T h e a f t e r s h o c k s e q u e n c e o f t h e n o r t h - w e s t K a s h m i r e a r t h q u a k e o f S e p t e m b e r 3 , 1 9 7 2 V . K . SRIVASTAVA (*) - E . K . S . C H O U H A N (*) - E A J I V N I G A M (*) R e c e i v e d on A p r i l 2 5 t h , 1975 S U M M A R Y . — T h i s p a p e r is a n a t t e m p t t o s t u d y t h e a f t e r s h o c k se- q u e n c e of t h e N o r t h w e s t K a s h m i r e a r t h q u a k e of S e p t e m b e r 3, 1972. b v a l u e of t h e s e q u e n c e is 1.59. T h e a r e a of a c t i v e s t r a i n z o n e is a p p r o x i m a t e l y 2.9 • ]01 3 s q . c m . T h e t o t a l a v e r a g e s t r a i n , a v e r a g e e l a s t i c e n e r g y a n d a v e r a g e s t r e s s of t h e r o c k b e f o r e slip a r e 3.3 • 10~5, 3.2 e r g s / c m 3 a n d 19.8 k g / c m 2 . T h e s t r a i n r e b o u n d c u r v e of t h e s e q u e n c e h a s been c o n s t r u c t e d w h i c h s h o w s a d u a l t y p e of r e c o v e r y w h e r e t h e c o m p r e s s i o n a l e l a s t i c c r e e p is fol- lowed b y t h e s h e a r c r e e p r e c o v e r y . T h e r e l a x a t i o n t i m e of t h e s e q u e n c e is a b o u t 0.7 d a y , s h o w i n g t h e K e l v i n b o d y like b e h a v i o u r of t h e u p p e r m a n t l e . R i a s s u n t o . — Q u e s t o s t u d i o è u n t e n t a t i v o di i n d a g i n e sulle r e p l i c h e del t e r r e m o t o del K a s h m i r n o r d - o c c i d e n t a l e del 3 s e t t e m b r e 1972. Il v a - lore b della s e q u e n z a è 1.59. L ' a r e a della z o n a di t e n s i o n e a t t i v a è a p p r o s s i - m a t i v a m e n t e 2.9-IO 1 3 s q . c m . L a t e n s i o n e m e d i a t o t a l e , l ' e n e r g i a m e d i a t o t a l e e lo s t r e s s m e d i o della r o c c i a p r i m a dello s l i t t a m e n t o sono 3 . 3 - I O - 5 , 3.2 c r g s / c m 3 e 19.8 k g / c m 2 . L a c u r v a di r i s p o s t a della t e n s i o n e della s e q u e n z a c h e è s t a t a c o s t r u i t a m o s t r a u n d o p p i o t i p o di r i p r e s a in cui la d e f o r m a z i o n e e l a s t i c a c o m p r e s - s i o n a l e è s e g u i t a d a l l a r i p r e s a di d e f o r m a z i o n e t r a s v e r s a l e . Il t e m p o di ri- l a s s a m e n t o della s e q u e n z a è circa 0.7 g i o r n i , m o s t r a n d o c o m e il c o r p o di K e l v i n si c o m p o r t i s i m i l m e n t e al m a n t e l l o s u p e r i o r e . (*) D e p a r t m e n t of A p p l i e d G e o p h y s i c s , I n d i a n School of Mines, D h a n b a d - 826004, I n d i a . 1 4 0 v . k . s k i v a s t a v a - r . k . s . c i i o u i i a n - r a j i v n i g a m 1 - I N T R O D U C T I O N The relocated epicenter of the N-W Kashmir E a r t h q u a k e which occurred on Sept. 3, 1972 at 16»48m31.64s GMT was at 35.95°N, 73.29°E. The unified magnitude of this shock was 6.2 and focal depth was 64 km. The aftershock which followed the main shock were dis- tributed over an area extending from latitude 35.5°ii to 36.5°lSi and longitude 73°E to 74°E respectively. All the d a t a are recalculated with the help of computer. The unified magnitudes of the aftershocks used in the present study ranged from 4.0 to 5.8. 2 - S E I S M I C I T Y O F IST-W K A S H M I R R E G I O N Kashmir region is very much seismically active due to syntaxial structure bend of the Himalayas. The epicenter of earthquakes are considered to coincide with the Main Boundary faults and any move- ment along this fault may cause earthquake. Fig. 1 shows the spatial distribution of the aftershocks of the September 3, 1972 with dislocation line and isostatic gravity anomaly map. The epicenters of the aftershocks of higher magnitude in the range of 4 to 5.9 are clustered in and around the main shock. A little north to main shock, the epicenters of the aftershocks are of magnitude below 4.0. But the distribution pattern of epicenters does not show any regular trend. However, the map clearly shows t h a t the epicen- ters of the aftershocks can be correlates with the dislocation line, presumably, the main boundary fault of the region, and they are concentrated in positive isostatic anomaly region. This association of positive anomaly shows t h a t the area is in isostatically over com- pensated. Thus this may be a cause of shallow shocks in this region, Antonio Marussi ( u ). 3 - F R E Q U E N C Y - M A G N I T U D E A N A L Y S I S . A well known relation between cumulative frequency of shocks and its magnitude is given by Gutenberg and Richter (9) in the form Log10A 7 = a — b M [1] t i i e a f t e r s h o c k s e q u e n c e o f t h e n o r t h - w e s t k a s h m i r 149 E P I C E N T R A L M A P F O R N W K A S H M I R L O N G I T U D E E F i g . 1 - E p i c e n t r a l m a p of N W K a s h m i r of S e p t e m b e r 3, 1972 e a r t h q u a k e . The constant b of this equation is related to the tectonic structure of the seismic region. Mogi (13) showed experimentally t h a t this con- stant b depends on the homogeneity of the material in the seismic region and on the distribution of applied stress. The value of b in- creases as the degree of heterogeneity increases and as the degree of symmetry of applied stress decreases. However, Scholz (10) has shown t h a t value of b depends upon the state of stress rather than the heterogeneity of the material in a region. Gutenberg and Ricliter (9) have studied in detail the Frequency- Magnitude relation for shallow, intermediate and deep focus earth- quakes. This relation has been also used by Chouhan (5) to study regional characteristics. Utsu (19), Suychiro (17), Chouan (6) etc., have shown t h a t the above relation is applicable to the aftershocks sequences also. Utsu (10) has summarised the magnitude distribution of the aftershocks in and 140 v . k . s k i v a s t a v a - r . k . s . c i i o u i i a n - r a j i v n i g a m near J a p a n and some other regions. He found t h a t the value of b lies between 0.5 and 1.5. Choulian et al (7) have also studied the magnitude distribution of " 6 " value for the aftershocks of the Assam Earthquake of August 15, 1950, and some other regions of India. They have found t h a t the b value lies between 0.5 to 1.1. Papazaclios et al. (14) have observed t h a t the value of b decreases for the aftershock sequence in the vicinity of Greece systematically with increasing focal depth of the main shock. I t is important to note t h a t there is practically no difference in the value of b obtained for the aftershock sequence and the earthquakes of the same region. A frequency-magnitude analysis for the aftershock sequence of the earthquake September 3, 1972 of NW-Kashmir has been carried out here. The resulting graph is shown in Fig. 2 and the values of a and b are computed using univariate least square procedure. The following relation is obtained Log N = 8.97 — 1.59 M [2] b value has been also calculated by using Utsu (21) maximum likelihood method, (M — Mm i n ) where M is the average magnitude for the series and Mmin is the minimum magnitude. The b value is found to be 1.5 by this method. The value of b for this sequence is rather large and this may be attributed due to low stress level in the region, Scholz (10). F u r t h e r this high value of b is also due to the small magnitude range taken here. Papazachos (I5) has shown t h a t the reliable b values are deter- mined only if this range is large enough for seismic sequence. 4 - S T R A I N R E L E A S E I N T H E A F T E R S H O C K S E Q U E N C E To study the elastic energy release behaviour in this sequence a most popular method of Benioff (2) has been applied. He has shown t h a t the potential energy J„ of a volume of rock V, possessing a coe- fficient of shear ¡x, strained an average amount s immediately before the earthquake is given by t i i e a f t e r s h o c k s e q u e n c e o f t h e n o r t h - w e s t k a s h m i r 149 M A G N I T U D E <- F R E Q U E N C Y M A G N I T U D E R E L A T I O N Pig. 2 - F r e q u e n c y - M a g n i t u d e r e l a t i o n c u r v e for S e p t e m b e r 3, 1972 e a r t h q u a k e . and the energy of released seismic wave (J) is J = r,/x V es/2 [5] where rj is the fraction of energy released as seismic waves, the rest being consumed in heat and displacement work. If 7-j is one, then entire potential energy is released as seismic waves. Thus for equation [5] strain s can be calculated if seismic energy J, the volume V and the coefficient of shear ¡a, are known. For calculating the energy, Gutenberg Richter's (10) formula is used log J = 5.8 + 2.4 m or log JW2 = 2.9 + 1.2 m [6] 140 v . k . s k i v a s t a v a - r . k . s . c i i o u i i a n - r a j i v n i g a m or J i / 2 = 10 (2.9 + 1.2 TO) [7] Fig. 3 is the elastic strain rebound characteristics curve for the after- shock sequence of Sept. 3, 1972 earthquake. There the time t of the aftershocks have been reckoned from the time of the main shock. Then the cumulative values of the calculated strain rebounds S — 2 ¡ J11'2 are plotted against "Z" which gives the accumulated strain rebound (times a constant C) increments of the aftershock sequence. This sequence consists of two segments of recovery, one linear which can be represented by the equation Li Ji/2 = A + B log t [8] A and B being constant followed by a non-linear segment which can be represented by the equation 2 ¡ Ji/2 = A' + B' ( l — e~a í l / 2) + C T? [9] where A', B', a, C and /3 are constants and T is wave period. This is a case where the compressional creep recovery is followed by a shear creep recovery. Compressional phase commences immediately after the main shock and the shear phase starts a few hours after the main shock. These interpretations are based on the empirical results ob- tained by Griggs (8) for rooks under compression and those of Michel- son's (12) for rocks under torsional stresses. Accordingly compressional creep recovery is caused by t h e elastic after working of the compres- sional stresses and the shear creep recovery also results by the elastic after-working of the shearing stress. The release of strain in two phases, compressional and shear has also been noticed by Benioff (3) Bath and Duda (') and Chouhan (°). The character of the strain rebound increments with time in Fig. 3 strongly resembles with the strain release behaviour of Kelvin Solid. The maximum S reached in Fig. 3 corresponds to the unstrained portion of the Kelvin body, the zero value of S to the loaded position. Eventually the curve is not expected to come to a complete levelling off, as in addition to the strain release, it must be expected t h a t a constant build up of stress occurs at a slow rate which, presumably, never comes to stop. Thus after a few years one would expect the same pattern to repeat itself. Thus the present behaviour of strain release can be explained in terms of elastic afterworking of Kelvin solid. t i i e a f t e r s h o c k s e q u e n c e o f t h e n o r t h - w e s t k a s h m i r 149 3 0 0 X 1 0 E R G S 2 0 0 w 100 - 1.0 T I M E I N D AY S 10.0 5 0 . 0 F i g . 3 - A c c u m u l a t e d elastic s t r a i n r e b o u n d i n c r e m e n t s (time c) of t h e S e p t . 3, 1972 e a r t h q u a k e of N W K a s h m i r . The time in which the strain drops to i j e times the initial value, called relaxation time, in this case is about 0.7 day. This relaxation time is also equal to the ratio v/fi, where ¡i is the coefficient of rigidity and v is the coefficient of viscosity. 5 - S T R A I N CHARACTERISTICS OF THE FOCAI, REGION Wilson (22) plotted aftershock epicentres to delimit the area of the strained zone involved in the Nevada earthquake of 193G. Since 1 4 0 v . k . s k i v a s t a v a - r . k . s . c i i o u i i a n - r a j i v n i g a m then the procedure lias been utilised by many workers such as Be- nioff (3), Tocher (18), Chouhan (5) etc. Further, by multiplying the area so obtained by the depth range of aftershock foci, the approximate volume of the focal region can be obtained. Other parameters can also be calculated from a knowledge of the energy released in the main shock and its sequence as follows. The spatial distribution of the aftershocks of the Northwest Kashmir earthquake of t h e September 3, 1972 is shown in Fig. 1. The distribution of aftershocks define a rectangular p a t t e r n which is perhaps t h e strained zone having the fault in the middle of the zone. Benioif (4) has described m a n y such cases where the distribution of aftershocks have lead to the delineation of the faults. The length of fault break in the present investigation is about 00 km and a width of the strained zone is about 44 km after applying a correction of the location of aftershocks. Thus the aftershock area is about 2.9 • 1013 sq.cm. We assume t h a t the average depth of the strain region is 50 kms, since the foci of many aftershocks were found down to this depth. The total volume of the strained rocks is V — 1.45 • 1020 cm3. The seismic wave energy of the principal shock is J = 4 . 7 • 1020 ergs. This gives an average elastic energy density of 3.2 ergs/c.m3. Assuming /i = 6 • 1011 dynes/cm2 at this is focal depths the value of the coefficient of viscosity (v) or better the mobility of the medium at this focal depth is of the order 3.6 • 1017 gm/cm/sec. From formula [5] of section 4 i.e., £2 = 2 J / f i V , [ 1 0 ] assuming rj = 1 and putting a = 6 • 1011 dynes/cm2. The elastic strain preceeding the principal earthquake is thus e = 3.3 • 10-5. The total strain release upto the end of the sequence is proportional to 2 J112 = 2.86 • 1010. For principal earthquake corresponding quantity is J 1 ' 2 = 2.1 • 1011. The elastic stress just before the fracture is roughly a = e[i = 6 • 1011 • 3.3 • 10"5 dynes/cm2 = 19.8 • 10° dynes/cm2 = = 19.8 kg/cm2. If "Z" = width of the aftershock region, the total relative slip during the principal shock is x = e • I = 3.3 • 10~5 • 4.4 • 1011 cm = 145.2 cm = 1.45 meter. t h e a f t e r s h o c k s e q u e n c e o f t h e n o r t h - w e s t k a s h m i r 1 4 7 This displacement is a rough approximation since e as used here represents the shear strain only very approximately. 6 - C O N C L U S I O N . The study brings out the following results: 1) The magnitude of the aftershocks are distributed according to the Gutenberg-Richter magnitude frequency relationship with value of b equal to 1.59 which is rather large in comparison to main shock. 2) The release of strain occurs in two phases, the compressional and shear. The remarkable feature of this sequence is t h a t the recovery is almost shear creep recovery with a small amount of compressional creep recovery. The relaxation time for the shear phase is found to be 0.7 days. Assuming rigidity /.i = 6 • 1011 dynes/cm2, the coefficient of viscosity, v, in the region is of the order of 3.6 • 1017 gm/cm/sec. 3) a) - The aftershock area is 2.9 • 1013 cm2 and the aftershock volume is 1.45 • 1020 cm3. b) - The elastic strain just before the main shock is 3.3 • H)-5. c) - The strain release by the main shock is 2.1 • 1 0 n . d) - The elastic stress just before the fracture is 19.8 kg/cm2. e) - The displacement along the fault plane is 1.45 meters. A C K N O W L E D G E M E N T The authors are grateful to Profs. J . Sing'h and R. K. Verma for discussions from time to time and for providing all the facilities to carry out the present work. Junior author acknowledges the financial support from the C.S.I.R. Scheme in the form of Junior Research Fellowship. R E F E R E N C E S F 1 ) B A t i i M . , D u d a S . J . , 1 9 0 4 . - Earthquake volume, fault plane area, seismic energy, strain deformation and relation quantities. " A n n a l i