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Approved for public release; distribution isunlimited.

Distribution authorized to U.S. Gov't. agenciesand their contractors;Administrative/Operational Use; 08 SEP 1967.Other requests shall be referred to Air ForceTechnical Applications Center, Washington, DC.

AFTAC USAF ltr 28 Feb 1972

197

STABILITY OF FREQUENCY-WAVENUMBER NOISE SPECTRA AT UBO

8 September 1967

Prepared For

AIR FORCE TECHNICAL APPLICATIONS CENTER Washington, D. C.

By

R. L. Sax

TELEDYNE, INC,

Under

Project VELA UNIFORM

Sponsored By

ADVANCED RESEARCH PROJECTS AGENCY Nuclear Test Detection Office

ARPA Order No. 624

BEST AVAILABLE COPY

STABILITY OF FREQUENCY-WAVENUMBER

NOISE SPECTRA AT UBO

SEISMIC DATA LABORATORY REPORT NO. 197

AFTAC Proj ect No.:

Project Title:

ARPA Order No.:

ARPA Program Code No,

VELA T/6702

Seismic Data Laboratory

624

581C

Name of Contractor:

Contract No.:

Date of Contract:

Amount of Contract:

Contract Expiration Date:

Project Manager:

TELEDYNE, INC.

F 33657-67-C-1313

2 March 1967

$ 1,736,617

1 March 1968

William C. Dean (703) 836-7644

P. 0. Box 334, Alexandria,Virginia

AVAILABILITY

This document is subject to special export controls and each

transmittal to foreign governments or foreign national may

be made only with prior approval of Chief, AFTAC.

This research was supported by the Advanced Research

Projects Agency, Nuclear Test Detection Office, under

Project VELA-UNIFORM and accomplished under the technical

direction of the Air Force Technical Applications Center

under Contract F 33657-67-C-1313.

Neither the Advanced Research Projects Agency nor the

Air Force Technical Applications Center will be responsi-

bile for information contained herein which may have been

supplied by other organizations or contractors, and this

document is subject to later revision as may be necessary.

TABLE OF CONTENTS

Page No.

ABSTRACT

PROCEDURE 1

TIME VARIATION OF THE SPECTRAL PEAK 1

Mean, Range, and Stability of Peak Power At Each Frequency 1

RESULTS 2

REFERENCES 3

LIST OF ILLUSTRATIONS

TABLE 1

TABLE 2

FIGURES

1. Unfiltered Noise

2. Unfiltered Noise

3. Unfiltered Noise

4. Unfiltered Noise

5. Unfiltered Noise

6. Unfiltered Noise

7. Unfiltered Noise

8. Filtered Noise Band

9. Filtered Ncise Band






ABSTRACT

Seven four-minute samples of the ambient noise were

subjected to frequency-wavenumber (F-K) spectral analysis

in order to observe the range and character of variatior.s

in the F-K power spectrum. The observations are derived

from the same normal population. The apparent variation

in the underlying noise statistics or processes do not suggest

gradual diurnal variations in the noise power, but large and

apparently random inter-day fluctuations.

PROCEDURE

The SDL wavenumber-frequency analysis program VFKSPTRM

due to McCowan and Jih was used to analyze seven four-minute

samples of ambient noise recorded at the UBO vertical array

on 14 April 1967, starting at 3/20/00.00, 4/42/00.0, 6/20/00.0,

9/00/00.0, 11/20/00.0, 14/00/00.0, and 15/1S/00.0. Spectral

peaks were observed at nearly infinite vertical velocity at

0.20 cps, 0.80 ops, 1.50 cps, and 2.00 cps. The variability

of power observed at these frequency was subjected to Bart-

lett's test for homogeneity of variance (Kullback, 1959).

For better accuracy the high frequency peaks were observed

after bandpass filtering in order to prevent leakage through

the spectral window due to the large. .20 cps peak.

TIME VARIATION OF THE SPECTRAL PEAK

Table 1 lists relative values of the spectral power

observed at different times during the day at the specified

frequency of F-K peaks observed in the noise. The vertical

wave number of the peaks is nearly zero in all cases.

The .2 cps noise power was taken from the F-K spectral

plots on Figures 1 to 7 with all observations normalized to

the mean at .2 cps. The strip at the bottom of the Figures

shew the array response. The other observations were taken

^rom the power spectral plots of band passed (.3 to 3 cps)

data on Figures 8 to 14.

MEAN, RANGE, AND STABILITY OF PEAK POWER AT EACH FREQUENCY

The arithmetic mean value observed for the spectral

peaks in the noise is taken from Table 1, as is the range

between the lowest and highest observation in the time inter-

val between 3/20/00.0 and 15/19/00.0. The parameter t is

measured for testing the hypothesis that the observed varia-

bility of variances is due to sampling and that the underlying

- 1 -

variance of the noise field is time invariant

7 i 7

2(BT) (B'X) I log S2/S? S2 = i t S? 1 7 . , 1

where B is bandwidth of frequency analysis

T is time-length of sample

X is length of the vertical array

B' is bandwidth of wave number analysis.

There is no spatial smoothing in the program, so B'X » 1.

This can be verified frcm the array response (using ? km. for

the length of the array). The smoothing of power in time re-

sults in B « .05 cps and the time-length of the sample is

204 sec. The results of the t test are shown on Table 2. For

acceptance of the hypothesis of homogeneity of variance t should

be less than 12.63 in Fisher's B2 distribution.

RESULTS

The probability of error in rejecting the hypothesis that

the .2 cps noise is stationary is considerably greater than

0.05, and therefore we should not reject, but the power for

acceptance of stationarity is probably low for this test. The

result for the 0.8 cps peak is also marginal. We reject sta-

tionary recognizing that the probability of error is close to

0.05 if the statistics and processes underlying the .8 cps peak

are indeed stationary. In the case of the high-frequency peak

at 1.5 cps and 2.0 cps respectively we can decisively reject

the hypothesis that the random variates underlying the observed

sample variances are from the same noraml population. The

high-frequency noise above 1 cps appears to be very non-stationary

when viewed over a 12 hour time span. There is no obvious diur-

nal trend in the observed spectral power of the high-frequency

- 2 -

peaks.

The character of the noise as seen on Figures 1 through

H shows a high degree of symmetry, indicating that energy con-

versions resulting in more up-going or down-going energy are

not "observed" to play an important role in the ambient noise.

There is no obvious indication of reflected P-pulses although

such noise may be obscured by the array response.

REFERENCES

Kullback, S., Information Theory and Statistics, Wiley, 1959,

p. 319.

- 3 -

.

c ftJ 0) 5:

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TABLE 2

Frequency Mean Powei- Range of Power t

9.7

Hypothesis of Homogeneity

Accepted . 2 cps 1.00 0.6«+-1.35

. 8 cps 0.06 0.03-0.10 12.9 ?

1.5 cpa o.om 0.001-0.037 91 Rejected

2.0 cps 0.017 0.002-0.055 98 Rejected

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Figure 13, Filtered Noise Band: Rolloff:

(.3<f<3cps) .leps

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Unclassified Swrutity ClaBgificjtion

DOCUMENT CONTROL DATA - R&D (Stcutllr elmttlllcmllon ol till», boar ol a6«lr«cl and intlmiimt annulmilnn muml bm mnimiiJ ivft.n ihm onnll »pan in zlttnlltal

ORietNATINC ACTIVI'V (Corpormlm tulhor)

TELLDYNE, INC. ALEXANDRIA, VIRGINIA

la REPONT •■CUftlTV C •.«■•■■'ICATieN

Unclassified 16 OBOUP

i MPONT TITLE

STABILITY OF FREQUENCY-WAVENUMBER NOISE SPECTRA AT UBO

4 OESCRIPTIVC MOTCI fTrpa al rapaM ml BSESlM dmlmt)

Scientific t. AUTHONf*) (Laal nun.. Ilnl nama. Inlilml)

$ax, Robert L.

• MC PONT DATE

September 8. 1967 • a CONTRACT OH I

F 33657-67-C-1313 ». P«CJ«CT NO.

VELA T/6702

'ARPA Order No. 6 24 jARPA Program Code No. 5810

flT TOTAL NO. OP P*oe»

24

T» NO. or nap«

1 • a. oRiaiNATnn'» RIPOMT NUMotnfSJ

197

*k. OTHin RfPORT uo(t).(Äny aAarmmkan *•• mar »• »aal»iarf ml» rmpott}

10. A VAILASILITV/LIMITATION NOTICCI

This document is subject to &pecial export controls and each trans mittal to foreign governments or foreign national may be made only with approval of Chief, AFTAC.

M. lUFPLEMENTARV MOTEt It. SPONSORIMO MtLITAHY ACTIVITY ,,,,„„„ . _-„„„ ADVANCED RESEARCH PROJECTS AGENCY NUCLEAR TEST DETECTION OFFICE WASHINGTON, D. C.

IS ABSTRACT

Seven four-minute samples of the ambient noise were subjected

to frequency-wavenumber (F-K) spectral analysis. In order to

observe the range and character of variations in the F-K power

spectrum. The observations are derived from the same normal pop-

ulation. The apparent variation in the underlying noise statistics

or processes do not suggest gradual diurnal variations in the

noise power, but large and apparently random interday fluctuations.

»

DD .'A 1473 Unclassified Security Clasaification

Unclassified Security Classification

KEY WORD«

Seismology

Microseism

Seipmic Noise

Spectrum

Stationarity

LINK A BOL» WT

UNK B ROLE. WT

tlNK C ROUC WT

INbTRUCTIONS I. ORIGINATING ACTIVITY: Enlar Ihe name •nd a^ldram* of Ihe contractor, eubcontraclor, grantee, Department of De- fence activity or other orcanltatlon (cotporal» au(Aor) Issuing Ihr report.

2a. REPORT SECUWTV CLASSIFICATION: Enter the over- all security cleaalflcallon of the report. Indicate whether "Reelrlcted Data" la included. Harking la I« be In accord- ance with appropriate security regulations.

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imposed by security clssslflcatinn, using standard statements ' auch s».

(1) "Cuallfled 'equeaters may obtain copies of thla repon from DDC."

(2) "Foreign announcement and dissemination of this report by DDC is not authorized."

(J) "U. S. Government agencies may obtain copiee of this report directly from DDC. Other qualified DDC users shsll request through

(4) "U. S. military agencies may obtain copies of this report directly from DDC Other qualified usera shall requcat through

(5) "All diatributlon of thla report is controlled. Qual- ified DDC users shall request through

If the report hes been furnished tc the Office of Technical Services, Depertment of Commerce, for ssle to Ihe public, indicate this fact and enter the pric, If known, 1L SUPPLEMENTARY NOTES: Use for additional explana- tory notes. 12. SPONSORING MILITARY ACTIVITY: Enter the name of the departmental project office or laboratory sponsoring (par- ing /or) the reaeerch and development. Include addreaa.

13. ABSTRACT: Enter an abstract giving a brlaf and factual aummnry of the document Indicative of the report, even though It may alao appear elsewhere In Ihe body of the technical report, if additional space la required, a continuation sheet ahall be attached.

It ia highly desirable that Ihe abstract of clansified reporta be unclassified. Each paragraph of the abstract shsll end with an indication of the military security classification of the in- fotisation In the paragraph, rapreaented as (TS). (*), (C). or (V).

There la no limitation en CSe length of Ihe abstract. How- ever, the suggested length la from ISO to 229 words.

14. KEY WORDS: Key words are technically mean'^gftil terms or abort phrases that characterise a report and may be uaad aa Index entries for cataloging Iha rapmi. Key words muat be selected so that no security claasification is required. Identi- fiers, such ss equipment model designation, trade name, military pteject code name, geographic locatlor. may be uaad aa key words but will bo followed by sa Indication of technical con- text. The assignment of link«, rules, and weights la optional

Unclassified Security ClaMlflcatioii

ft

J

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