T h e r e l a t i o n s h i p b e t w e e n t h e b o d y w a v e a n d t h e 

l o c a l m a g n i t u d e s f o r H i m a l a y a n e a r t h q u a k e s 

ir 
M . P . CHHABRA (*) E . K . S . CHAUHAN (*) - H . N . SRIVASTAVA ( * * ) -

H . M . CHAUDHITRY. 

R e c e i v e d o n D e c e m b e r 4 t h , 1976 

SUMMARY. — B o d y w a v e ( M B ) a n d l o c a l m a g n i t u d e (ML) w e r e d e t e r -
m i n e d f o r e a r t h q u a k e s o c c u r r i n g w i t h i n t h e e p i c e n t r a l r a n g e of 2 t o 10° 
f r o m N e w D e l h i d u r i n g t h e y e a r s 1 9 6 5 - 1 9 7 4 . T h e f o l l o w i n g r e l a t i o n s h i p s 
b e t w e e n t h e m w e r e f o u n d t o h o l d g o o d . 
M l = ( 0 . 9 5 ± 1.4) + ( 0 . 8 1 ± 0 . 0 6 ) M B ( A = 2» t o 5°) 
ML = ( 1 . 2 6 ± 0 . 7 6 ) + ( 0 . 7 6 ± 0 . 0 2 ) M B ( A = 5° t o 10°) 
ML = (1-00 ± 0 . 5 7 ) + ( 0 . 8 0 ± 0 . 0 1 ) M B ( A = 2° t o 10») 

T h e r e g i o n a l v a r i a t i o n of ( MCGS — -MB) h a s b e e n d i s c u s s e d i n t e r m s 
of t h e f o c a l m e c h a n i s m a n d o t h e r p a r a m e t e r s . I t h a s b e e n f o u n d t h a t 
(MCGS— MB) is p o s i t i v e n e a r I n d i a - N e p a l a n d T i b e t b o r d e r w h i l e e l s e w h e r e 
i t is g e n e r a l l y n e g a t i v e . 

RIASSUNTO. — L e m a g n i t u d o MB e d ML s o n o s t a t e d e t e r m i n a t e p e r 
q u e i t e r r e m o t i a v v e n u t i d u r a n t e gli a n n i 1 9 6 5 - 1 9 7 4 , e n t r o u n ' a r e a e p i c e n t r a l e 
c o m p r e s a t r a 2° e 10° d a N u o v a D e l h i . 

L e r e l a z i o n i c h e l e g a n o MB a d ML s o n o r i s u l t a t e v a l i d e e s o n o le s e g u e n t i : 
M L = ( 0 . 9 5 ± 1.4) + ( 0 . 8 1 ± 0 . 0 6 ) M B ( A = 2" t o 5°) 
ML = ( 1 . 2 6 ± 0 . 7 6 ) + ( 0 . 7 6 ± 0 . 0 2 ) M B ( A = 5° t o 10°) 
ML = (1-00 ± 0 . 5 7 ) + ( 0 . 8 0 ± 0 . 0 1 ) M B ( A = 2" t o 10°) 

È s t a t a d i s c u s s a l a v a r i a z i o n e r e g i o n a l e (MCas — MB) b a s a n d o s i s u l 
m e c c a n i s m o f o c a l e e d a l t r i p a r a m e t r i . 

L a d i f f e r e n z a s u d d e t t a h a v a l o r e p o s i t i v o al c o n f i n e f r a I n d i a - N e p a l e 
T i b e t , m e n t r e a l t r o v e r i s u l t a g e n e r a l m e n t e n e g a t i v a . 

(*) G e o p h y s i c s D e p a r t m e n t , I n d i a n S c h o o l of M i n e s , D h a n b a d , I n d i a . 
(**) I n d i a M e t e o r o l o g i c a l D e p a r t m e n t , L o d i R o a d , N e w D e l h i . 3, I n d i a . 



3 8 2 M. P . CIIIIABRA - R . K . S. CIIAUHAN - H. N . SRI VAST A VA - H . M. C H A U D H U R Y 

I N T R O D U C T I O N 

The m a g n i t u d e scales derived f r o m body waves and surface waves 
h a v e been widely accepted a f t e r t h e installation of world wide seismo-
graph system. However while using t h e m for e a r t h q u a k e s occurring 
within t h e epicentral distance of ten degrees, several difficulties are 
encountered. I n particular, surface waves of 20 ± 2 seconds period 
are rarely developed within this epicentral range to allow a c o m p u t a t i o n 
of Ms (surface wave magnitude). On t h e other h a n d , t h e use of t h e 
body wave m a g n i t u d e , MB has been recommended for epicentral 
distances larger t h a n 5 degrees. The d e t e r m i n a t i o n of MB is difficult 
when t h e initial motion within a few cycles of t h e onset of P - w a v e s 
is disturbed due to t h e complexities of t h e crustal s t r u c t u r e as generally 
observed for t h e H i m a l a y a n e a r t h q u a k e s . Also, MB c a n n o t be calcu-
lated for strong earthquakes, which r e n d e r t h e record white. 

For earthquakes occurring within 600 k m , t h e local m a g n i t u d e , 
ML first derived b y E i c h t e r for southern California based on the records 
of s t a n d a r d Wood Anderson Seismographs is generally used. Since 
however the magnification of t h e torsion seismometer is q u i t e low, m a n y 
earthquakes occurring in the H i m a l a y a n region are n o t recorded b y 
t h e m . Thus, t h e only a l t e r n a t i v e is t o use MB for such smaller events 
inspite of its limitations within 5 degrees. 

The object of this p a p e r is to s t u d y t h e relationship between MB 
and ML for t h e epicentral distance range of 2 to 10 degrees so t h a t 
t h e effects of using MB for A < 5 a n d ML > 5.5 m a y be b r o u g h t out. 
I n addition, t h e regional v a r i a t i o n of the C.G.S. m a g n i t u d e M, Mcas 
versus MN and ML has also been a t t e m p t e d in t h e light of t h e d o m i n a n t 
focal mechanism in different regions. 

D A T A A N D A N A L Y S I S 

For this study, t h e records of all t h e e a r t h q u a k e s with foci within 
t h e crust which occurred w i t h i n t h e epicentral distance of 2 t o 10 de-
grees f r o m New Delhi were examined for t h e years 1965 t o 1971. A 
t o t a l of 150 earthquakes were selected out of which MB a n d ML b o t h 
could be determined for 52 e a r t h q u a k e s only. Although t h e focal d e p t h 
determination were available only u p t o 1973 f r o m t h e Bulletin of 
t h e I n t e r n a t i o n a l Seismological Centre, we h a v e included those earth-





382 M. P. CIIIIABRA - R. K. S. CIIAUHAN - H . N . SRI VAST A VA - H. M. C H A U D H U R Y 

quakes occurring during 1974 for which reliable e s t i m a t e s of d e p t h s 
•were available f r o m I n d i a n Seismological n e t w o r k . The d a t a for t h e 
e a r t h q u a k e s is given in Table 1. 

The b o d y wave magnitudes, MB were d e t e r m i n e d b y using t h e 
Gutenberg E i c h t e r ' s relation, n a m e l y 

MB = log 10 + Q [1] 

Where Am*x is one half of t h e t h r o u g h to p e a k t r a c e a m p l i t u d e 
in microns, K is t h e p e a k magnification in t h o u s a n d s a t t h e period to 
be read f r o m the i n s t r u m e n t a l response characteristics of W W S S N 
Benioff system, T t h e period of t h e waves within (1 ± 0.3) records 
of t h e onset of P and Q is t h e d e p t h distance f a c t o r . I t m a y be men-
tioned t h a t t h e values of Q h a v e been t a b u l a t e d f r o m 2 degree onwards. 

The local m a g n i t u d e , ML was determined f r o m t h e t w o horizontal 
component torsion seismometers aligned in n o r t h - s o u t h and east-west 
directions. Since t h e magnification of these i n s t r u m e n t s has been set 
a t 1000 a t Delhi Seismological Observatory, t h e average of t h e m a x i m u m 
double amplitudes measured in b o t h t h e components (after allowing 
for t h e t r a c e thickness and reducing to ground a m p l i t u d e in microns) 
has been used to c o m p u t e ML- The plot of MB and ML is shown i n 
fig. 1 where details will be discussed later. 

R E S U L T S A N D D I S C U S S I O N 

F r o m t h e definition of MB and ML one m a y n o t e t h a t t h e r e is a 
v e r y narrow range of epicentral distance around 5 degrees where b o t h 
t h e m a g n i t u d e scales are theoretically valid. A search for such earth-
quakes gave us meagre d a t a (fig. 2). However in order t o e x a m i n e t h e 
effects of using MB for A < 5 and MR, > 5.5, two s e p a r a t e plots of M„ 
and ML were m a d e (fig. 1). The following relations h a v e been f o u n d 
to hold good by least squares m e t h o d s : 

M L = (0.95 ± 1.4) + (0.81 ± 0.06) M B ( A = 2° t o 5°) [2] 
M L = (1.26 ± 0.76) + (0.76 ± 0.02) M B (A = 5° t o 10°) [3] 
M L = (1.0 ± 0.57) + (0.80 ± 0.01) M B ( A = 2° t o 10°) [4] 

The relationship between MB and ML has been deducted earlier [2] as 

Mb = 1.7 + 0.8 ML — 0.01 J f L 2 



MB VERSES ML 

X - A 2* TO 5* 
O - A 5* TO I O*. 
DEPTH < 60 KMS 

4 4 4-8 5-2 5-6 6 0 6-4 6 8 7 0 7-6 

MB 

F i g . 1 - T h e r e l a t i o n s h i p b e t w e e n MB a n d ML f o r e a r t h q u a k e s i n H i m a l a y a s 
a n d n e i g h b o u r h o o d . 

6 - 8 

6 - 6 

6-4 

6 - 2 

60 
5-8 

5 6 

5-4 

5-2 

5 0 
4 8 

4.6 

4-4 

4-2 

M b V E R S E S M l 
A = 4 8 TO 5-5 
D E P T H < 6 0 Km 

4 0 4*4 4-8 5 2 5 6 6 0 6 4 

FIG- 2 MB 

F i g . 2 - T h e v a r i a t i o n of jlIB a n d ML w i t h i n t h e e p i c e n t r a l d i s t a n c e of 
4 . 8 t o 5 . 5 ° . 



382 M. P . C I I I I A B R A - R . K . S . C I I A U H A N - H . N . S R I V A S T A V A - H . M . C H A U D H U R Y 

Comparison of e q u a t i o n [4] with [5] shows t h a t MB t e n d s t o be equal 
t o ML a t m a g n i t u d e 5 i n t h e f o r m e r case while this v a l u e is a r o u n d 
m a g n i t u d e 7 in e q u a t i o n [5]. One of t h e possible causes m a y be t h e 
use of r e l a t i v e higher m a g n i t u d e e a r t h q u a k e s in deriving e q u a t i o n [5J. 
The large v a r i a t i o n of MB and ML on t h e basis of these relationships 
emphasizes t h a t no single relationship m a y be valid in t h e entire magni-
t u d e ranges. More d a t a is t h u s needed to establish MB versus ML 
relationship for m i c r o e a r t h q u a k e s i n t h e H i m a l a y a n region. Although 
several Wood Anderson Seismometers h a v e been installed recently 
along t h e H i m a l a y a n foot lulls, comparison of MB and ML has n o t 
been practicable d u e to t h e d i s t a n t location of t h e New Delhi Obser-
v a t o r y using s t a n d a r d i s e d seismograph s y s t e m . F o r such microearth-
quakes, a n e w m a g n i t u d e scale using t h e t o t a l signal d u r a t i o n is being 
developed whose results will be reported separately. 

Our results show t h a t t h e operational r e q u i r e m e n t s for r e p o r t i n g 
t h e m a g n i t u d e s of t h e e a r t h q u a k e s on t h e basis of New Delhi Obser-
v a t o r y can be a d e q u a t e l y n e t by e x t e n d i n g t h e local m a g n i t u d e scale, 
ML u p t o t h e epicentral distance of 10 degrees. 

The C.G.S. m a g n i t u d e is t h e average of t h e b o d y wave m a g n i t u d e s 
reported b y t h e s t a n d a r d i z e d stations all over t h e world a n d t h u s t a k e s 
i n t o consideration t h e effects of t h e source mechanism. The difference 
of MCGS — MB t h u s brings out t h e regional effects (fig. 3). Although 
t h e influence of t h e focal m e c h a n i s m on ML is less understood m a i n l y 
because of its restricted use, ( M C G S — ML) h a s also been p l o t t e d for 
t h e scale of comparison (fig. 4). Fig. 5 shows t h e focal m e c h a n i s m 
solution of some e a r t h q u a k e s in t h e same region, which h a v e been 
t a k e n f r o m t h e results of C h a u d h u r y et al., 1974 (2), Nowroozi (4), 
1972, T a n d o n and Srivastava, 1975 (7). 

Since t h e m a g n i t u d e s depend u p o n t h e focal depths, i t was desi-
rable t o s e p a r a t e t h e e a r t h q u a k e s occurring in t h e g r a n i t i c and basaltic 
layers. T a n d o n and D u b e , 1973 (6), using t h e body waves h a v e f o u n d t h e 
thickness of these two layers as 38 km and 13 respectively, for t h e 
H i m a l a y a n region. However some e a r t h q u a k e s h a v e occurred close 
t o t h e H i m a l a y a n foot hills where t h e c r u s t a l s t r u c t u r e and t h e g r a n i t i c 
layers are relatively less. Thus t h e e a r t h q u a k e s were grouped i n t o 
two focal d e p t h ranges n a m e l y 0 to 30 Ion and > 30 Ion b u t restricted 
to t h e c r u s t . 

I t m a y be seen f r o m lig. 3 t h a t n e a r t h e H i m a l a y a n Tibet a n d N e p a l 
border, MCGS — MB is positive for b o t h t h e focal d e p t h s and elsewhere 
it is generally n e g a t i v e . A l t h o u g h t h e n a t u r e of t h e f a u l t i n g (fig. 5) 



T A B L E 2 

E a r t h q u a k e m a g n i t u d e s 

¿\ = 5 ° t o 10°: d e p t h u p t o 60 k m . 

s . 
N o 

D a t e 
O r i g i n T i m e 

h m s 

L a t i t u d e 

°N 

L o n g i t u d e 

°E 

D e p t h 
in k m 

Mag. 
CGS 

A i n 
d e g r e e s 

Mb 
( D e l h i ) 

Ml 
( D e l h i ) 

1 12 1.1965 13 32 24 27 6 88 23 6 1 9 . 4 6 . 6 6 . 2 

2 29 1. » 20.06 02 4 35 6 73 6 41 5 7 1 0 . 0 5 . 7 5 . 6 

3 17 6. » 20 14 48 6 32 87 8 15 5 4 9 . 7 5 . 7 5 . 7 

4 11 1.1966 09 12 59 3 34 72 36 5 4 9 . 1 5 . 7 5 . 6 

5 24 1. » 07 23 07 6 29 9 69 7 26 5 8 6 . 7 6 . 2 6 . 5 

6 24 I . » 15 32 48 1 29 9 69 8 14 5 3 6 . 4 5 3 5 . 4 

7 02 2 . » 09 20 07 5 33 9 73 37 5 3 8 . 3 5 . 7 5 . 7 

8 09 2. » 08 22 17 9 29 8 69 8 16 5 2 8 . 7 5 . 8 5 . 9 

9 13 2 . » 19 09 47 4 29 8 69 7 9 5 1 8 . 7 5 . 8 6 . 3 

10 17 2. » 18 26 17 7 29 9 69 8 40 4 4 8 . 7 6 . 5 5 . 6 

11 04 3. » 06 01 05 30 0 70 0 33 4 4 8 . 4 5 . 8 6 . 0 

12 06 4 . » 01 51 51 8 35 73 54 5 1 9 . 3 6 . 4 6. 1 

13 01 8. » 19 09 55 1 29 9 68 8 33 5 8 7 . 3 6 . 3 5 . 9 

14 02 8 . » 05 41 37 4 30 68 8 32 5 2 7 . 5 5 . 9 5 . 5 

15 02 2.1967 07 37 54 9 39 7 75 5 39 5 3 1 0 . 7 6 . 0 5 . 0 

16 30 5. » 18 56 28 7 31 7 30 1 44 4 6 6 . 4 5 . 0 4 . 9 

17 11 2.1968 20 38 29 4 34 2 78 6 44 5 1 5 . 5 5 . 1 4 . 8 

18 03 3. » 09 31 20 2 34 7 72 3 43 5 2 7 . 1 5 . 4 5 . 3 

19 0 4 . 4 . » 01 44 26 4 24 6 66 33 5 0 1 0 . 3 5 . 6 5 . 7 

20 26 7. » 20 48 07 2 32 07 70 07 50 4 8 7 . 2 5 . 0 4 . 9 

21 26 6. » 00 46 13 8 37 7 69 9 16 5 2 10.0 6. 1 0 . 0 

22 18 11. » 05 05 04 3 33 1 71 1 41 5 3 6 . 8 5 . 6 5 . 1 

23 22 1.1969 19 42 21 8 32 2 70 23 4 7 7.1 5 . 8 5 . 2 

24 03 3. » 14 03 00 5 31 71 8 35 4 5 5 . 5 4 . 6 5 . 3 

25 10 4.1970 10 23 58 2 25 3 66 7 33 5 1 9 . 7 6 . 3 5 . 5 

26 12 5. » 22 07 39 4 27 5 67 5 7 4 7 8 . 5 4 . 7 5 . 2 

27 14 8. » 00 36 34 5 31 2 74 3 44 5 
2 5 . 2 5 . 7 5 . 4 

28 08 1.1971 23 52 16 3 29 1 69 1 19 5 2 7.1 5 . 7 5 . 8 

29 24 3. » 13 39 46 3 30 3 67 8 18 4 9 8 . 0 5 . 4 5 . 0 

30 21 12. » 09 54 40 35 7 73 4 15 5 7 1 0 . 0 6 . 2 6 1 

31 06 11.1972 10 56 14 26 8 88 4 59 4 4 9 . 8 5 . 6 5. 7 

32 20 1.1973 12 34 20 29 3 68 6 19 5 3 7 . 1 5 . 9 5 . 6 

33 24 2 . » 21 57 04 26 7 66 3 48 4 2 9 . 2 6 . 0 5 . 2 

34 09 2.1974 04 07 37 7 28 7 69 4 33 4 9 8 . 5 5 . 4 4 . 8 

35 07 4 . » 16 07 43 8 32 0 69 7 44 4 8 9 . 6 4 . 8 5 . 3 

36 03 8. » 04 08 13 9 35 4 71 7 20 5 0 10.3 6 . 0 5 . 4 





F i g . 4 - R e g i o n a l v a r i a t i o n of MCGS — ML o v e r H i m a l a y a a n d n e i g h b o u r h o o d . 



T H E R E L A T I O N S H I P B E T W E E N T H E B O D Y W A V E E T C . 3 8 9 

F i g . 5 - F o c a l m e c h a n i s m s o l u t i o n s of s o m e e a r t h q u a k e s in H i m a l a y a a n d 
n e i g h b o u r h o o d (see r e f e r e n c e ) . 

is generally of t h r u s t t y p e with different a m o u n t s of strike slip compo-
n e n t in different regions, t h e o r i e n t a t i o n of t h e nodal planes w i t h 
reference t o t h e New Delhi Seismological Observatory could t h u s 
be responsible for this t y p e of regional variations. The regional va-
r i a t i o n of ( M C G S — ML) is comparatively less m a r k e d (fig. 4) although 
this also gives a positive residual n e a r t h e H i m a l a y a n t r i j u n c t i o n . 

P a d m a n a b h a m u r t l i y , 1969 (5), has f o u n d negative residual f r o m 
( M C G S —• ML) a t New Delhi f r o m shallow e a r t h q u a k e s , b u t due to 
lack of d a t a , t h e regional v a r i a t i o n was n o t be a t t e m p t e d within 10 
degrees. 

Ignoring t h e regional v a r i a t i o n of (MCGS — MB) or ML t h e follow-
ing relations hold good (figs. 6 a, b). 

(MCGS — MB) = ( — 2 . 2 + 0 . 3 ) + ( 0 . 3 8 + 0 . 0 2 ) MCGS [ 6 ] 

(MCGS — ML) = ( — 2 . 3 + 0 . 3 ) + ( 0 . 4 5 + 0 . 0 2 ) MCGS [ 7 ] 

Comparison of [6] with [7] shows t h a t b o t h t h e scales ML or MB 
can be used with almost same accuracy u p t o 10 degrees f r o m New 
Delhi Observatory. 



P i g . Oa - T h e r e l a t i o n s h i p b e t w e e n ( M C G S — MB) a n d Macs 

F i g . Ob T h e r e l a t i o n s h i p b e t w e e n (MCGS — i l / t ) a n d 31, 



T H E R E L A T I O N S H I P B E T W E E N T H E B O D Y W A V E E T C . 

C O N C L U S I O N 

The above s t u d y brings out t h e following results: 

1) - The following relationships between MB and ML hold good. 
M L = (0.95 ± 1.4) + (0.81 ± 0.06) M B ( A = 2° to 5") 
M L = (1.26 ± 0.76) + (0.76 ± 0.02) M B ( A = 5» to 10") 
M L = (1.0 ± 0.57) + (0.80 ± 0.01) M B ( A = 2° to 10") 

The local m a g n i t u d e scale, ML can be used u p t o 10 degrees for 
t h e crustal e a r t h q u a k e s occurring i n t h e H i m a l a y a n Kritliar Sulaiman 
ranges. 

2) - Some regional variation of ( M C G S — M B ) has been n o t e d . 
( M B — MCGS) is positive for t h e H i m a l a y a n Nepal Tibet tri-junction 
and general negative elsewhere. 

R E F E R E N C E S 

(' ) BATII, M., 1973. - Introduction to Seismology, p . 112. 

( 2 ) C H A U D H U K Y , H . M . , S R I V A S T A V A , H . N . a n d S U B I I A R A O , J . V . , 1 9 7 4 . -

Seismotectonics investigation of the Himalaya. " H i m a l a y a n G e o l o g y " , 4 , 
p p . 4 8 1 - 4 9 1 . 

( 3 ) G U T E N B E R G , B . a n d R I C H T E R , G . F . , 1 9 5 6 . - Magnitude and energy oj 
earthquakes, " A n n a l i G e o f i s . " , 9 . 

( 4 ) N O W R O O J I , A . N . , 1 9 7 2 . - Focal mechanism oj earthquakes in Persia, 
Turkey, West Pakistan and Afghanistan and plate tectonics oj the Middle 
East. " B u l l S e i s m . Soc. A m . " , 6 2 , p p . 8 2 3 - 8 5 0 . 

( 6 ) P A D M A N A B H A M U R T I I Y , B . , I 9 G 9 . - Station magnitude Connections for Shil-
long, Poona and New Delhi. " I n d . J r . M e t . G e o p h y s i c s " , 2 0 , p . 275. 

( 6 ) TANDON, A . N . a n d DUBE, R . K . , 1 9 7 3 . - I n : " P u r e a n d A p p l i e d G e o p h y -
s i c s " , 1 0 5 . 

(7) TANDON, A. N . a n d SRIVASTAVA, H . N . , 1975. - Focal mechanism oj some 
recent Himalayan earthquakes and regional plate tectonics. " B u l l . S e i s m . 
Soc. A m . " , 65, p p . 9 6 3 - 9 7 0 .