A SOFTWARE PACKAGEFOR ANALYSIS

OF GEOPHYSICAL MEASUREMENTS

John Frederick Arfman, Jr.

United StatesNaval Postgraduate School

HPT-J 1A "FT G - 3 y Ss>

A SOFTWARE PACKAGE FOR ANALYSIS

OF GEOPHYSICAL MEASUREMENTS

by

John Frederick Arfman, Jr

Thesis Advisor H. A. Titus

June 1971

Approved {on. puhtlc A.ale.ai<i; dLi&iibuXion untunute.d.

>G

LIBRA**NAVAL ro£TCTADUAT3 SCHOOL

n 4T,jp. 939-10

A Software Package for Analysis

of Geophysical Measurements

by

John Frederick Arfman, Jr.Ensign, United States Navy

B.S., University of New Mexico, 1970

Submitted in partial fulfillment of therequirements for the degree of

MASTER OF SCIENCE IN COMPUTER SCIENCE

from the

NAVAL POSTGRADUATE SCHOOLJune 1971

C-/

LIBRARYNAVAL POSTGRADUATE SCHOOLMONTEREY, CALIF. 92940

ABSTRACT

A software package for general analysis of real time

series for geophysical data was developed. The package

consists of FORTRAN IV callable subprograms that are as-

signed different tasks such as input, output (either

printed or graphical) , initial data analysis and filter-

ing , spurious data rejection, FFT, and spectral analysis.

A geophysical problem involving detection of unusual deep

ocean pressures was analyzed.

TABLE OF CONTENTS

I. INTRODUCTION 6

II. A GEOPHYSICAL PROBLEM 7

A. STATEMENT OF THE PROBLEM 7

B. A MODEL 7

III. A SOFTWARE SIMULATION 14

A. GENERAL APPROACH 14

B. DATA INPUT 16

C. INITIAL SCAN OF DATA 17

D. ADJUSTING THE SAMPLING INTERVAL 18

E. FOURIER ANALYSIS 22

F. FIRST DIFFERENCING 25

GT'Tnn CTiTcn ?£

H. RECTIFYING THE SIGNAL 26

I. INTEGRATION 27

J. OUTPUT 2 8

IV. CONCLUSIONS 31

APPENDIX 37

COMPUTER OUTPUT 71

COMPUTER PROGRAM 7 3

BIBLIOGRAPHY 76

INITIAL DISTRIBUTION LIST 77

FORM DD 14 73 7 8

LIST OF TABLES

TABLE

I. SUBROUTINES AND THEIR FORMAL PARAMETERS 15

II. SIGNAL-TO-NOISE RATIOS 32

LIST OF FIGURES

FIGURE

1. SCHEMATIC OF UNUSUAL EVENT DETECTOR 8

2. VIBROTRON PRESSURE DATA ANALYSIS - SPURIOUSDATA GATE DISABLED 13

3. CONCEPTUAL OPERATION OF SUBROUTINE PACK 21

4. VIBROTRON PRESSURE DATA ANALYSIS - SPURIOUSGATE ENABLED 34

5. POWER SPECTRUM OF TIDE FILTER OUTPUT 35

6. POWER SPECTRUM OF DETECTOR OUTPUT 36

I. INTRODUCTION

The types of real time series considered here are geo-

physical processes. Usually, time is the independent vari-

able and such quantities as velocity and direction of flow,

temperature, and pressure are the dependent variables. In

the analysis and design of geophysical experiments, it is

useful to have at one's disposal a set of software sub-

routines to aid in this analysis. Thus, a software pack-

age for general analysis of real time series geophysical

data was developed. The package consists of FORTRAN IV

callable subprograms that are assigned different tasks such

as input, output (either printed or graphical), initial

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spectral analysis, and so forth. A geophysical problem

involving detection of unusual deep ocean pressures was

analyzed

.

II. A GEOPHYSICAL PROBLEM

A. STATEMENT OF THE PROBLEM

Throughout nature there exist many phenomenon that

occur only as "unusual events." In the realm of oceano-

graphy one such unusual event is called a tsunami. The

word tsunami comes from the Japanesse and means storm wave.

It is known that the presence of a tsunami is indicated by

a definite change in water pressure. Other information

concerning the velocity and direction of the current, water

temperature, salinity, and so forth, would also be useful

in the analysis and understanding of these events. However,

the infrequent rate at which tsunamis occur makes their

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these events, methods were devised to detect and record

them. The problem then is to logically design a detector

that will automatically sense the presence of a tsunami

and cause all the pertinent data to be recorded.

B. A MODEL

In order to determine the presence of an unusual event,

a detector which receives digitized pressure data was de-

signed [1] . Throughout the following discussion refer to

Figure 1 for the logical design of the detector. The de-

tector can be divided into six logically separate sections.

Data Input . Digital pressure sensors of varying

degrees of sophistication and reliability are presently

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available on the commercial market. Digital sensors

generally count the number of cycles of a pressure sensi-

tive oscillator over a given time interval. This summa-

tion in effect integrates the pressure signal. The

integration process serves as a low pass filter. That

is, high frequency pressure variations relative to the

sampling interval tend to average out, thus contributing

equally to each sample. This filtering of high frequency

variations might prove undesirable in some applications.

For this particular problem, however, almost all of the

high frequency variations are naturally filtered out be-

cause of attenuation of pressure variations due to ocean

depth.

It was determined thai the frequency band in which

tsunamis occur extends from \ to 30 cycles per hour.

Nyquist frequency theory indicates that in order to detect

a frequency of N cph , a sampling rate of at least 2N cph

is required. Hence the sampling interval was determined

to be one sample per minute.

Input Buffer . An input buffer receives the most re-

cent pressure reading in digitized form. The actual hard-

ware implementation of the input buffer is not part of the

problem. Conceivably the input buffer could be anything

from an acoustic delay line to a magnetic core.

The buffer is large enough to retain the most recent

121 consecutive samples. Hence, a two hour history of

pressure data is available for analysis at any one time.

Figure 2(a) is a plot of typical pressure data over an 80

hour period.

First Differencin g. The presence of a tsunami could

be indicated by an abnormal change in pressure from one

point in time to another. The phrase "change in pressure"

indicates that the derivative should be computed. As a

close approximation to the derivative, the positive first

difference was determined.

Incorporated within the first differencer was a spur-

ious data gate. Here each first difference was compared

against a preset threshold value. If the threshold value

was exceeded, then a sensor error (spurious error) was the

probable cause since deep-ocean pressure changes are rela-

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difference might falsely indicate the presence of a tsunami,

an excessive first difference was set equal to the previous

first difference. The threshold value was determined after

analysis of test data. First differencing, as computing

the first derivative, removes the mean pressure value and

suppresses drift. Figure 2(b) illustrates the effect of

first differencing on the data of Figure 2(a).

Tide Filter . The purpose of the tide filter is to

remove the effects of the diurnal and semi-diurnal tides.

This was accomplished by forming a weighted sum from the

sample data at h hour intervals. The coefficients were

determined from analysis of the tidal spectrum. The tide

filter output then is:

10

D«. = dP + - 3.920392-dP,. xn + 5 . 841800 -dP + , nt t t-30 • t-60

- 3. 920392- dPt . 9Q

+ dPt . 120

where dP is the first difference at time t [2]

.

Figure 2(c) shows the effect of the tide filter on

the first differenced data of Figure 2(b). Note how the

tide filter extended the effects of a spurious data value

when there was no spurious data gating.

Rectification . As Figure 2(c) shows, the output of

the tide filter presents an erratic picture of the changes

in pressure. In order to observe any trends in this data,

an integral over some fixed period of time needed to be

computed. Any integration of the tide filtered data

would only produce a result close to zero. This problem

was overcome by taking the absolute value of the data in

two ways; that is, the negative data values were made

positive so that the data was no longer distributed about

zero. The most straightforward method was to simply ignore

the sign (i.e., rectification) of each number outputted

from the tide filter. The second method was to square each

value. Figure 2(d) shows the result of squaring the tide

filter output.

Integration and Detection . The rectified or squared

tide filtered data was then integrated. The method of

integration was based on the solution of a differential

equation. The general form of the integrating function is:

11

y. + -,= e

a(y t

+xt ) > t = 1,2,3,... minutes

and where y, =,

a = a time constant associated with the inter-

val of integration,

x = the data to be integrated (rectified or

squared output of tide filter)

.

The value of a was determined experimentally via the simu-

lation (a = 1/60). Figure 2(e) is a plot of the integrated

tide filtered pressure data after the squaring process.

Dependent on the value of a, a critical threshold

value had to be chosen such that whenever the integrated

signal exceeded this value, a switch was closed causing

the contents of the buffer to be recorded on a tape or

otherwise be permanently recorded. At the end of a two

hour period of normal input the buffer would once again

be recorded. At this point the value of the integrated

signal would be tested again. If the integrated signal

was still greater than the threshold value, then the buf-

fer would again be recorded after two hours; otherwise

after two hours the testing is resumed as before. This

technique guarantees that a minimum four hour record will

be available for each event detected.

12

(a)

(b)

(c)

(d)

(e)

16

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si 48 64 hours 80

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FIGURE 2. (a) Pressure, (b) First Differenced Pressure (spur

ious Data Gate Off), (c) Tide Filtered Pressure,(d) Squared Tide Filtered Data, (e) IntegratedSignal Versus Time in Hours.

13

III. A SOFTWARE SIMULATION

A. GENERAL APPROACH

To be generally useful a software package must be able

to simulate a real system on the level of logical components.

That is, the basic information extracting procedures of the

system must be available for graphical or statistical anal-

ysis during the simulation. Accordingly, the following set

of eighteen FORTRAN callable subprograms was developed.

The subprograms and their associated formal parameter are

listed alphabetically in Table I. The subprogram UNIFRM

is a function subprogram and XYAXIS is an entry in DRAW1

.

Otherwise all the subprograms listed in Table I are sub-

routines. The various subprograms are explained in the

following sections according to their use in the unusual

event problem. Each subprogram is listed in its entirety

in the Appendix.

Each subroutine uses the variable FILE as its first

formal parameter. The meaning and use of FILE will be

given once here to avoid duplication in the sections which

follow.

FILE is a real-valued variable identifying the current

data file. This number is for user identification purposes

only. FILE is usually set equal to 1.0 or the DO-loop in-

dex if the simulation is being performed iteratively. When

a subroutine is called, a message is printed indicating

that the subroutine has completed its task. The message is

of the form:

14

SUBROUTINE FORMAL PARAMETERS PAGE

ANT IDE (FILE,

(FILE,

Y,

Y,

TIDE, L)

L)

26

CARDS 16

DRAW1 (FILE,

(FILE,

Y.

A.

L, YMAX, YMIN, LOG, XL,

B, N, ISN)

XI) 29

FFREAL 23

FFT (FILE, A; B, N, ISN) 23

FIRSTD (FILE, Y;DIFF, L, THRESH) 25

HARMON (FILE, Y,YH, L, HI, H2) 24

INTGRL (FILE x, Y, L, FTC) 27

OUTPUT (FILE, Y.

L) 28

PACK (FILE,ISEED

Y

)

, L, Y2, L2, IDEN, RAMP,19

POWER (FILE, Y. L, XL, XI) 25

RECSQR

(FILE, Y

(FILE, Y

(FILE, YYSTDEV)

(FILE, Y

(ISEED)

(XAL, YA1

v 9 t t n c "\

fl w

Ji-J

?± 1\C> J

, L, Y2, L2)

, L, YMEAN, YSTDEV, L2)

, L, YMAX, YMIN, YMEAN,

,L)

26

RESET 18

SCAN . 17

STATS17

TAPE 16

UNIFRM 22

XYAXIS 29

TABLE I.

Subroutine Names, Formal Parameters, and Page References

15

FILE NO. XX. X "message".

The digits XX. X indicate the current value of FILE. Execu-

tion of subroutine DRAW1 causes FILE to be incremented by

0.1.

B. DATA INPUT

CALL CARDS (FILE, Y, L)

CALL TAPE (FILE, Y, L)

Data input is accomplished by calling one of the above

subroutines. The meaning of each of the formal parameters«

is :

FILE - see Section III. A.

Y - A real, singly dimensioned array into \\rhich

the data is to be read.

L - An integer- valued variable equal to the size

of array Y. In subroutine CARDS, L must equal

the number of data elements to be read-in. In

subroutine TAPE, L may equal the number of

data elements to be read-in, or it may equal

the maximum size of Y as defined in the DIMEN-

SION statement of the main program. If an

end-of-file mark is encountered on the tape

before the L data elements have been read, the

subroutine halts and returns the number of ele

ments actually processed as the value of L.

These subroutines should be reloaded with the proper

FORMAT statements inserted before the simulation is run.

Currently the FORMAT is (10F7 . ,F10 . 0) .

16

C. INITIAL SCAN OF DATA

CALL STATS (FILE, Y, L, YMAX , YMIN, YMEAN, YSTDEV)

CALL SCAN (FILE, Y, L, YMEAN, YSTDEV, L2)

It is sometimes the case when geophysical data is being

recorded that the initial start up of the sensing device

intorudces spurious data which is recorded as valid data.

Used in series , subroutines STATS and SCAN can determine

the extent of any start up noise present in the data.

The meaning of each of the formal parameters is:

FILE - see Section III. A.

Y - A real-valued, singly dimensioned array con-

taining the data to be analyzed. Neither

subroutine alters the contents of array Y in

any way

.

L - An integer-valued variable equal to the size

of array Y.

YMAX - A real-valued number returned by subroutine

STATS equal to the maximum value encountered

in array Y.

YMIN - A real-valued number returned by subroutine

STATS equal to the minimum value encountered

in array Y.

YMEAN - A real-valued number returned by subroutine

STATS equal to the statistical mean of the

data in array Y.

YSTDEV - A real-valued number returned by subroutine

STATS equal to the standard deviation of the

data in array Y.

17

L2 - An integer-valued number returned from sub-

routine SCAN equal to the number of noise

dependent elements in array Y as determined

from the following procedure.

1) set 1=1, set ITEST=0.

2) If ABS(Y(I)-YMEAN)>2*STDEV then set

ITEST=0, set L2=I

;

otherwise, set ITEST=ITEST+1

.

3) If ITEST > 100 then return; otherwise

set 1=1+1, go to step 2.

D. ADJUSTING THE SAMPLING INTERVAL

CALL RESET (FILE, Y, L, Y2 , L2)

CALL PACK (FILE, Y, L, Y2 , L2, IDEN, RAMP, ISEED)

UNIFRM (ISEED)

The sample size of data to be analyzed can be adjusted

in two basic ways. First, the sampling interval may be

shifted forward by any specified amount. For example, if

preliminary analysis of the data indicates that the initial

data elements are in error, then the data file can be re-

set so that the record begins later in the sequence, there-

by skipping the bad data. This is accomplished by a call

on subroutine RESET. The formal parameters of RESET are:

FILE - see Section III. A.

Y - A real-valued, singly dimensioned array con-

taining the data to be reset.

L - An integer-valued variable equal to the size

of array Y.

18

Y2 - A real-valued, singly dimensioned array into

which the reset elements of array Y are to be

loaded. Arrays Y and Y2 may be the same

physical array in which case the skipped data

is overlayed and lost to further processing.

L2 - An integer-valued variable. On the initial

call to RESET, L2 equals the number of data

elements in array Y which are to be skipped.

On return, L2 equals the size of array Y2.

The second method of adjusting the sampling interval

involves increasing the density of the data points. This

is accomplished by a call on subroutine PACK. The formal

parameters of PACK are:

FT f P _ c e\ r* C rt r -f i Ap A

Y - A real-valued, singly dimensioned array con-

taining the data to be packed.

L - An integer-valued variable equal to the size

of array Y.

Y2 - A real-valued, singly dimensioned array into

which the expanded (packed) data of array Y

is to be placed. Arrays Y and Y2 may be the

same physical array.

L2 - An integer- valued variable. On the initial

call to the subroutine, L2 must equal the

maximum size of array Y2 as declared in the

dimension statement of the main program. On

return, L2 will equal the size of array Y2

19

as declared in the dimension statement of

the main program. On return, L2 will equal

the size of array Y2 if the subroutine com-

pleted successfully. The size of array Y2

can be determined from the formula (L-l)x

IDEN+1.

IDEN - An integer-valued variable specifying the

multiple of the current density that is de-

sired. The value of IDEN in part determines

the value of L2 that is returned to the main

program. IDEN can also be interpreted to

mean that IDEN-1 points are embedded between

each of the original points in array Y.

PwAM^ - \ v>r> al - v alue d ,ra ri?ble e^ual to the maximum

variability allowed when the embedded points

are being computed. If RAMP = 0.0 then the

embedded points are determined by linear in-

terpolation between successive Y values;

otherwise, the value of RAMP is multiplied

by a uniformly random number between -%, and

^, and this value is added to the interpolated

value

.

ISEED - An integer-valued variable that serves as the

random number seed for a random number gener-

ator. ISEED should be a six digit integer

equal to ±3(mod 8).

Conceptually subroutine PACK embeds the data as shown

in Figure 3.

20

(PRESSURE)

Y(I+1)

Y(I)

->

>A

embeddedpoints

"TRAMP

I

1 + 1

INDEX

FIGURE 3.

Conceptual Operation of Subroutine PACK where RAMP >

and I DEN = 4.

21

Function subprogram UNIFRM returns a uniformly random

number between -\ and ^. The use of UNIFRM is not re-

stricted to subroutine PACK.

The original data used in the simulation was based on

a four minute sampling interval. The detector, however,

was designed to operate on one minute data. Hence, to ob-

tain the proper sampling interval the following call was

made on subroutine PACK.

CALL PACK (FILE, Y, L, Y, LMAX , 4, 0.0, 103941)

LMAX equals the maximum* size of array Y as dimensioned in

the main program. Note RAMP equals zero.

E. FOURIER ANALYSIS

TAT T pFRFAT fPTLE ARM TSN^

CALL FFT (FILE, A, B, N, ISN)

CALL HARMON (FILE, Y, YH , L, HI, H2)

CALL POWER (FILE, Y, L)

Three areas of Fourier analysis are provided for in

the software package. Subroutine FFREAL returns the Fourier

cosine and sine coefficients of the data passed to it. Sub-

routine HARMON returns the approximation to the data passed

to it on the basis of the HI through H2 harmonics. Sub-

routine POWER returns the power spectrum of the data. Sub-

routine HARMON and POWER both call on FFREAL, and FFREAL in

turn calls on subroutine FFT. Subroutines FFREAL and FFT

are variations of Singleton's [3] algorithms for mixed radix

fast Fourier transform.

22

The formal parameters of subroutine FFT are:

FILE - see Section III. A.

A, B - Real-valued, singly dimensioned arrays. Ar-

rays A and B originally hold the real and

imaginary parts of the data and return the

real and imaginary Fourier coefficients.

N - An integer-valued variable equal to the num-

ber of real (or imaginary) data elements.

In the context of this paper, N=L/2.

ISN - An integer- valued variable. The magnitude of

ISN determined the step size of data in ar-

rays A and B. The sign of ISN determines

whether the complex or inverse transform will

be performed.

The formal parameters for subroutine FFREAL are:

FILE - see Section III. A.

A, B, - Real-valued, singly dimensioned arrays. The

original data values are alternately stored

in arrays A and B. On return, arrays A and

B hold the cosine and sine coefficients re-

spectively, of the transform.

N - An integer- valued variable equal to the num-

ber of elements in array A. In the context

of this paper, N=L/2.

ISN - An integer- valued variable. The magnitude of

ISN determines the step size within arrays A

and B. If the magnitude of ISN is 1, then

23

each consecutive element of the array is used

in the computations. If the magnitude is 2,

every other element is used. Hence, if the

data is contained within a single array, say

X, rather than two separate ones, the call

to FFREAL would be

CALL FFREAL (X, X(2) , N, 2).

If the sign of ISN is negative, then the in-

verse transform is computed.

The formal parameters of subroutine HARMON are:

FILE - see Section III. A.

Y - A real-valued, singly dimensioned array orig-

XUdxx^ ^OiH-aillliig Cii^ v-t a. i, a. t~ <-> u L, aiia-i.) *_ »_ ti .

On return array Y contains the Fourier co-

sine and sine coefficients as returned from

FFREAL.

YH - A real-valued, singly dimensioned array which

on return holds the approximation based on

the HI and H2 harmonic of the data originally

contained in array Y. This process involves

a double summation and could be time consum-

ing depending on the values of HI and H2.

L - An integer-valued variable equal to the size

of array Y (or array YH)

.

HI, H2 - Positive integer- valued variables indicating

which harmonics, HI through H2, inclusive, of

array Y are to be isolated.

24

The formal parameters of subroutine POWER are:

FILE - see Section III. A.

Y - A real-valued, singly dimensioned array con-

taining the data which is to have its power

spectrum computed. On return, the power

spectrum coefficients are in the first N=L/2

elements of array Y.

L - An integer-valued variable equal to the size

of array Y.

F. FIRST DIFFERENCING

CALL FIRST.D (FILE, Y, DIFF, L, THRESH)

Subroutine FIRSTD computes the positive first dif-

ference of the data in array Y, and returns the array of

first differences in array DIFF. The first and last ele-

ments of DIFF are zero. Subroutine FIRSTD is so coded that

arrays Y and DIFF may be the same physical array. By set-

ting THRESH to any computed value, any first difference

greater than THRESH will cause that first difference to be

set equal to the previous first difference.

The formal parameters of subroutine FIRSTD are:

FILE - see Section III. A.

Y - A real-valued, singly dimensioned array con-

taining the data to be first differenced.

DIFF - A real-valued, singly dimensioned array which

returns the positive first differences of the

data in array Y.

25

L - An integer-valued variable equal to the size

of array Y (or array DIFF)

.

THRESH - A real-valued variable against which each

first difference is compared. If the current

first difference is greater than THRESH

(threshold value) , then the first difference

is set equal to the previous first difference.

G. TIDE FILTER

CALL ANTIDE (FILE, Y, TIDE, L)

Geophysical events usually occur in the domain of other

less interesting phenomenon. In the case of the unusual

event detector, one such phenomenon is the effect of the

tides, both diurnal and semi-diurnal. Subroutine ANTIDE

(anti-tide) filters out the combined effect of these tides.

The formal parameters of subroutine ANTIDE are:

FILE - see Section III. A.

Y - A real-valued, singly dimensioned array con-

taining the data to be tide filtered.

TIDE - A real-valued, singly dimensioned array into

which the tide filtered data is placed. Ar-

rays Y and TIDE may be the same physical ar-

ray.

L - An integer- valued variable equal to the size

of array Y (or array TIDE)

.

H. RECTIFYING THE SIGNAL

CALL RECSQR (FILE, Y, Y2 , L, IRS)

Two methods of rectifying the data are provided. The

26

first involves taking the absolute value of each data value;

while the second squares each data value.

The formal parameters of subroutine RECSQR (rectify-

square) are :

FILE - see Section III. A.

Y - A real-valued, singly dimensioned array con-

taining the data to be rectified or squared.

Y2 - A real-valued, singly dimensioned array into

which the rectified or squared data is to be

placed. Arrays Y and Y2 may be the same

physical array.

L - An integer-valued variable equal to the size

of array Y (or array Y2)

.

IRS - An in Lege i- valued variable equal to 1 or 2.

If IRS = 1, then the data will be rectified

by computing the absolute value of each ele-

ment. If IRS = 2, then the data will be

rectified by computing the square of each

element

.

I. INTEGRATION

CALL INTGRL (FILE, X, Y, L, FTC)

Integration is performed by multiplying the sum of

previous data elements by a fading time constant (FTC)

;

that is some positive number less than unity. The form of

the integrating equation is:

Y(I) = EXP(-FTC) * ( Y(I-l) + X(I) )

27

where FTC is the fading time constant, and I is the index

of the current variable.

The formal parameters of subroutine INTGRL are:

FILE - see Section III. A.

X - A real-valued, singly dimensioned array con-

taining the data to be integrated.

Y - A real-valued, singly dimensioned array into

which the integrated data is placed.

L - An integer-valued variable equal to the size

of array X (or array Y)

.

FTC - A real-valued variable. A sample value of

FTC could be 1/60.

J. OUTPUT

CALL OUTPUT (FILE, Y, L)

CALL DRAW1 (FILE, Y, L, YMAX, YMIN, LOG, XL, XI)

CALL XYAXIS (XAL, YAL)

Two means of output are provided. Subroutine OUTPUT

prints out the first L elements of array Y. The page for-

mat of OUTPUT is 200 numbers with index numbers per page.

The formal parameters of subroutine OUTPUT are:

FILE - see Section III. A.

Y - A real-valued, singly dimensioned array con-

taining the data to be printed.

L - An integer-valued variable equal to the num-

ber of elements of array Y that are to be

printed. L may equal the full size of array

Y in which case a large quantity of paper is

usually generated.

28

Subroutine DRAW1 plots the first L elements of array

Y. The formal parameters of subroutine DRAW1 are:

FILE - see Section III. A.

Y - A real-valued, singly dimensioned array con-

taining the data to be plotted. Subroutine

DRAW1 does not alter the contents of array Y.

L - An integer-valued variable equal to the num-

ber of data points to be plotted.

YMAX, - Real-valued variables equal to the maximum

YMIN and minimum values to be plotted. If YMAX <

YMIN, then the plot is autoscaled.

LOG - An integer -valued variable equal to or 1

.

If LOG = 1, then the data in array Y is plot-

i,V_ U. VJll J- \_/ g . . JV^CXXO. NjcilV-.Iwi.JV_., A. J- l_IW^ \J

the data is plotted in the normal fashion.

XL, XI - Real-valued, singly dimensioned arrays con-

taining literal constants. The maximum length

string allowable is 40 characters. XL is the

plot label which may be blank, and XI is the

user's identification label.

The lengths of the plot axes are initialized to 20

inches for the x-axis and 8 inches for the y-axis. However,

these dimensions may be changed by calling XYAXIS. The for-

mal parameters of XYAXIS are:

XAL - A real-valued variable equal to the new length

of the x-axis in inches.

29

YAL - A real-valued variable equal to the new length

of the y-axis in inches. The value of YAL

should be less than 9 inches.

Subroutine DRAW1 (and XYAXIS) make use of the standard

plot package for the CALCOMP 765 plotter available on the

IBM 360 at the Naval Postgraduate School.

30

IV. CONCLUSIONS

In the detector, the question arose as to what was the

best value of the fading time constant used in the integra-

tion scheme. That is, given the form of the integrating

equation and that integration is naturally a low pass fil-

ter, what value of the fading time constant would produce

the most favorable signal-to-noise ratio? Three values of

the time constant were chosen, and the integration was per-

formed three times on the squared output of the tide filter

with a different time constant in effect each time. The

value of the constant used to produce Figure 2 was 1/60.

The significance of this value is that because of the struc-

ture of the inte a r?-tin a equation the contribution of a

single data value after one hour's integration would have

been reduced to one third of its original effect. This

value of the time constant was used. The other two values

of the time constant considered were 1/30 and 1/120.

Table II shows the results of two signal-to-noise ratio

computations using the three constants. The two hour

"threshold" level to noise ratio was computed by finding a

level such that the signal exceeded that level for exactly

two hours

.

The integrations were performed a second time but the

rectified rather than the squared output of the tide filter

was used. The ratios computed from these integrations are

also given in Table II.

31

i

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32

From examination of Table II, it was determined that

a value of 1/60 for the fading time constant gave the most

desirable results when the integration was performed on the

squared output of the tide filter. From inspection of the

output statistics of the first differences, the standard

deviation of the first differenced pressure data was ap-

proximately eight. Hence, a three sigma value of 25 was

chosen as the threshold value of the spurious data gate

in the first differencing subroutine. Figure 4 shows the

effect of the spurious data gate on the detector output

when this threshold limit was set at 25. Figure 4 also

represents a fading time constant value of 1/60 applied

to the integration of the squared output of the tide fil-

ter. (Compare Figures 2 and 4.)

The critical threshold value of the unusual event de-

tector was determined to be three times that of the back-

ground signal of Figure 4(e). Hence, the three events

detected in Figure 4(e) will cause the recorder to be ac-

tivated.

The power spectra [4] of the tide filter and detector

outputs are shown on Figures 5 and 6, respectively. In

Figure 5 the null power readings coincide with even cph

,

and the peaks coincide with odd cph. This result agrees

with the characteristics of the tide filter. The nodes of

the power spectral plot of the detector output do not ex-

actly agree with those of the tide filter because of the

effect of the integration process.

33

16 32 48 64 hours 80

Ai*4-4 t\Jk -A

m.MPS^

k

f IP 1

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16 32 48 64 hours 80

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16 32 48 64 hours 80

13

illj;j_lLi^ -^ ..':•» '» L»

16 32 48 64 hours 80

^0

#"\J j^jt

16 32 48 64 hours 80

FIGURE 4. (a) Pressure, (b) First Differenced Pressure (Spurious

Data Gate On), (c) Tide Filtered Pressure, (d) SquaredTide Filtered Pressure, (e) Integrated Pressure VersusTime in Hours

.

34

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75

BIBLIOGRAPHY

1. Titus, H. A., and Terman, F. W., "Detection of Non-stationary Processes," Proceedings of the FourthHawaii International Conference on System Sciences

,

p. 380-382, 1971.

2

.

Ibid .

3. Singleton, R. C, "An Algorithm for Computing theMixed Radix Fast Fourier Transform," Transactionson Audio and Electroacous t ics , V. AU-17, No. 2,

p. 95-103, June 1969.

4. Jenkins, G. W. , and Watts, D. G., Spectral Analysisand its Applications , Holden-Day, San Francisco,Caliiornia, p. 209-255.

76

INITIAL DISTRIBUTION LIST

No. Copies

1. Defense Documentation CenterCameron StationAlexandria, Virginia 22314

2. Library, Code 0212Naval Postgraduate SchoolMonterey, California 93940

»

3. Assoc Professor Harold A. Titus, Code 52TsDepartment of Electrical EngineeringNaval Postgraduate SchoolMonterey, California 93940

4. ENS John F. Arfman, Jr., USN7608 Harwood Avenue, N.E.Albuqueque , New Mexico 87110

77

UNCLASSIFIEDSecurity Classification

DOCUMENT CONTROL DATA -R&DiSecunly c las si t tc at ion of title, body of abstract and indexing annotation must be entered when the overall report is classified)

l originating activity (Corporate author)

Naval Postgraduate SchoolMonterey, California 93940

2a. REPORT SECURITY CLASSIFICATION

UNCLASSIFIED2b. GROUP

3 REPOR T TITLE

A SOFTWARE PACKAGE FOR ANALYSIS OF GEOPHYSICAL MEASUREMENTS

4 DESCRIPTIVE NOTES (Type of report and.inclusive dates)

Master's Thesis; June 1971S <u TMORiSi (First name, middle initial, last name)

John F. Arfman, Jr.

6 REPOR T D A TE

June 1971la. TOTAL NO. OF PAGES

79

7b. NO. OF REFS

4

la CONTRACT OR GRANT NO

6. PROJEC T NO

9a. ORIGINATOR'S REPORT NUMBERIS)

9b. OTHER REPORT NO(S) (Any other numbers that may be aa signedthis report)

10 DISTRIBUTION STATEMENT

Approved for public release; distribution unlimited.

I). SUPPLEMENTARY NOTES 12. SPONSORING MILITARY ACTIVITY

Naval Postgraduate SchoolMonterey, California 93940

13 ABSTRACT

A software package for general analysis of real timeseries for geophysical data was developed. The packageconsists of FORTRAN IV callable subprograms that are as-

signed different tasks such as input, output (eitherprinted or graphical) , initial data analysis and filter-ing, spurious data rejection, FFT , and spectral analysis.A geophysical problem involving detection of unusual deepocean pressures was analyzed.

DD, r

N°o

RvM473 (PAGE nUNCLASSIFIED

S/N 010) -807-681 1 78 Security Classificationa-31408

UNCLASSIFIEDSecurity Classification

key wo R OSLINK A

HOLE ROLE

Spurious Data Rejection

Tsunami

Real Time Series

Spectral Analysis

Nyquist Frequency

D,T„M.,1473 iback

I 01 Ot - 607-682 1 79UNCLASSIFIED

Security Classification

^Nvr 6»2 3 8 9 7

3 6

128334ThesisA653 Arfman

c.l A software package

for analysis of geo-

physical measurements.

238979iMVf 61

> o

Thesi s 128334A653 Arfmanc.l A software package

for analysis of geo-physical measurements.

thesA653

A software package for analysis of geoph

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