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which he considered to have occurred at least half a minute before the main movement.” It must be mentioned, however, that in Calcutta seismograms, there is no evidence of an earlier weak disturbance.
The seismograms of the Indian stations and also of the foreign observatories showed that the amplitudes increased gradually, interrupted by larger and larger impulses and that the surface waves were very large compared with the preliminaries. (Plates 25, 26, 27 and 28).
These features, according to Gutenberg and Richter?, are suggestive" of extended faulting or more probably, block movement. ” According to this view, the earthquake was the result not of an instantaneous process but took comparatively longer time during which long-period vibrations were set up, which disturbed the usual short-period waves.
The depth of focus of the earthquake. The depth of focus of an earthquake to which the normal international tables (Jeffreys-Bullen) apply is not known with exactness but a recent estimate by Jeffreysmakes it about 10 km. The destructive nature of the Quetta earthquake and the fact that the long-wave phases in the seismograms were exceptionally well-developed show that the depth of focus of this earthquake was smaller than normal. Seismograms at near observatories (distance less than 10) with good time-determinations are necessary if the depth of focus of a shallow earthquake is to be determined with any accuracy; in their absence, we have to examine whether any conclusion can be drawn from the "Z phenomenon ” or the deviations of S-Presiduals from those of a normal earthquake. If the mean value of the residual is positive (this is usually not very different at different distances), the presumption is that the earthquake was shallower than normal. Jeffreys is of opinion that +3 seconds is the maximum possible value of Z, which would occur if the focus were at the surface. In a few earthquakes such as the Santa Barbara earthquake of 1925 June 29, and the African Rift Valley earthquake of 1928 June 6, larger values of Z (+8 and +10 seconds respectively) have been obtained but these large values have been explained as being due to possible late reading of the S phase in the former earthquake and to the possible occurrence of two successive shocks within a few seconds of each other in the latter. In the present earthquake, the mean value of Z comes to +5.9 seconds, if we exclude those values of S-P which deviated more than £15 secs. from the mean. The number of observatories at which the times of arrival of the waves fulfilled this condition was 72. Of these, 56 observatories lay within the range of distance 40° to 60°. The mean residual S-P for these 56 stations alone was +6.1 secs. · This large positive value of Z greatly exceeds the maximum of 3 seconds suggested by Jeffreys for a surface focus. To see whether part of the discrepancy might be due to the fact that no correction was made to the travel-times for the ellipticity of the earth, S-P residuals were calculated after applying all the necessary corrections for ellipticity and using Jeffreys' new tables of travel-times of P and S for a continental surface-focus”. The mean S-P residual was now changed to +3.2 seconds considering all the 72 stations and to +.3.7 seconds considering only the stations lying in the range 40° to 60°. There is no large alteration in the nature of the distribution of the residuals about the mean (Figs. 3 and 4). The change
1 B. Gutenberg and C. F. Richter “ On Seismic Waves” (First Paper), Gerl. Beitr. zur Geoph., Vol. 43, p. 73, (1934).
2 H. Jeffreys, “ Further corrections to P, S and SKS Tables" M. N. R. A. S., Geoph. Suppl. 4, No. 3, p. 242, (1937).
S-P (0-c) Fig. 3.-"S-P” residuals using normal J. B. table. t, assumed to be 32m 599.
All stations; X X X X stations between 40° and 60°.
1 E. Tillotson, “ The African Rift Valley Earthquake of 1928 January 6" 3. N. R. A. S. Geoph. Suppl. 4, No. 1, p. 92, (1937).
E. Tillotson.“ T'urther note on the African Rift Valley Earthquake of 1928 January 6,” M. N. R. A. S. Geoph. Suppl. 4, No. 4, p. 315 (1938).
2 H. Jeffreys, Loc. cit.
Number of stations
S-P (0-c) FIG. 4.-“S-P” residuals using Jeffreys''continental surface focus table.' to assumed to be 32 m 59 s.
All stations ; X X X X stations between 40° and 60°.
of residual from +5.9 secs. to +3.2 secs. points to a position of the focus nearer the surface than that of a normal earthquake. There still remains too large a mean residual S-P to be attributed to accidental error. Figs. 3 and 4 show that there are two prominent peaks in the curve of residuals which are separated from each other by an interval of about 6 secs. It is probable that these fcatures are a consequence of the fact that the shock was not a simple one originating within a small area at a definite instant, but was the result of a comparatively protracted process.
The energy of the earthquake. To estimate the energy of an earthquake, various methods have been used. When the earthquake is shallow, most of the energy is in the form of long waves, and an estimate of the energy of these waves will therefore give a lower limit for the energy of the earthquake. We use the following simple relation which has often been used for this purpose. E=Mean energy per unit volume X21 R sin Ax thick
ness of layer in which the long waves travel x length of wave-train.
a? HV =4 113 p R sin A
R sin AS**
*The numerical factor 8 is often used instead of 4 in this expression. Since the mcan energy during an oscillation, which is partly kinetic and partly potential is equal to the maximum kinetic energy, its value per unit volume is
px 470?a ?
4 T'pao Rsin A. multiplied by 2 o R sin A gives only
where E is the energy conveyed by the long waves, p the density of the surface layer of the earth (~3 gm/c.c.),
from A the angular distance of the observing station
and V the velocity of the waves = 3.5 x 105 cm/sec.). There can be some doubt as to what value of H should be adopted. If
7.062 it is taken as the depth of penetration of Rayleigh waves, H
277 =l.127, according to Jeffreys, provided a is now taken to be the horizontal displacement. When the period of the waves is 10 to 12 sec., this depth is about 43 km. For a similar calculation, Tillotson1 used for H the thickness of the granitic layer assuming it to he 13 km. We shall adopt a value of 15 km. in our calculation.
Putting in the appropriate numerical values for the Quetta earthquake as recorded at Bombay, A=1340 km., T=10 to 12 sec. and H the assumed thickness of the granitic layer=1.5 x 106 cm. In the EW seismogram at Bombay, some of the excursions of the spot of light went outside the paper and one can therefore obtain only a lower limit to the energy of the waves.
The integral Santa
evaluated from the EW seismogram comes to be about 5x10-3 cm2 sec. In the NS component record also, the vibrations have been apparently obstructed on one side and we can only say that the value of the integral should have been greater than 5 x 10-3 cm2 sec. According to Rayleigh's theory of surface-waves, the amplitude of vertical movement should be about 1.5 times that of the horizontal in the direction of propagation. Actually the observed proportion is often different from this and in the absence
aldt of a vertical component seismogram, the value of
T2 ponding to the vertical component has been assumed to be about
aldt 5x 10-3 cm/sec. The total value of
from all the three T2
1 E. Tillotson,“ On an earthquake near Imotski,” M. N. R. A. S., 2, 8, p. 426, (1931).
components is therefore greater than 1.5 X 10 - 2 cm/sec. and the computed energy of the long waves of the earthquake greater than 3.2 x 1020 ergs. In a similar way, computing from the only available (E-W) component at Kodaikanal in South India and multiplying by 3, the energy of the long waves there was found to be 1-5 x 1021 ergs.
From the Göttingen (A=46°•8) records, the energy of the long waves in the different components was computed to be as follows :
No doubt there are considerable differences in the recorded amplitudes depending on the crustal structure at the recording station but the above values nevertheless give an approximate idea of the energy of the earthquake; it is clear that the energy must have been of the order of 1021 ergs.
(2) An attempt has been recently made by the Pasadena seismologists to introduce an instrumental magnitude scale for earthquakes. The scale is logarithmic and is based on the measured maximum amplitudes in the recorded traces of the shock in a standard seismograph. If the maximum amplitudes due to two similar earthquakes recorded at the same distance are in the ratio 10m: 1, the magnitude of the first shock is said to exceed that of the second by m. When the seismographs are
situated at different distances and are of different makes, even then the traces can be made use of to give an idea of the magnitude of the quake if the ground amplitude can be deduced from the trace. The equation connecting the maximum ground amplitude and the magnitude is (1) M=log a-log A.-2.5 where M is the magnitude of the earthquake, 'a' is the maximum, recorded ground amplitude and A. is a constant depending on the distance of the station from the earthquake centre, being the maximum amplitude in millimetres
1 B. Gutenberg and C. F. Richter“ On Seismic Waves" zur Geoph., Vol. 47, p. 119, (1936).
(Third Paper), Perl. Beitr.