with the orbital motion of the sea surface in [he up/down wa'e

tirection. From the data given by McConnell et al..1 5 this is

I a,1 = 0.894h 0/'. (21'

I v,%here Ih is the rmns wake height in meters. The mis wave height (in meters) can be

etimat,.d from wind speed (in meters!second., assuiming a Pieron.-Mosknwit7- mroe!

I for the sea surface giving

h = 5.33 x 10-3 U2 (221I Note ilhat the conunonly used sig•i-'•.f""t a. "' ftnt il. - . , - ,;,,-., 1.

1 a ".%,• •ý if. kit A All* 1/•.| i A., 4""' i t. - tol m. *I.

The combined orbital motion termn has a marked dependence on azimuthal angle at

low -razing angles. Both open ocean and e.. li...e•,-. daa hav ..... that, the angular

1 factor in Eq. 20 can be fitted by the expression

10- 0.0034 101 cos0 1,0 1 -<90I~ ~~~F F(o.0) = Jl-OO 3 II[1.0-0.0034 I 101- 1801 co;0 90 I< IO• 080c (23)

The azimuthal angle 0 is defined a.; 0, in the up-wave h,,.,, V•(,,,, ,.,,,o.,,, a,,.,A-,,

propagation is opposite to the wave front velocity vector). ±90( in the cross-wave head-

ing. and I8SO in the down-wave heading.

The factor F, (ft) in the orbital motion term of Eq. 20 describes the variation of the

S�spectral width with frequency. The normalited ,idth decrCeseý with increasi.n. fre-

quency a,,

SF 1()= 1.0- 0.0084(f- 25-

I figure 9 shows the final rcsuit for rl in the up-/down-wave direction for three seleciedfrequer.cies and a grazing angle of 60'. The frequcncy dependence given by Eq. 24 is

I shown in this ligure, as is the v"riatil with wave t ,,.ci,,,, b,,. 2! .,$

The model is %ell supported by data for the grazing angle range 0W-301 and the fre-

Squenc) range 15-60 kHz. The spcctrail width datta also agree .well ""ith Adar .A. .. par -

ularly at C hand (6.7 cm wavelength: see Valenzucla and Laing" and McConnell' 5 e1

I TR9407 ll-17

AD91 99453

UJNIVERSITY OF WASHIN~GTON - APPLiELJ PH~C LAGORATO __________

7ý

-C

CC1 002 0.04 0011 clo 02 C-4 0.7 1 2 3rms WAVE HEIGH- I~n)

Fi-tir 9. W, c hi~ derendte'nce O~f 1h' 17onnnalized spectral v.idth in th' up/doivn w~ave direr.tion al thzrLefircquenc-is.

The frequiency dependence given by Eq. 24 between 60 ki 1z and 10M Hz is simply an

extcrapolation based on data taken in the 15-60 kI-z range. No acoustic data were avail-

able at grazing angles beyond 60'; the suggested model is based o~i theoretical arguments

and radar data. Finally, it is possible to have, 2dditfin.-M sp"ctral spireading dUe% tv Dopjler

motion caused by the small-scale waves. This condition would exist only if backscatter-

ing were dominated by small-scale, or capillary, waves, as, dc,;cribeo by 0, (Eq. 9). The

effect on total speccral sprea J is riot signifleant. aind data presented in ikef~s. 15. 20. and 25

are well described using Eq. 20 without an additional term associated with capillary

Waves.

11- 18 TR 9407

Arw I) 99A['

I1 , UNIVERSITY OF WASHINGTON • APPLIED PHYSICS LABORATORY

C. FORWARD LOSS

I. Introduction

Models for high-frequency surface forward scattering and reflection are briefly

j surmnarized here. Supporting discussion and additional references to the literature are

given in Ref. 26. At high frequencies, incoherent scattering near the specular direction

I (forward scattering) almost always dominates over coherent reflection because of the

large roughness of the sea surface. Trkefore,, modeIng ,, of€ foFV1 ... V S, ,al-U.. i. ;I I *Aa1 .

rant for predicting the reduction in level and time spreading of acoustic signals. The pro-

perties to be modeled include the scattered intensity, frequency spreading, and statistics.

I For the high frequencies of interest here, the angular distribution of the scattered

intensity can be estimated using a facet-re flet.tion-,ype. m-de!. 26 .27 Data in support of

such a modeling approach arc reported by McConnell 28 and by Dahl and McConnell. 29

If relatively wide vertical and horizontal beam widths are involved, a detailed scattering

model describing the angular distribution of .......-.- *•.....1.. . .-.n....r... .... : ....

tion is not necessary to simulate typical propagation and reverberation conditions. In

such cases. the single bounce, fo-r;-','d scattered signal can be adequately represented by

an effective reflection loss. Invoking this approximation requires aat vertical beam

widths be >20" and horizontal beam widths be ?5°'. In the following we assume these

beam pattern criteria are approximately ,at,,ied.

2. Preliminary Discussion

The time-dependent received intensity after a surface bounce. excluding the direct

1 path contribution, can be written as

I I received (t) = !tot) ab ,(25)

where

I a! = total intensity (coherent plus incoherent) following the surface interac-tion, neglecting absorptionI

I TR 9407 11-19

Ar'A IQQAq1

______________UNIVERSITY OF WASHINGTON - APPLIED PHYSICS LABORATORY

al absorption factor due to bubbles.

The frequency spreading effects will beC descrfibled llafwr in Section ILAC. Tc f Acor 1

/E~a 0) can be written (see Section 11 of Rcf. 26)

ltola:() :- 'coh(fl + IA(t.) .(26)

%%here

cor = cohcrcnt (reflected) intensity

1()= incoherent (scattered,) intensity.

The coherent intensity shows no pulse elongation; the incoherent, or scattered.

intensity does. Thus. in g-ener~al. both I i#N ( ") an I(0) -#ntnbute #U^in thAf-t pa;ý o

the received si-nal with a duration equal to the transm~itted pulse length. whercas subse-

quently only 1,(t) is prc sent.

3. Effecive Reflection Loss for Foritard SterigiRerbrio mton

In reverberation. or total backscattering. ray paths involving surface bounces contri-

bute to the reverberation level, part icularly in shallow water or surface ducts. These Sur-

face bounces involve surface forward scattering, possibly reflection, and absorption dueto neUr-surface bubbles. In reverberation simulations involving a few bounces and usi Igwide vertical beams, it should be a good apoIlk, ...... tomode 1.11 o-,ac boune .a.

a reflection with the reflection loss given entirely' by the -surface bubble loss" (SEL).

Thus, the surface reflection loss RL is given by

RL (dB I =SBL(dB) 10Olog 10ab (27)

where the surface bubble loss, i& given by Eq. 28.

In this approximation. no loss is associated with scattering frorn the air/sea inter-

face. so in the absence ýif bubble attenuation this scattering is treated as a 0 dB reflection

loss. This approximate treatment of surface seatteriiig is justified when (he bcanis are

11-20 TR 9407

I ~ ~sufficiently wide (Ref. 26, Section nA) Ud 11 ~ ~ d~t owr

scattering can he ignored. The latter condition is met when the elongation hime L is small

I compared with the time scales over which the total reverberation Chnange., (set SeýCtionII.C.6i.

1 ~ ~In general, the 0 dB loss model for jurfc sctern shul Idn,1to j' C

latine volume and boundary reverberation involving wide beams and few surface

I bouncecs. Howe~er, in applications such as the simulation of target returns involving

pulses with high temporal resolution, it may be necessary to account for the. pulse elonga-

1 tion caused by the surface interaction (Ref. 26, Section V.C) and the concomitant reduc-

tion in peak amplitude.

I If more than about three surface bounces contribute significantly to the reverbera-

tion or target return, then the 10os o-wing- 10 anglrspreýalding.U1 1in te vertCica Cu~ becom

important. This loss arises because the cumulative angular spreading associated withrough interface interactions causes energy to arrive outside the main part of the receiver

beam pattern or to be lost in the bottom above the critical angle. For surface ductingsituations. angular spreading appcars as an effective duct leakage because energy is

I -Anal-fr h-dii.1'frdirected hi. -) !:Tin- angles greater. than- the Wr)clry , .. te ut ~o

tunately, very .-%mation is available on the loss due to angular spreading in

multiple bounces.

I 4. Absorption Due to Near-Surface Bubbles

IThe, e of bubbles near the surface can be described by a surface bub-ble loss, which is related to ab v'ia Eq. 27. A model for SRL is.'

SBL (dB) = .6x1-'u1.7f', V> Ž6 m/s (28a)

ISBL 013) =SBL(U= 6 mA) e 1 'U-6 .), L'<6xns ,2 )

1 where U is wind speed measured 10 mn above the slea surface, f is acoustic frequiency inkilohertz. and 0 is the nominal grazing angle of the surface bounce path (60> 0*). The

TR 9407 11-21

UNIVERSITY OF WASH!NG TON" APPLIED P-YSIvC, I ^0A=n 0VnO

model includes a wind speed threshold of 6 m/s to account for the threshold of bre, ing

waves (also known as the Beaufort velocity) and subsequent production of bubbles.

Figures 10-12 show representative model'd•/at,., comparisions fo'r dfinta lh

between 20 and 40 kllz in the open ocean 31 off California and in coastal waters1 3 off

Whidbey Island in Puget Sound. Because the data were collected at different grazing

angles, all data have been normalized to '10. The model provides a reasonable represe

tation of both open ocean and coastal data, with nearly all data points falling withZf

±3 dB of the predicted curves.

Scattering from bubbles will prevent SBL from becoming arbitrarily large. A nomi-

nal limit for SBL is 30 dB, ba;ed on ;cattering from, te underside of a unifor" layer of

near-surface bubbles. However, such a limiting value for SBL has not been observed in

x = Wh.dMey Island Expe-•nent

o= FLIP E x:wrime r

10"

±," dB ine-laottepeitdcn

-TR90

........ ..........- °="c c •

WIND SPEED (rm's)

Figure 10. C'omparisonz o~f SBL model predictions (solid line) with measured 20.kH: data .fromthe FLIP and Whidbey Island experiments. Data from various grazing angles have

been normalized to 10• grazing angle. Upper and lower dotted lines represent a±3dB intervaI about the predicted curi'e.

11-22 TR 9407

UNIVERSITY OF WAS 4INGTON APPLIED PHYSICS LABORATORY

15~x

x a Witey Is~an• Ex:enrnern

am FLIP Experment

10 . a

rS..°..

............. . .. .. .

co

00

5 10 isWIND SPEED (ints)

Figure) 1. Comparison of SB81 mode! predictions (solid line) iwith measured 30-kH-: data fromthe FLIP and Whidbey Island experiments. Data from various grazing angles havebeen nornalized to )O0 grazing angle. Upper and lower dotted lines represent a±3 dB interval about the predicted curvne.

15

x . W•'ibey Islard Expermen',

c FLIP Exp:emel.

10- x

". . . .. .. . . . . C '

0 ++

Co 5 ¶C 15WIND SPEED (ws'5J

Frigure 12. Comparison of SBBL model predictions (solid linej with measured 49-k-: data fromnthe FLIP and Whidbey Island experimnents. Data from various grazing angles havebeen normalized to 10' grazing angle. Upper and louer dotted lines represent a±3 dB inten al about the predicted curve.

TR 9407 I1- 23


data. because the patchiness of the bubble layer will nearly always admit some surface-

scattered energy to pass. Thus we suggest a nominal upper limit of SBLmax equal to

15 dB. This value is based on the SBL measurements reported by Thorsos.12 McConnell

and Dahl,b3 and Dahl."'

a. Depth-dependent formulation of the SBL modelThe formulation in Eq. 28 represents the ...-- 'y d--.... Int , t .. 114,1t.,,,-

tion for a surface-reflecting ray under isovelocity conditions. Since isovelocity is

assumed, however, the model cannot account for refraction effects, and in the case of ray

vertexing (0-40) the model becomes invalid. By ray vertexing, we mean the ray goes

through a turning point at depth z, because of refraction. This case is only important for

estimating SBL if the ray vertexes within 10 m of di surfaace, ie.. if"^ is 'lss thla l-im.

because bubble aatenuation will he extremely weak beyond this depth.

Below we provide an alternate depth-dependent formuation"'. of EQ. _18" that

accommodates rays vertexing within 10 ni of the surface. Two versions are given: the

first (Eq. 29) applies to an arbitrary sound speed po1-,file, ,rrIt ,pd (Pt, and .

to a linearized sound speed proftle. We recommend use of the Eq. 34 by linearizing the

sound speed profile in the top 10 m of water.

The version that applies to an arbitrary sound speed profile is

SL (dB =.13 2dz. (29)

where a(:) is the depth-dependent bubble attenuation coefficient, Z; is the vertexing

depth of the ray. and 0(z) is the local grazing angle at depth z. which is a function of the

sound speed profile. The attenuation coefficient is

a(z) = we' (30)

where LB (in meters) is the decay constant. or e-folding depth, for the exponential decay

and

11-24 TR 9407

UNIVERSITY OF WASHINIGTN & APPLIED PHYSI, S V I %ATOI

cx, = 0.63 x I0- 3 uL5 7f0-'5LB, U Z 6 m/. (3ia)

= a)(U = 6m/s~ e l.s) e 6I, U<6 m/s (31b)

A simple model describing L8 vs wind speed (in meters/second) for bubbles within

the resonant size range most relevant to torpedo frequencies is

LB=0.07x U (32)

This equation, which describcs incasurcmcnts repo.ted in. IR. 33., pdUC.es .. tIma... of_4r

LB that fall approximately between estimates derived from similar models reported in

Refs. 34 and 35.

The attenuation coefficient a(() is integrated between a depth of 10 m and Z-. and

multiplied by 2 to estimate the two-way denth-inte-grated bubbl, attCnUatin, Which j5

equivalent to SBL. For example. if the ray reflects from the sea surface, C, equals 0; if

the ray vertexes within 10 m of the sea surface, then z. is the vertex depth. The user is

cautioned that Eq. 29 has a singular point when 0(.z)-40 Which will cause .. u.r.. -cal

problems if not handled correctly.

b. Recommended version based on a linear sound speed profile

To estimate SBL for rays that vertex with.. in!0 rm of the. i., r "f .2.0. wreo-MMA"d

linearizing the sound speed profile in the upper 10 m such that it satisfies the form

c(z)=Co +gz , (33)where co is the sound speed at the surface, g is the so.1nd o"meed r-.adie,,n. ;in ;inve,.

seconds with g < 0 representing downward refraction, and z is depth measured from the

sea surface. The result is

SBL= 2okRce 2 \4(,/k60o) (34;

In Eq. 34. 4) is the tabulated probability integral, or error function. and is defined as

IS~TR 9407 II-25

IUNIVERSITY OF WASHINGTON* APPLIED PHYSICS LABORATORY

XI= (35) 1

The remaining variahles in Eq. 34 are I/Rc = the ray's radius of curvature, which is equal to cJ./I g I

C I = the sound speed at the vertex depth z . I

Oi(. -- local grazing angle (in radians) of the ray at 10 m depth

k = Rc/(2Ls). IThe argument "\'k01o) of 4 will in many cases be _>2. making 0 ncarly unity, and it is Isufficient to write

SBL (dB) = 2av'R,,L n2 e- (36) Ias the surface bubble loss for a ray that has vc.rtexed" :w"t- " -,. m oi .th ..ea " .

5. Model Usage Notes and Accuracy Ia. Model usage notes I

* The coefficients in the model are based on acoustic measurements made in the fre-

quency range 20-50 kHz. The model is therefore a high-frequency model; as a jbroad guideline, the model's applicable frequency range is 10-100 k.Hz. We note

that the SBL model has recently been shown to give results that are very consistent

with results from a model developed at the Nava! Uudersea Warf,.. Center fOr

ship sonar frequencies.3s 6

The effect of near-surface buhbles on the real part of the sound speed (known asthe sound speed anomal') is ignore,;.. since wihi

range the main effect of bubbles is attenuation, equivalent to the imaginary part of

sound speed. II

11-26 TR 9407 I

UNIVERSITY OF WASHINGTON, APPLIED PHYSICS LABOr )AiVy

I The model is based on measurements from a single surface bounce path. To com-

pute SBL for propagation channels involving multiple surface (and bottom) inter.;.>

tions. the total SBL is the sum of the individual SdL values computed for each

surface interaction. We caution that model performance for these conditions has

not been evaluated.

" The model does not address geographical dcpendencies. We i ct that. in gen-

eral. littoral waters and more pristine oceanic waters will differ in terms of bubble

properties. With few exceptions, however, bubble measurements rpotl-ed in-A the.

literature show within-region variability that tend% to obscure any between-region

variability, e.g., cf. Refs. 13 and 33. This fact. taken together with the data shown

in Figures 10-12 (showing both coastal and uca-i" ud"ta. suppor ue o ngie

model at the present time.

" Equation 28, rather than the alternate depth-dependent version in Eq. 29. should be

used when SBL is used as a submodel for surface backscattering (Section 11.B) AnA

ambient noise (Section 1I.D).

b. Model accuracy

" The model's uncertainty in comparisons w'ith th,. ,u,,it SBL, dautata,, is approxi-

mately ±3 dB. As a predictive model, however, we assign more conservative error

bounds of ±4 dB.

" Ping-to-ping fluctuations in SBL will be approximately bounded by -3 and +5 dB

about the predicted mean SBL value. These fluctuations are dominated by sea sur-

face scintillation, or the phase randomization that occurs in forward scatteri-g.

" The SBL model predicts the mean energy loss in surface bounce paths due to

extinction from near-surface bubblcs. where the el.crgy. o? tirte-integrated inten-

sity, can be modeled with a 0 dB loss in the absence of bubbles. Model perfor-

mance will be degraded in conditions under which the 0 dB loss case cannot be

assumed. Some examples where this could occur are as follows:

TR 9407 11-27

UNIVERSITY OF WASHINGTON APPLIED PHySICS LABORATORY [I

- The model is used to simulate data g..,theCred wi;th narrow, transmit and receive

beam patterns (see Section 11, Introductioni. In this case, the measured SBLwill be greater than the simulated SBL because the data undersample the

angular distribution of the scattered intensity,

- The model is used to simulate the loss in the peak value of short-pulse data.

A short pulse is defined as one with a duration time r much less than the

characteristic pulse elongation time L for surfac" sc,,atter.ed ar;va. lr. For

short pulses, the cnergy loss and the peak intensity loss no longer track each

other. The total energy will be underestimated when based on estimates of

peak intensity, resulting in data losses that are greate- than the simulated

losses. A rough guide is L < 4R. where L is in milliseconds and range R is in

kilometers. A more precise model for L is given in the Section II.C.7.

6. Coherent Reflection Loss

The combined effect of coherent reflection and incoherent surface forward scatter-

ing can often be modeled for wide beams by usi,,n-" no loss;: t.•h, effective reflection loss is

then determined entirely by losses due to bubble,. In a particular model application, the

coherent reflection loss (the loss due to the surface interaction and associated with the

coherent part alone) in Eq. 26 may be of interest.

The coherent intensity can be descrJbd with a reflection coefficient 262'

R = e-7: ,(37)

where X is the surface roughness parameter given by

41th sine7. - •. .(38)

where

h = rms surface wave height (m) (see Eq. 221

11-28 TR 9407

VI . UNIVERSITY OF WASHINGTON APPLIED PHYSICS LABORATORY

I ; = acoustic wavelength (m)

0 = specular grazing angle.

The coherent intensity is significant only when the wind speed and corresponding wave

height arc low enough that y < 2. For these conditions, bubble losses can ,e neglected.

The coherent reflection loss, RL. which is -10 logl0 R. is given by

I RLcoh (dB) = 305f 2 h2 sin2 8 , 39)

where f is in kilohertz, h is in meters, and a sound speed of 1500 m/s has been assumed.At high acoustic frequencies, the cohe•,,rent, ;int,%nsit is ,ian;r,,t ,nvly ,,hn IN#- s-ea

surface is nearly calm; for typical ocean conditions, Icoh(t) is negligible compared with

h(tn. We have includd the expression for coherent reflection loss (Eq. 39) for complete-

I ness. Its accuracy is good except at very low grazing angles (see Ref. 26. Section I').

1 7. Time-Dependent Intensity and Frequency Coherence in Forward Scattering

I a. Time-dependent intensity

i The surface roughness will again be assumed to be large (X > 2), ,,ince this limit

covers most cases of practical interest at high frequencies. We can neglect lcuh(t), o

I Consider a single surface bounce and. again, wide beam patterns. The energy, Jl),t)dt.

can be modeled with a 0 dB loss, but 4¢(t) itself will exhibit pulse elongation. (Bubble

I attenuation must also be included (see Eqs. 25 and 27). It is assumed here that such

attenuation does not change the form of the time depenudenccft' ,r,, i.,,,.,,,dA ...

characteristic elongation time, L, for 1,(t) can be estimated from (Ref. 26, Section V.CI.

L L- 2rjr, -- S.l0-e-0"%Ae) ,(40)rf + rZ c 9I

I TIR 9407 1T-29

S . ... . .. .. . I I

UNIVERSITY OF WASHINGTON.- APPLIED PHYSICS LABORATOPY

where

r1and r., = incident and scattered slant ranges alonrg thc specular path (mn)

C = speed of sound (m/s)

=specular grazing angli

s 2 = (large-scale) mean square surface slope

,to= tan- (S ).

The mean square surface slope s2 is estimated u.;ing

s2 0.0046 log, (2.1&U U > Im/s 0la)

=0.00.34 U < 1 (4 1b)

Equation 41 represents a logarithmic fit by Phillips3 to the optical glitter measurements

of Cox and Munk 3 The glitter rneasttrc~iicns were miaude 'froMi a sickove" ;ea

face which effectively removed surfacc wa~venunibr rompo~ients shorter than about

30 cm: hence they represejrt measurement of the 'iarge-scale" sea surface S!Opc.

Figure 13 show, the square root of Eq. 4 1. equal to large-scale slope s. compared

with acoustic estimates of s made, in open oce-a~n C.ndt;.Ain,,c T~hcet ina ý1%erderived by first measuring L and then inverting Eq. 40 to obtain an estimate of s. The

model for L bawed on Eqs. -40 and 41 described the data in Figure 13 to within an average

relafive error of ±30%1"(. Note that the spread in thfe data i& quite typical of sea Surface

slope measýuremnents.

If we use the expression for L given by Eq. 40. thc tiinc dependence of the scattered

intensity is

10A0

(r 0 0S~( (42.)

0('ýt/L)~~ - 01- T)L (

UNIVERSITY OF WASHiNGTON* APPLIED PHYSICS LABORATOAV

0.2 - -- - -r --

0 121r0

L

000

WIND SPEED) Jr's)

/- w•ir e P3. M odel 'o tri .vwa shl ope . s fqua/ to square root qft'Eq. 4!ai vs• estm ates of s (itriv, ed

firon mea~tureni.nts ofi L un~d int ersion (,(Eq. 40.

I where

"• I - t.,

t•=travel fimie for the .specular ray path referenced to the time

of transmit (U = 0)

o,= transm it pulse length (rectangula r pulse37

/(IW transmit pulse intensity

IAr unit area

i ~ and w here (P(x) is the probability in tegra l given i n1 Eq. '15. Equa tion 4 _2 ..... U~ U' ...

Sform for T.(t) for a single surface interaction l the generalization

to multiple bounces is

given in Ref. 26. Section V.C. An itlus irnion of !he coM tineJ effe,. (if increasing eirm-

gation time and increasing surface bubble loss is given in Figure 14, where (he scattered

intensity has beeii normalized by the multiplicative factor in Eq. 42, i.e.,

oAol~r, +r•r.

TR 9407 11-31

A~rI 199A4K

UNIVERSITY OF WASHINGTON- AFPLIED ,WiiCS LAiVRATIU;

For very short pulses, it is clear f ", .. A, 42 ..;' al i ' 1 A 1 l.... ... lt .. . . ,•..

sitv will not reach its final asymptotic (or peak) value. For modeling target returns. say a

single highlight, this reduction in intensi!y m 'ly be i ,- ,v, ,I 1 ,,, ,,Sin,, ,-,h,, w,.h h;n,lime resolution: the associated loss can be cstimated a, 10 log4)('Tc/L ). FinalT. it

should be pointed out that this loss and the elongation time L depend on the assumption

of an isoveloci:\ ocean. Strong det iaiior, s from, {hi; asstiption (e.g., a ra\ ihat is close

to 'ertexing at the sea surface) will invalidate the formulation for IA't given by Eq. 42.

1j1Doren b14ncC

TIMJE (msu

I-igure ]4 M'ode!e of rile su,?ice .for', ard bouwe' .ignaf illh~tr,•tij,z€ the e'ffec7s of nine eionfa-110on of rhe transmnitved ptd.e (" ? n7t¢ puh~c lengthJ and .su'1. ae bubb't' loss. Elon~ga.tion :timer and Hint1 .speed arc noted. Tire gnr:ing angle is 7.6r, thIc fu-quenc'v is25 kH:. til' source and receiver depths are both 50 ni, atnd the range i.€ 750 in. Thenoike level h,a.s been arbitrarily set at -- 1 dS.

b. Frequent) coherence

The inverse L-I (in hertzi is a measure of the coherence bandwidth of the chail-

neh': and therefire importunt both in designing av,'xeforms and in determining sif~nai-

processing strategies. Application of Eqs. 40 and 41 to estimate L"1 pro~ides a mearns to

11-32 TR 9407

A r%[D I O{ ':

UNIVERSITY OF WASH ING2TON. APPLlED PHY SN;C LAID3RAT0C%

obtain realistic estirnateN of~ the- coheenc bandwid for th4e channe as1% afUncionI Vf

bmoth acquisition geometry and environment. When coherence bandwidth L-' isIestimated. the relative error translates to anprnyinatclv ý.40c7 a~nd -201:%.

8. Frequency Spreadi-ag

IFor an incident high-frequenc% moriochurt--matic a. LC the %4;U!1dk~C frd&acligraaj~can be approximated asý a Gaussian spectral distribution about an unr-hifted centcr fre-

Iquency when X > ! (Ref. 26. Section V'1I: Ref. 41 ). If we aiwime a~ Pienrnin-Mnd-nv.it?surface wave spectrunm. the 3 dB spectral width of the forward-scattered signal is

given 42b%

Af3jB (Hz) = 0. 128 U ('sin 0 (43a)

I with U in mnetersisecond and f in kilohertz, or

(fHH7) = l.76 h'f sin8 043h)

Sith h in meters (Fq. 22 1. At low grazing angles. the spectral Npread of forwad scatter isI generall\ negligible, especia!ly In) compiarison to spectral widths associatec wi-th the lOng"

pulse len-ths typically used in practice (e.g.. the spread is 3 Hz at a frequency of 20 kHz,

I an rms., wave height of I m, and a grazing angle of 5').

Measurements hv Roderick 4 1 support Eq. 43. and its accuracy is considered satis-1 factory. Some differences can be expected when the s-urface wave spectrum deviates

from the Pierson-Moskowtkitz bpearaI f~iinn.

9. Statistics

After a surfaice bounce, the amplitude statistic-, over an ensemble of pings are ade-

Iquaiely described by the Rayleigh distribution 2. 434 wvhenevcr the roughness parametergiven by Eq. 38 exceeds -2. Deviations from. thie Ray'leig Inv l.^

I obsecrved in backscattering measurements involving small patch sizes. For example. datataken in Dabob Bay appear to deviate from the Rayleigh distribution for patch sizes

I TR 9407 11-33

A Mnr I AAAs C l

UNIVERSITY OF WASHINGTON * APPLIED PHYSICS LABORATORV

<10 m-, although this deviation was not observed for open ocean measurements.," These

observations should he viewed as a cautionary note for high-resolution systems that

emp!o\ narrow beams. Given a Rayleigh di--rihu"ion, the relative pfobauility of obtain-

ing a pressure amplitude (or envelope value), A, is given by

P(A)- A,- exp (-A -/2 ) (44)

%%here p is the instantaneous pressure and the angle brackets denote the ensemble aver-

aoe at a given time in the ping cycle. The mean square instantaneous pressure is related

to the mean square amplitude, or envelope value, by = i/2 <A 2 >. The equivalent

intensity distribution is

P(f) - exp (-/ I >) , (45)

where I is proportional to A 2. The models in Sections lI.C.3 and 11.C.6 pertain to the

mean .

For low roughness (Q < 2). a constant reflection coefficient plus a random scattered

component has been modeled with the Rician distribution.4-5-4 Since low roughnes con-

ditions seldom, occur at high frequencies. and sitice the Rician di-,,ribution is more con-

centrated about the mean than the RayIeigh distribution, we recommend use of the Ray-leigh disiribuiion.

D. AMBIENT NOISE

I. Ambient Noise Multipath Expressions

At frequencies above I kHz. the most ubiquitous source of ambient noise in the

ocean arises from the action of wind on the water surface. Above 50 kHz, thermal noisemay predominate when the levels of wind or other sources of surface-generated sound

(e.g.. precipitation and shipping) are very low. Of these other surface sources, only rainnoise will be treated here. Biologicals,,,,, of,,a ,.biet n ,-11 .;. , " nappig -11,

are examined in Section III.

I1-34 TR 9407

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I- UNIVERSITY OF WASHINGTON - APPLIED PHYSICS LABORATORY

I The resultant ambient noise model, tien, confsists of two types of noise originating

at the sea surface, namely wind and rain, plus thermal noise due to molecular agitation.

The total noise level detected W. the receiver " s

P,=Ps +P7 (46)

where

P, = total received noise power spectral density (pPa2-Hz)

IPS = surface noise power spectral density (lgPa2 /l1z)

P- = thernal noise power spectral density (pPa1-Hz).

I and the decibel equivalents are defined as

I NSL = 10 log P,

I Ns = 10 log Ps

NL 7 = 10 log P,.

The thermal noise term is given by

I L7 = -15 + 20 logf- DI - F (47)

where f is frequency in kilohcrtz and DI and E, respectively, are the directivity index and

I efficiency in decibels. 49

The surface-generated noise contribution is found by integrating over a uniform dis-

1 tribution of surface radiators, taking into laccount p ,oagin from ch, surf-.e to th,

receiver and the receiver beam pattern. To obtain realistic results in shallow water and at

I lower frequencies, the propagation model mu,,t include multipath contributions to the

total noise level, particularly for sites having hard bottoms.

Two equivalent exprcsions have been developed for implementation on a computer

to determine the noise level for directional receivers. The first expression is tailored to

computer codes that calculate transmission loss as a function of horizontal range, i.e.. the

i primary integration variable i., range.

I TR 9407 11-35

____________________________

UNIVERSITY OF WASH,,,0TONt, APPLIED PIivYSC-- LADOAMATCRY

Ps = A f br(OrO), o RV(B, a(R)h(R) dR , (48)0 paths

where

A = scale factor (function of wind speed. rain rate, and

frequency) or noise source level at the air/sea interface at

vertical incidence (iPPa9/iz/steradian)

N = surface radiation pattern including lo•s owing to a near-

surface bubble layer

(R) = a term that accounts for propagafien ant! interface

(reflection) loss

h (R) = "spreading" loss, from surface generator to receiver

b,(O,,O) = receiver beam pattern (intensity ratio)

R = horizontal range to surface generator

Rmz.x = maximum range for integration over surfacc area

8, = surface grating angle for ray between receiver and ,urface

0, = rdy angle at the receiver (positive angles being above

hori7ontal)

0 = azimuthal angle.

Multipaths are implicitly taken into account by summing over all relevant paths

connecting the surftce to the receiver at each range increment a.s, ,hown iti Figure 15a.

To determine the number of requisite path,, and Rma, for a given environment. several

11-36 TR 9407

I IUNIVERSITY OF WASHING"TONL' ,,APLIE uveROY1.S L ̂ 'oA DOCAORY

I trial runs are usually made in which the,,e , ,met,,er .,- iar,.e•pi,.,i! Ps "c '"""nmer f

a stable upper limit.The second expression for Ps, illustrated II Figure '5i 'M suied to :' .....

models that propagate a fan of ray tubes (indexed by elevation angle rather than horizon-

tal range) emanating from the receiver. In this case, the integration is over e!t:',!onr

angle and is given by .J(

PS= 27A r•HI .4tl r ~ (491

where

I and2B(Or) _J brO,4,O do (50)

Sand 2n _r

I H(O,) = X(0,) soier m o 10 (

-'in(Iskr 0

S•where 0, is a function of 0,.

Equation 49 conveni-rntly factors the noise into B(Or), a received noise beam pat-tern. ond HtOr). a propag&.ýion term wei-.hd•.r" bt" sa. " r.j;'ion p...ern, .0 ,A.

The summation term in Eq. 51 representts the absorption loss along each ray (tube) plus

the boundary bounce loss for each boundary interaction. The quantity M is the total

number of boundary interactiont, required for H(Or,) to conIvet.e and is as-ufmed to be

determined automatically in computer implementation of Eqs. 49-51. For example, if

two boundar bOthunce.s (M = 21 a.,re Sffir~f feor H(A I tt cotnvertgn Qr 9,5 of the |

that would be obtained for Al = o, then the transmission loss for the path from radiator R

show-n in Figure ISh is

TL2 = +C( sn + s 0 + RL(O8) + SBL(O,) (52)

III TR 9407 11-37

UNIVERSITY OF WASHtINGTON" APPLIED PHYSicS ,•Ae rnaTmov

Two-dimensionaluniform distribution

(a) Surface reflection of surface radtawors

Receiver 0,O

Bottom reflection

Two-dimensionaluniform distribution(b) Sof surface radiators

6 ~5 //, \.....Receiver

/ ' Radiated noise energy* i nondivergent withinL R / "": solid angle (there is no/ spreading loss)

Bottom reflection

Figure 15. Diagrams illhstrafin:g no o methods of calculazing tMe surface-gencrated n;i'. le:'elfor a h *ydropione located at depth D. corresponding to Eqs. 48 and 49. The methodshown in 15a uses range to index ra.'s from the surface to the receiver: tie inethod

in 15b uses the received elevation angle.

I11-38 TR 9407 I

IIUNIk ERSITY OF WASHINGTON * APPLIED PHYSICS LABORATORY

where 0. is the bottom grazing angle and si, s 2, and s, are the length;, shown in.

Fig. 15b. Expressions for the absorption coefficient ox, bottom loss RL, and 'surface bub-

I ble loss SBL are given in Sections 1, V, and !.C, res,- civel.y.

2. Simplified Expressions for Isovelocity, Deep Water Condltons

For isovelocity conditions and omnidirectional or highly directional hydrophones.

Eqs. 4& and 49 can be simplified to provide ana!ytica expressionM useful under a wide

range of conditions. An omnidirectional hydrophone is defined by br(6,0) = 1. Per-

forming the double integration (using numbers given in Section D.3) in Eqs. 48 and 49

1syields = 2MAE j(0.23ctD + 0 1) , (53)

where D is the hydrophone depth in m ..e.rS And is f#. la'nth' into- (aI-.ld #I.oI v1nrf

cross section for a near-surface bubble laye,. (An expression for P, in terms of the

I depth-integrated bubble density is gien by Eq. 5.) The quantity E, is the third-order

exponential integral function and is defined as

II EAW) "7 dt (54)

If both chemical absorption (a and bubble absorption (P.,) effects are negligible, Eq. 53

I reduces to

i PS 4 (55)

If. for example, the argument of E3 in Eq. 53 is less than 0.06, then the error in using

Eq. 55 in;tcad of Eq. 53 i.; less ""an 0.5 dB. .... ti.ons .53 and .5.. ..acd t o I.Val di.r...

path contributions to the noise and therefore 0- not include multipaths. Thus these

I expressions are most accurate for either the deep ocean or environments in which the

bottom is quite soft and has an associated high bounce loss.

I For narrow beams and relative! high ,r,,,nv a•ngve, the r ,''k M ,.,n c n .,

be approximated by

I1 TR 9407 11-39

__..... . ... ............ ...... . .. ......................... _ __ ___ ___ ___ __ ___ ___ ___ __ ___ ___ __


PS =A sinQ,, 10 2 U'a+SLelaf (56)

where 0, is the beam axis elevation angle. ra is the slant range to the surface for the

beam axis ray, and MQ is the equivalent solid angle of the receiver beam. This approxi-

mation relies on a small range of variation of sinO 1QSBPL'Q',zO over the beam pattern.

Tests using this approxinmation compared with evaluations of Eq. 48 have show.%n that, for

Oa > 25ý (mwhere 0.. is the elevation, angle of the solna-r: w. Flgjre l5 And"I"s"ZVý A6 V

(where A9 is the bcaniwidth in elevation angle). tihe results given by Eq. 56 are within

0.5 dB of those given by Eq. 48. This hold, true even for nonirovelocitv conditions and

realistic sound speed profiles because at high grazing angles the effects of the sound

.,peed profile are minimi7ed.

3. Surface~ Radiation Pattern (N)

The primary environmental quantities of interest in Eqs. 48 and 49 are A andNI.

Most studies of the surface radiation pattern N have shown good agreement with a dipole

radiation pattern for arrbienlt n.0:os Ata~ a h eas'~ Ac ibd win

speeds and frequencies. however. this radiation pattern is modified by a near-surface

layer of bubbles through which the noise generated at the air/sea interface must pro-

pagate. The resultant effective noise radiation pattern below this bubble laver 2 is

N(es) = 0 SL,~ sin: 0. (7

where the surface bubble loss is given by Eqs. 28a and 28b. Since SRL is inversely pro-

portional to sin%*. radiation at the lowest pra7.ing an.lesý is the most strongly affected by(he presence of an absorptive bubbD'le Rg- II 0,-r r6 0hos h. qc evqA It'a..,l

tion pattern (N) varies most rapidly with %%ind speed at the lowest grazing angles: the

variation at vertical incidence is small even at the highest wind speeds shown.

4. Nei.e Level at the Air/Sea Interface at Normal Incidence (A), Wind Effects

.Measurcmcnts of wind-generated noise have shown that wind speed is the main

environmental parameter governing the noise scale factor A. When the sea surface

11-40 TR9407

UNIVERSITY OF WASHINGTON', APPLIED PHYSICS LAUD0,0T •

F -" 10 mWs

' • 20 rn/s S-3: • , "

> "C I

Sm o ::4C 60oe:

GRAZING ANGLE (der)

rFitgurg 16. The tfective surfa' radiation panell sho'ing the dipole pattern at low itind

speeds. when near-.surface bubble ab.iorprion is negligible, and the increasingautrnuation of the nnoie leel. especially at lots grazing angle c. as bubble ahs(orp-

i lion increases with wind Npeed .f = 20 kHz),

becomes colder than the air above, however, the component of A duc to wind (A, ) alsobecome.s a function of the air,'sa cj,,,,, . - , ,. r,%,,v.,,,n.,. ,.,

20 kHz. this dependence on wind speed and air/sea temperature difference i% cxprcsCd

as

I J20.5 + 22.4 logU AT I C V > I mA

where AT = Tir - Ta and U is the wind speed in meters per second at a 10 m reference

height' ~ The temperature difference erin is ...... no"' "It,,,,, ,,1 ,,,,,

becomes significant for coastal locales with offshere winds or for enclo,,ed sea, during

the su'mnertime.

Ii TR 9.407 11-4 1

UNIVERSITY OF WASHINGTON,, APPLIED, P-n vS, ,AOV ^D Y_____

The frequency dependence of the noise leve! a! fhe sea surf'ace is

10 logA,,. = 10 logA,,.20 + 20.7- 15.9 logf, U > 1 i ns (59)

This is the noise source level at the air/sea internace (the effects of a near-surface bubble

layer have been incoqiorated into the expression for the radiation pattern. Eq. 571).

The araba ";t noise levels r"i" dfr (-An o, .... r,""t'-• ion.. Myroo, , a.. i..-

velocity, deep water situation can be compared to the Wenz curves throLugh the use of

either Eq. 55 (ignoring bubble effects) or Eq. 53 (which includes bubble cffccts through

the inclu,,ion of the depth-integrated totAl extinction cross section P3). The result of this

comparison is shown i. Figure 17a for frequencies from 1-100 kHz for 'severai sea

states. iThe wind speeds in meterý,second appropriate for each sea silite were 'ta-kef ftom

Table 2 in Section II.A.) There are three notable features: (1) the effect of bubbles is

predicted to be negligible at low sea states: (2) a! sea statc 0 ( ,Eq. 53 and 55 p:cdict

lower noise levels than the WVn.w curves, (3) at sea states other than ssO, Eq,,. 53 Lnd 55

predict higher noise levels than the Wenz curves. These last t~o features can be exam-

ined relative to a set of data acquired by. Farmer and LemnUA at4. 3.1 II 17t. l III, ...... ,", ,:i L ,,d,-,IC:U-1

of 0.5-25 nVx. Figure 17h shows tho,,e data along with the predictions of Wenz and

Eq. 53. indicating that Eq. 53 is a better ,redictor for the!.e dam: i.e.. the dr'.t,. show Mower

noise levels than the Wcnz predictions at low wind speeds and higher noise le%els at high

wind speeds.

5. Noise Level at the Air/Sea Interface at Normal Incidence (A),

Combined Wind and Rain Effects

Recent measurement, of rain noise in the open ocean have shown that the noise

Jcvel depends on both rain T"-_, and wind pd. ' The sCa2C fa 11r 1 ,I- .,, k,,, A, 2,-. ',

modeled simpl. by

I0 logA,:,, = b(U) + a(t) logRR RR >_ 10-2 miiwh (60)

11-42 TR 9407

I- -.........UNIVERSITY OF WASHINGTON* APPLIED PHYSICS LABORATORY

I ~>ss6

S........... - . --. , 6 • .I 60

SC c ss4%-s . • .. :•...

I ..... " •....-" • ".... -.- . .-"40 -ssO- ss2"....

2. ........ .Wen=

10 log (Eq. 55)II 10 log (Eq. 53, with a r._0)

3.5 4 4.5 5log (frequency, Hz)

I 20' 3TATION A- (b)-,J .-. 20 CAPE ST. JAMES--,

151.

E ..I ", ** '. * .a 6

Z ! .' Z10 Oog(Eq. 53. witha-O) 0

--- Wen2I ~~~~~~ .o •o o oto..j

NSL 4.3 kHz

F'gu'e 17. (a) Pressure received at an omnidirectional hydrophone car'ulathd via the Wenz

equation, via 10 log (Eq. 55,, which does not include bubbh eff''rts. and via 10 log(Eq. 53, vitht a = 0), which doe.% include b~abble effects. (.5) Wen: equation and R)log (Eq. 53. with a s 0) compared with data taken by Farmer and Lemon.""

II TR 94('7 11-43

UNIVERSITY OF WASHINGTON, APPLIED PHYSICS LABOFRATO') .. ,

where RR is the rain rate in millimeters/hlour aid the dependence on wind speed comes in

thrOLl-h the coefficients a and b;

"a =5.0+ 5.7(5.0- U), 1.5 U < 5.0, (61)15.0. U 11>5.0.

and

[41.6. U _< 1.5.b 50.0- 2.4(5.0 - U). 1.5 < U< 5.0, (62'1

150.0. 2: 5.0

As with the wind noise spectrum, the model for the frequency spectrum of rain noise %%as

obtained by making power law fits to measured spectra. To maintain simplicitN in theinodeled spectra, rain noise d..,34a tak.,n at A.. , . "'- V., .., 3 1""sf , . ,,' "

. jaoa ý t4IU A j) ; '

highly peaked spectra are not used in the fitting procedure (Refs. 58 and 59 show exam-

pes, of these highly pcaked spectra measured in a lake). The resultant rain noise spectra

are

10 lIorA, 2,1 - 10.0 logf I 5<f< I0. RR Ž_ 10 " wirdh.I0 IoA4,.,?1 + 49.0 logf- 59.0. 10 5f< 16. RR Z! 10-: rinnmh,

l~oA.=10 1og4,:ýj 16 •5f!ý24. RRŽ jO - mm/h,.1 l01og4,.,•.p-23.01ogf+ 31.7. 24 <f5100, RRŽ 10-2 mrn,1I

As with the wind noise spectra, a reference frequency of 20 kH-Li was chosen. The princi-

pal difference between the recommended spectra given in Eq. 63 and the highly peakedspectra men:io.',ed earlitcr cccit-,• vn. . .in . :iin t'.' ........ 1 .... .. .

that data on rain rate are primarily for rain rates less than 10 mm/h. There arc sparse data

which indicate that for rain rates greater than 10 mm/h Eq. 63 nay o'crpredict the notie

level by at least several deci'Vel., Therl'efofe %e recomiiiend ilih It, wifil- be u!,ed as the

model input for RR > 10 mm/h.

To find the scaling factor A when both wind and rain are present. simply add the two

contribution, as fo!lows:

o logA = O log(A, +A,) (64)

11-44 TR 9407

Swa~I &I to-iga R I ne-k -I M nff-ea.. n

UNIVERSITY OF WASHINGTON " APP," PHYS!CS LABeO A TR_6_0_=VII From Eqs. 58 and 60, it can be seen tha! neither contribution woei torn af zero wind

speed or no rain. In accordance with available data, we set A, = 0 when U < I in/s and

Ar 0 when RR < 10- mnm/h. Under these circumstances, either the hydrophone

sy'sten's self-noise or thcmial noise k the limiting noise: thermal noise tend, to be "d"r-

I inant at higher frequencies (above -30 kliz). The ambient noise levels predicted for an

omnidirectional hxdrophone in an isovelocity, deep water CnV'iron.ep t for vnriois corn-

binations of sea state (where the appropriate wind speed in meters/second for each sea

state was determined from Table 2 in Section IL.A) and rain rate are shown in Figure 18.

A comparison between the predictions of the ambient noise model and one set of data

from Ref. 55 is shown in Figure 18b.I6. Summary

I \'"e beliee the model ...... in Eq. 59 for...................... ..

sonably accurate. particularly for sea surface temperatures that are nearly the same as or

I warmer than the air above: in this case. the model is consistent with a large body of data

extending back to WWN, IT. The only signiticant deviation i.. when it is. .,nowing or ,,h,,r,I the air temperature is below free7ing or both" (in which case the niise level is con-

sistentlv 5 dB less than that given by Eq. 59). The quantity with Ie greawc5! degree of

uncertainty is the surface bubble loss effcct (Eq. 57). As discussed in Section II.C, SBL

displays a wide range of variability for a given wind speed.

The rain noise model, on the other hand, has much less data to support it. Also. it is

based on the occurrence of "'normal" rain. i.e.. rain containing droplets greater than

u2 nm in diameter. Reference 60 has shown that for "initty" rain the noise levels can be

30 dB higher than the model predictions for frequencies above 10 kH7. As an aid to the

user. Figures 19a and 19b shmi the received noise field (Eq. 48 or 49,) as a funt'ion ofelevation angle for frequencies of 5. 15. and 40 kHz and a soft mud bottom. The bottom

loss is large and increases with frequency, so that the effect of ambient noise energybeing scattered off thc bottom is minimal at 40 kH7 (Figur.C 19c).N Co,,,'"'n .. f. ,,"...

19b and 19d, which is the same xs Figure 19b but for it hard bottom, indicates the

significance of bottom type on the angular dependence of the ambient noise received.

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UNIVERSITY OF WASHINGTON. APPLIED PHYSiCS LABORATORY

Thermal noise at frequcncics below 100 kHz is u..-•,u, of fl;it ,-s.c.-, .. a

has received little experimental attention. Recent measurements, however. confirm the

thennal noise model presented here for omnidirectional hydrophones.54

7¢ ,(a)

7C

Cf

40'

) rain ram in mm/h3O.

20 .. 3. 3.7 57 4 4.-5 4.5 4.75 5log(frequency, Hz)

(b)

7:

40 •" .,, -

3O.... ss2- I0 log (Eq. 53. with m O)ss2.- dita from Rcf 55

' rain rat in mm/h

3.-5 a.3 3.75 4 4.2E 4.5 4.1t 1

log(frequency. Hz)

Figpri IS. 1aw 10 log f¢l-q. .33. with x a- 0( pltted fior five rain: razes and nm sea seYaCs.(b) Compari.son beti• cen 10 log (Lq. 53, with a =_ 0) and some of the data .fon;Ref 55.

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UNIVERSITY OF WASHINGTON * APPLIED PHYSICS LABORATOAY

In 5O fmKvZ to fm¶kI4z-~ 0.7 (sch mud', . P-0.7 (Wo:rnud:

- = .> ~, 30** ' 3

z ,. 4Xt

43D

9c 0 9w (d

1 0kz .5.

p ~ ~ ~ - 0 7 sd nd . haok

GOc*90' *9

z T

.... ... 4C.

Figulre 19. Polar dia gramns of MIOr) from Eq. 53. shoin~ jg elevation angle depenlence of thereceived noise field for a receiver at 120 in depth. a wsindl speed of 2.5 "vs. and aWater dept/h of 400 in. (a)-(c) For a bottom of soft mud wit/h a porosity% of 0. 7, bothhotiont loss and abso'rption increase rapidly, as t/he .fequencY A~ increased fromi5 k/iz &) 40 k/z-k the effect is most evident for the dowsn-lnokinR angles. (d) For ahard rock or gravel brotom at 15 k/-z. the levei.¶ for bottom-re ftected energy (iresignificantdv higher.

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REFERENCES - Section II

I. S.D. Smith. "Coefficients for sea surface %ind stress. heat flux. and wind profilesas a function of wind speed and temperature." J. Geophys. Res.. 93(C12).15.467-15.472 (December 1988).

2. J.L. Hanson. Winds. waves, and bubbles a the air-sea boundary. ./oims H,,pki-.sTeci,'a! Dixgst. 14. 200-20M k 1993).

3. N. Bo%%ditch. American Pracic,•l Navigator KU.S. Goverrim. ent Piriting Officc.19 5 8 .p. 1059.

4. R. 11. Fairbridge. Th' Encyclopcdia of Ocea.......... ,, ci,,,,, P,,i. Co., NewYork. 1966).

5. E. L. Bialek (compiler). Handbook of Oceanographic Tables (SP-681 (U.S. NavalOceanographic Office. Washington. D.C.. 1966).

6. Bunker Ramo. "A Guide to Sea State. with a l.isting of Visual and Tactile Clues"(source: Director of Marketing. Ocean Surveillance Systems. 31717 La TiendaDrive. Westlake Village. California 91361: undatcdi. I p.

7. D.G. Groves and L.M. Hurt, Ocean World Encyclopedia (McGraw-llill, Ne\xYork, 1980).

8. W. J. Pierson. Jr.. and L. Moskowitz. "A proposed spectral form for fully developedwind seas based on the similarity theory of S. A. Kitaigorodkii," J. Geophys. Res..69. 5181-5190 (1964).

9. D.B. Chelton, K.J. Hussey. and M.E. Parke. "Global satellite measurements ofwater vapour, wind speed and wave height." Nature. 294, 529-532 (1981).

10. P.A. Crowther. "Acoustical scattering from near-surface bubble layers." in Cavita.ticn and hinlwnogcneities in Undenrater Acoustics, edited by W. Lauterbom(Springcr-Verlag. New York. 1980). pp. 195-204.

II. S.T. McDanicl and A.D. Gorman, "Acoustic and radar sea-surface backxcauter-.'J. Geophyi. Re%.. 87. 4127-4136 (1982).

12. S.T. McDaniel. "Sea surface reverberation: A re\iey,," J. Acoust. Soc. Am., 94,1905-1922 (1993).

13. S.O. McConnell and P.H. Dahl. "Vcrtical inciderncc backscaiter and surface for-ward scattering loss from near-surface bubbles." OCEANS '91. /, 434-441. 1991.

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14. C. Devin, "Survey of thermal, radiation, and viscous damping of pulsating air bub-bles in water," J. Acoust. Soc. Am., 31, 1654-1667 (1959).

15. S.0. McConnell. J.G. Lilly, and G.R. Steiner, "Modeling of High-Frequency Sur-face Reverberation and Ambient Noise (U)," APL-LUW 7821, Applied PhysicsLaboratory, University of Washington, November 1978. (Confidential)

16. J. M. Monti, P.D. Koenigs. B. Niitzel, and H. Herwig. "The Influence of SurfaceRoughness and Bubbles on Sea Surface Acoustic Scattering," NUSC TR 7955,November 1987.

17. G. R. Garrison, S. R. Murphy. and D. S. Potter, "Measurements of backscattering ofunderwater sound from the sea surface," J. Acoust. Soc. Am., 32, 104-111 (1960).

18. S.T. McDaniel, "Diffractive corrections to the high-frequency Kirchhoff approxi-mation," J. Acoust. Soc. Amn., 79,952-957 (1986).

19. R. Waltzman and E 1. Thorsos, "High Frequency Bistatic and Monostatic SurfaceBackscatter Measured in the Open Ocean," APL-UW 2-82, Applied PhysicsLaboratory, University of Washington, October 1982.

20. S. 0. McConnell. "Remote sensing of the air-sea interface using microwave acous-tics," in Proceedings of OCEANS '83 (Marine Technology Society and IEEE.1983). pp. 85-92.

21. D.E. Barrick. "Rough surface scattering based on specular point theory." IEEETrans. Antennas and Propagation, AP-16, 449-454 (1968).

22. P. D. Mourad and D. R. Jackson, "High frequency sonar equation models for bot-tom backscatter and forward loss," OCEANS '89, Seattle, Washington, 1989.

23. E. C. Monahan, "Occurrence and evolution of acoustically relevant sub-surfacebubble plumes and their associated, remotely monitorable, surface whitecaps," inNatural Pkvsical Sources of Underwater Sound, 503-517, B. R. Kerman (ed.),Kluwer Academic, Boston. 1993.

24. B. Nibtzel, H. Herwig. and A. Schmidt, ""Acoustic and microwave backscatteringof the sea surface," IEEE OCEANS 93, Victoria, B.C., 1993.

25. G.R. Valenzuela and M.B. Laing. "Study of Doppler spectra of radar sea echo."J. Geophys. Res., 75,551-563 (1970).

26. E. 1. Thorsos, "Surface Forward Scattering and Reflection," APL-L'W 7-83, AppliedPhysics Laboratory, University of Washir :',on, May 1984.

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27. D. E. Funk and K. L. Williams, "A physically motivated simulation technique forhigh-frcquency forward scattering derived using specular point theory," J. Acousr.Soc. Am.. 915). 2606-2614 (May 1992).

28. S.O. McConnell, "Surface Forward Reflection and Scattering, Surface Back-scattering, and Ambient Noise Measurements Made During GCrV Adaptive SignalProcessing Test (11)." APL-UW TM 5-83. Applied Physics Laboratory, Universityof Washington. 1983. (Confidential)

29. P. 11. Dahl and S. 0. McConnell, "Measurements of Acoustic Spatial Coherence ina Near-Shore Environment." APL-UW TR9016. Applied Physics Laboratory.University of Washington, August 1990.

30. P. H. Dahl, "Revisions and Notes on a Model for Bubble A:tcnuation in Near-Surface Acoustic Propagation," APL-UW TR 9411, Applied Physics Laboratory.University of Washington, July 1994.

31. P.H. Dahl. "Bubble Attenuation Effects in High-Frequency. Surface ForwardScattering Measurements from FLIP." APL-UWN, TR 9307, Applied PhysicsLaboratory. University of Washington. May 1993.

32. E.I. Thorsos, "High frequency surface forward scattering measurements."presented at the 108th meeting of the Acoustical Society of America, October 1984.

33. P. H. Dahl and A. T. Jessup, "On bubble clouds produced by breaking waves: Anevent analysis of ocean acoustic meamuremnent," accepted by J. Geophys. Res..August 1994.

34. P.A. Crowther, H. J. S. Griffiths, and A. liansla, "Dependence of sea surface noisein narrow beams on windspeed and vertical angle." in Natural Physical Sources ofUndernv'ater Sound. pp. 31-44, B.R. Kernan. (ed.), Kluwer Academic Publishers,Boston, 1993.

35. M. V Hall, "A comprehensive model of wind-generated bubbles in the ocean andpredictions of the effects on sound propagation at frequencies up to 40 kliz.".1. Acoust. Soc. Am., 86, 1103-1117 (1989).

36. R.J. Christian. D.G. Browning. and D.G. Williams. "Revision." to an empiricalsurface loss model using a correction for pH-dependent attenuation." presented atthe 127th Meeting of the Acoustical Society of America. Cambridge, Ma,-sachuett,;, June 1994.

37. C. Ecka.rt, "The scattering of sound from the sea surface." J. Acoust. Soc. Am., 25.566-570(1953).

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S8. O.M. Phillips, The Dynamics of the Upper Ocean, Cambridge University Press,Cambridge. Massachusetts, 1977, pp. 177-179.

39. C. S. Cox and W. H. Munk, "Statistics of the sea surface derived from sun glitter,"J. Mar. Res.. 13, 198-227 (1954).

40. P. H. Dahl and A. AI-Kurd, "Time Spread and Frequency Coherence in AcousticForward Scattering from the Sea Surface," APL-UW TR 9405, Applied PhysicsLaboratory. University of Washington, May 1994.

41. W.I. Roderick and W.G. Kanahis. "Scattering coefficients and Doppler spectra ofspecularly scattered sound from the sea surface," J. Acoust. Soc. Am. Suppl. 1. 69,S96 (1981).

42. R. L. Swans and C.J. Eggen, "Simplified model of the spectral characterization ofhigh-frequency surface scatter," J. Acoust. Soc. Am., 59.846-851 (1976).

43. M.J. Pollack, "Surface reflection of sound at 100 kc," J. Acoust. Soc. Ani., 30,343-347 (1958).

44. D.C. Witmarch. "IUnderwater-acoustic-transmission measurements," I. Acousr.Soc. Am., 35, 2014-2018 (1983).

45. E.P. Gulin and K.I. Malyshev, "Statistical characteristics of sound signalsreflected from the undulating sea surface," Soy. Phys. Acoust., 8, 228-234 (1963).

46. S. Q. McConnell and J. G. Lilly, "Surface Reverberation and Ambient Noise Meas-ured in the Open Ocean and Dabob Bay (U)," APL-UXW 7727, Applied Phvsic-,Laboratory, University of Washington, 15 January 1978.

47. P. Bcckmann and A. Spizzichino, The Scattering of Electromagnetic Waves fromRough Surfaces (Pergamon Press, Oxford, 1963).

48. R.J. Urick, Principles of Underwater Sound (McGraw-Hill, New York, 1975), p.187.

49. J.G. Dworski and J. A. Mercer, "Ambient Noise and Its Impact on the QSAM Sys-tem." APL-UW TM 1-86. Applied Physics Laboratory, University of Washington,1986.

50. E. M. Arase and T. Arase, "Correlation of ambient sea noise," J. Acoust. Soc. Am.,40. 205-210 (1966).

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51. R.M. Hanson, "The effect of propagation conditions on wind-generated noise atreal shallow water sites," in Sea Surface Sound: Natural Mechanisms of SurfaceGenerated Noise in the Ocean. edited by B. R. Kennan (KiAuwer Academic Publish-ers. Boston. 1988), pp. 281-294.

52. D. DM. Farmer and D. D. Lemon, "'The influence of bubbles on ambient nois, at highwind speeds." J. Phlys. Oceanogr., 14. 1762-1778 (1984).

53. P.C. Wille and D. Geyer, "Measurements on the origin of the wind-dependentambient noise variability in shallow water." J. Acoust. Soc. Am.. 75. 173-185(1984).

54. S.O. McConnell. "Behm Canal Ambient Noise Measurements: Final Report."APL-LAV TIM 2-89, Applied Physics Laborator., University of Washington, April1989.

55. J.A. Scrimger, D.J. Evans, and W. Lee, "'Underwater noise due to rain-Openocean measurements." J. Acoust. Soc. Am., 85,726-731 (1989).

56. S.O. McConnell, M.P. Schilh. and J.G. Dworski, "Ambient noise measurementsfrom 100 fit to 80 k1lz in an Alaskan fjord." J. Acoust. Soc. Am., 91. 1990-2003(1992).

57. J. A. Nystuen, "An explanation of the sound generated by light rain in the presenceof wind," in Natural Physical Sources of Undenrater Sound, 659-668, B. R. Ker-man (ed.), Kluwer Academic, Boston. 1993.

58. J. A. Scrimger, D. J. Evans. G. A. Mclean. 1). NI. Farmer, and B. R. Kerman."Underwater noise due to rain. hail, and snow." J. Acoust. Soc. Am., 81, 794-86(1987).

59. J.A. Nystuen and D.M. Farmer, "The sound generated by precipitation strikingthe ocean surface." in Sea Surface Sound: Natural Mechanisms of Surface Gen-erated Noise in the Ocean, edited by B. R. Kerman (Kluwer Academic Publishers.Boston, 1988). pp. 485-500.

60. J.A. Nystucn, "Rainfall measurements using undervater ambient noise," J. A4cw,,!.Soc. Am., 79, 972-982 (1986).

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III. Biological High-Frequency Ambient Noise

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A. BACKGROUND

Invertebrates, fish. and marine mammals have long been known to be ambient noise

sources. Many of thcsc organisms produce Qound leves t w! n excess Oth

produced by purely physical phenomena (wind, wave activity, rain, etc.) and are often as

intense as those produced hy many electronic systems (e.g.. >200 dB at I n re I pPa). In

many cases. this noise may interfere with or otherwise disrupt our ability to utilize high-

frequency acoustic signals for detecting objects or for determining environmental noise

sources. Biological noise sources are af particula si"nif"c-nc* i shalr,, ,.:,,, There

is a need to develop a set of parameters that will allow estimation of the potential for.

and/or the levels of, such interference,

A principal source of ambient noise is snapping shrimp, though other invertebratescan contribute as well. Marine mammals, especially p•,rponiJses and dolphins, are a highlyvariable and unpredictable source of ambient noise. Many species of fish are also known

to produce persistent levels of ambient noise in many, especially tropical, environments.

Some data exist on these ,ources of ambient noise production. but m,,u,,ch of th,, da- ;.s

probably dated and may be seriously deficient at frequencies above 20 kHz. Somesources will he more difficult to predict than others, especially the more migratory

marine mammals. However, benthic or less migratory sources (e.g., fish) can be predict-able if measurements are available to establish a pattern of distribution, frequency ofoccurrence, and other abundance-related i.... nawa1.

B. GENERALIZED FREQUENCY DISTRIBUTION

Sonic generalization of these sources of biological ambient noise is possible:

(1) Frequencies less than 5 kHz will be strongly influenced by fish distribu-

tions.

(I2, Impulse noise producing a steady background level is dominated by

invertebrates and can be severe at frequencies of 10 to 20 kHL and higher.

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,UNIVERSITY OF WASHINGTON. APPLIED PHYSICS LAGORATORY

(3) Intermittent pulses or periods of high arnbicn; noise doimiiated by EC...."-

cation and vocali7ation by marine mammals at frequencies greater than

20 kllz will be a significant factor in sonic localiltes and extremely

difficult to predict.

A summary of some of thewe sources is eiven in Table 1.

Taiz'4 1. SiA,,;a! fhara(teritrics of some siqgificant sources oj IighItr,,qtuen0c biological

arnbient noise.

Frequency ofFrequency Range Peak Energy Pressure Level

Organism ("k-z) (kHz) (dB at I m re I pIPa)

Spiny Lobster 0.04-1.2 0.006--0.8 97

(PaIinuris spp.) 2.5-4.7Harbor Porpoise * 20-150 112

Common Dolphin 20-100 140Snapping Shrimp 2-2MK) 4-8 155Beluga Whale 40.O80, 120 160-180Sperm Whale 0.2-32 5-6 1Killer Whale 0.1-30 14 178Bottlenose Dolphin 15-130 100-130 >20M

"Unknown

C. GENERALIZED MARINE MAMMAL AMBIENT NOISE

No method is available to predict the occurrence of marine mammals ir. any

enironment., although the distribution of some mammals is known for broad areas. The

frequency spectra for some of the whlal,,s ,an"d po, li-. si.,..-" .,,I . Tal• . are sh.,, ,.,,w.. in

Figure 1. If marine mammal activity coincides with operations at a particular locality. it

may be necessary to suspend measurement efforts until these animals depat. Otherwise.

there will be periods of high-level aperiodic interference (biological ambient noisel

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.UNIVERSITY OF WASHING (ON APPLIED PHYSICS LABORATORY

8 bIN PEAK e

to M44 o 0 109 li

41 21. 6l' 601# PI41

is 046"1 PAX 23100 914&PEAK1O 5e 4I 41 It4 4K

ii414 PA bill SiLP S: il. i

4 -I ________

t o "a M i

10

�I '�Ilodsp 'c.HPPHOC IENA8

FREQUENCY (kHz)

Fig;#re 1. 7ione 3ignature and spectial romposition nf sounds from selected whahes andporpoises. fafter Busnel and Fish')

which will have to be accounted for or eliminated. Table 2 lists the species names of

additional whales and porpoises that are known to produce such sounds: howcvCr. the

exact spectral composition and levels of these sounds are unknown.

D. GENERALIZED SNAPPING SHRIMP LEVELS

The level of ambient noise produced b. snapping Ahrimp will depend on three con-

dition,: (1) the presence of suitable habitat. (2) the proximity of the listener to that

habitat, and (31 the operating frequency. The general location of snapping shrimp is

roughly bounded by 40'N to 40'S, approximately the bo""'dr. ,Of ,t'- I I C,,,thrm in

winter (see Figure 2i. In addition. water depths of less than 60 m within this general

region are more likely to contain snapping shrimp ppulations. Shrimp populations will

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-UNIVERSITY OF WASHINGTON I APPLIED PHVSICS LABORATORY

laibli' 2. Other whale' or dolphil: sperit-s :0wn~ protd:qwc 'ctsiorasoveAic pulas .

Organizsm Comments

CepI'atorIhync/:us spp. Coastal: southern hcmisphex(hlea.vy Sided D~olphin)

Grairp?4s grist w Oceanic: all occaný in temperate seag.(Risso's Eiolphin) including the Niediterr anean.

Gloht~ephala inelactia Oceaniic hut somne coastal. most of(long-Finned P~ilot Whale~i Norih Atlantic and southern h;rniispherc.Kogia hrei icep.N l-requently coastal:,Q'liemy Sperm Whale.) niobt of the tempe.rate oceans.Kogia simus Similar to K. breviceps.(Dvarl'Sperm Whale)Ld4gerorh *voJichus activis Contin.ntal shelf and shelf edee:(Atlantic Wrhitc-Shied Doiphin) North Atl'Antic.Lagenorh * ncIhu, afhirrostris Continental shelf and shelf edve:(White-Ileakeft Borlphin) North Atlantic

Lagenor/i* yrcIus ausrra!:s Coastal and shelf: tip of South. America(Pealecs Dolphin)bieenor1;vicI;'s aliscuris Southern hris~~(Dusk~y Dolphin)Liqrnorh ync/J!v ohhiquidepi~s Oceanic. bull son1i' cnzttal rhu;.(l1acific White-Sided D~olphin)Ph:ocm'riides dalli Shelf slope but sorne coastal:(Dall's Porpoise) North Pacific.Swenclla coerudeoalba Oceantic:. all N. Pacific.(Striped Dolph~in) all N. Atlantic and Mediterr.-axan.Srenefla tongirosits Oceanic predominantly but some proximity(Spinner Dolphin) to coastal waters.Srenefla plagiodoii Oceanic: Atlantic south of Cape Cod!(Spotted Dolphin) and in Caribbean.Steno bredanens.is Coastal: eastern Japan. eastern and wesiern(Rough-Toothed D~olphin)t Atlantic. occasional in central Atlantic.Tursiops aduncus Indian Ocean and Red Sea suhspecies of(Arablan Dolphirn T truncatus

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L- -r "F

-FtbrUary 116C

__ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ __ __ _ __ _ __ _ :: x :.. ..L ..J ......Figr' A~~tdided,~rihr~nj f sap:XXsunpacri~ O ounc ?~Sapn

shrip ae fond n te shdedarea;vhretr th bcrropt dpt/ is ei~than60X wi:hc ~ ~ ~ X bo:7 eiun ssiabe utrCi n eP.

bem~~tabndntwhrethrcar nm~o~hi~n pac~.aswi! c oud n oXosedimets uo'~i~ti~ of u~h bulders cobbes, orcoralrubbl. Saeo tc os

rockstrctue% re ko avo~ihl eniromens weres snd o mu ar no. PWh% o

Fiduent thorlodwiods of pibukojo snappin? shrimp acoditeos.no e l. napn

bn lose pbundant %-hr toer idiuarc nhrmIP,11 thielp.eak sswllhound pesr ee ofn indVi-

sdumeltsna canitngb o40 tough0 bouldrs.I cobbles, or~ spcral rble. hlc or othra!!yXOt

80d tred 1n bottom (sedimcurmaps. insuh rates athchurthe snccdtra wlevl he crticas wth

idcritify ~ ~ ~ ~ AD th1oatosof94ibes$apn sm rf

'..z , .'.

______________UN~IVERSITY OF WAS~iiNGTON *APPLIED PHiSiCS LABOPATUHY

pain

I tOS'. A

:r.vde-ey (Hz)oi

cure (aferce W'a aI BllV

SitnLfo h enrofa cocnrtf afsrm ildpn nthefeun)o

teof120I!.eeFigure 4). Gimarso n th e presence ofnnapping shrimp.niesetaa difrecnt in gen-V

erl rhrim snapsr 4il Seta tf 'subce-greaerathanovise-gandraind noise are alpo.vc himatreibounded byran n rite f ar freIquencie fobetheen 10te and 200 k Iz There the no pperve

diustuatien fry sheasne ocncnrton fof shrimp wille howendern ther ifangttm nrequenc ofupo

oprto (for. Than rexamlcthe ac tivte-wy of, eiheute thrimpsthmce ord ateuton othferqhen-hi

anieaso 0-2 wich then disturb 4the entepesneo snapping shrimp.thning-

Touned benerain oied falorf(fnk pcdlvlwt frequencye ewe 0ad20kz iser 0.s nodbse rved

5 ki lz to 175 kITLe, or approximately 260 dB ftrom 25 kHz to 175 kd-z (Figure 5). There is,

some direct evidence that shrimip snaps do not occur raridonmil but i;aiiheire IfrclunI

correlated with each other in bursts of pulses.

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1 11170I I , .- 60

* SAND

I g o' I.20 .-

• _ -.* .& ,"- L.

II .,,30,---4'- _!TRAVERS 3C'88

,-4 .TR.VERSE .

I '-C><'

• .- ...

40 0 4 6 8 X0SDISTANCE (kyd)

Figure~. 4. Variationl ,f shrimnp pwoise Ile'eI off California duringl rrav'erse,• over diflering bottorI sediment• and depth. Lerels shown use tlhe ov'erage of JO, 15, and 20 kll: ilevels.(af!er Iohnol etaZ I. fro -Ca, a d.B. I

I ~If clndiiions arc such that populations of snapping shrimp are potentially present.

a~sunie a level of 70 dB (for 5 kllz to 20 kHz) for the noise spectral level and makef adjiustments for frequency Ifor frequencies >20 kltz) and distance from the position of

the shrimp concentrattion (0.1 3 dB/k~z and 20 log range plus 2(x range, respectively). IfIit i's nighttime, add 8 dB. The estimateWllhe': , ,p;xint ,, d ,,, l ; .,o,. Ii ,,, ,.,, ,,,

low side. Actual values of the noise spectral level may deviate front this estimate by

I ~more than 10 dB. hut determining these values will require direct measurements in theenvironment of intcrest.

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II0110

0C 500 15 200

Frecu.ercy (kHz)

Fi itre 5. (he rplot of Pinltiple sin gle shrimp stnaps fromn S% Mnet Harbor showing the decline inspectra! let el itith~frequencY. (after Cato aPd Bell')

E. OTHER INVERTEBRATE NOISE SOURCES

A number of other species of shri nip. crabs, sea urchins, and barnacles are known to

produce clicks at v:arious frequencies. These are itemized in Table 3. These source% of

biological ambient noise are poorly studied, but may be of importance in some environ-

0 cn t'.

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Tabke 3. Other iniertebrates kno•wr o .rodu.. cn; ..

Organi sm Conmments

Shrimp in the genera Pontonia, Little is known about noise mechanismsand levels

1>'pton, and Coralliocaris Little is known about noise mechanismsand levels

Various species of fiddler crabs,especially in the genus Uca

The box crab Calappa flanmea Occurs in the Bahamas.

The black mussel Myrilii• edulix Produces pulse sounds at 1-4 kliz.

Some sea urchins:Evechinus chloroticus May produce sounds at 30 liz - 5 k11z.Strongylocentrotus drbba'hiensisDiadema setosUtn

North Atlautic barnaclesRawtnui ehuMetts Produces sounds similar to snapping shrimpBakinus balanoide.s Produces sounds similar to snapp;ng shrimp;

occurs in warm seas.Bahmets itinitinql'+itn Produces sharp clicks: oceanic, in warm seas

alarnu v perforatus Produces rythmic rubbing sounds:occurs in the Mediterranean.

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REFERENCES - Section III

I. R.G. Busncl and J.F. Fish (editors), Animal Sonar Siystems (Plenem Press, New

York, 1979), 1135 pp.

2 M.W. Johnson F. A. Everest. and R.W. Young. "The role of bnapping shrimp(Crangon and Synaipheus) in the production of underwater noise in the sea," Biol.Bull. Woods Hole. 93(2.). 122-138 (1947).

3. D. H. Cato and M. J. Bell. Ultrasonic Ambient Noise in Australian Shallow Watcr atFrequencies Up to 200 kHz. Technical Report MRI.-TR-91_23, MaterialsResearch Laboratory, 1991. 28 pp.

4. MN W. Widener, "Ambient noise levels in selected shallow water off Miami,Florida." J Acoust. Soc. Am., 42, 904-905 (1967).

BIBLIOGRAPHY - Section III

Alhers. V. M., 1965: Undernater Acoustics Hanudook-Il (Pern..Ivania Sw.. esity Prcs;), 356 pp.

Au, W.W.L., 1979: *'Echolocation signals of the Atlantic bottlenose dolphin (Tursiopstran catus) in open waters." in Animal Sonar Systems edited by R. G. Busnel andJ. F. Fish (Plenum Press, New York), pp. 251-290.

Busnel. R.G. (editor), 1963: Acouystic Behavior rf Anima!s (E,,evier. New Yor,,.933 pp.

Busnel. R. G. and J. F. Fish (editors), 1979: Animal Sonar Systems (Plenem Press, NcwYork). 1135 pp.

Cato. D. H.. and M. J. Bell. 1991: Ultrasonic Ambient Noise in Australian Shallow Waterat Frequencies Up to 200 kHz, Technical Report MRL-TR-91_23, MaterialsResearch laboratory, 28 pp.

Caldwell, D. K., J. H. Prescott, and M. C. Cald,, ell. 1960: "Production of pulsed sounds

by the pigmy sperm whale Kogia breviceps." Bull So. Calf. Acad. Sci., 65(41.245-248.

Diercks, J.K.. 1979: "Signal characteristics for target localization and discrimination,"in Animal Sonar Systems. R.G. Busnel and J.F. Fish (editors), Plenum Press. Neu,York, 229-308.

Ellis. R.. 1980: The Book of Iuhales, Alfred Knopf, Neu York. 202 pp.

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Fish, M. P., and W. H. Mowbray, 1970: Sounds of Western North Atlantic Fishes: AReference File of Biological Underwater Sounds, The Johns Hopkins Press, Bal-timore.

Hershkovitz. P., 1966: "Catalog of living whales," Bull. Smithsonian Inst., 246, 1-259.

Johnson, M.W., F.A. Everest. and R.W. Young, 1947: "The role of snapping shrimp(Crango and Synalpheus) in the production of underwater noise in the sea, Biol.Bull. Woods Hole, 93(2), 122-138.

Johnson, M.W., 1948: "Sound as a tool in marine ecology, from data on biologicalnoises and the deep scattering layer." J. Marine Res., 7, 443-458.

Knudsen, V.0., R.S. Alford, and J.W. Emling. 1948: "Underwater ambient noise."J. Marine Res.. 7.410.

MacGinitie, G.E.. and N. MacGinitie. 1949: Natural History of Marine Animals.McGraw-Hill, New York, 473 pp.

Martin, A. R. (editor), 1990: The Illustrated Encyclopedia of Whales and Dolphins, Port-land House. New York, 192 pp.

Nachtigal, P.E., 1979: Bibliography of echolocation papers on aquatic mammals pub-lished between 1966 and 1978," in Animal Son, r Systems, editcd by R. G. Busneland J. F. Fish, Plenum Press, New York. pp. 1029-1069.

Tavolga. W. N. (editor.), 1964: Marine Biuacoustics. Pergamon Press, New York.

Urick. R. J.. 1967: Principles of Undenrater Sound for Engineers, McGraw-Hil. , NewYork. 342 pp.

Walker. R. A.. 1963: "Some intense low frequency underwater sounds of wide geo-graphic distribution, apparently of bio!ogical origin," J. Acoust. Soc. Am., 35.1816.

Watkins, W.A., 1979: "Click sounds from animals Pt sea," in Animal Sonar Systems.

R. G. Busnel and J. F. Fish (editors), Plenum Prcss. New York. pp. 291-297.

Watkins, W.A., 1974: "Bandwidth limitations and analysis of cetacean sounds, withcomments on delphinid sonar measurements and analysis," J. Acoust. Soc. Am.,55, 849.

Watson, L.. 1981: Sea Guide to %7uiles of the World. E. P. Dutton, New York, 302 pp.

Widener. M.W.. 1967: "Ambient noise levels in selected shallow water off Miami.Florida." J. Acoust. Soc. Amn., 42.904-905.

Wenz. G.M.. 1962: "Acoustic ambient noise in the ocean: spectra and sources." J.Acoust. Soc. Am., 34, 1936.

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Wood, F.G., and W.E. Evans., 1979: "Adaptiveness and ecology of echolocation intoothed whales," in Animal Sonar Systems, edited by R. G. Busnel and J. F. Fish,Plenum Press. New York. pp. 381-425.

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I

IV. Bottom

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Introduction

This section contains the models for bottom forward loss. backscattering strength.

and bistatic scattering strength applicable ove"r the frequeny 1interVal AV-100 1Z. I the

forward loss and backscattering models are identical to those defined in the previous ver-

sion of this document.1 The bistatic model is new. The models employ a mixture of

theory and data fittinV and all use the same set of bottom parameters.This section is divided into four parts: S^^t;"n IV.A l;dcicc O, t•h ýv ,h,,,•, an,,

model inputs. IV.B treats the forward loss model, and IV.C and IV.D treat the back-

scattering and bistatic scattering models.

For those who want to make quick estimates of forward loss or backscattering

strength based on minimal knowledge of bottom type, we offer here a guide to relevant

tables and curves:

Bottom loss vs grazing angle

Use curves of Figure 1 (page IV- 19).

The loss is independent of frequency.

Backscattering strength vs grazing angle

Use curves of Figure 2 (page IV-26), which are computed for a ...requa..cy off 310 U,1.Iz.

More generally, consult Table 3 (page IV-23) and interpolate if necessary.

No similar plots or tables are available for the bistatic scattering model. To use the

mathematical cxpressions that constitute the separate models, model input parameters

must be determined. Section IV.A on model inputs provides the necessary information.

Once model inputs are available, they can be inserted in the equations for forward loss

(Section IV.B), backscauering strength (Section IV.C;. !r b•static sca.cr;_,• Str-,th

(Section IV.D) without further reading. The text explains the models and indicates theaccuracy that can be expected. The equations given for the three models are. srighhlfor-

ward, analytic expressions; however, the forward loss model involves considerably fewer

equations than the backscattering and bistatic models.

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It is important to understand a technical issue that arises in applying the models to

scattering near the specular direction. The loss model treats thc interface as perfectly flat

and gives the energy loss for perfect, mirror-like reflection. The two scattering models.

however, yield predictions for the angular spread of this energy due to interface rough-

ncss. If onc intcerates over this angul!ar spireadA, the totalk %.AL-rg6y will U- b jP A1 Jaro i%. ely

equal to the refilected energy predicted by the loss model. There is a danger of double

counting if the scattering and loss models are employed without an understanding of this

relationship. Rough bottoms such as rock and gravel present an especially difficult prob-

lem in this reg-ard. The forward loss model yields very low loss because it neglects

scatterino due to roughness. Such effects are the province of the bistatic model. but the

present version is not applicable to rough bottoms. The scattering model subsections

dIV.C and IV.D') contain brief discussions of this- isrsue.

A. MODEL INPUT PAR41METERS

This .section can be viewed as a "front end" dcsig .. d to allw se-rs teo Cbt'ainA area-

sonable estimates of the model input parameterN given various sorts of information about

the bottomn. Some us-ers may have only minimal information, c g.. a sediment name such

as "silty sand." Others may have a detailed geoacoustic characterization in terms of

physical parameters such as sedimnent sound speed and density. To accommodate a wide

rage of such possibilities. this s~ection is b~roken into Q "lmh of prtsc. Fol'oin s .. A' A.brief outline of each part intended to guide users to the material essential to the applica-

tion at hand.

1. Commnents on Ocoacoustic Modeling(This section is optional, but recommecnded, reading.)

2. Definition of Model Input Parameters(This is required reading for users intending to use the mathematicalexpressions that constituite the models).

3. Table for Model Parameters in Terms of' Sediment Name(This is the least ambitious; and Icast accurate approach to model inputpzu-ameters. This section is self-contained.)

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4. Model Input Parameters Using Grain Size(This provides a useful, but not always accurate parameterization in termsof a single. commonly encountered sediment parameter, grain size. Thissection is self-contained.)

5. Model Input Parameters Using Geoacoustic Data

(This section depends on material in Section IV.A.4.)

6. Refinement of Model Input Parameters Using Backscattcr Data(This supplements the methods discussed in Sections IV.A.3, IV.A.4, andIV.A.5.)

7. Use of Bottom Roughncss Data(This supplements the methods discussed in Sections IV.A.3, IV.A.4, andIV.A.5.)

1. Comments on Geoacoustic Modeling

Our modeling of the ocean bottom is confined to the top tens of ccntimcters because

of the high attenuation of sound in sediments at high frequencies. 2 The upper few cen-

timeters of sediment are more w.,terlike thin the- co-dimno tin di.eelp"er -- , ,i-ll t , foir

soft sediments such as silts and clays. Unfortunately. quantitative geoacoustic data on

this centimeters-thick transitional layer are almost nonexistent. With notable excep-

tions.3- the layer is either ignored outright or de.;troyed during proce-ing of the col-

lected sediment. However, the data available strongly suggest the existence ofsignificant gradients in porosity (hence density) alon.g with'" •--encra"'lly k•k r. . .. in.

sound speed and attenuation. These gradients start at or near the interface and connect

the more waterlike, unconsolidated sediments at the interface to the generally denser sed-

iments that characterize the deeper layers. These grad.ient" C.. ..... over ,.vcra, ccn;tmeter."

in depth. Preliminary theoretical calculations 9 show that these gradients can have

important effects on the interaction of acoustic waves with sediment, by determining the

effective impedance mismatch of the sediment/water interface. Long waves (relative to

the average gradient in geoacoustical parameters) do not see the gradient-the effective

impedance mismatch is determined by the bulk p.rprtfie" oaf the ,-imt. Shrt ,ave.s

see only the surface values of the sediment's geoacoustical parameters.

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Our modeling efforts were constrained b' the fact that there are not cnough !

tae'ou.s acoustic and geoacoustic data with the necessary level of detail to construct a

model of this interface that incorporates these effects in a realistic way. Our modeling

cftort, for bo)th backscatier' .-I-l forward loss afe therefoie based on the physical charac-

teristics of the uppermn, .- mnt, especially its density. Thus the sediments are

modeled ac a simple, scr, ý: ,mite fluid m %,,,,, ,,l .11;All, i 6 ........ to b" %' U &'" till ""'llv l h' -

geneous both in the horizontal and in the vertical. (Volume backwcauer contributions are

parameterized by an equivalent surface backscatter.) This avoids complicated models

which would have included more detailed physics, at the cost of ill-defined bounds and

poorly supported relationships for the appropriate parameters.

2. Definition of Model Input Parameters

Table I lists the geoacoumtic paraineters used as input, f,.VT butt, the f•ird ius.; wd

backscattering models.

Table, . Bottzoi parameters used as model inputs.

Symbol Definition Short Name

p Ratio of sediment mass density Density ratioto water mass density

Ratio of sediment sound speed Sound speed ratioto water sound speed

5 Ratio of imaginary wavcnumber to Loss parameterreal wavenumber for the sediment

72 Ratio of sediment volume scattering cro.,s Volume parametersection to sediment attenuation coefficient

y Exponent of bottom relief spectrum Spectral exponent

w11, Strength of bottom relief spectrum (cm ) Spectral strengthat wavenumber 21r/k = I cm-

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The bottom backscattcring model c ...io .-11 ;1- ;•' ... f, T-.. I', ". 4a

forvw-ard loss model employs only the first three. The bistatic model uses all of the inputs

from Table I except for oi which is replaced by three new parameters. A default pro-

cedure is provided for obtaining these parameters in terms of o;. The working assump-

tion is that the surficial characteristics of the sediment govern its acoustic properties.

Therefore, one should '-ve direct meaburements of the first three geoaco....ic .. .s

in Table I averaged over the upper few centimeters of the sediment, as well as direct

measurements of the others. Unfortunaely,. many oeoac•l•fic measurememnt Consist of

averages covering a depth of several tens of centimeters. Consequently a straightforward

method of assigning values to the parameters and compensating for likely bias is essen-

tial for practical applications of the model.

The water sound speed immediately above the bottom, c , enters the backscatter

and bistatic models through their dependence on the acoustic wavenumber,

k = 21rf/c " 2MAavelength.

3. Table for Model Parameters In Terms of Sediment Name

Table 2 relates standard sedirnen: types to .od.l input, ........ . T Vote .•mn:

name iN assumed to be the name appropriate to the bulk of the sediment, rather than the

surficial'scdiment. The user is cautioned that the density and sound speed ratios given in

this table are surficial values derived from model fitting and tend to be smaller than the

bulk values reported in the literature. The user is also cautioned that this table does notconstitute the APL-LV bottom in roeul ei. ny canto. Tc', •-qr M,,,tr ,a-,

intended as defaults for use in the absence of physical data on bottom properties. In par-

ticular, for a given sediment name, there is considerable spread in observed scattering

strength. Most of this spread can be ascribed to the parameters a2 and w2. as the output

is particularly sensitive to these parameters. The range of variation of these parameters

has been examined by fitting the model to unptib..ishcA sli ata, at. IV , ,.

sonal communication). In these fits the parameters of Table 2 were used, except that 02

and w_-2 were allowed to vary. One group of data was fit using the parameter for

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Tabl' 2. Model inpurs in tenn.s of .cdf,_nt. mi,:'.

!Bioilk ix,:.iIY Sou~nd SIVCJ Lv's vk'Iurn: Spcrwil S,-wcrJlSCrain ' Ru:io Ratio P,.ameler Parameter Epncri Stcrt;•h

Se~m..•tN-',: ] i~ze p t -- . o,__ _ -... i•r•

....--. 2 5:i (, 25 0 2(*e1.Wick2.w 2-.51' 0 (ill i4 0C j3 W(6

Cotil'. Gravel. Pet'.c . .I.&.) ' 74 m) (IL): o v it

Sand, (r cir :' . . .. 1..0 2 -P'. I .4

Sand ____ 40 Jiu )1 1 0(7 0(0 1667 O'kMI:- .5 (00](57".• '. . .. . j ,,:... IC o0" 63U 0I 02.

IV2 ?! "s 0(t'1630 -A' -2,',.a'Co..r.e SsdrJ. Gra.,el. Srd " 0 5 i"?1 1 .2.50 0.OiE39 004 3.^5 (0.(/457

MJa•,eI\ .1ddv Sand 1.0 151 1-2.141 0.01645 O"IX 4) W..

Me~lium Sani I1 A I.57.ý 1. o72 16. 00, 12 25 0,94___,

AMiOd' (raCv'l 2.0 (1.6.5 1.)1 Iw.I ,161 . 1.bi0 . 1: 25 0 l Q '14 ,

Finm. Sand. Stir, Sane 2.5 1.4!2 I 1073 U.010062 • .I.4 - .25: ( 1E,).tM ,dd ; ,S d 30 1 339 I.(I..1111 (I.( 72 09 .- (00 12,,

Ve% inc Samc 3.5 1.26t .06% 0 17 . ____________________

Claw%' Sani 4.0 1 224 1.0364 0 02 19 0.0w.. 3.2! O. .I I llCou'k. Silt 4.5 19M to 07ý 002158 0.0r., 325 60 7'

"Sdf- iilt. ] GI ,,c.a ,y . .j . s o - 1 1f-,9 0" 9 '9 o r 0 1,2 i 0('o,2 . . . . - - 0 T{'sI%

,,J-aun S:hi. S.ariS -Ci•.5--• 1 i--49 .• .9....5 . • •.76 . (.. .2! 005 ' sS 1 •. lu | 60 1.149 (is?73 (ICK,396 O.0(11 3 2. 0 OU10Fiii. Si:i. Cla~v\ Silt 6.5 ).14F (19S,61 0t.t41306, ()(911 _ I ID M 5 •X 1 S

.V ,d. (Ch.) . 0. 1. 14" 0(X49 (H;242 (110. 325 0 (t5.1

-V-r- Fii. Si,' 7." 1.147 0p3. 94 i-3 (lici [ .2!• W 0.2 Q (Y, 1•"

Sib lmND 1.4 (1ik iIýJ' 2 L foi't61; (ol 2 1)9 t(Y 1) 1 NCh- .a 9 .0 1.)4(,.5 (1 9M qt.,.( { 325

A. = 5.0. except that OY ranged from extremes of 0.C0001 to 0.OOS ith . ivt, . M" ,f ,, A

data falling in the range 0.0003 to 0.004. Anothcr group of data was fit using Al = 2.0

parameters; the extremes of 14 , were 0.00052 to 0.0j6. and about 70% of the data fell in

the range 0.0008 to 0.0086. In these fits., c, wa also adjusted t) imuprove the fit.

The sediment names are taken from the classification schemes of Wenrlortlh,t0

Lane.1 1 Inman2 Shepard,)3 and Folk.?4 The parameter At. given in the second column

of lable 2 is the mean grain size: it is included for completeness but is ines.sential for

most applications of the table. Mean grain, 017.6 N dfi.•niuA d in Section . .•".4. " \Or 4,1t.,

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Wentworth and Lane schemes, the Al. value given in Table 2 is the midpoint of the range

defined by the sediment name. The Inman, Shepard, and Folk schemes base sdiment

name on the proportions of three componcnt Si70e crlAsss r ihf-r than the mean grain Sije

The Al. values given for these schemes in Table 2 are not identical to those of the original

authors. but were chosen on the basis of consistency amone all five schemes and with

Section IV.A.4.

4. Model Input Parameters Using Grain Size

A useful sediment descriptor is grain size. It is usually measured in logarithmic

unit,, and denoted M1-.

do d

where d is the mean grain size (or "di2m.. er"), " 1 is ,lhe ref-.renc,.,e lngth (1 mnr) nd

the units of MA are denoted 0.

The foregoing comments about mcasuring the prop.e.. e.. ofA the , r' the" ,",

of the sediment apply to the grain size as well. Thus if the sediment consists of fine sand

with a several-centimeter layer of broken shel!, the grain size appropriate to the broken

shell should be used for At. Similarly, if a gravel bottom has a patina of sand, the grain

size of the sand is the relevant quantity, unless the layer is so thin as to permit acousticpenetration to the underlying gravel.

SWe offer parameterizations of the geoacoustic inputs in terms of the bulk grain sizeAM.. These parameterizations empirically relate M1. to the ass ,,um,"ed ti h -

teristics of the upper few centimeters of the sediment. This provides the basis for assign-

ing approximate parameter values in many cases of interest. Furthermore, sediment

nomenclature is based on M:. so one can estimate bulk grain size from the sediment

name and then. via our parameterizations, the model inputs. However, this path of least

resistance ha.q its price: the uncertainty in the ,.d,,, .Fed....., ,s.m., than.

accurate geoacoustic data are used to determine the inputs.

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._ UNIVERSITY OF WASHING, O,'* APPL193 PH I'SiC... LA E AT./- !

The empirical relationship. deinatdcu " ..............

our acoustic models and measured reflection loss and backscatter data, while remaining

consistent with the governing physics. In developing the,, rolatinnch;s , atam from three,

sutes played a dominant role. 9 The development was also guided by published geoacous-

tic relationships'" 5 and our earlier APL-UW modeling work.16' 17 The relationships

given below are defined only for - 1 1 M. !5 9.

P:

Pi

=10.007797ME-0.17057M. +2.3139, -5 Al. < 1

=-0.0165406M! + 0.2290201MA - 1.1069031 M. + 3.0455, 1 -At. < 5.3

- 0.0012973 M. + 1.1565. 5.3 < M :< 9

C-V- = (3)

0.002709 M.: - 0.056452 Al. + 1.271. ., A. <.,

= -0.0014881 MA + 0.0213937M3 -0.138..798!M. + 1.3425, 1 SM_ < 5.3

=-0.X)24?24 M. + 1.0019, 5.3 < M_ s 9

(Thcse pararncteri-alions allow for four CCIma.;,, I,.A.s o ..... r ...

All subscripts I refer to water and all subscripts 2 refer to sediment. Parameters p

and v are real quantities that are mcaurc.m of """e "ratios Of "-c .... ' "' a-a

opposed to complex) sound speeds of the two fluids. The density and sound speed ratio.s

agree with those of Hamilton and Bachman"' for -1 <M. < 1, where for re!.laij:ey

coarse sediments we expect at best a negligible, tenuous layer. For M: = 9. the sound

speed ratio again agrees with that of Hamilton and Bachman. while the density ratio

remains lower. For interm•ediate value; of l., b•oth p and v are smiller than the Har-lal-

ton and Bachman values.

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The loss parameter 8 is a dimensionless quantity involving the complex .sediment

acoustic w;\enumber k, k + & 2j:I-

k al2 v¢ I ln(10)

k 2r f4O0(

This definition can be related to the quality factor. Q.18 through the simple expression

28 = 1/Q. The loss parameter. 6, contains the sediment sound attenuation coefficient, a12 .

which is usually expressed in units of decibels per meter (it is discussed by Harmilton 2).

Hamilton's parameterization of ci,/f is reproduced below. N .ote ....a.t C,.,,,: ....... -,:n -u-,

be employed in Eq. 4. If a,/f is expressed in decibels per meter per kilohertz (as in

Hamilton's parameterization), c; must be expressed in meters per millisecond

(c = 1.528 m/ms is used in determining 8 from Hamilton's expression,, for rt2.f and

Eq. 4).

"= 0.4556. -15M <0 (5Mf

"f = 0.4556 + 0.0245 M., 0• M!. < 2.6

S= 0.1978 + 0.1245M. 2.6<_M, <4.5f

= 8.0399 - 2.5228 M. + 0.20098 M:. 4.5 M. < 6.0f

--=.-= 0.9431 - 0.2041 M. + 0.0117 M3, 6.0<- M. <9.5f

a,-= -0.0601. 9.5 AfM.f

The sound speed ratio parameterization is based on measured sound speed ratios

from three sites.9 The measured values correlated well with apparent critical angle

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behavior in the data. Also, the gradients I W%.,,,., velo,#It• ".Ae sle.•. ig,0lc two III z&.>•

On the other hand. the measured density ratios from these sites were discarded because

of the large scatter and vertical variations in porosity. Published bulk density measture-

ments and standard parameterizations were considered, but were not used because of

possible gradients which they do not incorporate. Rather. the acoustic models were fit to

data in order to determine the rel'atio" SiE----------"..........:-C ... , ... ...... , C:,.

ing consistent with the governing physics. However, it was found that the Hamilton2

parameterization for absorption gave satisf'actory res-its.

In the absence of information on scdiment volume scattering, the volume parameter

should be assigned the the foh , ioWvntflues:

o.2 = 0.002, - .0:5 MA < 5.5 (6)

02 0.001, 5.5 < M. 5 9.0

The dimensionless volume parameter is defined in Table 1. It is a surface scattering

parameterization of the volume scattering cross section when used in Eq. 66 (Section

IV.C.2I. There is considerable variation in the volume para eier, which sometimes take.s

on values differing by an order of ma nitude from those given above (see Section

IV.C.3).

The backscattering and bistatic models assume that the two-dimensional relief spec-

trurn is isotropic and obeys a power law for .a.cn...U.C. c" mparabie In, "' . ..

wavenumbe r:

W,, (K) =(h/0K)f w (7)

In this expression. K is the wavenurnbcr of bottom relief features- K = 2r/A, where A is

The associated wavelength: ho is a reference length, equal to I cm. Equation 7 requires

two parameters, the spectral exponent yand the spectral strength parameter i! 2 . Methods

of determining y and w.- from bottom roughness measurements are discussed in SectionIV.A.7. Here. the paramcterization of 7and W: is.coniue- -, te' i'.,-gr"ii- sue.

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In the absence of measurements, the spectral exponent is assigned the fixed value

y = 3.25 (8)

for all grain sizes. An average of available d4a"ta on ,spectral ,-,.n-,,,-,,, yieldo ,a .a,,

of 3.23 with a standard deviation of 0.44.

To parameterize the spectral strength, we start with a parameterization of the "-"

relief Ii of a 100-cm track, which is used to bui'd w'. The numbers in this parameteriza-

tion were chosen by fitting the backsCcattc'ing ,,nMde to datA.

h 2.03846 - 0.26923 1 M-1.0=.6-31 .0 -<M: < 5.0 , (9)ho 1.0 + 0.076923 .f.I.

= 0.5, 5.0<?4:9.0hoj

With these functions, the spectral strength is related to h for y = 3.25 as ......ow 17.

12 = 0.00207 h h0 . (10)

Note that wv, has units (cm 4); it is the only model parameter that is not diumnrsoionless.

This is the least accurate of the parameterizations (not considering Eq. 6) as there is wide

scatter in measured spectral strengths and weak co.rela.tion with grain size. Therefore,

Eqs. 8-10 should be viewed as reasonable defaults, not as predictors of the roughness

spectrum.

5. Model Input Parameters Using Geoacoustic Data

As noted earlier, measured sediment acoustic parameters often •show apprec.a..le

gradients in the upper few centimeters. The most significant vertical variations are often

confined to the density, while the sound specd and attenuation show smaller changes.

Because of these vertical variations, the preferred method for determining p. v, and 8 is

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direct measurement in the upper 10 cm using, unuistuStud core sampla., or f,-Siu prOt, s

with a resolution of at least 1 cm. This should be sufficient to resolve gradients to scales

appropriate for use in modeling applications at I0--100 klIz. Sampling of the. - .-rmI

portion of the sediment is not as important for the loss parameter as it is for the sound

speed and (especially) density ratios. This is partly because the loss parameter does not

vary greatly with sediment type and partly because the model.s are not particularly sensi-

tive to the loss parameter (save for the case of intromission; see below). However. themodels are strongly dependent or i...s.e .' n1%r ,l.,.riti,""ng.e, ', , rr,1 A,.

cosO, E I&. and on p near vertical incidence.

Some users may have access only to a sin,,,e ,im ,,ea ued 'U'".' gcu,,,IU,.. ,qua,-

tity. such as mass density or sound speed. In such cases, Eq. 2 or 3 can be inverted to

give a value for M:. If measured values are available for both mass density and sound

speed, inversion of the sound speed relation (Eq. 3) is the preferred means of determining

M:. Mean grain size can then be used to obtain the remaining input parameters using

other expressions in Section IV.A.4. Surficial vau.e. oIA, ,•h.e abso. .ption. ,... Aln. mist .. a.. be

used to obtain a value for the loss parameter, but Eq. 5 should not be inverted to obtain a

value for Af- in terms of the absorption coefficient because the uncertainty in this process

is too great. If a surficial value is available for porosity (denoted n and given in percent).

p can be obtained from

p = 2.66 - 0.0169n , 35 < n < 85 . (iI)

Equation II was derived by inverting a regression relation given by Hamilton and Bach-

man (p. 1903 of Ref. 15). With this value for p.Eq. 2 can be invertd .r i) -.. 1 Ir .1i

the other parameters can be obtained.

Some users may have access only to measured bulk' gcoeoustic quanticies. rather

than surficial values. If a measured value is available for M., it should be used in prefer-

enee to the bulk geoacoustic quartities, following ,hc procedures ,of Sec.ti;-n V•.A If

M, is not available, it can be inferred from the bulk geoacoustic quantities by using the

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following inverted forms of the Hamilton- Bachman 'S regres-io;n re.,tkina.

If the bulk density ratio is known:

At = 10.937 - "'128.25p - 177.12 , 1.22 < p < 2.05 . (12)

If the bulk sound ,peed ratio is known:

At. = 10.418 - \'369.64v - 363.09 , 0.99 < v < 1.22 . (13)

If the bulk porosity is known:

M. = 12.6575- \N220.5145.- 2.73972 n , 35 < n < 85 . (14)

6. Refinement of Input Parameters Using Backscattering Data

If backscattering strength data are available over at least a limited range of angles

and frequencies, this information can be used to determine model parameters via fitting.

This procedure is recommended only for dete"nrining those parameters W"hse ......... :""-

causes large variations in predicted scattering strength. For soft sediments (M. > 3.0).

such fitting provides a means of determining the sediment volume scattering parameter,

02. For harder sediments (MA _• 3.0), this procedure can be used to determine the rough-

ness spectral strength. Such acoustical determinations are preferred over estimates based

on sediment name or grain size, which can introduce large errors.

In the fitting procedure defined here, it is assumed that the parameters p, v. 8. and y

have already been fixed by the procedures given above. For soft sediienra;. (M. > 3.0), it

is assumed that sediment volume scattering is dominant. Accordingly, the roughness

spectral strength is temporarily set to zero and the volume p'r ine, er, i• qei t any

known value, e.g., 0.001. The resulting backscattering strength predicted by the model is

then compared with data, and a2 is adjusted to bring the model's results into agreement

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with the data. Since the backscattering cross section is proportional to c;,, this adjust-

ment is simple: e.g.. if the data arc 3 dB above the model, a- should be increased from

0.001 to 0.002. Once the volume parameter is determined, the spectral strength can be

"~turned on"' (assigned a value dettermined by thle proicedureý defifled earlier.) Aftei fthi

new set of parameters is incorporated, the model should be checked for consistency by

another comparison with data. If the roughness scattering, com-pnent~velii~,a

assumed in the fitting procedure, the model and duta will agree. If not, the procedure out-

lined here fails and cannot be applied.

For harder sediments (.11, 5 3.0). the volume parameter, c;,, is initially set to zero.

and the spectral strength, iv.- is assigned an arbitrary- value. It is subsequently adjusled

to produce agreement with data in exactly the same manner as, for the volume parameter.

There is a slight nonlinearity in the dependence of scattering cross section on st2, so

some iteration ma;' he rcquircud. Once a suitab~le value is Ifound., the se-dim-ent volumeý

scattering parameter is "turned on" and the consistency cheek is made as above.

7. Use of Bottom Roughness Duta

As a general rule, the backscatterIng rnod,- .0 sýsAJv tO both& VA LIM. ecraparameters for coarser sediments (M. < 3.5)i and becomes less sensitive for finer sedi-

ments.

From Eq. 7 it followvs that w, is the Vahle of the spectrum. for K = 14:0o. The spec-

tral exponent is limited in theory to the range 2 < y < 4. but practical considerations

(Section TV.C.3.1 place tile more stringent limi~ts

2.45 153.9 (5

If the measured % alUe of -1 falls outside these limits, one should use y = 2.4 or 3.9, which-

ever is closer to the measured value.

The normalization of the spectrum must be clearly defined if measured spectra are

to be used as model inputs. It is important to distinguish between the formal power law~

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spectrum (Eq. 7). which is infinite at zero wavenumber, and the measured spectrum.

which is necessarily finite. The measured spectrum must be normalized such that

J f W', ( K) dK, dKY =h (16)

where

x• Y K2 )'r (17)

and It is rms bottom relief. Note that the integral of E 6. 1, 1- 4.4-,,,,. for t,,, ,,, "

spectrum of Eq. 7. Still, Eq. 16 is useful because measured spectra are always finite. The

rms bottom relief is actually a function of the length of the window used to estimate the

spectrum. The same window length and taper must be used in estimating WV, (K) and h.

The preferred method for dete.mining y, --d wi is to do a straight-line reoressinn fit

to the two-dimensional relief spectrum plotted in log-log fashion. The fit should be made

at wavenumbers comparable to the acoustic wavenumber. which demands that the bot-

torn profile be measured with a resolution of I cm or better.

Most such measurements to date have been published in the form of one-

dimensional spectra rather than the two-dimensional spectra f,,"UC" U1,Vu,,.,

now relate one-dimensional spectral measurements to the two-dimensional spectrum

used in our model. The one-dimensional spectrum can be represented as follows:

W, ( K )=(h 0K 1 w (18)

with normalization

J W,(K)dK=/h2 (19)

The conversion to two-dimensional parameters is as follows 1:

7= + 1(20)

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UNIVERSITY OF WASHINGTON, APPLIED PHYSICS LABORATORY

r(1)2 = wjh 0 . (21)

R112 r( 2-2

i here r (xc is the ganmma function. 1 ,ie that the factor h. is present rne•e" y to balance

units in this expression.

Some spectra are presented in terms of spatial frequency. f,, rather than in terms of

wavenumber. K. The relation between wavenumber and spatial frequency is

K=2nf, . (22)

When spatial frequency is used, the one-dimensional spectrum can be represented as

01 (6=(hCof)-'y' 01 (23)

with normalization

4f, (A l, = h-. (24)

In this case, the conversion to two-dimensional parameters yand wi is as follows:

7 =y• + I , (25)

r( )2 = x I O*i 2 (26)

2

If the user does not have spectral data hut has data on rms relief for scales compar-

able to the acoustic wavelength. the spectral exponent should be taken to be

y=3.25 . (27)

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and the appropriate spectral strength is17

22Yy( y- 1 ) -21 4 -y)~

2h 'Q ,(28)32n r(3- Ly-

2

where L is the window length used in estimating h, where the latter is defined in Eqs. 16,

19. and 24.

8. Limits on .Modal Parameters

The following limits are recommended for input parameters. These limits afe

extremes suggested by a combination of numerical and physical considerations. Pub-

lished values of parameters fall withi these li.mts, but the extreme vqaues tin1r e Nk tn

be encountered in practice and may yield suspect results.

1.0 S Density Ratio • 3.0

0.8 5 Sound Speed Ratio _ 3.0

0.0 < Loss Parameter 5 0.1

0.05 Volume Parameter _ 1.0

2.4 : Spectral Exponent 5 3.9

0.0 < Spectral Strength (cm4) < 1.0.

Other parameters should be limited as follows:

0.05 Grazing Angle (deg) < 90.01400 < Water Sound Speed ("m" s) -" A

10.05 Frequency (kHz) : 100.0.

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B. FORWARD LOSS

The forward loss model is based on acoustic reflection rather than scattering con-

cepts. This is because much of the forward scattering data used in building the model

actually showci little pulse elongation. suggesting that the incident acoustic energy was

reflected rather than scattered. Available data on maill.-scae boilorn rfoUghrinss I. a2

support the modeling of forward scatter by forward reflection since they show that the

bottom ik often much smoother th3n the sea surfCe. In s,,,, .ppnc.tinon nb... I

spread of for%%ard-wcattered energy is import.nt. The bistatic model (Section IV.D) pro-

vides estimates of this spreading.

1. Statement ot' the Forward Loss Model

The following simple model is adopted for forward reflection loss. r0 . with 0 being

the grazing angle:

ro - 20 log,( IlR(0) (29)

R(O = (30)y,+1

y s9n8 (31)P(0)

P(0) = -K _ cos20 (32)

K: = 41 + is) .(33)

The idea of a Iossy Rayleigh coefficient was first published in an article by Macken-

zie,-' who quoted unpublished work by Morse. Note that R(0) (not the forward Ios, ro•

is a complex quantity, as are the quantitie, y. P(G), and KC.

Because this model does not include gradients and layering. it has no explicit fre-

quency dependence. The loss parameter, S. may be frequency dependent in general. but

it has no such dependence in our parameterizations.

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Figure 1 shows examples of forward loss for a var,..cty of _d.c: tot.. V_.j I.

represntative of the full spectrum of possible oceanic bottoms. The choices are taken

from Table 2.

2. Model Accuracy

The forward loss model is based on a limited set of data from three sites, and com-

parisons of the model with these data are given by Mourad and Jackson. 9 The data are

confined to the frequency range 20-30 kllz, and grazing angles are concentrated at small

values, typically between 50 and 30'. In addition, a single data point is available for each

site at vertical incidence (901). High-qui, .. L, ,.,,o -,-" da" % %" ,,"''AAi"A, , , ,"A ,h

sites. For the small angles, use of surficial geoaeoustic parameters resulted in model

errors that were about equal to the loss value. That is, for a soft, claycy bottom. the

prer Wcted loss at 50 was about 8 dB, and the data near this angle were within 6 dB of the

M

Z

C p i |" I

0I

0

0 -silt (Mz 6.0)01 _ - - - -_--sandy silt- -

L.. / ................. coarse silt ...............

... -- very finesand ..........

... fine sand -

,medium sand - -

S. ... ... coarse sand ........................ .. . .sandy gravel -oc -

" , ........ • rock ----

0.0 10.0 20.0 30.0 40.0 50.0 60.0 70.0 80'O 90 C'

GRAZING ANGLE (deg)

Figure 1. Cunres predicted by the forward loss model for generic bottom t.pes. The mode!input parameters are taken from Table 2. For a given set of input parameters, theloss modul ha.s no frequency depedulence.

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UNIVERSITY OF WASW..GT3 ... AP P . .... . ...... '..................

model prediction. For a hard ;an bottom, Ah .. :...,.. i .. .b . .. ,V d

the measured %alues ranged from a fraction of I dB to 2 dB. Errors of thc -amc magni-

tude occurred at 90'. These data were used in developing the reat:ivn'hin be.*tw=e'n -"rlin

size and model input parameters. As a result, use of grain size rather than measured

geoacoustic data actually gave a better model lit for this small data set than use of high-

quality geoacoustic data. but this is an artifact of the fitting process.

Because of the large fluctuations that can N: found in forward ,,cat,-ring ,am, ut,,,r,.

work should incorlporatc the effects of horizontal spatial variations in input parameters.,

s• hich may explain the large variation seen in measured forward loss.

In this model, bottom loss approaches zero as grazing angle approaches zero. This

is a reasonable approximation. provided bottom roughncss does not redirect acoustic

energy substantially away from the specular direction. The experimental data support

this assumption. as they tend to show low loss values as the grazing angle becomes sm.al. IIt must be noted. howevcr, that thVsc data did " l ,a.... , .... r than 3.. an 0a-0

they were gathered from single-bounce experiments. At longer ranges, multiple bottom

and surface bounces will render the reflection loss approach invalid if the angular spread

of the acoustic energy increases to a value exceeding the relevant system bearnwidths. In

such circumstances, a scattering approach is required. in principle. Such an approach

could be based on the bistatic S"catt""';"Alz ""d•"e;' ;" 0"I' '" TV.D.

The error incurred by using the present model in multiple bounce situations will be

greatest for relatively hard. rough bottoms, such a, ;and. gravel, and rock. For softer bot-

toms. roughness scattering should be less important, and the error should be correspond-

ingly smaller. For simulations that cannot employ a roughness ,caerino ap•,w,,h, it i,

necessary to introduce an effective loss that is greater than the loss given by the present

model, and possibly nonzero in the limit of small grazing angles. Such an effective los.,

depends on system parameters and propagation conditions, including the angular spread-

ing incurred by interaction with surface waves. That type of spreading will move a frac-

tion of the acoustic energy to higher angles where it is more readily absorted by the be!-

torn (Marsh and Schulkin 22 ). Quantitative prediction of these effects is difficult (Weston

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IUNfVERSITY OF WASHINGTON. APPi IED PHY1ICS LABORATOY'.

and Ching23). nevertheless, a fixed effecti•iVe 1"--"-o'' ;c c"^v".t;'i"v e,,M,, .... A ao

practical means of introducing scattering loss into acoustic simulations. For multiple

bounce situations, a minimum loss-per-bounce of 1.5 dR is recommended by Hall and

W atson.-

3. Numerical Considerations

Expressions 29-33 are all complex and are most simply evaluated by code that uses

complex arithmetic and treats the variables R (0). y, P (0), and 1 as complex numbers.

tThe square root in Eq. 32 is defined as the complex number whose magnitude is the posi-tive square root of the m....~ e ftear--A-,1 A. "'' .9-'-ýA.... &a ,I.1cl ,M,.%,• ....

of the argument. This definition removes the ambiguity about the sign of the square root.

C. BACKSCATTER

1. Introduction

The bottom backscattering strength model requires the six bottom parameters

defined in Table I and the water sound speed as inputs. Users who need only estimates of

bottom backscattering strength for generic bottom types may prefer to use Table 3 (corn-

puted using a water sound speed of 1529 m/s) or the curves of Figure 2 rathe ta

full model. Users that have physical data on bottom properties can obtain more accurate

predictions using the full six-parameter model which was developed to encompass a

%vider range of bottom types. The equations defining the model are straightforward. but

numerous. The model incorporates several submodels taken from the literature, suitably

modified and combined to give a reson•bly a,.crate, b ds.cit.,i,...,on o-f t y, s,;,

processes involved in bottom backscattering. Because the model is, in part. physically

based, it can be used to study such topics as

9 frequency dependence of scattering strength

* importance of scattering from sediment volume

9 classification of bottom type from backscattering strength

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"* extrapolation of measured data (in frequency, angle. and bottom properties)

"* estimation of bottom loss from backscattering strength

"• importance of various geoacoustic parameters.The ba.is for this model is documented M....ro ,,A and ,.... 9 a,,A ..... , .. th,

IVA lUjgU UJLAl 4A'U •/ ,vijq , tllMA -V I. AAM111ll.ll3 VId l III%.

mnodel have been given by Jackson and Brigg;.8 The model is a gencralization of the pre-

vious modcT. -- which was a simplification of the work of Jackson et al.16 Unlike its

predecessor. the prcsent model includes "slow- bottoms with a sound speed less than the

overlying water, and it incorporates a wider class of roughness types. It improves on thework by Jackson el al.16 in two ways: "h" .... ;"- InCd"-"c" a . .r .':":^ fa'h:--

wor by glf.ýllttt 1kim I II-l. ..I U 111I a 3111M1L, ILW ML,,gl~ , 9 MIMt0ll ,!l

and numerical integrations haie been replaced by efficient analytic approximations. The

present model assumcs that the properties of the bottom material are statistically homo-

gencous vertically and horizontally. Thus. as with the reflection model, layering and

vertical gradients are not included. McDaniel 26 has shown that layering can introduce

substantial effects in high-frequency hotto,., ......... :i,,

2. Equations for Bottom Backscattering Strength

Bottom backscattering strength. S,(0). is a function of the six parameters defined in

the introduction and also depends on acous!ic frequency..f .•in the .ra-.;n0 a-gl." .AA,

defined by Urick,: 7 Sb(O) is the decibel equivalent of the scattering cross section. which

is broken into two parts:

St, (19) = 10 10og 0 [ 0, (i0) + CT, (0) ],(34)

where

,0 = dimensionless backscatterimg cross section per unit.,olid angle per

unit area due to interface roughness

a.. 0 = dimensionless backscattering cross section per unit solid angle per

unit area due to volume scatlering from below the interf"-e.

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STable 3. Scattering strengths for generic bottom types.Rough Rock

An"-, 1 LH 15kHz k 20 klz 25 LIlt 30kHz 40kHz 60 kH 8)kHz 1(t •kH'. ,64 -24.9 -- 3.6. -231,0 .21.7 .20.0 .18.9 .18.0

" 24. -223 "21-1 .20.2 .19.4 -18.3 -16.9 -15.9 -15.?3 -21.6 -19.9 .18.8 18.0 .17.4 -16.4 -15.1 -14.2 -13.6

.18.4 -16.9 -16.0 -153 -14.8 -13.9 .12,8 -12.1 -11.57 -36.. .15.1 -14.1 ,13.5 .13.0 -12.3 -11.3 -107 -10.2

10 -14.0 .119 -122 -11.7 -113 -10.6 -9.1 -9.2 8.820 *9.4 -9.1 -86 -82 -19 -7.5 -6.9 -6.5 -6.249 -6.9 .6 1 .5.9 -5.6 *5.4 -5.3 -4.7 .4.4 -4.260 -6.1 -5.7 -53 -51 -4.9 .4.6 -4.3 -4.0 -3.870 -6.1 -5.7 -5.4 -5.3 -5.0 .4.7 .4.3 -40 -3.981) -6.4 -59 .5.6 .5.4 -5.1 -4.8 -4.4 .42 -4.085 .6.5 -6.1 .5.7 -5.5 -5.3 5.0 4.6 -4.3 -4.1

8S -6.6 -6.2 -5.8 -5.6 -5.4 -5.1 .4.7 I -44 -4.2X9 -6.6 .6.2 -5.9 -5.6 -5.4 -5.1 -4.7 -4.4 -4.29. -6.7 -6.2 -5.9 -5.6 -5.4 -5.1 -4.7 -4.4 -4.2

Rock- 10khz I5kilz20LHi25 kH, 30kHz 40kHz I 60ktHz. 80 k t1z 100kl.iz

"1 -52.0 -.V.4 '.477 .45.6 .44.0 41.5 -38.3 1.36.1 I -4.52 -45.7 -42.8 -404 -38.7 -37.3 -35.2 .32.4 -30.6 -29.23 .41.5 -38.3 -36.2 -.34.6 -33.3 31 . -29.0 / 27.3 -26.1S-35.7 -32. -30.8 -29.5 -28.41 -26.8 .24.6 --23.2 -22.27 .31 8 129.6 -27.3 -26.1 -25.2 -23.7 -21.8 -20.6 -19.7

10 -27.6 -25.1 -2^6 -22.6 . 21.7 -20.5 -18.q -17.8 -17.020 . 1.8 -17.8 -16 8 -16.0 -15.4 -14.5 -13.4 -12.6 -12.040 -13. : -I.3 -11.5 -11.0 -10.6 .10.0 -9.1 -8.6 -8.260 -1I.8 -10.6 -9.9 -9.4 -9.1 -8.6 -8K( -7.5 -?.270.L -10.1 -92 -8.1 -8.5 -8.3 -8.0 -76 -7.4 -7.1K. -6.h, -6.6 -6.9 .!.1 -7.3 -7.4 -7.5 -7.3 -7.2

. ? -3.6 -5.! -5.9 -6.4 -6.8 -7.2 .7.4 .7.4 -7.388 -2.8 .46 -5.6 .6.2 -6.6 .7.1 -7.4 -7.4 -7.3F•9 -416 -4.5 -3.5 -6.2 -6.6 -. _1 I-7.!.• -7.5 -7.4

90 -2.6 -4.4 -5.5 -6.2 -6.6 .7.1 1 -7.5 .7.5 -7.4

CobbleAng i00•Z 15z i . 20-kH, 25.kHz 30kHz 40khz 60ok1z SOM, IM00kH,

-49.4 -. .53 --5.9 -50.01 -48.5 -46.1 -43.0 -40.9 -39.42 .45.? -46.7 .44.7 -43.0 -41.7 .39.6 -37.0 -35.2 -33.93 .4?3 -1 423 .40.4 -38.9 -37.6 -35.8 .33.4 .31.8 -30.7, -3S.9 .36.6 .14.9 -33.6 -32.6 -31.0 -2.90 .2.,.6 -26.67.-i 5 -32.8 .31.3 -30.1 -29.2 -27.8 -26.0 .24.8 -24.0

10 .31.7 -29.8 -27.5 -26.5 -:5.7 -24.5 .23.0 -22.0 -21.22O -242 -21.6 -20.6 -19.9 -19.3 -18.5 .17.4 -16.7 -16.2

40 -186 -16.6 -15.9 -15.3 -14.9 -14.3 -13.5 -13.1) -12.6

70 .12.x• .12.2 -11.8 -11.6 -11.5 -11.5 -11.5 -33.5 -11..5

W, .66 .7.8 48.3 -8.8 -9.2 .9.8 -111.6 -11.0 -11.385 -3.4 -5.6 -6.7 -7.6 -8.2 -9.2 -10.3 -10.9 .11.28 K -2.3 -4.9 -6.2 .7.2 -7.9 1 -9.0 -10.2 -10.9 -11.389 -2.2 -4.7 -61 -7.1 -7.9 1-9.0 -10.21 -10.9 -11.3190 2.1 -4.? -6.1 -7.1 .7. 4.9 .2 .309 -11.3

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Table 3 (cont.)Sandy Gravel

Ano. ] 10kilz I5 kH7 20 kH, 25 kH? 10 kHz 40 k~z 60 kHz 80 kHz 1000 Iz1 405,s ".4s3 : 5 1 .503 -48. .46.0 443 .42.9"2 .41.4 .44,5 .46. -45.3 -44 2 .424 .40.1 -3t.5 .37..33 -41.4 .4 .9 -42.4 -41.3 1 40.3 -38.6 .36.5 -35.1 .34.05 .?8.2 .y3 7 -37.1 .36.0 -35.1 -33 8 -31.9 -30.7 -29.8" -.35.5 A34.4 -33.5 -32.5 .31.7 .305 -28.9 .27.9 .2?.1

I0 .32.2 X.0.7 -29.6 -28.8 -,1.1 -2, 1 -25.8 .24.9 -2-1.2, 25.9' .24.1 .23.1 .22.5 .22.1 -214 -20.4 -!9.7 -19.3

4,) -21.2 -203 -197 .19.3 -18.9 . 3... .17.6 -17.1 -16.8&I -IX 3 .1.. -.17.3 .16.8 -16.5 -16.1 -157 -15.5 -15.570 .14.7 -14.3 .14.0 -1.3.8 -13.17 .13.6 -13.9 -14.2 -145%"0 .7.5 .8.3 -9.0 -9.5 .9.9 .10.7 -12.0 -12.9 -13.68! J -3.2 .4 -6.7 -7.7 -8.4 .9.7 .11.3 -12.5 .13.3

Ns -1.; .4.4 .60 .7.1 .80 .9.3 .11.1 .12.3 -13.289 -1.71 -4.2 5.9 .7.0 .7.9 -9.3 -11.1 -12.3 -13.29 -1.6 . 4.2 .5.. .6 ... 7.8 .9.2 .11.1 .12.3 13.2

Coarse SandAr. 1 kH~z 1P5kHz 2( kHz 25-kHz 30(kHz 40 kH, 60 kH, 80) kHi- •I0 zl

I -542 -.50.5 -48.1 .46.S .47.1 -50.6 .50.5 -49.9 .. 72 -5(0.6 1 .47.2 -44.9 .43.6 .43.8 -46.0 .448 -43.1 .4).93 .4".h .44.8 .42 .41 6 -41.5 -42.6 .41.0 .19.5 -3f.Q5 -4'.4 -41.1 -39.4 -382 -37.9 .37. -35.9 -34.6 -33.67 .39. .38.0 -36.6 -35.6 .34.9 -34.1 .32.5 -31.3 M3.5

11, .3..9 .34.4 -33.2 -3.! j ,31.5 -30.3 &9 1-27.9 -27.2i^ -29.0 -27.8 -268 -26.0 .25.1 -24.0 -:3.0 -22A. -:1.6

4C ... -22.9 .22.4 -2.9 -21.4 -20.8 -20.2 I -19.6 -19.260 -1 -0.2 -9.6 .19.1 -I1 S -.1.6 .178 -1.3 -1'.:.0 -I ; .16.4 .15.8 .15.5 -I.5 -15.1 -147 -14.6 .14.7Z0 -9.6 -8.9 -8.6 -86 -8.9 .9.6 .10.5 -11.3 .12.085 2.7 -l. -3.9 -4.7 -5.6 -7.2 4.9 -201 -12.0xx M.) .41., -2.2 03.4 .4.6 -6.3 -8.3 -9.7 . -10.789 1.5 -06 -2.0 -3.3 -44 -6.1 -8.2 -9.6 -lo."290 1.6 -0.5. -2.0 .3.2 -4.4 -6.1 -8.2 .9.6 -o.;

Medium Sand'A.0-i- - -Hz 30kHz 40kHz 06kHz 80kH7 ItOkHi

..61, -57.7 .55.1 .53.0 -51.4 -49.1 -49.2 -50.8 -50f0_ ! -2.? -51.4 -49.6 4;<.1 -45.9 .45.5 -45.9 -449

3 . I; .?0.7 .48.7] -47.1 .45.8 -438. .42.8 -42..t -41.5S .476 .458 -4-4.4 -43.1 -421 -494 .38.6 -37.6 .36.6

-43.4 -42.0 .40.9 .39.9 .39.0 -317 6 .35.4 .34.2 -33.31 - -37.3 ..36.1 .34 -34.1 -32.7 -30.5 -29.820 9 30 I -29.4 -28.8 -28.3 -27.4 -25.7 -24.0 -24.240t -2.4.4 -24.1 -2. ....•t9 -23.7 , -3.5 -23.1 .22.'4 .22.0 -'.

60 -".6 .2.. .21.8 .21.5 '21.2 -206 -20.1 .19'. -19.5'C' 20.4 -19.6 -18.9 -183 .A .7 .I's4 .16.9 -16.6 -16.480 13.2 .12.0 -11.4 .11.0 0.8 -20.6 .].1 .121.7 -12.25 .. o -4.7 ," .4.9 -5.2 -5.5 -6 -8.2 .9.5 1.-04

s 1 -03 -1.5 .2.5 -3.4 4.F -7.2 -8.7 9.9.69 2 0.3 -1.1 -22 .3.1 -4.? .7.0 .S.6 .99(' . , .O -2.1 .3.1 4.6 .70 .8.6

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Table 3 (cont.)Very Fine Sand

Ang. I0kHO ? 15kHz 20ktz" 25 kliz 30kM, 4-kH? 6.. . .. kH.. IOUklz1 .662 .64.0 -62.3 .60.9 -59.7 .57.8 -.55.0 .52.9 .-5.42 .58.8 -57.6 -56.5 -55.6 -54.7 -53.3 .51.0 -49.3 .47.93 -53.4 -52.7 -52.0 -. 1.3 -50.8 .49.7 -48.0 -46.6 -45.45 .45.9 -45.5 -45.? -- 4.9 -44.6 .44.0 .43.0 -42.1 -41.3

-40, .40.6 -40.3 -40.3 .40.1 .39.8 .39.1 .38.5 •.37.9

10 -35.6 -35.5 M35.4 -3!.3 -35.2 -35.0 -34.7 -34.3 .-402 .27.: -.27,. -21.1 -27.1 -27.1 .27.1 -27.0 -27.0 -27.040 .250 .25.0 .2.4.9 .9 -249 .24.9 .24.9 .24.9 .24.6

611 .23.4 -23.8 -23.8 .23.7 -23.7 .23.7 .23.6 -23.5 -23.570 . 23.3 .23.2 -23.1. -23.1 -22.9 .22.7 -22.5 -22.380 .21.9 .21.4 -21.0 -20.6 i -20." -19.5 -18.7 -18.3 -18.085 -16.9 .15.2 -14.1 -13.5 -13.1 -12.8 -12.5 -12.6 .12.988 -5.2 -5.0 .5.2 ! 53 .5.9 .6.8 -8.2 -9.4 -10.389 .0.2 .1.4 .2.5 .3:5 43. .5.6 -7.5 -. 9 -10.090 1.8 -0.3 .1.7 529 .7.4 -8.9 .10.0

Silt (a2 = 0.001)

1.. OkHz 5klz 2k z 5kH1 3OkH? 1 40kHz ) klz 80khlz I00ktlz1 -60.7 -60.0 -59.3 -58.7 j -58.2 -57.3 -55.8 -54.7 -53.82 .51.9 .51.7 -51.5 -51.3 -51.1 .50.8 -50.2 -49.6 .49.13 .46.9 -.0601 -46.8 46.7 -46.6 -46.5 -46.2 -45.9 -45.75 .41.4 -41.3 .41.3 -41.3 -41.3 .41.3 -41.2 -41.2 -41.17 .38.4 -38.4 -38.3 -38.3 -38.3 -38.3 -38.3 -38.3 -38.3

10 -35.7 ...35. -3. 357 -35.7 .35.7 -35.7 -35.7 -35.720 0 1.8 -31.8 -31.- -31.8 -31.8 -31.k .31.8 -31.8 -31.840 -28.8 -22.8 -2h6, -28.8 -28.8 .28.8 -28.8 .28.7 -28.7

) -27.4 -27.4 -27.4 -27.4 .27.4 .27.4 -27.4 -27.4 -27.470 -27.11 -27.0 -27,0 -27.0 -27.0 .27.0 .26.9 -26.9 -26.980 -26.6 -26.5 -2f.4 -26.4 -26.3 -26.2 -26,0 -25.7 -25.585 .25.4 -25.0 .24.6 .24.2 -23.9 -23.2 -21.9 -2109 -20.388 .18.0 .16.0 -14.6 .13.7 -13.1 -12.5 -12.1 -12.3 -12.689 -8.0 -7.0 -66 .66 .6.8 .7.3 -8.4 -9.5 -10.490 1.8 .0.1 -.. 6 .21.7 .3.6 .5.2 -7.1 .8.6_ -9.8

Silt (a 2 " 0.0003)"An-. K 10kHt 15kH7 20kllz '25kHz 30MHz 40ikHL 60kHz 8'kHz 100 kkHz

1 -660 .65.2 -64.5 -63.9 .63.4 -62..4 .61.0 .59.8 -58.92 -!7.1 -569 -56.7 -56.5 -56.3 -56.0 -55.3 -14.8 -.54.33 -52.) -52.0 -52.0 -51.9 -51.8 .51.7 .51.4 -2.2 .50.8

-466 -46.6 46.5 -46.5 -46.5 -46.5 .46.4 -46.3 -46.?"-43.6 -43.6 -43.6 -43.5 -43.5 -43.5 -43.5 -43.5 -43.4

10 -40.9 -40.9 .40.9 -40.9 -40.9 .409 -40.9 -40.9 -40.920 -37.0 -37.0 .37•.) -37.0 .37.0 .37.0 -37.0 -37.0 .37.040 -140 -34.0 -34.0 -24.0 .34.0 -34.0 -33.9 -33.9 .33.960 -32.6 -32.6 -32.6 -32.6 .32.6 -32.6 -32.5 -32.5 -32.570 -32.2 -32.1 -32. -32 1 -321 -32.0 -31.9 -31.8 -31.780 -313 -31.1 M.3.9 -30.7 -30.5 j -30.2 -29.6 -29.2 .28.75 -.28.5 -27.6 -269 -26.3 -25.8 J -.4.8 -23.0 -21.7 .22.1

8S .18.4 .16.2 -14.8 -13.9 .133 -12.6 -12.3 .12.4 -22.,89 -8.0 -7.0 -6.7 -6.7 -6.8 -7.3 -8.5 -95 -101.490 2.8 -6.2 -1.6 .2.7 -3.6 -5.1 -7.2 -87, -9.8

"TR 9407 IV-25

ADB 199453


0

Generic Model Curves, 30 kHzS................................. ro u g h ro c k ....................................... .,,

...-....... . . .. .. . . r o u g h r o c k

----- --e-y fine sand .S... silt, Mz =6.0, o2 =k0.001 ..-

"sit M 6.0, o0 .......000..

0

F-igure 2. Model curves for backscamrering strength at 30 kH for generic bosan m d vps. The

model input parameters are taken from Table 2.

These two scattering cross• Sections are functions of the six parameters defined in Table 1.

Evaluation of these cross sections involves numerous equations, w~hich arc dcve!oped in

the following subsections, beginning with the roughness scattering cross section and end-

ing with the sediment volume scattering cross section. No superfluous or intermediate

equations arc pre.sented: all of thc following c4quatiann must be incluued in code to e,,idu-

ate the bottom backscattering strength.

a. Roughness scattering cross section, 0 ~r(0)

Three different approximations are used,,, fr he ,.,,,,.h,,,,s ,,,at,.e,.;n, ,.,.-,s S•hc,,;.,,.r(.. For smooth and moderately rough bottoms (e.g.0. C;2 silt, and sand), the rough-

ness scattering cross section is computed using the Kirchhoff approximation for grating

angles near 9Oe and the composite roughness approximation for all other angles. For

rough bottoms (e.g., grave] and rock), an empirical expression taken from the previous

JV.26 TR 9407

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UNIVERSITY OF WASHINGTON" APPLIED PHYS!CS LABORA.TORY ..

vers-ion of this model is used.I'-25 The follo),wing dirsussinn di-ve lops each Of thCSC

approximations in turn, providing only those expressions needed for computation. The

final result for O, (0) is given in Eq. 62, which is an interpolating expression that

automatically shifts from one approximation to ,mother.

KirchhoffTAl)pro.xitin:io

In the Kirchhoff approximation, it is cony. -ient to redefine the roughness parame-

ters in terms of parameters cc and CJ of the so-called ustrctur iiU "

a = I _ 1 (35)2

and' 6

2 a w2 r"(2 - ot) 2- 2C n 2 (2= 2~(36)Czt h4i (0 - ar) F(I + oor(6'

Note that there is a physical constraint on y equivalent to 0 < a < 1.

The Kirchhoff approximation yields an integral for the backscattering cross section

(for example, see Ishimaru29) which must be integrated numerically or otherwise approx-

imated. A simple approximation has been developed for this integral based on special

cases for which exact analytical evaluation is possible.9 The resulting approximation for

the Kirchhoff backscattering cross section, ak, (0), is

'ao' (0) ~ b q,. I R (90P) 12" 4

~r (O = _ ,0-40° (37)8it [cos4'" (6) + a q2 sin4 (0)1 2u

=0. 0 < 4W.

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-_UNIVERSITY OF WASHINGTON - APPLIED PHYSICS LABORATO7Y

The Kirchhoff cross section is set to zero at angles less than 40', where the composite

roughness approximation is used. The abrupt jump at 40' will not be seen in the model

output because a smooth interpolation is used at angles greater than 40'. Equation 37co ntain s the fo llo w,,in g I" L.. ...... .....LIIILI LOA 4 J

parameters derived from thr. j,..,•, fu.ati. n .. a n

q= C• 21 Ex k2 (38)

8a 1 +1 2a

a = I(39)

I II2 2

a 2- r(-.40( (40)2a

It also contains R(901). the complex Rayleigh reflection coefficien! (Eq. 30) evaluated at

normal incidence.

Composite Roughness Approxi"n ;""

In the composite roughness approximation, the small-roughness perturbation

approximation is used with corrections for shadowing and large-scale mis bottom

slope.:' The large-scale rms slope. s, is defined as the positive square root of

(2) k (41).• _ 211 -a)

IV-28 TR 9407

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UNIVERSITY OF WASHINGTON' APPLIED PHYSICS LABORATORY

where k is the acoustic wavenumber. It is convenient to break the composite-roughness

cros•s section into two factors:

ac, (0) = S (0. s) F (0, pr s) , (42)

where S (0, s) is the shadowing correction and F (0, a,.. s) i a ,•!opf aperaoing inPera!l

to be defined. Following Wagner,"'

1 -s)- Ic (43)S (0, S) -(43O

2Q

where

Q -I1'? C-1 - t II - err (01 (44)4t

and

tan (0)(4t = •(45)

S

In Eq. 44, erf (t) is the error function. In Eq. 42, the function F (0, a,,r, s) is (he small-

roughness perturbation cross section averaged over bottom slope.

We approximate the slope averaging integral" by a three-point Gauss-Hfermite qua-

drature32:

F (0. o,,r, S) = lT- 1, an apr (0 - On) ' (46)n=-I

a-, =a1 -0.295410, a(,= 1.181636 , (47)

0- - = 1.224745 OJ, Oo = 0.0 (48)

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UNIVERSITY OF WASHINGTON - APPLIEU PHYSICS LABORATORY

The parameter 0,, is the rmis slope. s, converted to angular units a, follows:

0., = SO,(49)it

where the parameter 0. is simply an angle of 180', defined to avoid confusion as to radi-

ans vs degrees. In Eq. 46, the argument of a;pr sometimes falls outside the interval

0~-9W over which a.,, is defined. If the argument is zero or negative, it should be set to

0ý'. This is equivalent to tie composite roughness rule of setting the contribution to zero,

as the cross section vanishes at 0--. If the Xqrgumcnt is getrthan Onf, it can ke cmt te

901. This choice is arbitrary-. the composite roughness cross section at 90' will not con-

tribute to our final resuilt.

The function G~pr (0) is the bottom backscattering cross section in the small-

roughness perturbation approximation. We use a modified version of Kuo's expression

for this functioni':

ci,, (8) =4 k sin ()I1' (0) 12 11% (K,). (50)

In this expression. Y (6o is the complex function

[p sin (0) +P (0)],

where P (0) and Kc are as defined in Eqs. 32 and 33.

The power spectrum. IV-. for random bononm Aresitof aprpears Jn En. 50. It;

evaluated at the wavenumber

K9 14 k 2 ens2 (6. + (k/lO9]I2 (;2)

The term involving k11O has been added to the usual expression for the argument of the

specrum.This is done to avoid the singularity in the power-law spectrum at zero

IV-30 TR 9407

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wavenumber (i.e., as 0-.90c): this somewhat arbitrary modification of the uwual ,mall-

roughness expression only affects the cross section for grazing angles near 90', and these

angles are unimportant owing to the inte, ,!a•i•on sche-m used.

Large-Roughness Scattering Cross Section

The observed scattering strengths for gravel and rock bottoms are relatively large

and imply roughness parameters that fall "o"' Sde t,,, ra ofV.. Jdity %if th, ,,. ch

and composite-roughness approximations. For these cases. an empirical fit taken from

this model's predecessor 'I.. is used for the large-roughness cros. scMnn,.AA- (0):

Or. 0.0260 1 R (9Q0) 12ir0 , (O) = 1 sin " +0.810'. (0_T- ý0 o.122(

I 02 1 2 1+ 91++ II+2.60,1"•0"

The sound speed ratio determines the critical angle, 0c, -. :h is defined as

0, = cos-' (1A:) v 2 1.001 (54)

0, = 2.5613' v < 1.001

For bottoms with v < 1.001. the critical angle is set to a fixed value, as in the prede-

cessor model. This artifice led to problems when the earlier model was applied to sedi-

ments with low sound speeds. The interpolation used in the present model circumvents

this problem because such sediments usually have small, roughe,. n A h,,h case the

composite roughness model (which includes a physically correct treatment of low sedi-

ment sound speeds) is invoked. The parameter s is the large-scale slope defined in

Eq. 41. Although this parameter is defined in the context of the composite roughness

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UNIVERSITY OF WASHINGTON. APPLIED FHYSiCS LAbGOnAT;....

model, it is useful even when that model is invalid. The large-roughness cross section

uses the following additional parameters:

n - 0.7263 (.s)-1/ (55)

0.04682 1; "-.25 [ [- 2 2 , I1 34 (56)

1 15 0

lnterpolation Between'c Appro.inlawions

Interpolation of the various approximations employs the following function:

f -(57)1 + C,

The first interpolation is between the Kirchhoff and composite roughness approximations.The interpolated cross section will be denoted ,r (M). with the, ,.. .. rpf 'iznifN'.n.

"medium roughness."

,all" (0) =f(x) aW4.. (0) + [1 -f(x)] 0~-, (0) , (58)

where

Cos(O) - cos(O I (9

0.0125

cos (61,m)= +4j 4 (60,

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UNIVERSITY OF WASHINGTON. APPLIED PHIYSICS LA6GOATORY

1 1C4 = (1000) +~ 2aq)a .(61)

The interpolation shifts between the Kirchkf,, .... o 0,x1,,,A-I."kaA" ,- , a.a;,.,, .1anc ,e,"a, 90

anti the composite roughness approximation at smaller angles. The changeover occurs in

the vicinity of 0 ,jB, which is approximately equal to the angle at which the Kirchhoff

cross section has fallen 15 dB below its peak at 90.

The Kirchhoff cross section, Ilk, (0), acconts for the angular spread of energy that

would be perfectly reflected if the interface were flat. The issue of double counting

arises in modeling vertical-incidence or "fathometer" sonar echoes. If it is important to

simulate the time and angle spread of thi; energy, the "'.ackscatt. mo.dc" can" .c... ud, but-

the forward loss model could be used if these spreads are deemed unimportant. It would

be improper to combine thc outputs of both approaches; this would -he double coun.ning,

The final interpolation, between the large roughness and medium roughness cross

sections. gives the roughness scatterin, - cr " p;'e arin-i, , 34.

01 (8) =f(5) ,,7 ()+ -f (M afl, (0) . (62)

The argument of the interpolating function is

(Oan- s - er) (63)

The parameters Or and A8 are refr.enc ,.,,. ,4,6,,-,..,,. st , ,

0, = 7.0' AB = 0.50 . (64)

b. Sediment volume scattering cross section, av (0)

The term (;,(0) in Eq. 34 describes volume scattering by the bottom material. An

expression for sediment volume scattering including refraction and transmission loss at

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-UNIVERSITY OF WASHiKGTON - APPLIED PHYSICS LABORATORY

the sediment-water interface was published by Stockhauscn." This expression is gen-

eralized to allow for the effect of absorption on the transmission coefficient of the

sedinentlwater interface and in"orpate shadowing" a btt A r an-

gous to Eq. 42:

oY, (0) = S (0. s ) F (0. aý,, 5 (65)

To ealuate F (0;, r, ). Eq. 46-49 are used, with c;,,, replaced by

5 8 c; I I - R (0) 1 sin. (0) (6O/,. (0) - 2 ' 66)v lnl0 I P(0) I1 lmI P(0) )

The function P(O is given in Eq. 32. Equati,,,,, 66 co..ects a 'ypographical "ior occur-

ring in previous publications." 9 in which the exponent 2 of the reflection coefficient,

R (0), was omitted.

The volume scattering parameter, a2 . is treated empirically. That is. it is not deter-

mined by measurement of sediment physical properties but rather is dctennried by com-

paring the model with backscattering data. The empirical approach to sediment volume

scattering is in contrast to the treatment used for interface roughness scattering. where

the roughness spectral parameters I and air. maliriawc IaC rcop og1a 01.% or

other means. Analogous to this, there has been recent work on the physics of sediment

volume scattering" " This work can be used to relate 02 to measurable corre!3t.iC.n

functions or spectra describing sediment inhomogeneity. Such an approach is used. in

fact. in the bistatic model presented in Section IV.D. Boyle and Chotiroa'-"9 have

argued that sediment volume scancring may f;oii he dLe to t he gtainimaes of sediments

or the presence of small gas bubbles. In such cases, sediment correlation functions may

not provide a suitable characterization, but the parametcr t7 may bc •,.nera! -.,,- %I-

encompass such mechanisms.

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I I - UNIVERSITY OF WAS4INS3TON AtPPLED PHYSICS LASOPATGAV

3. Model Accuracy

The following comments on model accuracy are primarily derived from published

reports on comparisons of this model with data from well characterized sites.8'9 Because

thi,, model is similar to it& predecessor.1 earlier model-data comparisons 5"6.1'7 40 are also

of value and are reflected in the discussion "cre.

Generally speaking. model accuracy improves as the quality of bottom characteri -

zation improves, and model predictions are most accurate when the grazing angle is not

too small and the bottom roughness is not too large. The following estimates of model

uncertainty are rouo'h estimates ba.ed on e-' ... 1,, J"U&,,a% .. a.. than. statistial

analysis. Model "uncertainty" is defined as the largest difference expected between the

model's prediction and measured data, neglecting errors in the data and discarding obvi-

ous outliers.

For rock and gravel bottoms, model uncertainty is approximately 10 dB for grazing

angles greater than 15" and probably greater for smaller angles. Model uncertainty is

approximately 3 dB for well-characterized sand and silt bottoms for grazing angles

greater than 5'. For poorly charac:crized bottoms.. , un..rAtAiti' of VA.O... 5MI"k A) dB

and 10 dB can be expected for sand and silt bottoms. respectively.

Because the model incorporates many of'the known mcchan.;.m., €..r bt ... ,t-

scattering, it is reasonable to use the model to extrapolate measured scattering strength

data to other frequencies, grazing angles, or bottom parameter values, Such extrapola-

tions are expected to be most accurate for sand and silt bottoms.

For soft bottoms (MV. > 3), the model is most sensitive to the -,,r',mtr r," dei,,-rib.

ing sediment volume scattering. As noted earlier, this parameter is best determined by

backscattering measurements. in which case the model becomes essentially a means of

extrapolating in angle and frequency. As more and more data have accumulated.. t has

become clear that c% varies over a wide range. The largest reported values are about 0.1

and were obtained by direct measurement of sediment volume scattering. 4.

IS dB is evident in the references cited here, and a range of 30 dB has been observed in

TR 9407 IV-35

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unpublished work by K.Y. Moravan on low-frequency bottom reverberation. These deci-

bel values can be taken to be the range of scattering strengths observed for so~ft bottoms

of nominally the same type.

For harder bottoms (Af-~ < 3). the model is sensitive to the, spectra!, ,aramtre rs on Ad

iv:. The situation here is more favorable than for soft bottoms. Measurements of these

parameters are available at some sites. and the range of variation in these paratmeters is

not particularly great when translated inito variation in- scattefing strength. Prroblemsý

have arisen in applying the model to sites where the spectral exponent approaches thelimits given in Eq. 15. The two know.,n y^mlc r a An., sand4r;. sie w1here 2~' 3.9

was measured. and a coarse-shell bottom,6 where 'I = 2.47 was measured.

The model is consistent with oluder dat j.r, the 11c AlC e X ce pt foV r iIthe; '. 4C' 1 4*

the model yields a more rapid falloff of backscattering strength with decreasing grazing

anale than some of the earlier data. More recen! dL-at, such as those cited in the

model/data comparisons above and those reportcd by Boebme et al .'45 Boehrne and Cho-

tiros. 46 and Gensane, 4 7 confirm this more. rapid falloff.


The gamma and error function-, used in the model can be computed to sufficient

accuracy using approximations found in Ref. 48. It should be noted that the argument of

the gammia function soet.e %fall o Utid "the % ra d -. , "fld 991 fia". reqJUIre Le ofthe relation F (y + 1) = x I- (A). Numerical problems may be encountered if the exponen-

tial and error function arguments in Eqs. 43 and 44 become too large. To avoid such

difficulties, the shadowing function can be set to unity if the parameter t, defined in

Eq. 45, exceeds 2. Similarly, if the argument of the interpolating function, Eq. 57, is less

than -40. set f(x) = 1; if the arg-ument is Ureate -Tha , av t "1 kA .

The scattering strengih defined by- Eq. 34 and subsequent equations approaches

negative infinity as the grazing angle approaches Rcro. This presentis pro'blem; in, appli-1

cations where a look-up table is used for scattering strength with entries at Oc.,1', 2', etc.

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UNIVERSITY OF WASHINGTON., APPLUED PHYSICS LABORATORY

It is expected that angles of 0.0010 and -g'r"xv nro-cont n m-mcrica! diffi-,lty. For

angles smaller than this, we recommend that the model output at 0.001 be used. The

equations in this section have been written so as to be neutral with respect to the choice

of angular units (radians or degrees). Complex expressions (Eqs. 51 and 66) are con-

v*enienth' coded using complex arithmetic as noted in Section IV.B.3.

D. BISTATIC SCATTERING

The bottom bistatic scattering model is a generalization of"te back.sca..Cring mou.. -

presented in Section IV.C, and is dccumented in Ref. 49. Like the backscattcring model.

the bistatic model treats scatterir. from both interface roughness and sediment volurme

inhomogencity. The input parameters for the bistatic model are identical to those for the

backscattering model, with the exception of the volume scattering parameters. The sin-

gle parameter, a,, used in the backscattering model is replaed, by three parame

Since most users will not have values for these parameters, a simple procedure is given

so that a2 can be used instead. The bistalic model employs three angular variables.

definc .n Figjure 3.

z

Figure 3. Bistatic scattering geometry. The angle 0, is the incident grazing angle, 0, is thescattered grazing angle. and 0, is the bistatic angle.

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UNIVERSITY OF WASH!NGTONt APPL'! i HUYSv LA a ,On ,A 'v

The bistatic model has been compared with historical data, but these comparisons

are not rigorous owing to lack of adequate physical data. Bistatic data and accompany-

ing, physical data suitable for model testing are currently being obtained under the Coas-

tal Benthic Boundary Layer Program, ....... ')b thE IN ...... REsearch La.b.. oratoriy.

The bistatic model embodies several features that are physically reasonable but

untested experimentally. As illustrated in Figure 4. for hard (sandy) bottoms, interface

bcattering dominates sediment volume scattering away from the specular direction. whilethe opposite is true for soft (silt and clay) bottoms ... 5). The b"ust",,,I .........

strength exhibits a peak near the specular direction owing to interface scattering. This

peak is broader in the vertical plane than in the horizontal plane (for example. compare

Figures 4a and 4c and 5a and 5c0; both widths decrease as the incident grazing angle

decreases. In directions away from specular. the scattering strength is predicted to be a

slowly vatying function of the bistatic angle (the c:hang,, II poln VI.I.. .",a|ItLI I , I.

This can be seen in Figures 4c, 4d. 5c, and 5d.

The approximations used in this model fail for rough bottoms (e.g.. graei and

rock). For the special case of backscattering, the model produces results similar to, but

not identical to, the backscatterinz model and is consitCe t:h •a•;labl, back.catterine

data for bottoms with small to moderate roughness (e.g.. clay, silt, and sand).

1. Model Inputs

Table 4 lists the input parameters for the bigtatic model, The parameters y;, wv, and

preplace the volume scattering para..eter, .. B ,eo.r delltnincg t"Ie addItional 01-121 paramll•-

ters. defaults will be provided for users who wish to employ only the backscattering

model inputs of Table 1.

= 3.0 (671

-1.0 (68)

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.... .... ..

.. ... ..... , ...

z

.~~~~~ ....... ......

a

Si • • •c. ,I• . • •. • --

Z'

I. "-;

CC

I. '", * '•

(upý 419..*ZS suu~ttv• (aP) qls'uaus luu.mIft

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UNIVERSITY OF WASHI,"GTO'%' Al'PPLIED,, P1YS!C'S L A~C^ATADY

aB..

L IL

> >

4,

tc~

12 .,~.

k -- -

(or 8pL-,jlrx s(p ~m'lu~

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UNIVERSITY OF WASHINGTON. APPLIED PHYSICS LABOR.ATOPY

Table 4. Bottomi parameters used as inputs to the bisatic model.

Symbol Definition Short Name

p Ratio of sediment mass density Density ratioto water mass density

t Ratio of sediment sound speed Sound speed ratioto water sound speed

SRatio of im aginary wavenum ber to Loss parameterreal wavenumber for the sediment

73 Exponent of sediment inhomogeneity spctrum Inhomoveneity exponent

113 Strenrith of sediment inhomogeneity spectrum Inhomogeneity strength(cm-) at wavenumber 2n/. = I cm-1

P Ratio of cumpressibility to Fluctuation ratiodensity fluctuations in the sediment

7 Exponent of bottom relief spectrum Spectral exponent

$2 Strength of bottom relief spectrum (CM4 ) Spectral strengthat wavenumbcr 2n/X = 1 cm-1

40 8 c2 (2h 0 )"yt

w r= _n•n )10)) (69 )

The expression for w I is general and can be used with values of y3 and It other than

those given above. Ideally. the parameters ,.X, w., and pi should be assigned values based

on measurements of sediment inhomogcncity. At present. such a characterization of sed-

iments is in the realm of research. 37'." There is no compilation of relevant inhomo-

gcneyit data. Consequently, these parameters will be deined buodiled pre*sripTionc

for estimating these parameters in terms of grain size, etc., will not be given.

Sediment inhornogeneities are described in :1he1C. model by "hre"ve ... I "• "al -'

for compressibility and density fluctuations. These fluctuations are normalized by divid-

ing by the mean values of compressibility itnd density; the normalized compressibility

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UNIVERSITY OF WASHINGTON, APPLiED PHiYSiCS LABORATORtY

and density fluctuations are denoted "tK ( r ) and y,, ( r ). respectively. It is assumed that

the fluctuations in sediment compressibility and density are tied together by a simple pro-

portionality relation,

YK ( r )=p(r). (70)

The model parameter p is expected to have values in the neighborhood of -1, because

density and compressibility tend to be ,nnicrreaI -e. Ftod r AV eAm-pl, if 3 looC,,n,;,,. of theA

sediment produces a 10% decrease in density, then there will be a corresponding

increase in compressibility of about 10%. The argument for this anticorrelation is based

on the experimental fact that sediment sound speed is a rather slowly varying function of

density.15 That is, a 10% change in density is likely to produce a much smaller percen-tage change in sediment sound speed. Sce .... ,d spe•ed dAepnd, An ,.,, ,•,, ,.,.•,,.t ,f

compressibility and density, it follows that density and compressibility changes must be

anticorrelated in order to produce the observed small change in sound speed. Note, how-

ever that pa = - I is a default value and that the model aulows" any value for ji.

We assume that the fluctuations in density and compressibility are spatially station-

at). so that power spectra can be defined as Fourier transforms of the corresponding

fluctuation covariances,

W,-,p (k,)- (2 f e-L.r <ya(r(,+r)jp(ro)>d1r , (71)

where the dummy subscripts a• and P can be taken to be any combination of p and K.

We assume that the spectrum for density fluctuations obeys the following powerlaw,:

.':PPV 4 ( , j h 3.0 < <5.0 (72)( k, h0 )•"'

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UNIVERSITY OF WASH "V'GTON a APPLIED PHY$4YCS LAOV.,•AIMT¥

Equation 70 then forces the following expr.ssicn. fo" the ......... f.,,. u....natt 'bU4 A-0I IM. JJ1U t % .y I tU4Jt UJ!

spectrum IVKK(k;.) and the cross spectrum WpK(k,.):

w KKA ( k, ) =- A(73)( k%. h o )

and

IVK ( k, ) - (74)( k,. ho0 )Yt

For the sake of simplicity, three-dimensional isotropy is assumed for the sediment inho-mogeneity. This is reflected in Eqs. 72-74 in that these spect,. dep-nd on"l on it. _'...

nitude. k,. of the three-dimensional wavevector. k,. Layered sediments, by definition, do

not possess three-dimensional isotropy. It is an open question whether a more compli-

cated. anisotropic sediment model is needed at high firequencies.

Where grains and bubbles are the dominant causes of sediment volume scatter-in.g3 8"39 it may be possible to mimic the proper volume scattering behavior by adjusting

.t. y.•. and w. which then should be regarded as empirical, rather than physical, parame-

ters.

As noted above, the inhomogeneity exponent, yý, is restricted to the range 3.0 to 5.0.

The parameter p should be restricted to the range -10.0 to 00 The ;"c.... -

strength, wi. is restricted by the limits of 0.0 to 1.0 imposed on 02. Thus w 3 must be in

the range 0.0 to the value obtained by inserting c2 = 1.0 in Eq. 69.

2. Equations for Bottom Bistatic Scattering, Stre.,gth

The bistatic scatteringing strength will be defined in exactly the same fashion as the

backscattering strength, the only diffcr,.n, c '"" 'bn 'hat .o.re agular va..iab."c; are

required. The bottom bistatic scattering strength will be written in the form

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UNIVERSITY OF WASHINGTON, APPLIED PHYSICS LA0;AT ORY

Sb (Os, 0• , 1 0 Ilogic, es• O, 0'.. e, )+ C;( ., 0 • 0,f Ms. 7)

AM for backscattering. the bistatic scattering cross section is decomposed into two

components--one. o, (0 o. q, 06 ), for scattering from the rough interface and one.

a, 1 0,. o,. 0, ). for scattering from sediment %olume inhomogencities. In the following.

all of the ntibered equations are necessary for "'""'"°';n"" "r ;,r,,,.1,; ri-,l,, nr,s

given except in the body of the text as unnumbered equations.

a. Definition of geometric parameters

The angles .;. O6.. 0i appeaning in Eq. 75. are defined in r.'igJure 3. These arc the

same angles employed by Lang and Culvcr.51 but our notation is slightly different. The

"incident grazing angle" is denoted 0,, the "scattered grazing angle" is 0,. and 0, is the

"bistatic angle," defined as the difference in azimuth between the scattered and incident

directions. In general, one needs four angles. two grazing angles and two azimuths. but

only the azimuthal difference is h,.,, !.. ,.s. hmorn sufloir, Ire mmlrnd to be

laterally isotropic.

It is useful to define some geomntrical fqCtnS tht", ... . a; ear ;n 19tr, ' .

for the roughness and volume scattering cross sections. In terms of the various angles,

these geometric parameters are

A (1 + sin 0, sin O0 - cos 1B cos 0. cos 5 )I• (76)

AZ. = (sin0 1 + sinO,) (77)

and

I

A,= (cos 2 o, - 2 cos 0, cos 0, cos ., + cos.0, )t1/. (78)

IV-44 TR 9407

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UNIVERSITY OF WASHINGTON - APPLIED PHYSIC'S LPi30;MAT0;Y

Note that A = vit+A~ These parameters are related to (he differenee between

wvavevecbors in the scattered and incident directions, normalized by dividing by 2 k.

Equations 76. 77, and 78 represent, respectiel, the% mAgide the519U%% norml component,

and the transverse component of this normalized difference.

We will define the "specular direction" by 0, = 0i,, 0. This the direction of

mirror-like reflection from a flat. horizontal interface. In the specular direction. A, = 0.The correspondenCe between a gvnscatte-ringv and the. a-ua -,.#ls s o

unique. For example. the specular direction can also be specified as 0, = 180' - 0,.

0,= 18W~.

b. Roughness scattering cross section

Two different approximations are used for tile roughness scattering cross section.

a, (Os 0,. o, ). The Kirchhoff approximation is used for scattering near the specular

direction, and the perturbation approximation is, ~ud 'for all other U-1ecin Thi.s

approach is somewhat different than that used in the backscattering model, where the

perturbation approximation is "improved" by applying composite rougahness averalginga.

This is a means of accounting for the large-scale random slope of the bottom. but is

dropped in the bistatic case where such averaging becomes very cumbersome mathemati-ca~ll%. An additional difference is that th empiica ^ros eto sdfrvrog

bottoms in the backscattering, model is not used because it has no bistatic generalization.

K'irchhzoff Approximzation

Analosous, to the monostatic expression of Eq. 37. the approximate bistatic Kir-

chhoff croý,s section can be expressed in the following form:

FA~r (8,. 0'. 0,) I IR(84 3 ) 2IA' b q, 11+ 00AJ I8n 1 sý ' (79)

I.Sla+a q2 Ae 20t

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UNIVE RSITY OF WASHIG1O, 0TO PP I.ED PH YerotCS LA DO R AT•Y•R Y

The numerator factor involving A' artificially increases the Kirchhoff contribution for

directions far from specular (note the text following Eq. 84). Because the interpolation

scheme favors the smaller of the Kirchhoff and perturbation cross sections. it suppresses

the Kirchhoff contribution cxcept near thie specullar directi.,n. In Eq. 79 : as defined

in Eq. 35, and q, a. and b are as defined in Eqs. 38-40. The function R ( 0j, ) is the com-

plex plane-wave reflection coefficient for a flat interface separating water and sCdime-nt

(Eq. 30i. This, coefficient is nor evaluated at normal incidence as in the backscattering

model. Rather. in accordance with work by Thorsos (private communication), the local

tilt of the interface is assumed io be such as to cause spe.ulr reflection in the sattered

direction. This is the dominant process for scattered angles near the specular direction,

and Thorsos finds that this approach -;V'CS ;mprnoved .nccracr, y hbitat;i Qca.tteri.;n, W; ith

this assumption. the reflection coefficient is to be evaluated at the grazing anglk

0,, = sin- A . (80)

Perturbation Approximation

The bistatic form of the scattering cross section computed in the perturbation

approximation•,.,9 16, can be put in the foilowing form conenient for computation:

Opr (ePs. o. ) 1 1 +R(o, ) 12 I1 +R((0), 12 10G W2 (AK , (810,

4

where

G=(l/p-l )i . 0 -1O 0, C050_p )P ( !p(+!- 8.. ." (82)

The parameter AK in Eq. 81 is the "P. ,:g wavenumber." modified to avoid difficulty

with the singularity at K = 0 in the relief spectrum. W2 ( K ) (Eq. 7).

AK = 2 k ( A, + 0.000) . (831

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- UNIVERSITY OF WASHINGTON * APPLIED P-YSiCS LASORATO'V

hIterpolation Berecen Approxunafl'-s

The bistatic model uses an improved Kirchhoff-perturbation interpolation scheme in

which the smaller of the cross sections takes precedence. Th;s procedure is based on the

fact that, for a power-law relief spectrum, the perturbation approximation overpredicts

scattering near the spccular direction owing to the singuk-.I.ty "- thu rLi.c - pc...t AuL at.

zero wavenumber. In contrast, the Kirchhoff approximation tends to overpredict in other

directions. 5"-'-5- This overprediction is particularly bad for horizontal scattering, where

the Kirchhoff approximation yields a finite cross section while energy conservation

demand- that the cross section vanish. The interpolation scheme used here is

II

The smaller cross section will dominate if the parameter il is negative. The value ri = -2

is recommended.

The issue of coherent vs incoherent scattering is not addressed by the present

model. In fact, it is assumed that all sc.aered ener..y is in.-oherent. If surfce ha,

very little roughness, the scattering strength will be sharply peaked in the specular 6.rec-

tion. and the height and width of this peak will be such as to give approximately the same

energy flux as the forward loss model in Section W.B. If the forward 1os; model is uced

to account for energy scattered near the specular direction, O, should not be used for this

purpose, as this would be double counting.

c. Sediment volume scattering cross section

If composite roughness averaging is not used, the bistatic generalization of Eqs. 65

and 66 is

Ir + I +R(Oi )f 2 I 1 +R( 3 ) 12, (0, p, M I) = em ) 0

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UNIVERSITY OF WASHINGTON.- APPLIED PHYS;CS LAGORMATOW;

where o,. ,j is the volunc scattering cro s "c c due to %J,

is the resulting interface scattering strength to be inserted in Eq. 75. Following Hines,35

TaneR'. and Lyons and Anderson,?' perturbation theory is used to obtain the volume

scatterintg cross section,

1 0 1it + scos0Ojcososo,-P(O, )P iOs)1: W•o(Ak. (,6.

The spectrum W0', is given by Eq. 72. and

Ak =k 4A4+(Re {P(iOj +P()0+}P )] (87)

is the Bragg wavcnumbcr.

3. Model Accuracy

The bistatic model is compared with a ,,11,,,t,,cd .,t of1 , histrical data An ,,,j,.=. 4:1.These comparison, qualitatively verify some of the features of the model but are not

sufficient for a quantitative assessment of model accuracy because no physical data were

available from which to estimate model inputs. The model predicts that scattering

strength varies slowly with bi.static angle in the vicinity of the backscatter direction. This

feature is supported by comparisons with .•,jioriCa., da... IU The ..... m.d.

found to be in reasonable agreement with tne backscattering model in comparisons for

Iwo experimental sites having silty and sandy bottoms. Thus, for smooth and moderately'

rough bottoms (e.g., clay, silt, and sand), the accuracy of the bistatic model in directions

near backscattering should be comparable to the accuracy of the backscattering model.

The bista:ic model is not expected to have useful- accuracy 1br rouh gravelv ard r.ck bot-

toms owine to failure of the scattering approximations used. Specifically. if the

difference between the bistauic and backscat!ering models becomes significan! (-3 dB ,or

more) when using the same input parameters and equivalent angles, the bistatie model

IV-48 TR 9407

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UNIVERSITY OF WASHINGTON , APPLIED PHYSICS LAORAT8OR ....

should not be used. Near [he specular dr:CCtin• , the bUS . ,d,,,t, Lde l t,%-,, ,- ,ai,,,Y

th- sane acoustic intensity as the forward loss model and so has similar accuracy in thik

resoe( i. 7he model's prediction for the angular spread nf near-mneriiAr tenergy has not

been tt sed experimentally, however.


The expressions used in computing the perturbation approximations for roughness

and volume scattering are conveniently coded using complex arithmetic in the fashion

noted in Section TV.B.3. To avoid negative infinities in the scattering strength. values of

0, or 0, that are within 0.001' of eithe"" 0' olr l8O, ,hiold be roar.,ced, Wu,, M.I0 eor

179.999. To avoid underfiow and overflow, the following quantities should be limited to

be no smaller than 10"' 5: ak, (Eq. 79), the denominator of Eq. 79 (after exponentiation).

and r;,,. (Eq. 81).

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REFERENCES - Section IV

I. APL-UW High-Frequency Ocean Environmental Acoustic Models (U), APL-UW8907, November 1989. (Confidential)

2. E.L. Hamilton, "Compressional wave attenuation in marine sediments," Geophy-

shcs. 37. 620-646 (1972).

3. M.D. Richardson and D.K. Young. "Geoacoustic mo"e"; and b ..... "' .... -IGeo'.. 38, 205-218 (1980).

4. K. B. Briggs. M.D. Richardson, and D.K. Young. "Variability in geoacoustic andrelated properties of surface sediments from the Vene7uela Basin, Caribbean Sea,"Mar. GeoL 68. 73-106 (1985).

5. S. Stanic. K.B. Briggs, P. Fleischer. R.I. Ray. and W.B. Sawyer, "Shallow-waterhigh-frequency bottom scattering off Panama City. Florida." J. Acoust. Soc. An:..83, 2134-2144 (1988).

6. S. Stanic. K. B. Briggs. P. Fleiseher. W. B. Saw. yer. and R. 1. Ray. "'High-frequenc%acoustic backscattcring from a coarse shell ocean bottom." J. Acousi. Soc. Am., 85.125-136 (1989).

7. K. B. Briggs. P. Fleischer. W. H. Jahn. R. 1. Ray, W. B. Sawyer, and M. D. Richard-son. Investigation of High-Frequency Acoustic Backscattering Model Parameters:Environmental Data from the Arafura Sea, NORDA Report 197, Fcbr, ar, 1989.

8. D.R. Jackson and K.B. Briggs "High-frequency bottom back.scatte, ing: Rough-ness versus sedimen! volume scattering," J. Acoust. Soc. Am.. 92.962-977 (1992).

9. P.D. Mourad and D.R. Jackson. "High frequency sonar equation modt S for bot-tom backscatter and forward loss." in Proceedings of OCEANS "89 (Ma..ne Tech-nology Society and lEEr, 1989), 1168-1175.

10. C. K. Wentworth. "A scale of erade and class for elastic sediments," J. Geolhgv.30. 377-392 (19221.

11. E.W. Lane. "Report of the subcommittee on sedimentary terminology." Trans.AGU. 289. 936-938 (1947).

12. D.L. Inman. -Measure for describing, the size distribution of sedimer s.'" J. Sedi-menWt Petrol.. 22, 125-145 (1952).

13. F. P. Shepard. "Nomenclature based on s .,d,-slt-cla. rattio;.J. Z ¢*J: .. e.rv"..24, 151-158 (1954).

14. R.L. Folk. "'The distinction betveen grain size and mineral composition insedimentary-rock nomenclature." J. Geology. 62. 344-359 (1954).

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15. E. L. Hamilton and R.T. Bachmann, "Sound velocity and related propertie.; ofmarine sediments," J. Acoust. Soc. Am., 72, 1891-1904 (1982).

16. D. R. Jackson, D. P. Winebrenner, and A. Ishimaru "Application of the compositeroughness model to high-frequency bottom backscattering," J. Acoust. Sof. Am.,79. 1410-1422 (1986).

17. D. R. Jackson, Third Report o. "TTCP Bottom Scattering Measurements: ModelDevelopment, APL-UW 8708. September 1987.

18. C. S. Clay and H. Medwin, Acoustical Oceanography (Wilcy, New York. 1977). p.491.

19. K. B. Briggs, "Microtopographical roughness of shallow-water continentalshelves." IEEE J. Oceanic Eng., 14, 360-367 (1989).

20. D.R. Jackson, A.M. Baird, J.J. Crisp, and P.A.G. Thomsom, "High-frequencybottom backscattering measurements in shallow water," J. Acoust. Soc. Am., 80.1188-1199 (1986).

21. K.V. Mackenzie, "Reflection of sound from coastal bottoms," J. Acoust. Soc. Am.,32. 221-231 (1959).

22. 11. W. Marsh and M. Schulkin, "Shallow-water transmission," J. Acun. &,,, Amp..34, 863-864(L) (1962).

23. D.E. Weston and P.A. Ching, "Wind effects in shallow-water acoustic transmis-sion.- J. Acoust. Soc. Am.. 86, 1530-1545 (1989).

24. H. R. Hall and W. H. Watson. An Empirical Bottom Reflection Loss Expression forUse in Sonar Range Prediction, NUC Tech. Note 10, Naval Ocean Systems Center,San Diego. July 1967.

25. APL-LTW Ocean Environmental Acoustic Models, Revi;ion I (U), A-% VW, 3-T40,June 1984. (Confidential)

26. S. T. McDaniel, Effect of Variations of Sediment Properties on High-Frequency SeaFloor Reverberation. TM 88-23, Applied Research Laboratory, Pennsylvania StateUniversity, February 1988.

27. R.J. Urick, Princip/e. of Underwater Sound (McGraw-Hill, New York., 1983.

28. A. M. Yaglom, An hitroduction to the Theor. of Stationar. Random Functions(Prentice-Hall, Englewood Cliffs, New Jersey. 1962).

29. A. Ishirnaru. Wave Propagation and Scattering in Random Media, Volume 2, Multi-ple Scattering, Turbulence, Rough Surfaces. and Remote Sensing (Academic Press.New York, 1978.).

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30. S.T. McDaniel and A. D. Gorman. "Acoustic and radar sea surface backscatter," J.Geoplhys. Res.. 87.4127-4136 (1982).

31. R.J. Wagner, "'Shadowing of randomly rough surfaces," J. Acoust. Soc. An 41,138-147 (1967).

32. B. Carnahan. H. A. Luther. and J.O. Wilkes, Applied Numerical Methods (Wiley.New York, 1969). p. 116.

33. E. Y. Kuo, "'Wa'e scattering and transmis.ion at irfegular suffaces." J. Acoust.Soc. Am.. 36. 2135-2142 (1964,.

34. J. 11. Stockhausen, Scattering from the Volume of an Inhomogcneous Half-Space.Report No. 63/9. Naval Research Establishment, Canada., 1963.

35 P.C. Hines. "Theoretical model of acoustic backscatcr from11 a =1,,,,th ;Cah,, ." if.Acoust. Soc. Am., 88. 324-334 (1990).

36. D. Tang. "Acoustic wave scattering from a random ocean bottom," Ph.D. thesis.Massachusetts Institute of Technology and Woods Hole Oceanographic Institution.June 1991.

37. A. P. Lyons and A. L. Anderson, "Acoustic scattering from the seafloor: Modelingand data comparison." J. Acoust. Soc. Am.. 9.5. 2441-2451 (1994).

38. F. A. Boyle and N. P. Chotiros. Bottom Penetration at Shallow Grazing Angles 11,ARL-TR-92-12. Applied Research Laboratories, The University of Texas at Austin,June 1992.

39. F. A. Boyle and N. P. Chotiros. Bottom Backscatter From Trapped Bubbles, ARL-TR-93-15, Applied Research Laboratorics. The University of Texas at Austin. July1993.

40. H. Boehme, N.P. Chotiros. and D.J. Churay, High Frequency EnvironmentalAcoustics, Bottom Backscattering Results. ARL-TR-85-30, Applied ResearchLaboratories. The University of Texas at Austin. October 1985.

41. R.A. Stewart and N. P. Chotiros. "Estimation of sediment volume scattering cross.section and absorption coefficient," J. Acou.t. Soc. Am., 91, 3242-3247 (1992).

42. C. M. McKinney and C. D. Anderson. "Measurements of backscattering of sound.;ore the ocean bottom." J. Acoust. Soc. Am., 36.158-163 (1964).

43. H.-K. Wong and W.D. Chesterman. "Bottom backscattering near grazingincidence in shallow water," 1. Acoust. Soc. Am.. 44. 1713-1718 (1968).

44. A.V. Bunchuk and Yu.Yu. Zhitkovskii, "Sound scattering by the ocean bottom inshallow-watcr regions (review)," Sor. Phys. Acoust., 26, 363-370 (1980).

IV-52 TR 9407

ADlR 1 994c

UNfVERSITY OF WASHINGTON, APPLIED PiH'V;CS LABOPATGO;V

45. H. Boehme, N. P. Chotiros, L. D. Rolleigh. S. P. Pitt, A. L. Garcia, T. G. Goldsberrv,and R. A. Lamb, "Acoustic backscattering at low grazing angles from the oceanbottom. Part 1. Bottom backscattering strength," J. Acoust. Soc. Am., 77, 962-974(1985).

46. H. Bochme and N.P. Chotiros, "Acoustic backscattering at low grazing anglesfrom the ocean bottom," J. Acoust. Soc. Am., 84, 1018-1029 (1988).

47. M. Gensane. "A statistical study of acoustic signals backscattered from the sea bot-tom," IEEE J. Oceanic Eng.. 14, 84-93 (1989).

48. M. Abramowitz and 1. A. Stegun (editors). Handbook of Mathematical Functions(Dover Publications. New York, 1965).

49D. R. Jackson. A Model for Bistatic Bottom Scattering in the Frequency Range10-100 kHz. APL-UW 9305, August 1993.

50. T. Yamamoto, "Velocity fluctuations and other physical properties of marine sedi-ments measured by crosswell acoustic tomography," J. Acoust. Svc. Am. (submit-ted, 1994).

51. D. C. Lang and R. L. Culver, A High Frequency Bistatic Ocean Surface ScatteringStrength. Technical Memorandum 92-342, Applied Research Laboratory, Pennsyl-vania State University, December 1992.

52. E. 1. Thorsos. "Exact numerical methods vs the Kirchhoff approximation for roughsurface scattering." in Computational Acoustics, Vol. 11: Algorithms and Applica-tions. edited by D. Lee. R. L. Sternberg, and M. H. Schultz (North-Holland, Amster-dam, 1988), pp. 209-226.

53. E. I. Thorm i, "The validity of the Kirchhoff approximation for rough surfacescattering t mic a Gaussian roughness spectrum," J. Acoust. Soc. Ant.. 83 78-92(1988).

54. R.J. Urick, "Side scatt,..- of sound in shallow water," J. Acoust. Soc. Ant., 32,351-355 (1960).

55. S. Stanic, E. Kennedy and R. 1. Rap. "Variability of shallow-water bistatic bottombackscattering." J. Acoust. Soc. Am.. 90. 547-553 (1989).

TR 9407 IV-53

AnR19QAq1

V. Arctic

AMR I JQAql

UNIVERSITY OF WASHINGTON* APPLIED PXYS!CS I6A, V_•5n_7___v

In! roductiott

For arctic operations, a nonridged ice surface can be modeled similarly to the open seasurface. However, when ice is ridged, the under-ice keeuls act as 4,.l • M i;LUcICVitb ad1U HIt

be treated differently. In modeling an ice keel, one can use either an "acoustic model" or an"ice block model,' depending on the level of effort and the ice information available. An

acoustic model that relates keel reflections to ridge dimensions and seasonal conditions is

directly applicable and thus probably preferable. Modeling a keel as a pile of ice blocksrequires an idealistic assumption as to keel stnuCture ad .a detaile knowled.. o, V1e r"feI--

tivity of various ice surfaces. The greater effort may not necessarily provide a more accu-rate model. In this section, we provide parameters for either choice of model.

For many applications (e.g., measuring ice thickness from below), sound speed andabsorption in the ice are important. Expressions for on,,,, pee , s a func-,,o ofi cnl;vi,.

ity and temperature of the ice, average vertical sound speed as a function of thickness andair/ice interface temperature, and absorption as a function of temperature and frequency are

given in Section VA.

The ice cover, when formed in calm weather or in sheltered locations, is fairly flat anduniform. The backscattering and forward scattering from this ice are important to the mod-eler in two ways: (1) as an upper boundary to the medium in nonridged ice, and (2) as one.urface of blocks in ice keels. In Section VB we ,ic-,lue a.stm, %,"u".y offrward st,.,.,

near-normal "reflectivity," and low-angle backscattering from nonridged ice.

In Section V.C we discuss the formation of ice ridges and the .a.ica prope'ti- Ofthe corresponding under-ice keels, which act as large false targets for acoustic systems. Thetarget strength distributions for these false targets are provided in Section V.D. They can be

used directly in acoustic modeling or as a verification of the results of ice keel modeling.

There are not enough data to offer guidance about how to vary the distribution for seasonalp ,"* iS app..C.I.. e 10, o hp. 1 .... e rf:o,or site-specific conditions, except for one curve th,, ,s ,pl,.,to, s e .... -

bution curves in both fall Pnd spring were given in the previous version of this document(APL-'W TR 8907). They arc not shown here because they are classified.

TR 9407 V-I

AfR 1994ql

UNIVERSITY OF WASHINGTON - APPLIED PHYSICS LAGOGAT0RV

For more detailed modeling requircnnents ^e.g., for a moving -latfom),ls wC "rovid

information on ice keel reflectors-their spacing in a keel and their angular response pat-

tern. These can be used to compute such values as the number of pings from a moving tor-

pedo that will detect a keel reflector and the variation in target strergth from ping to ping.

Ice keel reflections depend on frequenCy a,• •ul.e .,. .. Examp .. .. III ,,

dependence are given to help select optimum parameters. Also, the interference between

reflectors depends on these parameters and may be a consideration in their selection. The

results of some measurements and studies of this interference are given.

A. SOUND SPEED AND ATTENUATION

I. Vertical Sound Speed as a Function of Salinity and Temperature

The density and porosity of the ice depend on the salinity and temperature. This depen-

dence is summarized in equations of Biot1 2 and Cox and Weeks1'3 :

p = PpI/÷ (l-1 3 )PS (la)

p•S (lb)

Pf= pS- pf S + pS

Ps= 917.0- 1.403 x 10-T (c)

pf = 1000.O+0.S f.(T) (ld)

S = - 3.9921 - 22.7T- 1.0015TZ - 0.19956T', (le)

where p is the bulk density, P is the porosity, S is the bulk salinity, Sf is the brine salinity,

p/ is the brine density. ps is the ice frame density. and T is the temperature. The densities

are in kilograms per cubic meter. the salinity in parts per t..ou.an. and, 'e temperature in

degrees Celsius..

Ice supports both compressive and shear waves. Recent measurements of these speeds

as a function of salinity and temperature1 have been used to derive the following relations:

V-2 TR 9407

ADB 199453


C = r , m/s (2b)

Kef = 9.49 x 106 ( - 1.403) p, N/rm2 (2c)

9 eff = 3.38 x 106 (1 - 2.790) p, N/0m, (2d)

where c, is the longitudinal wave speed, c, is the shear wave speed. Kff is the bulk modulus.

gI,,fis the shear modulus, and P and p are determined from Fq. 1. It i; important to note that

the moduli KeD-and lieffphysically must be positive. Thus when the porosity becomes large

enough that the moduli would be nega.•tive, a default v~ue of zero shoiAod be ,,•ed. . .re. 1

400

D

3000

2000

0 0

0 0.05 0.10 0.15 0.20VOLUME FRACTION OF POROSITY

Figure 1. The longitudinal (cl) velocity data (shown as open squares) and shear (c,,) velocitydata (shown as open circles). Least.squares fit curmes to the data are also shown.The largest errors come in determining porosities from the salinity and temperatureof the samples. This uncertainty increases with porosity.

TR 9407 V-3

ADB 199451


shows both the data from which these equations were derived and the model curves result-

ing from their implementation. In Ref. 1 the moduli are related to Biot parameters. In Ref.

4 they are used in a model for determining the reflection coefficient for sea ice as a function

of S. T and frequency, f.

2. Average Longitudinal Sound Speed as a Function "" 1"-'- c....... an ,Ir .ceInterface Temperature

The average acoustic speeds through the icc canopy arc ofic•, for 1o-

efforts and ice thickness measurements. By using a simple model for the salinity profile in

first-year ice and assuming a linear temperature profile from the airrice to the ice/water

interface. one can determine vertical speed profiles and subsequently average speeds using

the results of Eqs. 1 and 2.

The average speed of the longitudinal wave c! in the vertical direction is of particular Iinterest. For this reason polynomial fits were derived' for the average longitudinal wave

speed as a function of thickness. d. in meters and air/icc interface temperature, T. in degree; ICelsius. I

Cae = F, (d) + F2 (d) T, + F (d) T,.+ F4 (d) T3:i., .(,3a)

F, (d) = 2661.92 + 482.514 xd (3b) I- 191.152 xd 2 + 28.1133 xda

F2 (d) = -134.744 + 62.3017 x d (3c)

-25.7015 x d2 + 3.82128 x d

F, (d) = -.7.24730 + 3.34510 x d (3d)

-1.38910 x d2 + 0.206891 x d

F4 (d) = -0.129668 + 0.059669 x d (3e)2 d3-0.024812 x d + 0.003696 x d

Figure 2 indicates the ice thickness and temperature regimes where the above fits are useful. I

V-4 TR 9407

ADR 199493


3800 I (a)

Surface Temperature. -26^ 1

V 3600 - 0

C C34O0

8cL 3400 _ _

Surface Temperature. -21 !CO:'

S32001 :,-'D "l3 20 Integration Results

" + 0 Polynomial Fits

30001O 1 2 3 4 5

TOTAL THICKNESS (m)3800 . (b)

J ==• •,.• .•! Thickness a 3.0 m3600 m

Thickness 0.5 m

34004

I ~00*

~3200 D0o & Integration Results+ 0 Polynomial Fits

3000t 'I "40 -30 -20 -10 0

SURFACE TEMPERATURE (-C)

Figure 2. Part (a) shows the average longitudinal velocity as a function of thickness for rNdifferent air/ice surface temperatures. Part (b) show-s the average longitudinal velo-city as a fiuncion of air/ice surface temperature for t'o ice thicknesses. The figuresshow results of numerical integration of the velocity profiles and compare the poly.nomial fits in Eq. 3 with the integration results. They indicate tfle ice thickness andtemperature regime where the polynomialft.s are useful.

TR 9407 V-5

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-- UNIVERSITY OF WASHING7ON - APPLIED PHYSICS LABORATORY

3. Attenuation as a Function of Temperature

M :Cammon and McDaniel suggested a form for attenuation5 as a function of tempera-

ture and frequency which is based on the assumption that intergrain friction is the cause of

absorption in ice. Their equation is

a = k7 (-6/T) 3 , (4)

where ot is absorption in decibels/meter, k is a constant, f is frequency in kilohertz, .- d T

is temperature in degrees Celsius. Recent experiments6"7 were aimed at determining

whether Eq. 4 captures the correct dependences. The results indicate that, away from the

3-5 cm thick skeletal layer at the bottom of the ice, Eq. 4 can ,,1.. Uscd wit• 0.18 S k 5 0.3.

Within the skeletal layer, Eq. 4 can be used as an approximation with k = 1.0.

B. SCATTERING AND FORWARD ENERGY LOSS FROM

UNRIDGED ICE

1. Forward Scattering

The rms roughness of unridged ice is typically much larger than an acoustic wave-

length for frequencies greater than 10 kldz. Therefore. the interaction of high-frequency

acoustic energy with unridged ice is most properly conside-ed a scattering process. How-

ever, there arc cases in forward scattering where only an estimate of the energy lost into the

ice is needed, and the process can be ire'tied by assigning;, -an€e.cer;,,,c,- on ce;-,,,.-, .

For this reason. this subsection starts with a discussion of energy losses given in term! of

reflection coefficients. Subsequently, expressions are given in terms of scattering.

a. Energy loss

Unridged ice reflects sound so well that a surface-reflected signal will ofte'r overlap the

direct-path signal and cause interference. Experimental results 8 are shown in Figure 3 for

the reflection coefficient at 25 kHz as a function of angle for unri.ge. ice. Resuts at 45 KIi-

V.6 TR 9407

ADB199453

UNIVERSITY OF WASHINGTON* APPLIED PHYSICS LABORATORY

a

I-

a1 00

U4.

a

a•- I .. .I , , ..

10.0 20.0 20.0 40.0 50.0SpecuLor IncLdent AngLe

Figure 3. Average of reflection coefficient. R,!, vs grazing angle for data from Rur; 31, 33.and 37 of Ref. 8.

for the same experimental geometries gave similar values- i.e., no obvious frequency

dependence was observed. For grazing angles up to ^5%. Figu-re 3 suggests using an average

reflection coefficient loss in the range of 4-5 dB. Figure 3 and the modeling of Ref. 4 indi-

cate that for higher grazing angles a larger loss is to be expected: the losses seen near nor-

mal incidence are given in Section VB.2.a below.

The reflection loss quoted in the last paragraph is for growing spring ice. A monitoring

of reflections 9 near the coast in the Beaufort Sea showed that lhe arrival of warm water from

the Alaskan Coastal Current changed the character of the surface by melting but brine chan-

nels and making it more porous, with a result,;cg ir,.,-,, of nlw IA dB in fht rCflCCtiOn

loss.

TR 9407 V-7

ADB199453


b. Scattering coefficient

Similar to the facet scattering contribution to scattering from ,he !ocean s,,,.re, ,

high-frequency approximation 10 can be used to arrive at the forward scattering cross section

IR-,, sec4...._ × ( tan2y" 5cr(y) = ,K -R1 .• !S e xp •- - -. 5

where

INIcos20 O- 2 Cos Of Coses Cos + co-slestd ly = sin 0 , + sin ID S

the ang..lc e, 0f , are measured relative to the mean surface as shown in Figure 4. The

angle "1 is the facet reflection angle." IR1- accounts for the energy loss into the ice, and s

is the two-dimensional rrn; ;lope of the rough .wate..ce inte face.

The results in Section VB..la can be used to get an empirical estimate of the energyloss factor IRij (quoted there in decibels. but needed here in nondecibel form). Altema-tively, a more theoretically bawed method (f calculating the energy losses is given in Ref. 4

z

V

-~ /l

R

Figure 4. Measurement gometnr..

V-8 TR 9407

ADB 199453

UNIVERSITY OF WASOONGTON * AFPLIED i•VSCS LAbUHATIPV.

where porous meda theor", a, . ,, TVL A U...U LU .... 11 ... : . L.. II

coefficients.

An estimnate of the rms slope, s, was determined in Ref. 12 based on the experimentai

rc;u!tt, in Ref. !3. This ertimate was based on a scattering strength expression equivalent to

Eq. 5 and examination of the puke e.on.g.tion s.... n.--- i s & ragio-, ....s It'. ,, c -•

tered off the ice surface. The results indicate a slope range of

tan (4.2) _< .s tan (6.4c). (6)

Equation 5 should not be used for grazing angles less than about twice 6.4'. For shal-

lower grazing angles. the effects of shadowing aMb i ..M.Pt. ...... ,, , Ua NC.SS WIC

method of approximately incorporating shadowing effects.

c. Time-dependent intensity after forward scattering

The expressions for the time-dependent intensit%. or "pule elongation,* givcn in Eq.

42 of Section 11 can be used for the Arctic if Eq. 6 is used for rms slope and the rcshlt is

multiplied by the R1 (f the la!-! subsectiin. i.e.,

IRIO. 0 'T<0

-0 ( JC71-) -) T - )/T) I-T,,

where the symbols arc defined in association with Eq. 42 of Section 11.

TR 9407 V-9

ABiR 1 994

UNIVERSITY OP WASHINGTON - APPLIED rfl,1StCrQ LABORATORMY

2. Near Normal Incidence

The discussion of icc keel rcflections; i Section V... indic-i"; thva? tho I.Aro,-r r,-tfprtnnc.

probably corne from ice block face,, that arc nearly normal to the acou~stic beam. The high

angle reflection from the face of it block of arctic ice is therefore very important, and has

motivated the APL mecasurements of normia- i neidenrce reflection; fromn cxpanso;ofI

unrideci ice and fromn ice blocks cut from such a surface.

a. Unridged ice amplitude "reflection- coefficient

The normal- incidence reflection and scattering from the under-ice surface are iticaured

b5 placing, a transducer beneiith the ice and projecting sound upward. The return is used do

dciernunc an "effcctive" ~lcin ~ ~ t~t~fo

both coherent reflectior. and incoherent scitkr. The amplitude reflection coefficients mea-

sured in this wa\ have bcen plotted in Ficure 5. Some measurements by Stanton et al. ifor

a very thin ( 10 cm i icex shret oni an o~utdoo~r pond of salt water are added for compa~ison. Aleast squares fit to all the reSults% tdahed line in Figure 5) is our recommendation for a sim-

ph: -effeciive- reflection coctmi ciecnt R.#. 4 no'rm-A

R4= 0.46- 0.19 log (f)

where f is the frequtenc) in kilotwcrt/. The relationship is lim~ited to frequencies of 2-

200 W.-I and assumres beams! al leas! it fc\, degreesý wide. Below 7, kHz. there are no data:

the line provides a convenient transition to the maximumi R o (f 0.4. which corresponds to

that expectcd from the mis.match be-t\%een water and icc. Above 200 kllU. %\v recommtend

u% in g an R, of 0.04, w hich I s repre scin "'., ; f "f ,-4AC 1;('.. 1-6 Mnnr,f',44i Ics ! t Mbtan;"d to% Ate.

Equattio'n 8 is a purely empirical expression. A semiernpirical -based result for the effec-

tive reflection coefticient iý, sho%%nr as a solid cune in Figure 5. This re~ult is based or, a

measured longitudinal sound speed profiletn in the ice in conjunction with a theoretical

rx~pression' 5 for the reflection cueflficient as a ni,~i'v ronw f recy for a medium with ai

continually varying sound speed. This semiempirical reflection coefficient is given by

R= 2.3-4783 + 5.17682 0.34449 x log (f) (ga[lo ~fJ 2 log~f)

V-10 TR 9407

UNIVERSITY OF WASHINGTON* APPLIED PHYSICS LABORATORVY . ......

0.4 #_ICE EANO:PY

APlotter O phere"0. * 22x22 022x22 on o0,w

C_iE ,

0RTIFICIPL SEq IE

C "1 Stant•n.Jkzek. •o* 14

0)0

C-0

• 0.1 .. ............ ................

-- ! -

IC 2"0 so :30 200Freqaerncy (kHz)

Fag'aure 5. ,MIeasied rrflection coefficients for the underside of fht ice canopy. Data from anAPL-L'II ice blo & e.perirnept and fiom Stanton ct al. IS are included for comparkon.The dashed line is a least square.v fit to all data below 2114 kH:(R, = 0.46- 0.19ogf). The solid line is the theoretical result calculated using aopical sounpd speed prafile %ithin the ice (see text near IFq. aki. All measurementswcre taken at 28-m range expett flur the 22 x 22 transducer on the arm, which % as at

2 m.

Ice keelh arc made up of ice block%, and largec reflections come from block face.; nearly

normal to the acoustic beam. The reflection coefficients measured above can be Used to pre-

dict the target ,trengths of the~c faces. One caveat is that some faces may not have a skeletal

layer, in which case the reflection ighs" be Jýt.' "• . ¢Am t..... r....C'....

are so near the same range that interference occurs (see Section V.Dj.

b. Scattering from an Ice block

In spring 1988, we measured normal-incidence reflections at 20--80 kMl1 from the end

of a cylindrical ice block. In this experiment, blocks with diameters. of 27. 38. 58, and 84 cm

TR 9407 V-Il

______________UNIVERSITY OF WASHINGTON~ - APPLIED PHYSICS LABORATORY

were individuallyv depressed below the surface so that when acoustic pulses were transmit-

ted from beneath thc floe the block's reflections were separable in time from the reflections

off the underside of the ice canopy. A sourcEi/recei1vcr placed 301V blo the lock wa&ý

moved horizontally to measure the angular response pattern. Precise calibration waf5

obtained by replacing the block with an invcrted pan of the samei diameter, filled with air.

In the left-hand pane] of Figure 6. returns from the air/water interface of the pan at

three of the five frequencies air.- conmp-ard Ui1- thetheory $%or 6A f1k. &" V ",- %'-

;also good for a pressure relief surface). In this theory. the 1w-get strength. TfS. for wave-

length ý an3 incident angle R is given h\,16

TS= cosO(91TS=l0loc[tR., : j 0 4 s

where a is the radius oif the plate, 3 2 ka sinO, k is the wavenumber. and J, is a Bessel

function. The anplirudc. refle-t ion -oc 1.111 u- .C 1t ahI- Uý"1,61ý1#

loss at the stirf.ace. which rna% he due to impedance change. roughness, or sonmc other cause.

In the right-hand panel of Figure 6, the ice reflection niea~urerve4ntt; afe pktoted f10i

comnparison with theory. The returns are considerably lower than on the left. but still indi-

cate the side lobes observed for dhe air surfawe. A! !lýe !om freq.,en-iies th, !ancid-r rp!enm,

pattern follows the flat plate theory. but at the higher frequencies roughnecss play s an inipor-

tant role. a% indicated by the filling in of the nulls. After thc block was removecd, the bottomsurface wis measured a~nd futind io hive a ýa`-t- *. .. -1.. I .... *--lv 'nUcm

3. Low Angle Backscatter

In areas of the Arctic where the ice has fruzen with \ erý little disturbance from wiad orcurrent. such a,ý in narrowN leads. the resuhing qirf cc it. suffcel vfa aduiomt

acoustic backscattering can be treated similarly ito the hackscattering from an open sea sur-

face.

This backscatterine. or surface reverberation, was measured at 20 and 60 kl-z under

refro7en lead-, at sevcral ice camps in 1973-1975."- 19 In 1992, measuremients, were made

V- 12 TR 9407

AM~ I QQAq1


30 3'--0---.z3,-

20 20 kHz] 20 20 kHz

10o 10

0 1 00"

.10 -10:

-20 - -20~\o.3.0-30 .30

40 40.

300 3 .

40kHz 20 40 kHz:, L"1 0a, 10:7

w 0 iu 0

W w .20 ,, r,.,cc .30 I , -30 0. 0. 0

~ 40 ----- ~- .40 AL 4 .4.

3030.,I I

20 .. 80 kHz 20 - 80 kHz

10 4 0

.I. rr' '': - ":

-10 10 -5 0 $ 10

INIETANGLE (dog) INCIDENT ANGLE (dog)

cylinder ice cylinder

Figure 6. AfeLasurfment•" of t/he target strength of t/h end face of a 60 cm diameter cy.lindler of

air antd of a 58 cm diameter cy'linder of ice. As the transducer was moved horizon.

tally beneath the c'linder, the incident angle varied from )0• in one direction to 10&

in the opposite direction.

TR9407 V-13

.10 -S 0 5 10 10 .5 0 6 1

UNIVERSITY OF WASHINGTON' APPLIED PXYQ:CS LACCCRATCgY-

at 100-300 kHz both in a laboratory.. tn 2o .,d ;. , 4e•d21 Th, b,.,.ca..eri,, o, ... h

was found to increase with frequency and with grazing angle. The measured results arc

shown in Figure 7. Three equations were derived for the modeling of backscattering at

selected frequencies:

Ss= -35 + 19 log sine 20 kHz (0la)

S,= -31 + 24 logs•inO 60 kHz (10b)

Ss =-72 + 25 logf+ 15 log sinB 10(--300 kHz, (10c)

where S, is the backscattering strength in decibels,f is the frequency in kilohertz, 0 is the

grazing angle (valid for 6c-45' only). and the logarithms are to base 10.

0

1 -0 S,, -72 + 25 Iog., f 15i log,, sina

C,•0[330'

S& & 1982Z W

S1974-1976 1973197640

20 50 100 200 500FREOUENCY (kHz)

Figure 7. Surlfce ret erberation measurements for flat sea ice. 1973-1976 and 1982. The 1982data are a combination of laboratory" tank measurements and arctic field measure.ments.

V- 14 TR 9407

Mr 0 I QAZI


C. ICE KEELS

I. Formation of Ridges

Arctic ice is subjected to various environmental forces and is continually undergoing

some sort of transformation. In the sumnmer, ablation on top and melting below reduce the

quantity of ice. In the vinter, freezing increages the thickness and coverage of ice. Variable

winds and currents cause the ice floes to be forced together or spread apart. If floes of thin

ice arc forced together. one may ove.lap the other and raffiting occur,. If to s f i

slide past each other while in contact, a shear ridge is produced. If the compressed ice floes

are thick, pressure ridges are created, either at the po;- r :a. or fuilowing cracking of

the floe. These pressure ridges are generally largei, wiore spectacular, an-d, from our ,,.ser

vations at many ice camps, more common than shear ridges. It should be noted, however.

that the ridging process often involve, both shear and pressure components, The ice :' a

shear ridge tends to be in small chunks with a ground up appearance. whereas that in a pres-

sure ridge is composed of discrete blocks of many sizes.

For the ice blocks in a ridge, the relation between the long axis. L. and the thickness. :.

has been found to be reasonably well represented by22

L= 2.04 t + 0.72. (11)

where L and r are in meters.

2. Ridge Structure

The portion of the ridge above sea level is the sail, and the part below is the keel. Using

a kinematic ridging model based on fe-xura, faie•, .,, the r;ia,;n ,o,,h4'Anic,., P,•,.,rr,.

and Coon2: found the sail height to be limited by the thickness of the constituent blocks.

This was corroborated b. the measurements of Tucker et al. 2 Empirically, the sail height

has been found to depend on the square root of the average block ihickness in a ridge. 24

The ratio of keel draft to sail height of ridges has been shown to vary widely from 3 to

9. Kovacs25 reported a ratio of 4 or 5 from measurements and sonar profiling of five ridge

TR 9407 V-15

A•I' 1 QQA•


structure,. in the Bering- and Chukchi seas. Kovacs et al.26 found a ratio of 3.3 for a multi-

year ridg using coring and sonar profiling methods. Kozo and Diachok 2 7, gave a ratio of 5

for ridges in the Greenland S~ea by Col-Aparinbg Ulhe diVibto of4S- AAWiA ob4nd rmair-borne laier profiles with the distrihution of keels obtained from submarine under-ice pro-

files. Francois-'ý determnined ratios of 4.4 to 9.3 for both first-year and multiyear ridges near

Ice Island 1-3 by comparing data obtained from topside ,:~eying with data obtained from

under-ice profiling with an unmanned stibmersi1"'-. Garrison et aL.2 showed a ratio of 7.5using supposedly one-to-one correspond-.0:-ý ntweenC- #toP;id I-a.e prfle A ,od.- -

sr:' -cfiles obtained in the Bc-alif. Sea. A theoretical value of about 8 was obtained by

Parmerter and Coot.. *.. " Ig model23 based on calculations of limits on sail height and

keel draft as a func*: n of ice thickness.

Considerina these results, we reCommendA 116,ina draft-to-sa1i ratio of A fo. er acutlc

modeling, unless one of the above measurements seems more appropriate for the intended

locale.

3. Keell Statistics

Ice keels atre imiportant not ortly becaiuse they are a hindrance tc) unriutv aiefnvglo

but because of their effect on acoustic propagation and backscittering. Statistical informa-

tion on the properties of the keels is needed for analysis Of bomh Nh~cjtrira and fo~rwa,ýrd

To compute a distribution fuNctioin fhr ice keel dA-ft, a t-1l A-s frt I.- dcfincd. Thi.

is achieved using the analogous Rayleigh criterion in optics to define a keel as a downward

protrusion of ice with a trough on one side of the maximum draft that is at least halfway

toward the local level ice surface. which is arbitrarily defined as a draft of 2.-5 in. Expressed

mathemnatically, a feature with maximum draft, d. is a keel if the trough on one of the sidesis Jess than (d + 2.5) / 2 deep. This is aun arbitray efinitio of ka kee, aInd oel m e

with complex shape or odd size. it is not very satisfactory. It is used here, nevertheless.

because of the lack of a better one, and because it has been used by several other investiga-

tors.3031 Ilavinia used the same definition of a keel, we can compare our probability density

functions with theirs.

V- 16 TR 9407

ADR I99491


Straight-segment inder-ice profilesI hve Ueen ob.,aind ,ith;, n....... n.""r b6v

submarines during the SUBICEXs in which APL participated. The probability density func-

tion for ice keel drafts is shown in Figure 8. The figure shows best fits to the exponential

,'() = B exp (-bi) for keels with a draft, h, between 5 and 19 m (where N(h) is the number

of keels per kilometer with draft h). For the fall, use B = 4.0 keels per kilometer and b =0.47 per meter, for the spring, use B = 5.6 an,,d b = 0.38. The iniCa,,t ...f .er kee, i th.

fall than in the spring, which is reasonable since in the fall freezing is just beginning and

less ice is a'ailable for ridging. The spring distributions show fairly large differences

between the years. probably a function of the local conditions during freezing. Overall, our

data from the Beaufort Sea show fewer keels than data obtained in the central Arctic byother investigators.

E 10' . . . .............. Spring 1976, 35 km------- Fall 1982, 92 km- -.... Spring 1986, 38 km

LL 100 . Spring 1988, 62 kmr•c-- Spring 1988, 202 km,- - - Spring Average

LU I0.1 "

w 5 10 15 20KEEL DRAFT (m)

Figure 8. The distribution of maximnum drafts. of ice keels ob.srt-ed in thu undir.i.C profi~lr;obtained along given track v of a submarine.

TR9407 V-17

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D. ICE KEEL REFLECTIONS

In the Arctic, the returns from ice keels21'32--4 dominate all other forms of acoustic

backscatter. When short pulse lengths are used, the returns appear to be from discrete reflec-

tors. which, at times-, interfere. Some return; are certainly a combination of 11w) refllectoii,

perhaps three or four at timne;, that appear at the samne range. In this section, we summarize

what we have lea-ned about ice keels from an examination of somet !vpical refleCtinn-z

Sonmc modeling- is also included.

1. Point-Like Nature

W~hen a weapon -freque ncy transducer is rotated to make a 360' scan of the ice, using a

pulsed cwk transmuission, the return from indi%,iduall point-like reflectors will rise and fall.

rep~licating the beam pattern. Also, when a split-beam transducer is used, the left-right

phase difference varies uniformly to show the chaneoine dircection Ms the trtnsduce~r rm

If there are t%%o reflectors spaced a feN% degrees apart in azimuth, the return will be-in

to rise as the first is approached: then. a-, the two echioc; combfine, Ithe ampiillitud" II depitcolon thc relative phasc of the two echoes. This; relative phase depends on the range difference

and could he any value by chance. Figure 9 show; thc returns for pairs of reflections a! the

same range that overlap in a7zimuth. In the overlap region. the amplitude depends on the rel-

ative phase of the returns from the two reflectors. In (a) it follows the patterns well, but in

(b) the two overlappin.- returns "addj c0.rstruc,,*i.I

For the many reflectors that we have examined in this manner, about half hav'e a good

match to (he transducer pattern and hawe well-behaved p~hase angles, while (he other half

show definite signs of interference. This; ratio will hold true when implementing an ice keel

reflection model with the reflector denst reo;ne n the .v wii o ar-nh.

2. Reflector Density

A detailed examination of icc scans at an icc camp in the fall of 1984 -. showed that

there were 5.3 keels per square kilometer and that on the average each keel had 30 reflectors

V-I18 TR 9407


2 wayTransducer

TARGE'! Patien (a)STRENG 'Pt \ Rarge . i• m

15 35

Range =157fn? b

-2C 2 2

155

SCANJ AZIMJT-4I 1,,',

Figurte 9. Scans pa.st inteifering ice keel reflectors. The measured target strength devialte.from the tran iducer pattern ithen the reflet tions overlap.

and occupied an area with dimensions of 176 x 43 m. The actual shape of the kee! may be

less elongated because only one side of the keel i.s observed acoustically. Also, the keels

often meander in plan view.

The average density given above corresponds to an average reflector spacing within the

keel of 16 m. assuming that each reflector was an individual one. However, the overlap-

ping of echoes from reflectors indicates that they are more closely spaced. A suidy of ihe

interference between reflectors at different frequencies indicates a spacing of 3-4 ni (see

Section VD.4 below). The density of reflectors is no doubt hiohly variahl I in nvure Foir

modeling, we recommend using an averar'e spacing of 6 m.

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3. Response Pattern

An experiment in 1986 was designed to measure returns from a keel that fored after

the ice :anip was; occupied. WNe measured bistatic reflections at 20 k~lz using a receiving

transducer at a range of 110( m and a portable- omnidirectivlal trJA Im:ng tiandumcer yp-i-

tioned 15 mn from the keel. As the transmitter was lowered, sonie lrgpe echoes for succes-

sive pings shiowed a ý -rt~ical responsýe patter with a 3' wvidth (to -3 dB reduictions in targ-!

sitrcpgth for an equivalent moncistatic arrangemient). This agrees well with the ice block

response pattern at 20 kl-z shown in Figure 6, pos.-ihly indicating that the keel reflectors

had dimensions, similar to thc 58 cm udiai-eter jioe hbloc' A smarexperim-ent repo-mud by

McD4Iniel3lt showed somewhat narrower vertical response patterns. Wec have no hori7on1tal

response mea-kirements. but since ice keel blocks tend to be larger horizontally than veri-

cal1y. we assume that the horizontal pattern should be somewhat narrower.

4. FrequencY Dependence

An example of some returns from ridged ice at ranges of 560-1050 m is shown in Fig-ure 101 Th e o rd in.Ite i s t a r,!-t s o I e g1 h thAe g ' j! r 0po1,1,in a 4"- __.

to another indicates a decrease in keel reflecti\vit\ with increasing frequency. Some Inca-

surements for two selected keels (designated Keel A and Keel C) show the average amipli-

tude (convertcd to target strength ) decrcasing a aauu V1.9 ±-0 dIAA. cn'iUI II)

An experiment was perormed in 1986 in which the frequency of successive pings wa;shitedby k~.33 A close look at the returns in Figure 12 ihow httedtisi h

return vary greatly with small changes in frequency. There is no continuous trend, but rather

avariation that is thought to be duC to #th% 01"crercr4 Iewe C~~ kcun Sfro

reflectors at nearly the same range.

A measure of this variation with frequency is shown by the cross correlation of ampii-

tudes for two rcturns 2 kl-z apart in frequency (see Figure 13).3 The two 20 kHz pings

were from successive sets; thus t~hey spar t.hC othr% intm,. Th~ ~h ~ zo5

that time changes were not an influence. A 2 kHz shift. causes the correlation to drop below%

0.80. A computer simulation3 was run of the cot~eeation of randomly spaced reflector-, for

V-20 TR 9407

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________UNIVERSITY OF WA SHINGTON *APPLIED PHYSICS LABORATORY

F10-

20 kHz

U-20-

F v 'kHz

-30 .I~ JfII'P

8100 001201

TIME (ins)

Figure 10. An e-xample of fit,~ returns from the same ridged ice af tllree frequencies. !nterval Fis selected for expansion and wratmeni later. A general decrease in target strengthwith frequency is observed.

T*R9407 V-21

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0 0 T I

W Pulse

0 v 000-(ins)

C 0g .100.

'C

-2C 1.0

LU3 Keel A**.. 04

1.

20 30 43FREQUENCY (kHZ)

Figure II. A decrease in target strength n iW, incrt.-Sing.frequency is observed for two keels atrange 500 in at the 1986 ice camp. Each target strength is calculated for the aver-age amplilude of all rcflectors in tMe kee!.

a 0.4 ms pulse. According to the simulation. the measured correlations for Keel A would

indicate more than 73 refledorý in a 12 ms interval (see Figure 14). Considering a trans-

ducer beam 12: wide (two-way) and a range of 440 m. this, would correspond to a uniform

reflector spacing of less than 3.3 nm. For such a ,1•,1e number ref,.nor-, h,,,,e., ,,o

cross correlation is only weakly dependent on the number of reflectors, and thus cross cor-

relation doe" not give an accurate delermination of their number.

5. Modeling of Ice Keels

A model of an ice keel was developed by Ellison37 in which he built up a keel by stack-

ing ice blocks of random size and orientation. He then summed the reflections from allblock faces, using target strength response ,,rvs for n,.;m;A idsurfc., 16 Wiýt th. .Ad.utt...

of several parameters. his model gave a targct strength distribution that was similar to our

measured target strength distribution. This approach is a difficult one. Most ridges do not

V-22 TR 9407

Db 435 Fiche 2 06/24/95 05DSIA14453

UNIVERSITY Of WASHINGTON APPLIED PHYSICS LABORATORY

Frrquency

""A •20 kHz0 ... , I. ..... g jl, r• i

-31 L-

A _________________22 kHz

- b 2 , k H z

c 26 kHz

-30 -V 1• . 28 kiz

I, - p'* . 1".,

-30li

0 50 k00

I RELATIVE lIME (mns)

Fgigere 12. A comparison of returns at several frequencies for inrerm~al F in Fi•gu' IJ. Pulse.kengtl; is I nis. Inidvidual peaks in: fth retunl are aftost unre'cgni',ab, wlicn the'

i .f'eqtuency changes by 2 kHz.

TR9407 V 23

ADB 199453

TIME BETWEEN PINGS (s)1.0 25 5 10 15 20 15 10 5

== •0

I=U 0.9

0.8 0 /e . o *

< 0.7 ',20 22 24 26 28 30 35 40

FREOUENCY COMPARED (kHz)

Fhietre 13. An;p!itude correlation between the 100 ms samples of the closely spaced pingsshown in Figure 12. Each is compared with the 20 kHz return. Tie time betweenreturns varied from 5 to 25 s, as shown at 'he top of the graph. The correlationdrops sha rpy for a change of 2 kHt: infrequcncy.

z w 1.0

* "0.4 ms Pulse Length

S°I. ..... .... ... ...x .. .......

X ""r - -•- -� - -x- Keel A

.-.------- -'C c 0.7 • iI l

0 1o 100 150NUMBAI OF REFLECTORS IN 12 ms INTERVAL

Fi"itrc 14. "he modeled decrase in cross-(requencv correlation as the number of reflectorsincreases. The results are an aterage for 50 random selections of reflector ampli-tude and range. The dotted lines indicate the standard deviation. Correlation mea-surements .for returns from Keel A are shown by a dashed line. The intersection ofthe dashed line )it;h tile x-line gives a prediction of the number of reflec.tors inKee! A.

V-24 TR 9407

ADB 199453

UNIVERSITY OF WASHINGTON, APPLIED PHYSiCS LA6;ATI0;V

look like a pile of rectangular blocks. And .h... "o1l b'" sa" €"" "' "• bo.. For

confidence in the model, we need more checks along the way--e.g., a comparison between

modeled and measured reflections for an actual keel of known overall dimensions.

The desired model is one that converts an observable feature of an ice field to keel tar-get strengths. Satellite im"ges, aria" l photography- anse pr11i- give irformtiOn

ridge sails. only, and the correspondence between sails and keels in older ice is not suffi-

ciently known. The most likely usable observable feature, when an area of operation has

been specified. is an under-ice profile obtained with a submarine.

Bishop et al. 38 took an under-ice proffle , obta2ined, with , a ,,marjnP and , modeled ;,c5

keels to suit, using Ellison's ice keel model. They then predicted the acoustic return along

the submarine's track and compared the .averagc reverberation levels with the reverberation

levels measured with a fonvard-looking acoustic transducer mo..unted on 111C b "" "' ":

Although the agreement for specific areas along the track was poor, the averages for a 1 km

track agreed within a few decibels. The greatest source of error wa. the inconpatibi!ity

between the narrow-beam profiler and the wide beam of the transducer used to measure the

ice reflections; i.e., reflections were being included that came from keels too far off the pro-

file track to be detected.

A less basic model than Ellison's. but one with more accuracy and immediate useful-

ness, would be an "acoustic" model. Such a model would use anmpirically U- :r--' ""d

relationship between target strength distribution and the characteristics of the keels

observed in the under-ice profile. The data needed to deteryine this relationship ,re not

available.

II

TR 9407 V-25

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UNIVERSITY OF WASHINGTON. ADPLIED PHYSICS LABORATORY

REFERENCES-Section V

L. K. L. Williams and R. E. Francois, "Sea ice elastic moduli: Determination of Biotparameters using in-field velocity measurements," J. Acoust. Soc. Am., 91, 2627-2636(1992).

2. M.A. Biot. "Thcory of propagation of ciastic waves in a fluid-saturated porous solid.11. Higher frequency range.'* J. Acoust. Soc. Am., 28. 179-191 (1956).

3. G. F. N. Cox and W. F. Weeks, Equations for Determining the Gas and Brine Volumesin Sea Ice Samples. CRREL Report 82-30. Cold Regions Research and EngineeringLaboratory. Hanover. NH. 1982.

4. G. S. Sammclmann, "Biot-Stoll model of the high-frequency rcflection coeffiCje.,, ofsea ice."J. Acoust. Soc. Am., 94, 371-385 (1993).

5. D. A. McCammon and S. T. McDaniel. "The influence of the physical properties of iceon reflectivity." J. Acoust. Soc. Am.. 77,499-507 (19851.

6. K. L.. William,,. G. R. Garrison. and P. D. Mourad, "Experimental examination ofgrowing and newly submerged sea ice including acoustic probing of the skeletallayer." J. Acoisi. Soc. Am., 92. 2075-2092 (1992).

7. G. R. Garrison. R. E. Francois. and T. Wen. "Acoustic reflections from arctic ice at 15-300 kHz." .1. Acoust. Soc. Am.. 90. 973-984 (1991).

8. K. L. Williams. R. E. Francois. R. Stein. and J. C. l.uby, Acoustic For'ard ScatteringBeneath the Arctic Canopy at 25 and 45 kH7.: Experimental Procedure and Results.APL-U•W TR 9118, September 1991.

9. R. E. Francois, G. R. Garrison, E. W. Early, T. Wen. and J. T. Shaw, Acoustic Measure-ments Under Shore-Fast Ice in Summer 1977 (U). APL-UW 7825, March 1981. (Con-fidential

10. Tolystoy and C. S. Clay, Ocean Acoustics (American Institute of Physics. New York,1987*1.

11. D. E. Banrick. "Rough surface scattering based on the specular point theory." IEEE J.Trans. Antenna% Propag.. A P.1. 449-454 (1968 .

12. 6. S. Sammelmann, "High-frequency forward scattering in the Arctic.",I. A coast. Soc.Am., 94. 302-308 (1993).

V-26 TR 9407

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__UNIVERSITY OF WASHINGTON- APPLIED PHYSICS LABORATORY

13. K. L. Williams and D. E. Funk. "Acoustic Forward Scattering Beneath the Arctic Can-opy at 25 and 45 kHz: Experiment and Specular Point Theory," APL-LUV 9110. Sep-tember 1991.

14. T. K. Stanton. K. C. Jezek. and A. J. Gow, "Acoustical reflection and scattering fromthe underside of laboratory grown sea ice: Measurements and predictions." J. Acoust.Soc. Am.. 80, 1486-1494 (1986).

15. D. Winebrenner. "Acoustical backscattering from sea ice at high ft,,rquenc ies" ,TUW TR 9017, January 1991.

16. R.J. Urick. Principles of UnderwaterSOU1J ... r,, -7,,.. ,.- Yor,, .1983.

17. G.R. Garrison. E. A. Pence, and E.W. Early, Acoustic Studies from an Ice Floe NearBarrow, Alaska, in April 1974. APL-UW 7514, February 1976.

18. G.R. Garrison, R.E. Francois, and E.W. Early, Acoustic Studies from an Ice Floe in theChukchi Sea in April 1975. APL-UW 7608, August 1976.

19. G.R. Garrison, E.A. Pence, E.W. Early, and H.R. Feldman. Studies in the Marginal IceZone of the Bering Sea: Analysis of 1973 Bering Sea Data (U), APL-LUW 7410, Sep-tember 1974. (Confidential)

I 20. R.E. Francois and T. Wen, Use of Acoustics in Localizing Under-Ice Oil Spills, APL-UW 8309, June 1983.

I 21. G.R. Garrison. R.E. Francois. and T. Wen, Acoustic Returns from Ice Keels, 1982 (U),APL-UNW 8311, May 1984. (Confidential)

i 22. W.B. Tucker II. S.S. Devinder, and J.W. Govoni, "Structure of first-year pressurcridge sails in the Prudhoe Bay region," in The Alaskan Beaufort Sea. Ecosystems andI Environments. (Academic Press, Orlando. FL, 1984), pp. 115-135.

23. R.R. Parmerter and M.D. Coon, "Model of pressure ridge formation in sea ice," J.I Geophys. Res., 77,6565-6575 (1972).

24. W.B. Tucker Ill and J.W, Govoni, "Morphological investigations of first-year sea iceSpressure ridge sails," Cold Regions Science and Technology; 5. 1-12 (1981).

25. A. Kovacs. -On pressured sea ice," in Proceedings ofan international Coan'erence n11Reykjavik, Iceland. 1971 (National Research Council. Reykjavik, 1971).

IITR 9407 V-27

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26. A. Kovacs. W.F. Weeks, S. Ackley. and W.D. H-ibler ITT, A study of a multiyear pres-sure ridge in the Beaufort Sea. AlIDJEX Bull. 12. University of Washington, Seattle,1972.

27. T.L. Kozo and 0.1. Diachok. Spatial variability of topside and bottomnside icc rough-ness and it,, relevance to underside acoustic reflection loss. AIDJEX Bull. 19. Univer-

gieo Wsinton. Seattle. 1973.

28. R.E. Francois, High Resolution Observations; of Under-Ice Morphology. APL-Ok'77 12-. March 1977.

29. G.R. Garrison. R.E. Francois. E.NkW Early, and T. Wen. Comprehensive Studies of Arc-tic Pack Ice in April 1976. APL-UW ,7724, May 1978.

30. P. W'adhams and R.J. Horne, An analh,ýis of ice profiles obtained by submarinc sonar inthe Beaufort Sea, J. Glaciol.. 25. 401-424 (1980).

31. F. Williams, C. Swithinbank, and G, d Q. Robin, ^A subriarine ;onar sawdyv of wtc~tic-pack ice," J1. Gliwiol.. i5. 349-3621 (1975).

321. G.R. Garrison, R.E. Francois. and T. X%'cn. "Ice keels as false targets (U)," ANT~ J.Underwater Acou.¶t., 30. 423-437 (1980). (Confidential)

3.1 G.R. Gairrison. R.E. Francois, and TI Wen. Ice Keel Reflections NMe.'sur.ed in Srn1986 (U). APL-LrW 8912), April 1989. (Confidential)

34. C.R. Garrison. R.E. Francois. T. WVen. and R.P. Stein. Acoustic Reflections from. aNewly Formed Ice Keel (U). APL--W, 8507, September 1986. (Confidential')

35. Garrison, R.E. Francois, T. Wken. and R.P. Stein. Reflcctionq from Ice Keels. 1984 (U).APL-UW 3-86. December 1987. (Confidential

36. ST. McDaniel, Vertical Spatial Coherence of Backs.catter from Ice Keels (U). Tech.Note 86-172. Applied Research Laboratory. Pennsylvania State University., October1986. (Confidential)i

37. W.T. Ellison. Simulation Studies cof tinder-Ice Acoustic Scattering, (U). CambridgeAcoustical Associates. Inc.. 54 Rindge Ave. Extension, Cambridge. MA. October1980. (Confidential)

38. G.C. Bishop, XV.T. Ellison, and L.E. Mellherg, "A~ simulation model for high-fre-quency under-ice reverberation.�~ 1. Acoust. Soc. Am., 82, 275-2.86,iJuly 1987.

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REPORT DOCUMENTATION PAGE I___ ft ___01,_u €I c e:-i : g ec! riq - lot for 0•4•e4rof 5in0om a•,dr ! e arvited " Cv.' I haw Pot reswrse. ,nkiudng nb. t o ,,e fo" f m st',-g n *..,l s's. m lcr,, hg data IoUJc.., gathem, ; sAd

inamtaosg he :*-a -selel. and tev.ouirr the WW4I"c1b at ,norraa. oSed eoowdea r 1ga.9ing t*ti, wg.den emmate or ay other moper. as " ceoflotW ofl• o ,f'ce•..r . in.dg sug$goa •oo'ci eWrift.t " & t.rd.-. t0 Wasi.- O" kes: c.a'Ier Srvm s, Dir•eI'Irs, fof Wtorma'ho Opershns arnd RePAot 121 S .•, 4W1 Davis Highway. Siae 12^4. Alr, 0gi, VA 222'0432. sid lo-th Ie lrc4 04 ,: ftfant id Ftl~ig~aty Armin, OfC#" e- Vtamagiurwrd grid Bufet. Wastgt?,. DC 2CS03________________I 1. AGENCY USE ONLY (Loam W/ant) 2. REPORT DATE '. REPORT TYPE AND DATES COVERED

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I 6. AUTHOR(S)

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I REPORT NUMBERApplied Physics LaboratoryUniversity of Washington APL-1-JW/TR W7

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Distribution authorized to Department of Defense and DMID contractors only; SoftwareDocumentation. Date of Determination: April 1995. Other requestLsall be referred tothe Chief of Naval Research. 800 North Quincy Street. Arlington, VA 22217-5660.

13. ABSTRACT (Maxlmum 200 #ot0s.

I This report updates several high-frequency acoustic models used in simulations and system design by Navy torpedo and minecountermeasure programs. The models presented augment and supersed those given previously in APL-UW technical note7-79 (August 1979) and its successors, APL.UW technical reports 8407 and 8907. The report addresses the interaction of high-Sfrequency acoustic energy with the ocean's volume, surface, bottom, and ice. It also addresses ambient noise generated byphysical processes at the ocean surface and by biological organisms. The results are given in a form that can be exploited insimulations. The relevant fundamental experimental and theoretical research by APL and others upon which these models arebased is available in the references.

I

14. SUBJECT TERMS IS. NUMBER OF PAGESSpeed of sound; absorption coefficient; surface reverberation, volume reverberation, bottom 195reverberation: surface forward scattering and reflection; bottom forward reflection; ambient noise: 16. PRICE CODEarctic acoustics; sea state; ocean higb-frequency acoustic models: ocean environmental models

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Code N53(CDR Chris IHill) CommanderN534 (Bruce Northridge) Submarine Development Squadron TW, EIVE

Box 70Commander Naval Submarine Base-New LondonNaval Sea System; Command Groo CT 06349-5200A nton: DC 2 5 1Artn: Code N714 (LCDR Jessie Carmen. Oceanographer)

Atm: Code 91PMO-401 (George Tsuchida) CommanderPMO-407 (MIWV) (J. D. [Jim] Grembi) Submarine Group NINEPEO (1MW) (Dale G. Uhler) Bangor,WA 98315PEO (USW) (Timothy E. DougBrs)Angor APEO (USWT) (James N,. Thompson) Atm: Code N73 (LCDR Jun Hill. Staff Oceanographeri

IADB 199453

TR 9407 Initial Distribution ListMay 3, 1995

7170 0. S. ISteve) Stanic)Superintendent 7174 (Robert W. Farwell)U.S. Naval Postgraduate School 7174 (Richard H. Love)Monterey, CA 93943 7180 (Paul J. Bucca)

7180 (Cgorge A. Kerr)NA\T LABORATORIES 7181 (Stanley A. Chin-Bing)

7330 (Ming-Yang Su)

Commander 7333 (Kevin G. Briggs)Naval Air Warfare Center-Aircraft Division (NAWCAD) 7430 (Samuel G. Tooma)Patuxent. MD 20670-5304 7431 (Michael D. Richardson)

Atn: Claude Martin. MS-29. Blde. 3169 (Staff) Commander

Commander Naval Surface Warfare Center

Naval Air Warfare Center-Aircraft Diision Carderock Division

Wajininster. PA 18974-5020 Bethesda, MD 20084-5000

Atn: Library Attn: Library

Code 4.5.5.3.6 (Arthur W. Horbach, Bldg. 2) Director

Commanding Officer Naval Surface Warfare Center

Naval Command, Control & Ocean Surveillance Center Detachment Puget Sound

RDT&E Divtsion 530 Farragut Avenue

53560 Hull Street Bremerton. WA 98314-5215

San Diego., CA 92,152-5000 Atm: Code 704 (C. P. Henson)

Attn: Code 0274 Technical Libratry (Cathy Wright. 712 (Mike Schilt)

Librarian)02211 (Parr'ica A. Marsh) Commanding Officer532 (Robert W. Floyd) Naval Surface Warfare Center532 (Robet W. Flo)es)Coastal Systems Station78 (Paul M. Reeves) 60 et1lewv9782 (Bob Dukclow)783 (Robert J. Vent) Panama City, ML 32407-7001

807 (Jack T. Averyj Attn: Code E29 Technical Library10M (Elan Moritz)

Commanding Officer 130B (Raymond Liam)Naval Oceanographic Office 130B (Joseph L. Lopes)1002 Balch Boulevard 130B (Gary S. Sammelmnan)Stennis Space Center. MS 39522-5001 130B (Cynthia C. Weilert)Att: "technical Library 3110 (Kerry W. Commander)

Code N33 (Thomas A. Best -Database) 3110 (Robert V. Croft)

N333 (Richard H. Simmens) 3110 (William C. Littlejohn)

N341 (Robert F. Joyce - Product) Commander

Commanding Officer Naval Surface Warfare Center

Naval Research Laboratory Dahlgren Division, Detachment White Oak

4555 Overlook Avenue, S.W. 10901 New Hampshire Avenue

Washington. DC 20375-5000 Silver Spring. MD 20903-5000

Atti: Code 5200 l.ibrarv Attn: Library7100 (Edward R. Franchi - Head. Code AI0 (Charles F. McClure)Acoustics) R02 (Bernard T. DeSavagc. Jr.)71210 (Marshall 1t. Orr)7142 (Fred T. Erskine) Officer in Charge

Naval Undersea Warfare Center

Commanding Officer Arctic Submarine LaboratoryNaval Research Laboratory 49250 Fleming RoadDetachment Stennis Space Center San Diego, CA 92152-7210Stennis Space Center. MS 39529-5004 Ann: Code 906 (Robert M. Anderson)

Atm: Code 7170 (Roger W. Meridcth)7170 (Joe Posey)7170 (Dan J. Ramsdlale)

2


Commanding Officer LNIVERSITY LABORATORIESNaval Undersea Warfare CenterDivision Keyport The Johrs Hopkins UniversityKeypon, WA 98345,5000 Applied Physics Laboratory

Atn: Code 50 (Ernest E. Varnum - Weapons Johns Hopkins RoadSytitems Test Group) Laurel, MD 20723-6099

5540 (Glen A. Anunson) Att: Lee Danztler57 (Alan L. Lindstrom)70C1 (Robert Helon) The Pennsylvania State University

Applied Research LaboratoryCommander P.O. Box 30Naval Undersea Warfare Center State College, PA 16804-00.30Division Newport Attn: Library1176 Howell Street Carter L. AckermanNewpert, RI 02841-1708 Lee Culver

Atm: Code 0262 Technical Library Ralph Goodman22101 (Anthony F. Bessacini) Edward G. Liszlka2211 (Ma S. Davis, Jr.) Francis R. Menotti821 (James G. Kelly) Harvey S. Piper. Jr.8212 (Robert N. Carpcntcr) Dennis W. Ricker8212 (Adam Mirkin) Frank W. S)mons, Jr.8219 (Carl J. Albanese)823 (David Goodrich) University of California, San Diego842 (Frank E. Aidala. Jr.) Scripps Institution of Oceanography8423 (Carlo,; M. Godov) P.0. Box 60498423 (John R. Ventura) San Diego, CA 92166-6049

Attn M. Buckingham

Officer in Charge C. DcMouscievNaval Undersea Warfare CenterNew London Detachment Universiht of California. San DiegoNew London. CT 06320-5594 Scripps tIstitution of Oceanography

Attn: Library Marine Physical Laboratory, 0701Code 101 (Robert F. Laplantc) P.O. Box 6049

2122 (Albert Dugas. Jr.) San Diego, CA 92166-60493112 (Raymond J. Christian Atn: William Kuperman, Director3122 (Henry Weinberg) William S. Hodgkiss3122 (Thomas H. WbeeleiS3123 (Rudolph E. Croteau. Jr.) University of Texas at Austin33A (Joseph M. Monti) Applied Research Laboratory3314 (Roger J. Tremblay) P.O. Box 80293421 (David S. Cwalina) Austin, TX 7E713-802961 (Charles J. Baas)6291 (Gary N. Leticcq) Attn: Nicholas P. Cbotiros

H. Boebme

DEPARTMEN'T OF DIEFENSE I. WellmanTonm Muir

CommanderAdvanced Research Projects Agency INDUSTRY AND CONSULTING AGEXCiE,3701 North Fairfax DriveArlington. VA 22203-1714 Alliant Techsysteins In'.

t 600 Second Street NortheastAtm: William Carey 1oinNX 54

CAPT Bruce Dyer Hopkins, MN 55343Charles Stewart Attn: Paul Greenblat (MNW 1-2881 Ii

John Reeves ('MS-2865)

Defense Technological Information CenterCameron Station, Bldg. 5Alexandria. VA 22304-6145I

i


Alliant Techsystems Inc.Marine Systems Division6500 Ilarbour Heights Park-wayMukiltco, WA 98275-4844Attn: Ken Caproni (MS-4D16)

Analysis & Technology Inc.2341 Jefferson Davis Highway. Suite 1250Arlington. VA 22202

Atm: Eleanor Holmcs

Arete AssociatesP.O. Box 8050La Jolla. CA 92038

Atm: Don W. Miklovic

Hughes Aircraft Co.Aerospace Defense Section Surface SystemsGround Systems GroupP. 0. Box 3310Fullerton. CA 92634-3310

Manning Systems Inc.115 Christian LaneSfidell. LA 70458

Atm: Marshall R. Bradley

Planning Systems Inc.7923 Jones Branch DriveMcL.ean, VA 22102Aim: Charles W. Holland

Ravtheon Electronics Ss sterns Division528 Boston Post RoadSudbury.MA 01776Att: Stanley Chamberlain

Science Applications International Corporation (SAIC)P. 0. Box 1303McLean. VA 22102

Atm: Anthony I. Eller

Science Applications International Corporation (SAIe)P. 0. Box 658Mashpec. MA 02649

Atm: Ruth Keenan

Tracor Applied Sciences, Inc.35 Thomas Griffin RoadNew London, Cl 06320-6498Attn: Sean IM. Reilly

4

DEPARTMENT OF THE NAVYOFFICE OF NAVAL RESEARCH

800 NORTH QUINCY STREETARLINGTON, VA 22217-5660 IN REPLY REFER TO

5510/6Ser 93/17019 Feb 97

From: Chief of Naval ResearchTo: Administrator

Defense Technical Information Center (ATTN: RSR)8725 John J. Kingman RoadFt. Belvoir, VA 22060-6218

Subj: CHANGE IN DISTRIBUTION STATEMENT

Encl: (1) Copy of Report Cover 04D-i- /97 'IY3(2) Copy of SF 298

1. It is requested that the distribution statement for APL-UW TR 9407 report be changed to "A"- Approved for Public Release; Distribution Unlimited.

2. Since I do not know the AD number, enclosures (1) and (2) are provided for your information.

3. Questions may be directed to the undersigned on (703) 696-4619.

PEGGY LAMBERTBy direction

unclassified ad number - dticarctic (sound speed and attenuation [in ice], scattering and energy...

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