Travel times of P from deep-focus Indian earthquakes

232

Physics of the Earth and Planetary Interiors, 17 (1978) 232—248 © Elsevier Scientific Publishing Company, Amsterdam — Printed in The Netherlands

TRAVEL TIMES OF P FROM DEEP-FOCUS INDIAN EARTHQUAKES R.C. AGRAWAL School of Research and Training in Earthquake Engineering, University of Roorkee, Roorkee, UP. (India)

(Received November 4, 1977; accepted for publication November 11, 1977)

Agrawal, R.C., 1978. Travel times of P from deep-focus Indian earthquakes. Phys. Earth Planet. Inter., 17: 232—248. In this study all the deep-focus earthquakes occurring in the Indian region (6°—37°N; 70°—100°E) during the years 1936—1969, and which were widely recorded, have been investigated. An iteration process was used in revising the epicentres and 87 of the 108 earthquakes converged. P times for the Indian region for 0° ‘~ ~ e 105°have been cajculated and are generally greater than the Jeffreys-Bullen P times at almost all distances except for the range 90 ~ ~ 16°.Anomalous regions have been found both in the upper mantle and in the lower mantle.

1. Introduction The Jeffreys-Bullen (J-B) time tables have had a long run as “world average” tables. However, even when they first appeared some anomalies were apparent. Some of the anomalies were due to systematic errors and others remained unexplained. It is a well-known fact that there are considerable regional differences in the travel times of all the bodywave phases, and a world “average” is no longer acceptable to many geophysicists. The most significant evidence for the regional differences was brought forward from a study of the Gnome residuals by Romney et al. (1962) and Herrin and Taggart (1962). Lehmann (1955, 1962, 1964) and Jeffreys (1954, 1958, 1962) had already reported the existence of regional differences. Later, the precise studies by Carder (1964) and Gogna (1967) of the travel times of P waves from nuclear explosions in the Pacific confirmed the earlier reports of such differences in the travel times of body waves up to 20°epicentral distance, The recent work in the last decade has shown that the deviations from 1-B times contain a regionally dependent component (Arnold, 1965; Husebye, 1965; Bolt and Nuttli, 1966; Carder et al., 1966; Cleary and

Hales, 1966; Herrin et al., 1968b, Douglas and Lilwall, 1970). The residuals, found by the above authors using different materials and methods, correlate quite well (Hales and Herrin, 1972). Thus, cornbining the data from earthquakes in different regions has been proved to be only of doubtful value (Jeffreys, 1966). Regional differences of 8 s have been established (H. Jeffreys, pers. commun., 1975), but overall there is a shift of approximately 2 s with respect to J.B travel times for most of the distances. In comparison, very few seismological studies on the structure of the earth below the Indian subcontinent have been made. Recently, some work has been done on the travel times of certain regions of the Indian subcontinent. Tandon (1954), while studying the great Assam earthquake of 1950, analysed the P times and concluded that the residuals (with respect to 1-B P times) are positive for most of the ranges. He reported a P~velocity of 7.9 ±0.02 km/s for the Assam region. Kaila et al. (1968) carried out a detailed study of P travel times from shallow-focus earthquakes occurring in northerly azimuths from India. They found negative residuals (with respect to J-B times) up to 19°epicentral distance varying from ito 10 s, and positive residuals for 330 ~ ~ ~ 50°,with an

233

average excess value of 4 s. They obtained a P~velocity of 8.31 ±0.02 km/s a very high value indeed. Kaila et al. (1969) studied the upper mantle of the Hindu Kush region from 28 deep-focus earthquakes. They found a P~velocity of 8.21 km/s at a depth of 45 km, which is a little higher compared to P~velocities of other regions of the earth. Subsequently, Kaila et al. (1970) have studied P and S travel times of shallow-focus earthquakes, occurring in different directions from India and recorded at Indian stations. They found a consistently higher P~velocity (varying from 8.20 to 8.43 km/s) compared to other regions of the earth. They analysed the residuals with respect to 1-B tables and concluded: —

“As against the northern direction, i-B residuals in ~ other directions for ~ ~ 33°are mostly negative with an average value of 3 to 4 S.”

They found considerable variations in P travel-time curves in various directions from India compared to i-B travel-time curves, but, with minor variations, these curves agreed well with the travel-time tables of Herrin et al. (1968a), except in the northern direction, Thus, they also gave evidence for lateral inhomogeneities in the upper mantle. Nag (1966) studied travel times of earthquakes up to 27°epicentral distances as recorded at Indian stations and found significantly positive residuals. He obtained a P~velocity of 8.0 km/s. Tandon (1967) studied the upper-mantle velocity of the Hindu Kush region by using Gutenberg’s method. He found no low-velocity layer in the mantle for P waves, but concluded that the P velocity remains nearly constant at 8km/sup to a depth of 160 km. The regional differences in P-wave travel times observed over various parts of the earth stimulated the investigation of travel times of principal phases using deep-focus earthquakes occurring in the Indian region. In this paper, P times have been studied.

2. Selection of data The region studied here extends from latitude 6° to 37°N,and longitude 70°to l00°E.All the signifi. cant earthquakes, satisfying the criteria mentioned

below and occurring in the Indian region during the years 1936—1969 and which were originally deemed suitable for this investigation, were taken from the bulletins of the International Seismological Summary (I.S.S.) (from 1936 to 1963) and the International Seismological Centre (I.S.C.) (from 1964 to May, 1969). Criterion No. 1. Since this study is limited to deepfocus earthquakes, the focus should be below the Mohorovi~iédiscontinuity. This criterion has an obvious significance (see Chapter 1 of Agrawal, 1975). Criterion No. 2. The earthquakes should be well observed in wide ranges of epicentral distances and azimuths. Those earthquakes having the observations of P and S refracted through the core were preferred to enable us also to study the PKP and SKS phases. According to the above-mentioned criteria, 108 earthquakes were selected, and are listed in Table I. Every earthquake has been assigned a number in order to facilitate the description, wherever necessary. The distribution of the epicentres of the earthquakes is shown in Fig. 1. Looking at the epicentres, it becomes clear that deep-focus earthquakes are not very prevalent on the Indian subcontinent. There are two main clusters of the epicentres: one in the Hindu Kush area, the mountainous region in Afghanistan, and the other near the India—Burma border in the east. Both these areas are tectonically active. The depth of the earthquakes ranges from just below the Mohorovi~iédiscontinuity to 240 km. According to Wadati’s (1928) classification, such earthquakes should be termed “intermediate-focus earthquakes”. But in the present work the more general term “deep-focus earthquakes”, as used by Turner (1922) and acceptable to many other seismologists, has been used for earthquakes occurring below the Mohorovi~iédiscontinuity. Many of the selected earthquakes have depths as small as 0.005 R and a few have depths even smaller. Therefore, in such cases it is easier to calculate the times at short distances because less extrapolation is needed to reduce them to surface focus (Jeffreys, 1970). Herrin et al. (1968b) also used only those earthquakes which had depths of less than 250 km.

234 TABLE I The selected earthquakes No.

Date

Time (h ms)

Epicentre

Depth (R*)

lat. (°N)

long. (°E)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37

1936 1937 1937 1938 1938 1939 1939 1940 1941 1942 1942 1943 1943 1948 1948 1948 1949 1950 1950 1951 1951 1952 1952 1952 1953 1953 1954 1954 1954 1954 1955 1956 1956 1956 1956 1956 1956

Jun. 29 Oct. 29 Nov.14 Apr. 14 Aug.16 May 27 Nov.21 Mar.19 Jan. 21 Jan.30 Mar. 22 Feb.28 Sep.09 Feb.04 Sep. 07 Sep. 28 Mar. 04 Feb.15 Jul. 09 Jan. 06 Jun. 12 Jan. 15 Jul. 05 Oct. 18 Jun. 06 Nov.05 Feb.26 Mar. 21 Apr. 11 Jul. 10 May 14 Mar.03 Apr.06 Jul. 03 Jul. 12 Jul. 16 Sep. 19

14 30 15 07 26 31 105810 0116 30 042755 03 45 37 11 01 44 043557 12 41 41 121208 02 08 29 125433 040609 04 45 22 08 15 18 21 36 46 10 19 30 143659 16 10 24 05 17 20 2240 39 02 31 38 17 19 51 21 26 19 0110 18 08 21 39 1846 18 23 42 17 1053 32 225654 13 35 43 10 13 48 071138 23 26 17 15 01 26 15 07 11 23 47 48

36.20 37.00 36.30 22.50 22.50 24.30 36.30 36.30 27.20 06.10 36.30 36.30 36.30 23.80 36.30 22.30 36.70 11.20 36.70 36.50 36.30 23.80 36.70 36.70 11.00 36.70 36.80 24.20 36.40 36.60 36.60 23.10 36.40 36.60 22.62 22.24 23.88

70.70 70.50 71.00 94.50 94.50 94.10 71.00 71.00 92.00 95.10 71.00 71.00 71.00 94.80 71.00 94.10 70.50 93.30 70.50 71.00 71.00 94.80 70.50 70.50 93.00 70.50 71.40 95.10 70.80 71.10 71.30 94.20 70.70 71.10 93.95 95.73 94.79

0.030 0.020 0.025 0.010 0.005 0.006 0.025 0.010 0.024 0.013 0.020 0.030 0.015 0.005 0.025 0.005 0.030 0.010 0.030 0.030 0.030 0.010 0.030 0.030 0.005 0.030 0.015 0.030 0.025 0.030 0.030 0.005 0.030 0.030 0.005 0.001 0.011

~38 39 40 41 42 43 44 45 46 47 48 49 50

1956 1956 1958 1958 1958 1958 1958 1958 1958 1958 1958 1958 1959

Oct. 13 Nov.14 Jan. 06 Jan. 13 Feb. 17 Mar.07 Mar. 22 Mar. 28 Mar.28 Sep. 18 Sep. 25 Dec. 10 Feb. 01

08 2112 005128 01 54 39 20 14 36 05 18 42 06 55 32 10 11 33 04 09 36 12 06 24 20 52 04 065404 0343 43 03 13 35

36.32 36.67 36.97 11.79 36.50 36.55 23.53 36.39 36.51 36.49 36.59 36.35 36.69

71.28 71.10 71.09 92.79 70.68 70.68 93.80 71.02 70.98 70.70 70.11 71.28 70.95

0.009 0.008 0.007 0.003 0.028 0.027 0.003 0.032 0.024 0.020 0.029 0.012 0.032

235 TABLE I (continued) No.

51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101

Date

1959 1960 1960 1960 1960 1961 1961 1961 1962 1962 1963 1964 1964 1964 1964 1964 1964 1964 1964 1964 1964 1964 1964 1965 1965 1965 1965 1965 1965 1965 1965 1965 1966 1966 1966 1966 1966 1966 1966 1966 1967 1967 1967 1967 1967 1967 1967 1967 1967 1968 1968

Time (ii m s)

Mar.02 Jan. 09 Feb.19 May19 Jul. 18 Feb.04 Jun. 19 Jun. 27 Jul. 06 Oct. 09 Apr. 23 Jan. 22 Feb. 27 Feb. 28 Mar. 20 Mar. 27 Jun. 03 Jun. 13 Jul. 12 Jul. 13 Aug.17 Sep. 26 Oct. 21 Feb. 18 Feb. 25 Mar. 14 May 30 Jun. 01 Jun. 18 Jun. 18 Dec. 05 Dec. 15 Mar. 06 Jun. 27 Aug.28 Oct. 02 Oct. 18 Oct. 22 Nov. 19 Dec. 15 Jan. 04 Jan. 13 Jan. 30 Feb. 08 Feb. 15 Jul. 02 Aug.15 Dec. 10 Dec. 18 Jan. 29 Jun.12

15 51 41 07 24 04 103653 020656 0054 08 085150 17 04 37 07 03 56 23 05 32 15 59 18 0955 13 15 58 43.7 ±0.12 15 1047.8 ±0.10 17 47 07.0 ±0.14 19 0053.2 ±0.18 04 30 36.1 ±0.14 02 49 17.2 ±0.12 17 35 58.3 ±0.10 20 15 58.8 ±0.10 105847.0 ±0.11 14 42 54.0 ±0.20 0046 02.6 ±0.13 23 09 19.0 ±0.12 04 26 34.7 ±0.13 10 34 06.9 ±0.14 15 53 06.2 ±0.08 08 48 19.7 ±0.35 04 3248.5 ±0.13 0118 39.0 ±0.15 08 17 38.1 ±0.12 22 01 38.7 ±0.25 04 43 47.4 ±0.10 02 15 57.2 ±0.72 10 59 18.1 ±0.16 104301.3 ±0.25 04 31 48.7 ±0.76 20 34 37.4 ±0.65 03 03 24.4 ±0.58 07 42 30.7 ±0.60 02 08 03.1 ±0.47 11 26 46.0 ±1.20 14 04 30.3 ±0.46 21 05 30.0 ±0.70 17 17 48.0 ±0.77 05 57 30.5 ±0.59 08 32 39.7 ±0.64 09 21 03.3 ±0.18 18 43 33.8 ±0.58 10 51 36.4 ±0.29 05 00 09.3 ±0.19 0429 21.7±0.57

Epicentre —

lat. (°N)

long. (°E)

36.44 36.47 36.57 36.31 07.22 24.86 36.49 27.53 36.49 36.42 25.67 22.33 ±0.027 21.65 ±0.024 18.28 ±0.037 23.47 ±0.037 25.82 ±0.032 25.88 ±0.031 23.00 ±0.039 24.88 ±0.020 23.51 ±0.024 25.32 ±0.047 29.96 ±0.031 28.04 ±0.028 24.97 ±0.029 23.63 ±0.032 36.42 ±0.021 25.93 ±0.066 20.13 ±0.030 32.01 ±0.042 24.94 ±0.029 23.34 ±0.058 22.00 ±0.026 31.49 ±0.030 29.71 ±0.033 36.38 ±0.023 24.41 ±0.038 24.28 ±0.034 23.04 ±0.031 18.35 ±0.031 21.51 ±0.026 23.55 ±0.062 23.94 ±0.028 26.10 ±0.027 23.13 ±0.046 20.33 ±0.029 33.21 ±0.037 31.05 ±0.036 22.49 ±0.033 29.46 ±0.042 36.44 ±0.016 24.83±0.025

70.60 70.08 71.04 71.14 94.44 95.34 70.87 99.07 70.34 71.16 99.59 93.58 94.40 94.44 94.39 95.71 95.69 93.95 95.31 94.67 94.18 80.46 93.75 94.21 94.64 70.73 95.80

94.83

±0.027 ±0.022 ±0.028 ±0.043 ±0.033 ±0.030 ±0.038 ±0.023 ±0.024 ±0.085 ±0.031 ±0.029 ±0.022 ±0.024 ±0.020 ±0.055 ±0.026

87.59 ±0.030 93.67 ±0.022 94.46 ±0.047 94.47 ±0.022 80.50 ±0.028 80.89 ±0.027 70.79 ±0.029 94.81 ±0.045 94.87 ±0.042 94.28 ±0.029 95.32 ±0.032 94.43 ±0.023 94.19 ±0.068 94.72 ±0.034 96.14 ±0.025 93.80 ±0.040 93.99 ±0.025 75.71 ±0.052 93.56 ±0.033 94.88 ±0.030 81.71 ±0.045 70.39 ±0.017 91.94±0.028

Depth (R*)

0.028 0.031 0.028 0.010 0.010 0.017 0.025 0.013 0.027 0.032 0.010 0.0043 ±0.00083 0.0091 ±0.00069 0.0020 ±0.00097 0.0096 ±0.00089 0.0129 ±0.00110 0.0139 ±0.00075 0.0043 ±0.00110 0.188 ±0.00051 0.0122 ±0.00067 0.0198 ±0.00150 0.0025 0.0006 0.0019 ±0.00072 0.0097 ±0.00069 0.0271 ±0.00041 0.0108 ±0.00130 0.0076 ±0.00089 0.0016 ±0.00098 0.0023 ±0.00069 0.0101 ±0.00120 0.0120 ±0.00083 0.0026 ±0.00100 0.0005 ±0.00048 0.0222 ±0.00045 0.0061 ±0.00120 0.0084 ±0.00093 0.0061 ±0.00086 0.0073 ±0.00084 0.0080 ±0.00068 0.0034 ±0.00180 0.0080 ±0.00070 0.0009 ±0.00100 0.0028 ±0.00120 0.0028 ±0.00086 0.0015 ±0.00096 0.0004 ±0.00060 0.0189 ±0.00088 0.0014 0.0283 ±0.00031 0.0010±0.00083

236 TABLE I (continued) No.

102 103 104 105 106 107 108 *

Date

1968 1968 1969 1969 1969 1969 1969

Time (h m s)

Oct. Oct. Jan. Mar. Mar. Apr. May

03 12 25 05 10 28 21

15 2056.0 19 06 27.0 23 34 28.4 19 33 22.9 19 04 02.7 12 50 17.3 15 31 59.8

Epicentre

±1.70 ±1.60 ±0.15 ±0.21 ±0.21 ±0.67 ±0.20

Depth (R*)

lat. (°N)

long. (°E)

18.30 31.60 22.98 36.41 36.47 25.93 36.47

94.98 76.10 92.40 70.73 70.92 95.20 70.18

±0.140 ±0,230 ±0.030 ±0.015 ±0.018 ±0.027 ±0.017

±0.097 ±0.290 ±0.024 ±0.017 ±0,026 ±0.023 ±0.025

0.0101 0.0200 0.0025 0.0273 0.0256 0.0056 0.0302

±0.00250 ±0.00018 ±0.00034 ±0.00036 ±0.00099 ±0.00034

R is the radius to the Mohorovi~iódiscontinuity as used in the i-B tables,

3. Revision of parameters

where

Before analysing the data to compute the times, the four parameters of all the earthquakes, namely origin time, latitude and longitude of the epicentre and focal depth, were recalculated by an iterative process, where weight is attached to an observation according to its residual. The recalculation of the parameters was made because the uncertainties in the estimates of the parameters were not given by the I.S.S. and because it is also desirable to recalculate the parameters of research work. The values of the parameters, given in the bulletins, were taken as trial values for the recalculation of the parameters and J-B tables were used as trial tables, The epicentral distances and azimuths are calculated using the formulae given by Bullen (1963). After calculating the residuals at all the observing stations of an earthquake under consideration, the equations of condition were formed as follows: let T be the correction needed in the trial time of origin, x andy the displacements needed in the trial epicentre to the south and the east, respectively, measured as angles seen from the centre of the earth, and h’ the correction needed in the trial focal depth; the correction to the origin time would then contribute T towards the time of travel and the displacements x andy would contribute (x cos ~ —tv sin øXdt/d~)[where (x COS 0 y sin 0) gives the change of distance for a small change of epicentre], and h’ would contribute h’(dt/dh). A typical equation of condition is then: —

T ÷(x cos 0

—

y sin 0)(dtfd~)+ h’(dt/dh)

=

t0

—

(1)

t

0 and t~are the observed and calculated travel times, respectively; ~ the azimuth of the station from the trial epicentre measured from north through east; i~ the epicentral distance of the station; and dt/d~and and dt/dh are calculated from i-B tables at trial epicentral distance ~ and trial depth /s. The number of equations is so large that it is difficult to handle them without the use of an electronic computer. An electronic computer, IBM 360 model 044, at Delhi University was used for this purpose. Jeffreys’s (1970) method of uniform reduction was used in giving proper weights to all the residuals. The solution of the above-mentioned equations in turn gives the estimates of the four parameters. The solution is said to have converged only if, during the iterations, the differences between two consecutive values ofT, x, y and h’ are less than 0.01 s, 0.0 1°, 0.01°and 0.0001 R, respectively. In all, 87 earthquakes converged. Table II lists the revised parameters of these earthquakes which retain the numbers assigned in Table I.

4. Computation of P times The parameters listed in Table II are used for calculating the residuals at all distances for all 87 earthquakes separately. (1)Reduction of the data to the surface. It is well known that combining data for different earthquakes of different focal depths would give errors large enough to affect the accuracy of the present

237

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Frequency of Epicentree (Other Places)

Fig. 1. The distribution of epicentres.

work. Therefore, it was decided to reduce the data of all earthquakes to the surface, using Gogna’s (1975) tables. Only distances for the complementary rays were needed to be calculated and these distances were added. Since the travel times and the velocity distri-

bution used are compatible, the times did not need to be calculated. After reducing the data to the surface, the data for all earthquakes were combined. The weighted means at intervals of 1°epicentral distance were calculated.

238 TABLE H The revised parameters No.

1 2 3 4 7 8 11 12 J5

16

Time (h m s)

* *

*

17* 18 * 19 20 21 * 23 24 25 * 26 27 28 * 29 30 31

33 34 35 * 36* 37 38 39 40 41 * 42 43 44 45 46 47 48 49 50 51 52 53 54 55 * 56 57 59

14 30 11.30 ±0.735 07 26 34.30 ±0.894 1058 14.80 ±0.701 0116 31.50 ±0.543 11 01 42.20 ±0.210 04 35 54.65 ±0.993 0208 30.91 ±0.621 12 54 32.90 ±0.929 08 15 19.60 ±0.684 21 36 45.30 ±0.995 1019 27.52 ±0.623 14 3655.30 ±0.986 16 1020.71 ±0.765 05 17 19.20 ±0.527 22 40 40.70 ±0.717 17 19 47.21 ±0.309 21 26 15.63 ±0.428 0110 16.71 ±0.950 08 21 36.31 ±0.438 1846 13.73 ±0.405 2342 13.03 ±0.706 1053 31.91 ±0.329 22 56 52.93 ±0.432 13 35 42.33 ±0.324 07 11 36.81 ±0.332 23 26 15.62 ±0.393 15 01 24.83 ±0.845 150709.40±0.983 23 47 46.8 ±0.204 08 2110.71 ±0.469 0051 27.70 ±0.448 01 54 37.63 ±0.403 20 14 35.44 ±0.992 05 18 40.61 ±0.292 06 55 31.04 ±0.298 10 11 33.11 ±0.773 0409 35.21 ±0.323 12 06 23.81 ±0.303 2053 0.11 ±0.250 065403.51 ±0.332 034342.11 ±0.329 03 13 34.00 ±0.226 15 51 40.72 ±0.298 07 24 03.33 ±0.230 10 36 52.00 ±0.245 02 05 55.44 ±0.341 0054 11.91 ±3.073 08 51 49.44 ±0.588 17 04 35.91 ±0.249 23 05 31.33 ±0.504

Epicentre

Depth (R)

lat. (°N)

long. (°E)

36.47 ±0.06 36.28 ±0.07 36.77 ±0.06 22.83 ±0.08 36.22 ±0.01 36.04 ±0.07 36.36 ±0.06 36.41 ±0.06 36.39 ±0.07 22.78 ±0.09 36.53 ±0.05 11.03 ±0.09 36.54 ±0.08 36.39 ±0.05 36.51 ±0.08 36.45 ±0.03 36.38 ±0.04 10.91 ±0.12 36.39 ±0.04 36.36 ±0.04 24.43 ±0.04 36.40 ±0.03 36.50 ±0.04 36.54 ±0.03 36.32 ±0.03 36.51 ±0.04 22.56 ±0.05 22.18±0.16 23.53 ±0.02 36.25 ±0.04 36.63 ±0.04 36.88 ±0.04 11.83 ±0.14 36.36 ±0.03 36.37 ±0.03 23.46 ±0.08 36.30 ±0.03 36.47 ±0.03 36.28 ±0.02 36.51 ±0.03 36.28 ±0.03 36.58 ±0.02 36.39 ±0.03 36.42 ±0.02 36.50 ±0.02 36.32 ±0.03 07.32±0.09 24.87 ±0.07 36.43 ±0.02 36.43 ±0.04

70.77 ±0.04 70.20 ±0.04 70.75 ±0.07 94.44 ±0.02 70.69 ±0.03 70.68 ±0.06 71.09 ±0.10 70.66 ±0.04 70.93 ±0.05 94.25 ±1.01 70.66 ±0.03 93.58 ±1.02 71.33 ±0.06 71.09 ±0.04 70.94 ±0.05 70.95 ±0.03 70.63 ±0.04 92.93 ±0.15 70.63 ±0.04 71.25 ±0.04 95.16 ±0.02 70.78 ±0.03 71.07 ±0.04 71.19 ±0.04 70.76 ±0.03 71.17 ±0.04 94.05 ±0.04 95.67±0.03 94.60 ±0.01 71.12 ±0.05 70.96 ±0.04 70.99 ±0.04 92.86 ±0.03 70.65 ±0.03 70.60 ±0.03 93.68 ±0.07 71.04 ±0.04 70.97 ±0.03 70.66 ±0.03 70.11 ±0.04 71.20 ±0.04 70.88 ±0.03 70.62 ±0.04 70.07 ±0.03 71.04 ±0.03 71.03 ±0.04 94.33±0.07 95.22 ±0.06 70.83 ±0.03 70.38 ±0.06

0.031 ±0.0011 0.031 ±0.0011 0.028 ±0.0011 0.010 ±0.0027 0.028 ±0.0013 0.007 ±0.0019 0.024 ±0.0013 0.026 ±0.0015 0.026 ±0.0008 0.001 ±0.0005 0.027 ±0.0008 0.008 ±0.0044 0.030 ±0.0006 0.029 ±0.0005 0.030 ±0.0009 0.027 ±0.0007 0.027 ±0.0008 0.004 ±0.0032 0.027 ±0.0006 0.012 ±0.0007 0.023 ±0.0011 0.025 ±0.0006 0.027 ±0.0006 0.030 ±0.0005 0.028 ±0.0004 0.029 ±0.0005 0.003 ±0.0012 0.001±0.0018 0.012 ±0.0013 0.009 ±0.0009 0.007 ±0.0007 0.007 ±0.0006 0.003 ±0.0009 0.027 ±0.0004 0.026 ±0.0004 0.003 ±0.0010 0.031 ±0.0005 0.024 ±0.0004 0.018 ±0.0005 0.029 ±0.0005 0.011 ±0.0006 0.031 ±0.0004 0.028 ±0.0004 0.031 ±0.0003 0.027 ±0.0004 0.010 ±0.0005 0.017±0.0043 0.017 ±0.0007 0.025 ±0.0004 0.027 ±0.0004

239 TABLE II (continued) No.

60 62 63 64 65 68 69 70 72 74 75 76 77 78 79 80 81 82 85 87 88 89 90 92 93 94 95 96 98 99 100 101 104 105 106 107 108 *

Time (hms)

* *

*

*

*

15 59 17.52 ±0.291 15 58 46.44 ±0.784 151048.33±0.456 1747 06.51 ±0.777 19 00 52.92 ±0.708 17 36 00.44 ±0.618 20 15 59.11 ±0.339 1058 47.81 ±0.885 0045 58.31 ±0.818 042635.25±0.611 10 34 07.08 ±0.620 15 53 05.53 ±0.443 08 48 19.90 ±0.77 1 04 32 47.60 ±0.624 0118 39.71 ±0.714 08 17 37.84 ±0.575 22 01 39.22 ±0.840 04 43 47.00 ±0.676 104300.51 ±0.316 20 34 37.41 ±0.604 03 03 24.40 ±0.686 07 42 30.61 ±0.762 02 08 03.60 ±0.692 14 04 29.90 ±0.520 21 05 29.81 ±0.863 17 17 48.14 ±0.802 05 57 30.40 ±0.684 08 32 39.31 ±0.749 18 43 31.92 ±0.391 1051 32.66 ±0.730 05 00 08.73 ±0.385 04 29 21.41 ±0.752 23 34 27.10 ±0.664 19 33 21.92 ±0.351 19 04 01.83 ±0.361 12 50 16.51 ±0.827 15 31 58.80 ±0.436

Epicentre

Depth (R)

lat. (°N)

long. (°E)

36.36 ±0.03 22.15 ±0.04 21.53±0.06 18.24 ±0.11 23.46 ±0.05 23.08 ±0.06 24.83 ±0.04 23.57 ±0.09 29.95 ±0.07 25.02 ±0.08 23.70 ±0.07 36.37 ±0.04 25.96 ±0.07 20.04 ±0.04 31.90 ±0.07 24.92 ±0.03 23.42 ±0.09 21.99 ±0.03 36.34 ±0.03 24.29 ±0.03 23.04 ±0.04 18.33 ±0.04 21.35 ±0.10 24.02 ±0.06 26.09 ±0.03 23.24 ±0.10 20.19 ±0.08 33.20 ±0.04 22.51 ±0.06 29.32 ±0.07 36.41 ±0.04 24.81 ±0.03 22.97 ±0.00 36.39 ±0.04 36.46 ±0.03 25.90 ±0.03 36.53 ±0.04

71.20 ±0.04 93.52 ±0.04 94.21±0.05 94.42 ±0.03 94.38 ±0.05 93.78 ±0.06 95.27 ±0.03 94.54 ±0.08 80.53 ±0.09 94.18 ±0.06 94.52 ±0.05 70.72 ±0.06 95.78 ±0.05 94.78 ±0.03 87.41 ±0.07 93.67 ±0.02 94.22 ±0.07 94.46 ±0.02 70.75 ±0.04 94.72 ±0.04 94.28 ±0.13 95.30 ±0.04 94.23 ±0.06 94.77 ±0.05 96.15 ±0.03 93.82 ±0.07 93.83 ±0.07 75.76 ±0.05 94.98 ±0.05 81.96 ±0.07 70.34 ±0.05 9L94 ±0.03 92.40 ±0.03 70.62 ±0.05 70.86 ±0.06 95.19 ±0.03 69.91 ±0.07

0.032 ±0.0004 0.012 ±0.0012 0.009±0.0008 0.002 ±0.0011 0.009 ±0.0010 0.004 ±0.0011 0.019 ±0.0006 0.020 ±0.0091 0.001 ±0.0033 0.002 ±0.0008 0.009 ±0.0008 0.027 ±0.0005 0.011 ±0.0013 0.007 ±0.0010 0.002 ±0.0011 0.002 ±0.0008 0.009 ±0.0012 0.012 ±0.0010 0.022 ±0.0005 0.008 ±0.0009 0.006 ±0.0010 0.007 ±0.0011 0.008 ±0.0008 0.008 ±0.0008 0.001 ±0.0013 0.003 ±0.0012 0.003 ±0.0010 0.001 ±0.0011 0.019 ±0.0009 0.001 ±0.0049 0.028 ±0.0003 0.001 ±0.0011 0.001 ±0.0010 0.027 ±0.0005 0.025 ±0.0004 0.005 ±0.0012 0.030 ±0.0004

Parameters using all the data.

(2) Smoothing. The mean residuals were plotted against the epicentral distances. There was a sharp bend in the travel-time curve at about 17°epicentral distance, the observation points before the bend appearing to form a straight line and those beyond tending to lie on a smooth upward curve, Therefore, it was decided to fit a straight line to the observations for 1.5°~ ~ 15.5°by the leastsquares method. This hypothesis did not agree with

the data since x2 was found to be too large. For smoothing the times for 19.5°~ ~ 104.5°, the method of summary values, as described by Arnold (1968), was applied. Twenty-four summary points were obtained. Using these summary points, the times at 1°intervals were calculated by using the third divided difference for each interpolation. The contribution to x2 was much larger than the expected value for the hypothesis to be in agreement with the data.

240

where 2 h2cr~= 1, and a denotes the standard deviation. On trial, h = 0.4514 and a = 1.57. Computing 2236 exp(—~h2),the frequency distribution was calculated and is given in Table III as “Calculated (1)”. Here 2236 is the frequency at the mode and ~r are the deviations of the residuals from the assumed means. The difference between the observed and calculated (1) values are given in Table Ill and designated “0 — C”. This difference (0 — C) Suggests that the required reduction of frequencies should average 142. This number is subtracted from the observed frequency and a new frequency distribution, designated “Calculated (2)” in Table III, is obtained. Computing the mean and standard deviations from the new frequency distribution, we obtain: mean +0.0796; a = 1.62 and h = 0.44 This repeats the previous estimates fairly closely. For calculating the weights, the value of Jeffreys’s parameter j.i(~~)must be calculated. Here, ~i(~ 1) is the ratio of the estimated reduction to excess density at the mode. Thus, P(~r)is given by:

By reconsidering the observations of each earthquake, it was noticed that some of the earthquakes had either positively dominant or negatively dominant residuals. Therefore, the frequency distribution of the residuals in different ranges of distance had to be found. From the frequency distribution of the residuals, it became apparent that the modes of the distribution, in different ranges, are not at zero. To bring the modes to zero the residuals for all the ranges were combined only after subtracting the assumed means. A summary of the thus combined frequency distribution of the residuals is given in Table III. The mode of this distribution is now approximately at our zero. Table III shows that there are also larger residuals, There are many reasons for the existence of these large residuals. Some of the possible reasons for their presence have been summarised by Jeffreys (1970). Therefore, these residuals are dealt with by a modified law of error, the “method of uniform reduction”. In this method, the residuals are grouped by intervals and counted; then a constant is subtracted from the number in each interval, leaving the central group isolated and a mean and a standard deviation are found from the reduced central group (ieffreys, 1936). It was shown later that this method is a fairly accurate one because a weight is attached to each observation

/~(~r) = 142/2236

=

0.0635

Using this value of P(~r),the weights are calculated by the formula: 2~)I~ (2) Wr = [1 I1(~r)exp(h These are+ given in Table IV. Adopting these weights, the mean residuals at an interval of 1°epicentral dis-

according to itsobservation residual (Jeffreys, 1961) — the weight of a particular being calculated according to the degree of probability of normality. For the application of the method of uniform reduction, an estimate of the precision constant, h, was made by considering the residuals between —1.5 and +1.5 s, and those between —3.5 and +3.5 s [this method has been described by ieffreys (1936)]. These residuals were 5426 and 7937 respectively, giving the equation: erf(3.5 h)/erf(l.5 h) = 7937/5426 = 1.4628

tance were calculated. The unsmoothed times are plotted against the epicentral distance and it is found that indicating there is a sharp bend at about 18°epicentral distance, a discontinuity at this distance. Therefore, it was decided to study the times for the ranges 0°~ l4,5°and19.5°~ z~‘~ 104.5°separately and find the times for the remaining distances by interpolation.

TABLE III Observed and calculated frequencies of P residuals ~r for

Observed Calculated (1) (0—C) Calculated (2)

00 ~

8

_7

—6

—5

—4

—3

33 0 33 0

51 0 51 0

100 1 99 0

137 14 123 0

255 86 169 113

427 774 357 990 70 —216 285 632

—2

~ 1050

—1

0

1

2

1127 1823 —196 1485

2236 1563 818 2236 1823 990 0 —260 —172 2094 1421 676

3

4

5

6

7

8

492 357 135 350

287 86 101 145

188 14 174 46

134 1 133 0

86 0 86 0

68 0 68 0

241 TABLE IV

TABLE V

Calculated weights from eq. 2

Calculated travel times from eq. 3

Residual

*

0.00 ±1.00 ±2,00 ±3.00 *

Weight

Residual

0.94 0.92 0.87 0.70

±4.00 ±5.00 ±6.00 ±7,00

*

Weight 0.36 0.08 0.01 0.00

These are the deviations of the residuals from the assumed mean residual of the range.

4.1. Times for L~~<14.5° A straight-line fit to the observation points up to 14.5°epicentral distance gave the solution: a+ where l0~’=(~—7.5),a= 112.9186±0.8424 and 2 = 95.16 on 12 degrees bof=freedom, 136.8507which ±0.4302 with x is too large. It was noticed that the t=

contributions to x2 at 3.5°,5.5°and 8.5°are exceedingly large. Arnold (1965), while studying the Japan region, fitted a cubic to the observations of P up to 15°epicentral distance. Jeffreys (1970) concluded from his earlier studies that a cubic —with the coefficient of the cubic term being small and definitely negative — fits the observations for near distances quite well. Therefore, a cubic fit was also tried, which gave the solution: t =a + + where 10z~’= (~ — 7.5), a = 112.984 ±0.7542, b = 138.4024 ±0.3 123 and c = —6.4574 ±0.0342 with x2 = 31.23 on 11 degrees of freedom, which is still too large for the hypothesis to be acceptable. In cornparison, contributions to x2 from 3.5°,5.5 and 8.5° were larger, and the major contribution to x2 came from these three points. It was thought from the exceptionally large contribution to x2 at the 3.5°and 5.5°epicentral distances that this was due to some property of the region at a depth of about 150 km. These points (3.5 and 5.5 ) were therefore left and a cubic fit was tried which gave the solution: 3

t—a+bL~+ci~ where a

=

9.2321 ±0.4113,

(3) b

=

13.9145

±0.2133

Distance, ~ (deg)

dt/d~ (s/deg)

Time, t (s)

0.00 9.2321 139134 1.00 23.1455 139070 2.00 37.0525 138039 3.00 50.9464 138746 4.00 64.82 10 138486 5.00 78.6696 138162 6.00 92.4858 137774 7.00 106.2632 8.00 119.9951 13.73 9.00 133.6753 136218 10.00 147.2971 11.00 160.8541 13. 5 0 12.00 174.3399 13.4858 13.00 187.7478 13.4079 14.00 201.0716 13.3238 ___________________________________________ = —0.00108 ± 0.0009 with x2 being 10.84 on 9 degrees of freedom, which is satisfactory. Thus, the times for ~ ‘cZ 14°epicentral distances were taken from eq. 3. The calculated times are given in Table V.

and c

4.2. Times for 19.5°~

~ 104.5°

The times for the range 19.5°~ ~ ~ 104.5°were smoothed by using the method of summary values. For this purpose, all the data were divided into 12 ranges of distance. For each range of distance two summary points were calculated. The summary points were obtained with the help of a T.D.C. 12 electronic computer available at the Department of Mathematics, Kurukshetra University, Kurukshetra. From the summary points, the smoothed times at the desired epicentral distances were calculated by interpolation, using third divided differences (Jeffreys and Jeffreys, 1966). Here, x2 was found to be 215.51 on 60 degrees of freedom, which is a fairly large value. It was noticed that the major contribution to x2 came from the points at2l.5°,35.5°,42.5°,46.5°,61.5°, 68.5 76.5 79.5 86.5 and 91.5 epicentral distances. The large contributions to x2 at these points are either due to the anomalous region or to the anomalous properties of the stations recording observations at such distances, The second reason, though ,

,

,

.

.

242

possible, is not very sound. The lower mantle has also been found to be considerably heterogeneous by a number of other workers. Bugayevskii (1964) obtained anomalous regions in the ranges 36°—37°, 51°—53° and 70°—73°. Toksöz et al. (1967) found discontinuities at 35°, and 70°epicentral distances. Niazi and Anderson (1965), from an array study, confirmed the existence of discontinuities at 19°and 35°epicentral distances. Kaila et al. (1968) found changes in the slope of their travel-time curve at 19°,22°and 33° epicentral distances. Johnson (1969) found anomalous regions near the 34.5 40.5 49.5 70.5 and 81.5°epicentral distances. Hales and Roberts (1970) claimed the universality of a discontinuity at 42°epicentral distance. Enayatollah (1972), from array measurements, found sudden changes in the velocity gradient at 19.5°,29°,40°,46°,54°,80°,86°and 90°epicentral distances. Hales and Herrin (1972) also mention changes in the character of the curve at the 34°,40°,48°—50°,59°and 80°epicentral distances, After omitting the anomalous points mentioned above, the summary points are recalculated, and are given in Table VI. The smoothed times at the desired epicentral distances were o1~tainedby interpolation by third divided differences. Test of goodness of fit yielded a x2 value of 58.29 on 50 degrees of freedom, which is satisfactory. 530

,

,

4.3. Allowance for the upper layer The time given by eq. 3 at ~ = 0°is 9.2321 s. Owing to some error in the estimation of the depth, the time at ~ = 0°will be affected. The observations of pP, which have two more transits through the crust than P, are quite useful in finding the torrection to the time for vertical travel. 4.4. Use ofpP observations

,

In finding the corrections, there is an ambiguity arising from the fact that the corrections had to be determined in terms of one of their number. Thus, an additive constant had to be found. The depth below the Mohorovi~iódiscontinuity may be suitably estimated by the use of P time tables alone, for these are internally consistent, but no information regarding the upper layer can be obtained. The problem can be settled by estimating the depth of focus by using (pP — P) times and hence determining the additive constant. A table of (pP — P) times is given in the i-B tables for the earthquakes originating at different depths. Since these intervals are independent of the origin time and nearly independent of the distance, an independent estimate of the depth of focus can be found. For one observation of (pP — P), we can write an

TABLE VI Revised summary values Azimuth range (deg)

First summary point, t

19.5—24.5 31.5—37.5 38.5—44.5

19.9422 26.2086 32.3230 39.4911

45.5—51.5

46.4696

52.5—58.5 59.5 —65 .5 66.5—72.5 73,5—79,5

53.4471 60.3468 67.3787 74.4402 81.3814 90.2632 98.3721

25.5—30.5

80.5—87.5 88.5—95.5 96.5—1043

277.1707 339.2606 393.0774 454.8013 510.8908 563.8568 613.1691 659.0243 701.9697 740.2462 784.4346 821.6981

Second summary point, t

±0.0614 ±0.0727 ±0.0823 ±0.0532 ±0.0536 ±0.0487 ±0.0676 ±0.0691 ±0.0684 ±0.0774 ±0.1297 ±0.0962

±0.0629 373.2874 ±0.0687

23.5969 30.0547

315.3040

36.7330

431.1748 490.8332 541.1110 594.0627 641.2601 684,5895 721.3428 762.2997 805.4572 844.5008

43.9119 50.3824 57.6428 64.6017 71.4833 77.9025 85.6212 94.7712 103.4319

±0.0769 ±0,0509 ±0.0551 ±0.0544 ±0.0693 ±0.0672 ±0.0750 ±0.1030 ±0.0807 ±0.0953

243

vations. These were Nos. 19, 23, 25, 26, 28, 29, 30, 31, 56,105 57, and 59, 107. 63, 64, 75,No.39 78, 82, 85, 33, 90, 34, 95, 39, 100,51, 104, Of 68, these

equation of condition of the form: (at/ah)I~~~(~h) = (0 — C)~pp

(4)

where 6h is the correction to the depth of focus, and the right-hand side of the equation is the residual taken at the depth determined by the P time tables alone, The time from focus to the epicentre, ~ t, which will constitute ~5h= 0, is: 2~t =

(at/ah) Ip,~roah

had scattered observations and was thus rejected. The (pP — P) residuals were obtained with respect to (pP — P) times of the i-B tables; (pP — P) residuals were analysed by the method of uniform reduction. Equations of condition of the form of eq. 4 were constructed, and 5t was calculated for each earthquake by eq. 5 which is given in Table VII. Let us consider the path between two points on the surface, shown ina Fig. Let T~.be the time of vertical travelasthrough layer2.with a constant velocity,

(5)

knowing that at ~ = 0°:~t/~hfor P is half that for (pP — P) as the latter travels twice through the upper layers

Pg~of

a single-layered crust, where Pg dT~/di~. The time of travel T2, shown in Fig. 2 is given by: 2)i/2 (6) T2 (T~+ p~~

Of the 87 earthquakes used to calculate the times of P, 28 earthquakes had a series of suitable pP obserTABLE VII Estimates of 6 t for different earthquakes Earthquake No. 19 23 25 26 28 29 30 31

0.0428±0.0018 —0.0289 ±0.0022 0.2045 ±0.0216 0.8813±0.1121 0.4046 ±0.0343 0.2618±0.0100 0.5263 ±0.0023 0.1185 ±0.0522 0.1929 ±0.0014 0.4781 ±0.0144 0.2363 ±0.0011 —0.4017 ±0.0843 0.6318±0.0077 0.8813±0.0927 0.5646 ±0.0666 0.5382±0.801 0.0032±0.0011 1.0003 ±0.0231 0.3325 ±0.0422 —1.0229±0.3699 0.5117±0.1415 0.5099 ±0.0887 0.0328 ±0.0004 0.4901 ±0.0014 0.6978±0.0126 0.2776 ±0.0006 0.6537 ±0.1341

33 34 51

56 57 59 63 64

68 75 78 82 85 90 95 100 104 105 107 *

(0

Estimate of St

—

C)

Weight

(0

20.30 35.53 22.02 11.24 41.37 7.07 19.95 19.07 33.11 17.15 13.47 23.26 15.22 38.60 35.11 13.48 15.93 13.74 14.83 18.61 24.64 23.28 15.40 43.25 25.18 57.98 15.30

0.0870 0.1345 0.0178 0.2954 0.0045 0.0058 0.0355 0.0481 0.0210 0.01 75 0.0103 0.5469 0.0864 0.2954 0.05 14 0.402 0.1120 0.4389 0.0000 1.8515 0.0302 0.0296 0.0930 0.0232 0.1296 0.0036 0.0998

—

C)2 (*)

(average value of öt) — (estimated value of St). Average value of 6t

26 degrees of freedom which

is satisfactory.

W(O

—

C)2

1.7661 4.75 19 0.3920 3.3203 0.1862 0.0410 0.9173 0.9173 0.695 3 0.3001 0.1387 12.7209 1.3150 11.4024 1.8047 0.5419 1.7842 6.0305 0.0000 34.4564 0.7441 0.6891 1.4322 1.0034 3.2633 0.2087 1.5269 =

0.3378 ±0.0397 s. x2 is found to be 25.08 on

244

polation, using the divided differences formula: -

(9)

Fig. 2.: Travel path between two points on the earth’s surface.

where The time for the entire path ~ is given by: fl~) = Tg(~ 1)+ 2T2(~2)

j(~) —I(~) 2 -

which can be approximately written as: 2P1~2 T1(~1) T1(~)— Thus:

0

T 1(~)+ (2Tv/PgXp~ —

(7)

This is a very useful expression for stripping off the thin layers. Using eq. 7, the constant term obtained by eq. 3 can be modified to account for travel through the upper layer, i.e. the time at z~ 0°.Using eq. 7, the time of one vertical travel is found by: 112 = 6.4723 s = t0/2(1 —p~/p~) where t 0 = 9.2321 s, p0 = 13.9 134 s/deg and Pg = 19.85 ±0.11 s/deg This estimate of Pg is found for Europe by Jeffreys (1952), and has been used here because no suitable estimate of Pg accompanied by standard error is available for the Indian region. The calculated correction of 0.3378 s is added to this value of T~to give the corrected T~.Using this value, the time at distance i~= 0°is obtained by using eq. 7, which becomes: =

,

..0

,

26.24s It is respectively. evident from Table VIII that dt/dL~.attains a minimum at i~= 99°and then increases for greater values of ~. This increase in dtfd~is clearly impos-

2P~2

=

—

The times for 15°,16 1, 180 and 19 0 epicentral distances, calculated by the above formula, are 3m 3477S 3m 47.89~,4m 00.89s, 4m 13.7 i~and 4m

7T4) = T1(~)+ 2T2(~2)— or T(&)

~2

9.7139 ~

Thus, the final formula representing the times for 0°~ ~ 14.5°becomes: 3 (8) t=9.7139+13.9145i~t—0.00108i.~ therefore 0.4818 s should be added to the times for all the distances to account for an increase in the times through the upper layers.

sible for first arrivals according to ray theory, and is 15 13 11

(a)

9 7 >

‘-5 3 Distance (deg)

1 0 — .-~4 E 2

20 ‘

40

60

80

100

I

0

E -1

U)

4.5. Times for 15° ~

L~~

19°

Fig. 3. a. Final P travel-time curve calculated for

distances to

105°. b. Deviations of final travel-time curve (a) from i-B

The times for

150 ~

<190

were found by inter-

times in seconds.

245

TABLE VIII Times ofP for 0°~ ~ ~ 105° Distance, ~ (deg)

J-B times m

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49

0

1

2

3

4

5

6

7

8

Smoothed times, t s 06.8 21.1 35.4 49.7 03.9 18.1 32.2 46.3 00.3 14.2 28.0 41.7 55.3 08.7 21.9 35.0 48.0 00.7 13.2 25.5 37.0 47.4 57.5 07.4 17.1 26.8 36.2 45.4 54.5 03.5 12.5 21.3 30.1 38.8 47.5 56.1 04.6 13.0 21.4 29.8 38.1 46.3 54.5 02.7 10.8 18.9 26.8 34.7 42.6 50.3

m 0

1

2

3

4

5

6

7

8

s 09.71 23.63 37.53 51.43 05.30 19,15 32.97 46.74 00.48 14.16 27.78 41,34 54.82 08.23 21.55 34.77 47.89 00.89 13.71 26.24 38,30 49.41 00.00 10.03 19.59 28.83 37.87 46.80 55.67 04.49 13.29 22.04 30.75 39.43 48.07 56.71 05,33 13.95 22.56 31.11 39.58 47.92 56.10 04.12 12.00 19.84 27.65 35.43 43.19 50.94

Smoothed i-B P times (s) 2.91 2.53 2.13 1.73 1.40 1.05 0.77 0.44 0.18 —0.04 —0.22 —0.36 —0.48 —0.47 —0.35 —0.15 —0.11 0.19 0.51 0.74 1.30 2.01 2.50 2.63 2.49 2.03 1.67 1.40 1.17 0.99 0.79 0.74 0.65 0.63 0.57 0.61 0.73 0.95 1.16 1.31 1.48 1.62 1.60 1.42 1.20 0.94 0.75 0.73 0.59 0.64

dt/d~ (s/deg)

13.91 13.91 13.89 13.87 13.85 13.82 13.78 13.73 13.68 13.62 13.56 13.49 13.41 13.32 13.22 13.12 13.00 12.82 12.53 12.06 11.11 10.59 10.03 9.56 9.24 9.04 8.93 8.87 8.82 8.80 8.75 8.71 8.68 8.64 8.64 8.62 8.62 8.61 8.55 8.47 8.34 8.18 8.02 7.88 7.84 7.81 7.78 7.76 7.75 7.73

246 TABLE VIII (continued) Distance, ~ (deg)

i-B times m

50 51 52

Smoothed times, t s

Smoothed i-B P times (s)

58.67 06.28 13.75

0.67 0.68 0.55

7 61

—~

9

S

58.0 05.6 13.2

m

9

dt/d~ (s/deg)

53

20.7

21.09

0.39

7’25

54 55

28.0 35.4 42.6 49.8 56.8 03.8 10.7 17.5 24.3 30.9 37.5 44.0 50.4 56.8 03.1 09.3

28.34 35.54 42.73 49.93 57.10 04.22 11.24 18.13 25.86 31.44 37.92 44.40 50.83 57.22 03.60 09.87

720 719 720 717 712 7:02 6.89 6.73 6.58 6.50 6.46 6.43 6.39

70

15.4

16.03

71

21.5

22.15

0.34 0.14 0.13 0.13 0.30 0.42 0.54 0.63 0.56 0.54 0,42 0.40 0.43 0.42 0.50 0.57 0.63 0.65

72

27.5

28.17

0.67

5.92

73 74

33.4 39.2

34.09 39.92

0.69 0.72

5.83 5.72

75

45.0

45.64

0.64

5.64

76

50.7

51.28

0.58

5.56

77

56.3

56.84

0.54

5.52

02.36 07.83 13.27 18.68 24.03 29.33 34.54 39.66 44.66 49.55 54.34 59.05 03.70 08.33 12.96 17.58 22.18 26.77 31.32 35.85 40.36 44.85

0.56 0.53 0.57 0.68 0.83 0.93 1.04 1.16 1.16 1.15 1.14 1.05 1.00 1.03 1.06 1.08 1.08 1.07 1.02 1.05 1.06 1.05

56 57 58 59 60 61 62 63 64 65

10

66 67 68 69

78 79 80 81 82 83 84 85

11

12

86 87 88 89 90 91 92 93 94 95 96

97 98 99

13

01.8 07.3 12.7 18.0 23.2 28.4 33.5 38.5 43.5 48.4 53.2 58.0 02.7 07.3 11.9 16.5 21,1 25.7 30.3 34.8 39.3 43.8

10

11

12

13

6.38 6.27 6.16 6.12 6.02

5.41 5.30 5.21 5.12 5.00 4.89 4.71 4.66 4.63 4.63 4.62 4.60

4.51

247 TABLE VIII (continued) Distance, ~ (deg)

iB times m

100 101 102 103 104 105

14

Smoothed times, s

s

Smoothed J-B P times (s)

49.34 53.83 58.32 02.81 07.30 11.79

0.94 0.93 0.92 1.01 1.10 1.19

m

48.4 52.9 57.4 0L8 06.2 10.6

14

r

probably caused by the apparent dispersion of the travel times beyond 99°,arising from failure at many stations to detect the first arrival of the attenuated P waves (Taggart and Engdahl, 1968). The same situation was met by Herrin et al. (1968a) while preparing the 1968 P seismological tables and they arbitrarily fixed dt/d~at the minimum value of 4.5643 s/deg for i~ = 99°.In this study we have fixed the minimum value of dt/d~at 99 which is 4.49 s/deg for ~ = 99°.Taggart and Engdahl (1968) remark here that this creates an artificial diffraction boundary or discontinuity for P rays at a radius of 3565.36 km, but the velocity distribution above the discontinuity is not affected by assuming that dt/d~is constant beyond 99°epicentral distance. Thus, the finally obtained times for P for 0°< <105°are given in Table VIII and are shown in Fig. 3a. The difference of P times calculated for the Indian region from the J-B P times are shown in Fig. 3b.

dt/d~

(s/deg)

(4) The lower mantle is also found to be quite inhomogeneous. Large values of x2 atepicentral distances of 21.5 ,35.5 ,42.5 ,46.6 ,61.5 ,68.5 76.5°,79.5°,86.5°and 91.5°indicate the presence of anomalous regions inside the earth at approximate depths of 450, 850 1000, 1150, 1600, 1900, 2100, 2350, 2500 and 2800 km, respectively.

,

5. Conclusions (1) P times for the Indian region have been calculated for the range 0°
Acknowledgements This work was undertaken by the author at the Department of Mathematics, Kurukshetra University during his stay there as a C.S.I.R. Research Fellow. The author expresses his sincere thanks to Dr. M.L. Gogna of Kurukshetra University for suggesting the problem and taking a keen interest in the work. He thanks Dr. S.D. Chopra, Professor and Head of the Department of Mathematics of Kurukshetra University for providing the necessary facilities. The author is extremely grateful to Prof. Markus Bath of the Seismological Institute, Uppsala for revising the manuscript. Financial support from the C.S.I.R., New Delhi, and U.G.C., New Delhi, is also gratefully acknowledged.

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