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THEORETICAL DEVELOPMENT FOR LOW DISTORTION BROADBANDING OF SEISMIC DATA

Lewis J. Pinson, et al

ENSCO, Incorporated

Prepared for:

Air Force Office of Scientific Research

1 June 1973

DISTRIBUTED BY:

National Technical Information Service U. S. DEPARTMENT OF COMMERCE 5285 Port Royal Road, Springfield Va. 22151

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NATIONAL TECHNICAL INFORMATION SERVICE

EIMSCO.IIMC. 5408A Port Royal Road

Springfield, Virginia 22151

Phone: (703) 569-9000

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THEORETICAL DEVELOPMENT

FOR LOW DISTORTION BROADBANDING

OF SEISMIC DATA-INTERIM

TECHNICAL REPORT

AFOSR CONTRACT NO: F44620-73-C-0Ü64

TR-1002-01

June 19 73

Sponsored by:

Advanced Research Projects Agency rfClUI ARPA Order No.: 2 50 6

Prepared by:

BNSCO, INC. 8001 Forbes Place

Springfield, Ya. 22151

A I h Technicp1 Pi ector

birector, iss Division

y:Q./::, ̂ c3 — Principal Investigator

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Theoretical Development for Low Distortion Broadbandiflg oi" Seismic Data - Interim Report

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Lewis J. Pins on Paul V.', Broome

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1 Juno 197. • a. C O'i 1 U AC : OH CHANT '.„

l:44620-73-C-0Ü64 fc. PHOJEC T NO

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Approved for public release; distribution unlimited

11 iU t'F'L LM t f. T A R V NOTES

Tech, Other

13. AMSThACT

A "sof of exa scismi are de LP and

12. SPONbOHiNG MIUllAWY ACTIVITY

AF Office of Scientific ResearcV 1400 Wilson Blvd. NPG Arlington, Va. 12209

t" zero-memory non-linearity is modeled to demonstrate effects mple non-linearities on multiple event signals and micro- c noise. Non-linearities of the order of 1 percent and less monstrated to increase noise levels significantly in certain SP bands.

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ARPA Order No:

Progran Code:

Cont ractor:

Effective Date ol Contract

Contract Expiration Date:

Amount of Contract :

Contract Number:

Principal Investigators:

Program Manager:

Title:

Sponsored by:

2506

5F10

ENSCO, INC.

1 April 19 73

31 December 19 73

$54,712

P44620-73-C-0064

Paul K. Broome 713-569-9000 Lewis J. Pinson 713-569-9000

William Best 202-694-5456

Theoretical Development for Low Distortion Proadbanding of Seismic Data

Advanced Research Projects Agency ARPA Order No. 2 506

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TABU; or CONTENTS

TECHNICAL REPORT SUMMARY

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Page

1.0 INTRODUCTION' 1-1

.0 TECHNICAL DISCUSSION

2.1 The Problem

2.2 Sine Kavc Input?

2-1

2-1

2-6

2.3 Non-Linear Lty Effccrs on Microseisr.n c Noise 2-8

3.0 CONCLUSION AND COMMENTS 3-1

4.0 REFERENCES 4-1

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TECHNICAL REPORT SUMMARY

The goal of this research effort is to perform an

investigation of the effects of seismometer non-linearities

on received signals and to improve understanding of the

effects of distortion, caused by seismometers, on later

data processing.

Seismometers are designed to convert earth motion into

electrical signals. In an ideal seismometer, this conversion

would take place without distortion. In an actual seismo-

meter, one must contend with several types of distortion.

These distortions affect the type and potential success of

all later processing steps. Without proper consideration

for the errors committed by the transducer, one can, in fact,

come to false conclusions regarding the characteristics of

the original signals.

Non-linearities in present seismometers make it difficult

to utilize spectral discriminants to solve the "interfering

event" problem. The potential advantage of increased bandwidth

for improved spectral discrimination is eliminated for non-

linear instruments because the problem uith non-linearities

increases as the bandwidth of the instrument is increased.

A "soft" zero-memory non-linearity is described in

Section 2.1 and used to model the non linear effects of seismo-

meter:.. Results of application of this non-'incarity model to

the signal (see 2.2) and noise spectra (sec 2.3) demonstrate

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that non-1incaritics of the order of It can significantly increase

noise levels in frequency bands of interest. Also, spurious

cross-product terms are generated which could easily be mistaken

for low-level events.

For modeled non-linearity levels ranging from 0.1°. to 31,

when applied to microseismic noise spectra, resulted in peak

spectral noise increases ranging from 1 to 33 db for displacement

noise and from 1 to 21 db for acceleration noise. Noise levels

in selected long-period and short-period bands increased by as

much as 30 db for the 30o distortion level. The example non-

linearities are demonstrated to cause significant increases in

noise levels for non-linearities of the order of l-o and less.

The severity of the problem depends of course on the exact

non-linearity levels to be expected in actual seismometers.

Efforts to date have indicated that an expected upper

bound on non-1inearilies is II; however, very little information

concerning the definition of this distortion level is available.

There is a noticeable lack of reliable test data to verify

expected le\ols of non-linearities.

Definition and implementation of non-linearity test pro-

cedures are required before reliable bounds can be placed on

seismometer non-linearity levels. A preliminary representation

is given of desirable features of su:h test procedures.

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1.0 INTRODUCTION

The goal of this research effort is to perform an

investigation of the effects of seismometer non-linearities

on received signals and to improve the understanding of

the effects of distortion, caused by seismometers, on later

data processing. This work will also lead to improved methods

of combining data from co-lojated seismometers so as to reduce

the effects of these distortions. The availability of modern

data processing equipment makes it possible to utilize new

approaches to seismometer design and utilization so that

distortion effects are minimized.

Non-linearities in present seismometers make it difficult

to utilize spectral discriminats to solve the "interfering

event" problem. The potential advantage of increased band-

width for improved spectral discrimination is eliminated for

non-linear instruments because the problem with non-linearities

increases as the bandwidth of the instrument is increased.

Although it has been generally accepted that analog

recording has been a limiting factor in both the broadband

and the interfering-event problems, this is most likely not

the case. The analog recorder can faithfully record and

play back, without need for switching, over a dynamic range

of nearly 100 db. The background noise level rises with the

signal level, however, so that only about a 30 to 40 db sub-

range can be Utilized in the broadband case. Even with this

1-1

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reduced dynamic range for the recorder, Ron-linearities of

the order of n in the seismometer are sufficient, to make

the seismometer the limiting factor rather than the recorder.

This is illustrated in Section 2.0 for the simple case of

multiple sinusoidal signals. The effect of non-linearities

on the microseismic noise spectrum is also illustrated.

A "soft" zero-memory ron-linearity is described and used

to rodel the non-linear effects of seismometers. Results of

application of this non-linearity model to the signal and

noise spectra demonstrate that non-linearities of the order

of It can significantly increase noise levels in frequency

bands of interest. Also, spurious cross-product terms are

generated which could easily be mistaken for low-level events.

Thus the relative effects of non-linearities are demonstrated.

The next step is to determine acceptable levels of non-linearities

for actual seismometers and to recommend methods for verification of these levels.

1-2

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2. 1 The Prob lorn

Scismoncters arc designed to convert earth motion into

electrical signals. In an ideal seismometer, this conversion

would take place without distortion. In an actual seismometer,

one must contend with several types of distortion. These

distortions affect the type and potential success of all later

processing steps. Without proper consideration for the errors

COmnitted by the transducer, one can, in fact, come to false

conclusions regarding the characteristics of the original

signals.

The characteristics of most transducers are similar. The

primary design specifications which influence signal distortion

are :

• Banduidth - 'Ihe effect of instrument bandwidth

is to distort the signal by emphasizing certain

frequency components at the expense of others.

• Dynamic Range - The dynamic rang? is the difference

between the instrument's self-noise and the maximum

signal that can be accepted without exceeding a set

level of amplitude distortion. An instrument with

inadequate dynamic range will either distort strong

signals by clipping them, or mask weak ones with

additive noise.

2-1

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• Linearity - The effect of non-linearities is to

distort the relative amplitude of signals. The

effect of these non-linearities on signals is not

uniquely revcrsable by later data processing.

Dynamic range can be improved by digitizing the output

data at the seismometer. This eliminates noise sources

extraneous to the seismometer itself. However, this does

not solve the non-linearity problem. In fact, it will be

shown that improved dynamic range can make the non-linearity

be the limiting source of distortion. Thus, it is desired

not only to improve dynamic range but to reduce the effects

of non-linearities also.

Non-linearities are a result of such factors as imperfect

springs which cause a non-linear compliance, hysteresis ei-

st iction effects which influence damping, and the accuracy of

the electromagnetic (u other) pickup. It is theoretically

possible to reduce these to almost any desired limit if cost

and size are not limiting factors. However, some non-linearity

will always exist in seismometers, and should be included in

a modeling approach to minimizing distortion in seismic signals.

The effects of non-linearities can be seen in either the

time domain or the frequency domain. If the input is a com-

plicated function of time, it can be considered to be equivalent

to a Fourier series with many terms. The effect of the non-

linearities on the output is to create energy at all sum-and-

difference frequencies which existed at the input.

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by: Consider, for example, tlic non-lincur response represented

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where

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a

the input time function

1

the output time function

the distortion for an input of v ■ 1

The response curve represented by (1) is shown in Figure 1.

In order to relate the distortion to real signals, the response

curve is normalized to the input rms value. Thus, a specified

distortion level of "a" means that y = x-a when x is at its

rms value. The distortion level increases for x greater than

its rms value and decrease? to zero as x goes to zero.

Because of the nature of the non-linearity model, the

transfer function goes to zero slope, then negative, as the

cubic term predominates. As a safeguard against the negative

slope, a clipping level is defined where the slope goes to

zero. This level is a function of the value of "a" and is

given in Figure 1 for example values of "a" from 0.11 to l,co.

The expected non-linear response and its point of action

aie not well understood. Figure 2a illustrates two examples

of how the non-linearity might react with earth motion. In

the top port of the figure the non-linearity acts on earth

acceleration. In the bottom part of the figure the non-linearity

acts on earth displacement. Oilier questions concerning the

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LINEARITY

DISPLACEMENT RLSPOXS]

POST-

FILTERING

a) NON-LINEARITY POINT OF ACTION

MICROSEISMIC

NOISE

b) ANALYSIS MODEL

Figure 2: Non-Linearity Analysis

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point of action Include whether the mv -linearity is mechanical

(springs, et.-.) transducer-related (moving coi] pick-off,

capacitor measurement, etc.) or electronics related.

For t!.'; analysis model shown in Figure 2b used in this

program, input and output spectra were compared for three cases

1) multiple simsoid, 2) displacement microseismic noise, and

3) acceleration microseismic noise. Result.-, of the application

of the non-1inearit/ model in Figure 1 to these three cases are

• iscusscd in the remainder of this section.

2 . 2 Sine Wave Inputs

Signals consisting of equally weighted sinusoids were

generated and processed through the non-linearity. The input

spectrum for a signal consisting of two sinusoids at frequencies

fj and f2 is shown in Figure 3. As illustrated in the output

spectrum (sec Figure 3) for this case, cross-jiroduct terms arc

generated by the non-linearity which have amplitudes about

40 tc 50 db below the true signal components. The value of

"a" in this case was II,

Several conclusions can be drawn from this example:

1. The distortion added by even a good seismometer

can l)e appreciable when viewed in the frequency

domain. Since this is the case, recorders which

have specified dynamic ranges of 30 to 40 db are

adequate to record the dan generated through these seismometers.

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Figure S; Effect of Bxanple Onc-Percem Non-Linearity on Sine Wave Input Signals.

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2. Th< generated spectrum is complex for this simple

case. It would be difficult to remove the non-

linear effects, especially if mixed in with other

effects such as linear filtering.

3. The added components occur over a much wider

frequency band than is occupied by the original

s ignal.

4. One ould suspect low-level signals in the presence

of strong peaks as being spurious.

2.3 Non-Linoarity Effects on Microscismic Noisr

A model for microscismic noise (DISPLACEMENT MODEL 3)

covering the period range from 0.1 to greater than 100 se.onds

was synthesized using measurement data from various sources

[1] [2] [3]. An alternate model (DISPLACIiMHiNT MODEL 4) based

on more detailed measurement for long period noise including

the peak at 18 seconds was also developed [4]. These two dis-

placement noise spectra are shown in Figure 4. A program was

devised for generating a noise time signal which exhibits the

spectral properties shown in Figure 4 and covering the range

from .002 llz to 8 Hz (.125 to 500 seconds period). These noise

time signals were then processed through the non-linearity and

comparisons were made between input and output spectra.

Estimates for the corresponding acceleration spectra were

obtained by doubly differentiating with respect to time the

displacement curves. Results of this process are shown in

Figure 5 for noise models 3 and 4.

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Results of application of the non-linearity model to

displacement noise are shown in Figure 0 for the two noise

models. Input spectra are shown as solid lines and output

ipectrt are shown for values of distortion (at rms) of

0.1ct, 0.3", 1,01 and St. As would be expected the high

ener-y microseismic peak at approximately 6-seconds when

passed thru the non-linearity model :auses significant

increases in noise energy at the third harmonic level

(approximately 0.4 Hz) and at the In* (difference) frequencies.

A si-nificant increase in a portion of the 20-40 second band

is observed. Peak differences as high as 33 clb at 0.4 Hz are

observed with peak differences in the LP b ad at 37-roximately 12 db.

The results cf Figure 6 indicate the expected output

spectra for a non-linearity acting on the earth displacement

if the Input spectra are truly representative of earth dis-

placement noise. It is emphasized that these input spectra

are based on measurement data and arc in fact seismometer

output spectra upon which non-linearities (if present) have

already acted.

Figure 7 shows results of the non-linearity model acting

on the acceleration microseismic noise. Results are similar

for both models 5 and 4, the major difference being the

notch at 18 seconds for model 4. The result of the non-linearity

is to fill in this notch and for both models is to increase

energy in the low frequencies and near the third harmonic.

The increase in low frequency energy for the acceleration model

is more pronounced because of the relative levels of low and

high frequeno energy at the input. That is, for the acceleration

noise model, significant energy in the range from 1 to 8 llz

is also pumped down into the LP band.

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Peak spectral noise increase occurs in the LP band and

ranges from about 1 db for a •« 0.11 to about 21 db for a = 3%.

Thus, for an instrument with non-linearities acting on the

acceleration input to the instrument, the non-linearity levels

examined would cause significant degradation of the system

performance.

Figures 6 and 7 demonstrated relative spectral noise

increases due to the described non-linearities. Of concern

also is the relative total noise increase in finite SP and

LP bands of interest. A spectral integration scheme was

employed to compute relative input and output power in

representative long-period and short-period bands. Results

of this computation for displacement and acceleration noise

models 3 and 4 are given in Figure 8.

Because of the sharp slopes of the noise curves and the

logarithmic frequency scale, energy in the selected SP and

LP bands is very sensitive to the exact bandpass limits, and

results of the bandpass integration in some cases may not

appear to agree with Figures 6 and 7. The point to be made

by Figure 8 is that gross differences in bandpass noise levels

are observed for non-linearities of the order of II and thus

reduce the effective signal-to-noise performance of the system.

This degradation of signal-to-noise ratio can seriously impair

the ability to detect low-lev.1 events in the given LP and SP

bands.

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3.0 CONCLUSIONS AND COMMENTS

It has been demonstrated that a wideband seismometer

exhibiting the example non-linearity would produce an output

spectrum which could seriously degrade overall performance.

For the interfering event case there would be confusion in

trying to separate low-level events from cross-product terms

of larger events.

For the case of low signal-to-noise it is demonstrated

that in certain spectral bands, the example non-linearities

increase noise levels sufficiently to completely mask low-level

events. The severity of the problem depends of course on tho

Txact non-linearity levels to be expected in actual seismo-

meters. Efforts to date have indicated that an expected upper

bound on non-linearities is It; however, very little information

concerning the definition of this distortion level is available.

There is a noticeable lack of reliable test data to verify

expected levels of non-linearities.

Definition and implementation of non-linearity test

procedures are required before reliable bounds can be placed

on seismometer non-linearity levels. Figure 9 is a preliminary

representation of desirable features of such tests. The idea

is to compare broadband instrument results with those from

"standard" SP and LP instruments.

A major task in implementing the ideas represented in

Figure 9 is the definition of "standard" seismometers. Ideally

they would be linear; however, it Blight be sufficient that they

respond only to specific passbands such that out-of-band energy

is in no way coupled into the passband.

20 3-1

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1 ■ ■ ■»" " mw^^^mim^wKv^mmm^m fw^m^mm^^mm

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SHORT PERIOD

"STANDARD" SEISMOMETER

^ 'D

LONG PERIOD

"STANDARD" SEISMOMETER

BROADFAN?

SEISMOMETER

A D

A

COMPARATOR

LONG PERIOD

MATCHED EILTER

SHORT PERIOD

MATCHED FILTER

Figur« 9: Candidate Tost Method for Evaluating Relative

Non-Line lit ics.

3- 21

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4.0 REFERENCES

1. Brunc, J. and Oliver, J., "The Seismic Noise of the

Earth's Surface", Bull. Seis. Soc. Am.. Vol. 49, No. 4,

Oct. 1959, pp 349-353.

2. Sykcs, L., "High-Gain, Long-Period Seismograph Station

Instrumentation', Vol. 1. AFOSR-TR-71-2372. Lamont-

Dohcrty Geological Ohservatory, 31 Mar. 1971, pp 12-14.

3. Carder, D., "The Requirements of a High-Sensitivity

Seismograph Station", VESIAC Report, Institute of

Science and Technology, University of Michigan, Oct.

1963.

4. Savino, J., McCamy, K. and Hade, G. , "Structures lr

Earth Noise Beyond Twenty Seconds - A Window for Earth-

quakes", Bull. Seis. Soc. Am., Vol. 62, No. 1, February

1972, pp 141-176.

22

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