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UNCLASSIFIED AD NUMBER LIMITATION CHANGES TO: FROM: AUTHORITY THIS PAGE IS UNCLASSIFIED AD480406 Approved for public release; distribution is unlimited. Document partially illegible. Distribution authorized to U.S. Gov't. agencies and their contractors; Critical Technology; MAY 1965. Other requests shall be referred to Air Force Technical Applications Center, Washington, DC. Document partially illegible. This document contains export-controlled technical data. usaf ltr 25 jan 1972
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Page 1: UNCLASSIFIED AD NUMBER LIMITATION CHANGES · The travel times for all body phases tabulated in the Jeffreys and Bullen SeismoJogical Tables (1958) have been calculated by interpolation

UNCLASSIFIED

AD NUMBER

LIMITATION CHANGESTO:

FROM:

AUTHORITY

THIS PAGE IS UNCLASSIFIED

AD480406

Approved for public release; distribution isunlimited. Document partially illegible.

Distribution authorized to U.S. Gov't. agenciesand their contractors; Critical Technology; MAY1965. Other requests shall be referred to AirForce Technical Applications Center,Washington, DC. Document partially illegible.This document contains export-controlledtechnical data.

usaf ltr 25 jan 1972

Page 2: UNCLASSIFIED AD NUMBER LIMITATION CHANGES · The travel times for all body phases tabulated in the Jeffreys and Bullen SeismoJogical Tables (1958) have been calculated by interpolation

B - M

"> KJ M sS^.^:

uS raff ~ o SHR--.-i^;. «■II : ' HH

iS :-

INTERPOLATED ,IEFFR=YS AND PULLEN SEISMOLOGICAL TABLES

D D C

1W APR2 01S56 jij

THIS nrcu^E'lT iS SUBJECT TO SPECiAl £■■ -i c-rcLs AMO vm TRftHSMtim ToKblGHGCVERNMEMTSORFOREl^ HAT10HÄL MAY BE MAOE CNIY WiTH PRi^H APPROVAL OF CHtEF^rWS.

THE BEDTSCHNICAI» CORPORATiaN

a.«.i»LANP, Tt:x.^^Il

-_ „_. .,-,v..~«~—^—i^-Aiitv-^J--;;^

Page 3: UNCLASSIFIED AD NUMBER LIMITATION CHANGES · The travel times for all body phases tabulated in the Jeffreys and Bullen SeismoJogical Tables (1958) have been calculated by interpolation

BEST AVAILABLE COPY

Page 4: UNCLASSIFIED AD NUMBER LIMITATION CHANGES · The travel times for all body phases tabulated in the Jeffreys and Bullen SeismoJogical Tables (1958) have been calculated by interpolation

TECHNICAL REPORT NO. 65-35

INTERPOLATED JEFFREYS AND BULLEN SEISMOLOGICAL TABLES

by

H. S, Travis

AFTAC Project No: ARPA Order No: AR PA Code No: Contractor:

Contract No;

VT/40.,P 104-6« 8100 The Gv;otechnical Corporation, Garland, Texas AF 33(657)-i2145

THE GEOTECHNICAL CORPORATION 3401 Skiloh Road T: ? n^^sST irSJ»l£CT TO SPECIAL Garland, Texas I . ' , C!'::;T-GlS AFÖ EACH TRANSf,";"Al

TC FGKEoH GGVErfaOTS OR Füi-tiSN mmm. mt DE MIDI: ONLY mn PKIOR

AH^GVAL CF CHiff^FB!«.

ü May 1965

Page 5: UNCLASSIFIED AD NUMBER LIMITATION CHANGES · The travel times for all body phases tabulated in the Jeffreys and Bullen SeismoJogical Tables (1958) have been calculated by interpolation

CONTENTS

ABSTRACT

1. INTRODUCTION

2. DESCRIPTION OF METHOD

3. NUMERICAL TECHNIQUES 3. 1 Lagraugian interpolation formula 3.2 Linear interpolation formula

4.

5.

6.

REMARKS

INDEX OF PHASES

INTERPOLATED JEFFREYS AND BULLEN SEJSMOLUGICAL TABLES

Page

1

2

$ 3 4

4

5

TR 65-35

Page 6: UNCLASSIFIED AD NUMBER LIMITATION CHANGES · The travel times for all body phases tabulated in the Jeffreys and Bullen SeismoJogical Tables (1958) have been calculated by interpolation

ABSTRACT

The travel times for all body phases tabulated in the Jeffreys and Bullen SeismoJogical Tables (1958) have been calculated by interpolation for distance intervals of 1 degree at each of the 14 focal depths established by Jeffreys and Bullen. Travel times have been similarly derived for the phases "diffracted P" (P at distances beyond 105 degrees) and "PKPPKPPKP, " based on data extrac- ted from the Gutenberg and Richter travel-time charts (1934-1939), The cal- culations were effected by means of a digital computer program principally emtloying Lagrange's four-point interpolation formula. This report discusses the techniques involved and presents the fully interpolated tables in a convenient form.

TR 65.35

Page 7: UNCLASSIFIED AD NUMBER LIMITATION CHANGES · The travel times for all body phases tabulated in the Jeffreys and Bullen SeismoJogical Tables (1958) have been calculated by interpolation

INTERPOLATED JEFFREYS AND BULLEN SEISIviOLOGICAL TABLES

I. IN'IROBUCTION

This report prestnts a fully interpolated version of the Jeffreys and Bullen (J-B) Seismological Tables and discusses the manner in which it was gen- erated. The travel times for all teleseismic body phases contained in the J-B tables are given for diotance intervals of 1 degree at each of the 14 standard J-B focal depths. The times are tabulated in a convenient reference form very similar to that employed for the "P1' and "S:' phases in the existing J-B tables. Tra/el times are similarly presented for the phases "diffracted PH

{P at distances beyond 105 degrees) and "PKPPKPPKF. " based on data extracted from the Gutenberg and Richter travel-time charts.

These interpolated J-B tables have been calculated as a convenience for seis- mologists who must have frequent access to accurate, closely resolved (in distance and depth) travel times for ail phases. The only phases in the exist- ing J-B tables listed for distance intervals of 1 degree at all depths are "P" and "S. " It is anticipated that the tables will save m^ny hours of needless, repetitious manual interpolation on the part of analysts trying to identify and associate phases, Particular application is seen for compiling seismological bulletins, such as those assembled under the Long-Range Seismic Measure- ments Program, which routinely involve a vast amount of table lookup for accurate association of phases.

Section 2 of this report discusses ia detail the interpolation and computational methods used to create the interpolated tables, and section 3 specifies mathematically the interpolation formulas used. Section 5 provides an index of the phasei available, thair various branches, and the ranges of distance

Jeffreys, Harold, and Bullen, K. E, , 1958, Seismological tables: British Association for the Advancement of Science Publication

^Gutenberg and Richter, 1934-1939, Seisnnic wave papers, I-IV: Gerlands Beiträge Zur Geophysik

TR 65-35 -1-

Page 8: UNCLASSIFIED AD NUMBER LIMITATION CHANGES · The travel times for all body phases tabulated in the Jeffreys and Bullen SeismoJogical Tables (1958) have been calculated by interpolation

Jeffreys and Bullen, op. cit.

TR 65-35 -2-

i over which they are tabulated. Depth phases such as "pP" and "sS" are not included because of the ease with which their times can be calculated from the "P" and "S" tables.

2. DESCRIPTION OF METHOD

A program for the Control Data 160-A digita) computer was written to inter- polate the existing Jeffreys and Bullen seismological travel-time tables and tabulate the results. Primarily, the program employed the Lagrangian four- point interpolation polynomial to interpolate between the times; however, when four points could not be obtained, a linear interpolation method was used. For each phase where it was necessary, the program first calculated by inter- polation the depth allowances at all standard J-B depths for distance intervals of 1 degree. Depth allowances in the Jeffreys and Bullen tables are generally given at distance intervals of only 10 degrees. Subsequently, the interpolated depth allowances were subtracted from the surface times of the phase to obtain the corrected travel times at depth. In some cases, the times for surface focus were given at 5-degree intervals and also had to be interpolated for each degree.

For core phases other than "PKP, " "SKS, " "PcP, " and "ScS, " the allowances for depth had to be obtained by first determining the dt/dA at 1-degree intervals for each phase's surface travel-time curve. Then the allowance 5^r depth were taken as equal to those given (or interpolated) for the above core phases at distances where dt/dA were the same. For example, to obtain the desired depth allowance for the phase "SKKS" at 150 degrees for depth ?. 06R, it is determined that dt/dA at that distance is 5.5 sec/degree, which is matched by "SKS" at 94 degrees. Therefore, the depth allowance for "SKKS" at 150 degrees for depth 0. 06R is equal to that for "SKS" at 94 degrees and depth 0, 06R. 3 For those phases whose depth allowances were not defined by the J-B tablea, such as "PP" at 10 degrees and depth 0,06R, the times were left blank.

Travel-time tables were tabulated for those phases which produce multiple com- binations, such as "PcSPKP. " Tables for the phases "ScPPKP" and "PKPScP" (or PKPPcS) were tabulated by obtaining the proper depth allowances (for ScP and PKP, respectively) by th3 atandard procedure and subtracting these times

i

Page 9: UNCLASSIFIED AD NUMBER LIMITATION CHANGES · The travel times for all body phases tabulated in the Jeffreys and Bullen SeismoJogical Tables (1958) have been calculated by interpolation

from :.he surface times of "PcSPKP. " The travel times for äiffrac^ed nP" and ^FKPFKFPKP11 were obtained from the Gutenberg and Richter travel- time charts at distance intervals of approximately 0, o degree and at depth intervals of 100 kilometers. From these, travel times were determined for distance intervals of 1 degree at thi standard J-B focal depths.

Generally, the times for each phase given in the standard Jeffreys and Bullen travel-time tables represent average times with standard errors of under 1 second. Inevitably, the interpolated tables presented erein have the same error; however, it should be pointed out that possibilities of small disagree- ments with the standard tables arise from the smoothing technique introduced. In the majority of cases, the interpolated times agree to 0. 1 second with the standard tables. However, the derivatives (dt/di) of the travel-time curves for several of the more exotic body phases (e.g. , PKPPKS) were so erratic the interpolation technique employed smoothed over these points. Conse- quently, the times differ occasionally from a linearly interpolated time. The magnitude of the disagreement is generally less than half a second.

3. NUMERICAL TECHNIQUES

3. 1 LAGRANGIAN IKTERPOLATION FORMULA

Numerical four-point interpolation (Hildebrand, F. B. , 1956) can be obtained from the Lagrangian interpolation polynomial of degree 3 expressed in the following general form:

y(x)= £ Mx)f'xk; k=0

where:

y{x) is the Lagrangian interpolation polynomial of degree 3 that approximates the assumed continuous function f{x).

f(xjt) is a series of discrete ordinate points (corresponding to abcissa values XQ. X|, X2. and X3) representing the function to be approximated.

4Ibid

TR 65-35 -3-

Page 10: UNCLASSIFIED AD NUMBER LIMITATION CHANGES · The travel times for all body phases tabulated in the Jeffreys and Bullen SeismoJogical Tables (1958) have been calculated by interpolation

and the desired Lagrangian coefficients are given by:

^k(x) = (x-x0) . . . (x-xj^.,!) {x-xk+l) . . . (X-X3)

{xk-x0). . . (xk-Xk-iMxk-xjcf i). -. {xk-X3^

where vhe factors (x-xk) and {xk-xk) are to be omitted in the products. Thus, a vaJv i of y may be calculated for any value of x by means of the Lagrangian polynomial. To obtain the highest degree of accuracy, the value of x should be centered between the two innermost data pcintp (xj and X2).

3.2 LINEAR INTERPOLATION FORMULA

Linear numerical interpolation (Hildebrand, F, B. . 1956) between two tabular points can be obtained from the following formula:

f(x)«f(x0) + (X'X0)

(X^XQ) fl.X,) . f{Xn)

where:

f(x) is a function assumed to be linear between the two tabular points, XQ and xj.

4, REMARKS

The interpolated Jeffreys and Bullen seismological tables are also available on punched cards.

TR 65-35 -4.

Page 11: UNCLASSIFIED AD NUMBER LIMITATION CHANGES · The travel times for all body phases tabulated in the Jeffreys and Bullen SeismoJogical Tables (1958) have been calculated by interpolation

5. INDEX OF PHASES

PHASE BRANCH

1. P 2. P diff i. S 4. PP 5. PS 6. SS 7. s? 8. PPP 9. PPS

10. PSS li„ SSS 12. SSP 13. SPP 14. PcP 15. PcS )i. ScS 17. ScP IS. PKP

DISTANCE RANGES PAGE

19. PKS

20. SKS

21. SKP

22. PKKP

AB BC DEF

AB BC DEF

AC DEF

AB BC DEF

AB BC DF

0o-lC5o 9

105°-150° 12 o'-io/ 14

10°-180° 17 50°-140° 22 10°-180° 25 4^°-140° 30 10°-220° 33 60°-180° 39

100°-220° 42 10°-220° 45 90°-220° 51 45°-180° 55 0°- 80° 59 0°- 70° 61 0°- 80° 63 0'- 80° 65

143°-180° 67 143"-147° 68 110°-180° 68

13 >0-14&0 70

130°-140" 70 l-.-o-i80o

70

70°-133^ 73 99°-180° 74

ISO'-HS"' 77 130P-140° 7? ),r,4o-180° 77

104°-126° 80 93°-126° 80 r -162° 81

TR 65-35 .c.

Page 12: UNCLASSIFIED AD NUMBER LIMITATION CHANGES · The travel times for all body phases tabulated in the Jeffreys and Bullen SeismoJogical Tables (1958) have been calculated by interpolation

PHASE BRANCH

23. PKKS AB BC DF

24. SKKS AC DF

25. SKKP AB BC DF

26. SKKKS ABC

27. PcPPKP AB DF

28. PcSPKP AC DF

DISTANCE GANGES PAGE

2v. ScSP

30. JcSPKP ABC D

31. ScPPKP AC DF

32. PKPPcP AB DF

33. PKPPcS or PKPScP AC

DF 34. PKPScS

ABC D

35. PKPPKP DF

36. PKPPKS or PKPSKP B

DF

134'-146' 86 100°-146 86

0*-168' 87

85*-243° 92 0o-173o 96

134,,-x460 101 100° "146*' 101

0'-i68o 102

90°-370°

82°-187° 132°-180°

110o-1949

1278-180,'

s o 112 -140 11Z0-1300

l60o-Z0b' IZV-ISO0

110o^194,' 12'o-180o

9 S 82 -187

UZ9 -180°

110o~194D

127e-180o

1600-2060

i2r-180o

0e-i4no

ü o 75 - 84

0e-145o

107

114 116

li8 120

122 122

124 125

127 129

131 133

135 137

139

142

1 6 146

TP 65-35 -6-

Page 13: UNCLASSIFIED AD NUMBER LIMITATION CHANGES · The travel times for all body phases tabulated in the Jeffreys and Bullen SeismoJogical Tables (1958) have been calculated by interpolation

PHi3 iSE BRANCH

37. PKSPKP B

•DF 38. SKPPKP

B DF

DISTANCE RANGES PAGE

39. SKSP 115"-205° 158 40. PKPPKPPKP 446-104o 161

TR 65-35

f

75°- 84° 150 0o-i45o 150

75 - 84 154 0o-145o 154

Page 14: UNCLASSIFIED AD NUMBER LIMITATION CHANGES · The travel times for all body phases tabulated in the Jeffreys and Bullen SeismoJogical Tables (1958) have been calculated by interpolation

6. INTERPOLATED JEFFREYS AND BULLEN SEISMOLOGICAL TABLES

Page 15: UNCLASSIFIED AD NUMBER LIMITATION CHANGES · The travel times for all body phases tabulated in the Jeffreys and Bullen SeismoJogical Tables (1958) have been calculated by interpolation

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Page 17: UNCLASSIFIED AD NUMBER LIMITATION CHANGES · The travel times for all body phases tabulated in the Jeffreys and Bullen SeismoJogical Tables (1958) have been calculated by interpolation

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Page 18: UNCLASSIFIED AD NUMBER LIMITATION CHANGES · The travel times for all body phases tabulated in the Jeffreys and Bullen SeismoJogical Tables (1958) have been calculated by interpolation

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Page 19: UNCLASSIFIED AD NUMBER LIMITATION CHANGES · The travel times for all body phases tabulated in the Jeffreys and Bullen SeismoJogical Tables (1958) have been calculated by interpolation

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Page 20: UNCLASSIFIED AD NUMBER LIMITATION CHANGES · The travel times for all body phases tabulated in the Jeffreys and Bullen SeismoJogical Tables (1958) have been calculated by interpolation

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Page 58: UNCLASSIFIED AD NUMBER LIMITATION CHANGES · The travel times for all body phases tabulated in the Jeffreys and Bullen SeismoJogical Tables (1958) have been calculated by interpolation

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Page 59: UNCLASSIFIED AD NUMBER LIMITATION CHANGES · The travel times for all body phases tabulated in the Jeffreys and Bullen SeismoJogical Tables (1958) have been calculated by interpolation

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Page 69: UNCLASSIFIED AD NUMBER LIMITATION CHANGES · The travel times for all body phases tabulated in the Jeffreys and Bullen SeismoJogical Tables (1958) have been calculated by interpolation

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Page 81: UNCLASSIFIED AD NUMBER LIMITATION CHANGES · The travel times for all body phases tabulated in the Jeffreys and Bullen SeismoJogical Tables (1958) have been calculated by interpolation

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Page 94: UNCLASSIFIED AD NUMBER LIMITATION CHANGES · The travel times for all body phases tabulated in the Jeffreys and Bullen SeismoJogical Tables (1958) have been calculated by interpolation

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Page 95: UNCLASSIFIED AD NUMBER LIMITATION CHANGES · The travel times for all body phases tabulated in the Jeffreys and Bullen SeismoJogical Tables (1958) have been calculated by interpolation

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Page 96: UNCLASSIFIED AD NUMBER LIMITATION CHANGES · The travel times for all body phases tabulated in the Jeffreys and Bullen SeismoJogical Tables (1958) have been calculated by interpolation

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Page 145: UNCLASSIFIED AD NUMBER LIMITATION CHANGES · The travel times for all body phases tabulated in the Jeffreys and Bullen SeismoJogical Tables (1958) have been calculated by interpolation

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Page 158: UNCLASSIFIED AD NUMBER LIMITATION CHANGES · The travel times for all body phases tabulated in the Jeffreys and Bullen SeismoJogical Tables (1958) have been calculated by interpolation

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Page 168: UNCLASSIFIED AD NUMBER LIMITATION CHANGES · The travel times for all body phases tabulated in the Jeffreys and Bullen SeismoJogical Tables (1958) have been calculated by interpolation

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