Statistics o f Indian earthquakes - Frequency energy 

distribution 

R . K . S. CIIOUHAN ( * ) - Y . K . SHRIVASTAVA ( * * ) 

R e c e i v e d on December 20th, 1973 

SUMMARY. — Frequency-magnitude and energy-magnitude distribu-
tion of the Indian earthquakes have been studied f o r both shallow and 
intermediate earthquakes using data f r o m 1910 to 1969. Secular energy 
released b y the Indian earthquakes has been studied by considering cumu-
l a t i v e energy release and it is found that these results m a y be used to estimate 
the size of largest conceivable earthquakes f o r shallow and intermediate 
f o c a l depths. 

RIASSUNTO. — Dai dati reperiti dal 1910 al 1969, è stata studiata la 
distribuzione della frequenza-magnitudo e dell'energia-magnitudo di ter-
r e m o t i a carattere superficiale e intermedio avvenuti in India, nonché l'e-
nergia secolare liberata da questi ultimi considerando l'energia totale libe-
rata. Si è t r o v a t o che questi risultati possono essere usati per valutare l'in-
tensità, per quanto grande essa possa essere, di terremoti a f u o c o super-
ficiale e intermedio. 

1. - INTRODUCTION 

G u t e n b e r g a n d R i c h t e r i n t h e i r m o n u m e n t a l w o r k " S e i s m i c i t y 

of t h e E a r t h a n d a s s o c i a t e d p h e n o m e n a " ( 5 ) h a v e s h o w n t h a t t h e r a t e 

of e n e r g y r e l e a s e d b y e a r t h q u a k e s is e x t r e m e l y i r r e g u l a r f o r t h e w h o l e 

w o r l d . T h e s i n g l e y e a r 1906 a c c o u n t s f o r a b o u t o n e n i n t h of t h e g l o b a l 

e n e r g y r e l e a s e , so t h a t t h e a v e r a g e a n n u a l r e l e a s e b e t w e e n 1907-1952 

( * ) D e p a r t m e n t of Geophysics, Indian School of Mines, Dhanbad-
826004, I n d i a . 

( * * ) D e p a r t m e n t of Geophysics, Banaras Hindu University, Varanasi-5, 
I n d i a . 



()0 K. K. 8. CHOUHAN - V. K. SHKIVASTAVA 

is only 11.0 X 1020 ergs while the average between 1906-1952 is 
12.4 x 1026 ergs, using energy magnitude relation 

log E = 12.0 + 1.8 M [1] 

where E is the energy in ergs and M is the Richter's magnitude. 
Intermediate shocks show that the maximum energy was releas-

ed in 1910 and 19.11 owing to two large earthquakes in these years. 
The ratio of average annual energy release in shallow, intermedi-

ate and deep earthquakes is 31:4:1 according to Gutenberg and Rich-
ter (5). But in the year 1920 this ratio was 265:2:1 i.e. about 98% 
of the entire energy released in shallow earthquakes. Similarly 
in the year 1969, Chouhan and Das (3) reported that about 98% of 
the energy was released by shallow earthquakes. 

The energy released in different magnitude ranges for shallow, 
intermediate and deep shocks is found to decrease with the value of 
magnitude. 

The number of shocks decreases with depth. According to Gu-
tenberg and Richter (5) the number of shocks decreases to a minimum 
at a depth of about 450 km, there being a clear rise to a minor maxi-
mum at a depth of about 600 km, beyond which the number falls 
off very rapidly. Ritsema (8) while considering the distribution of 
intermediate and deep shocks of varying magnitudes with depth, 
found that the curves showing variation of earthquake number show 
maxima at depths of 80 to 90 kms and 220 to 280 kms with a minor 
maxima at a depth of about 180 kms. These general results can be 
confirmed by use of small agreegate numbers in the range of times 
and magnitudes considered statistically. Thus, there is no general 
agreement on the distribution of earthquakes with depth, however, 
these results are expected to be different in different geographic re-
gions of the world. 

2 . - O B S E R V A T I O N A L D A T A 

For the frequency-energy distribution of shallow and intermediate 
earthquakes of India, the data has been extracted from Gutenberg 
and Richter (5), Seismological Bulletins of India Meteorological De-
partment, I.S.S. bulletins and U.S.C.G.S. bulletins in addition to other 
sources; the span of time being sixty years (from 1910 to 1969). The 
magnitudes used here are all Richter's magnitudes 31 ^ 5. 



S T A T I S T I C S OF I N D I A N E A R T H Q U A K E S - F R E Q U E N C Y E N E R G Y E T C . ()1 

For calculations of energy from the magnitude values M , the 
following relation of Gutenberg and Eichter (") have been used. 

log E = A + B M [2] 

where A = 1 1 . 8 and B = 1.5. 

3 . - F R E Q U E N C Y - E N E R G Y D I S T R I B U T I O N 

Annual frequencies of all the earthquakes of different magnitudes 
M in the range of 5 to 8.6 have been calculated using all the earthquakes 
that have occurred since 1910; for magnitudes 5 to 5.2 the time span 
is 13 years. Thus, the frequencies of shallow (N.) and intermediate 
earthquakes (Nt) have been determined and given in Table 1. Annual 
energy released by shallow (Es) and intermediate (Et) earthquakes 
of different magnitudes has been calculated using equation [2] and is 
also tabulated in Table 1. 

Figures 1 and 2 show the frequency-energy distribution of earth-
quakes against magnitude, the general shape of the figures being 
approximately parallelogram defining the boundaries of the frequency 
and energy of different magnitudes in the range of 5.0 to 8.6. These 
figures clearly show that the frequency of earthquakes is maximum 
when the energy release is minimum or vice versa, a well known fact 
in earthquake seismology. In seismology these facts are expressed 
by representing logarithmic dependence of E the seismic energy 
and N the earthquake frequency, on magnitude M. These relations 
are known as energy-magnitude (Eq. 2) and frequency-magnitude 
relations as given by Gutenberg and Eichter (5) in the form 

log N = a — bM [3] 

where a and b are constants. 

However in the present analysis the energy magnitude relation 
has been assumed logarithmic and then the energy values are cal-
culated as given in the Table 1. The slope of the two sides of the ap-
proximate parallelogram (not shown in the figures 1 and 2) may take 
any shape depending upon the values of B and b. I t has been ob-
served by Utsu (10), Chouhan (4), Page (7) that the value of b varies 
from 0.4 to 1.5 and Bath ( l ) has also shown that the value of B may 
be taken as 1.44 also, apart from Gutenberg-Eichter's value of 1.5. 
Thus we can say that the slope of E changes from 1.44 to 1.50 while 



6 2 R . K . S. C H O U H A N - V . K . S H R I V A S T A V A 

T a b l e 1 - A N N U A L F R E Q U E N C Y A N D A N N U A L E N E R G Y R E L E A S E D B Y S H A L L O W 

A N D I N T E R M E D I A T E E A R T H Q U A K E S OF D I F F E R E N T M A G N I T U D E S D U R I N G 

T H E P E R I O D 1 9 1 0 TO 1 9 6 9 W I T H M ^ 5 . 

Annual frequency of Annual energy released by 
earthquakes Magnitude earthquakes ( X l O 2 0 ergs) 

Shallow (N.) Intermediate 
(Ni) 

(M) Shallow (E*) Intermediate 
(Ei) 

1- 2. 3. 4. 5. 

0.0167 8.6 1182.00 

0.0333 — 8.3 592.00 — 

0.0333 — 8.0 210.00 — 

0.0667 0.0167 7.7 149.30 37.39 

0.1334 — 7.6 211.40 — 

0.0667 0.0333 7.5 74.80 37.36 

0.0333 — 7.4 26.45 — 
0.0833 0.0167 7.3 46.10 9.30 

0.0667 0.0167 7.2 26.54 6.60 

0.0500 0.0167 7.1 14.45 4.70 

0.0667 0.1167 7.0 13.31 23.28 
— 0.0167 6.9 — 2.35 

0.0833 — 6.8 8.30 — 
0.1167 0.1500 6.7 8.20 10.62 
0.0167 0.0833 6.6 0.83 4.17 
0.1500 0.3167 6.5 5.32 11.24 
0.0167 0.0500 6.4 0.42 1.26 
0.2167 0.2167 6.3 3.86 3.86 
0.1000 6.2 1.26 — 
0.1834 0.0667 6.1 1.60 0.59 
0.3167 0.2344 6.0 1.99 1.47 

0.1334 0.0500 5.9 0.60 0.23 
0.2334 0.1167 5.8 0.72 0.36 
0.3000 0.4834 5.7 0.66 1.06 
0.2334 0.1334 5.6 0.37 0.21 
0.3334 0.4000 5.5 0.37 0.44 

0.5834 0.3500 5.4 0.46 0.28 
1.3669 0.2500 5.3 0.78 0.14 

3.6900 0.8330 5.2 1.47 0.33 
3.7600 1.0000 5.1 1.06 0.28 
2.6900 2.0700 5.0 0.54 0.41 



S T A T I S T I C S OF I N D I A N E A R T H Q U A K E S - F R E Q U E N C Y E N E R G Y E T C . ()1 

A N N U A L F R E Q U E N C Y ( N S ) A N N U A L E N E R G Y R E L E A S E ( E S ) I N E R G S 

10 10 IÓ1 
. 20 21 22 23 ,„24 
10 10 10 10 10 10 10 

-7.5-

Fig. 1 - Frequency-energy distribution of Indian earthquakes against 
magnitude M ^ 5 for a period of 60 years, from 1910 to 1969. The figure 

shows the distribution for shallow earthquakes. 

A N N U A L F R E Q U E N C Y ( N ¡ ) A N N U A L E N E R G Y R E L E A S E ( E i ) l N E R G S 
10' 10" id1 i o 2 i o 1 9 I O 2 0 io21 I 0 2 2 

7.5-

Fig. 2 - Frequency-energy distribution of Indian earthquakes against 
M 5 for the same period of fig. 1. The distribution is for intermediate 

earthquakes. 



0 4 R . K . S. CHOUHAN" - V . K . S I I R I V A S T A V A 

the slope of N changes from —0.4 to —1.5. Hence, when the values 
of B are 1.4 (approximately) to 1.5 and b 1.4 to 1.5 then the shape 
of figures 1 and 2 becomes parallelogram. For all other values of b the 
general shape of figures 1 and 2 is quadrilateral tending to a triangle 
for small values of b. These observations may be interpreted in sup-
port of energy magnitude relations of Gutenberg-Ricliter (°) and 
Bath where they have used the upper limit of the slope of frequency 
magnitude relation. 

These relations can be expressed mathematically by combining 
the equations [2] and [3] in the form 

N (E) = C.E.-i»"»-1 [4] 
where 

10 {a+Ab/B) 

° = ¿ i n f o -

where N(E) dE is the number of earthquakes with energy between 
E and E + dE. 

Here it may be mentioned that in U.S.S.B, the frequency-energy 
relation is used in the form 

log n(K) — G — v K [5] 
where 

K = log E and v = bjB 

which is similar to relation [4], 

4. - SECULAR ENERGY RELEASE 

In the years 1913, 1919 and 1953 the energy released by earth-
quakes was less than 1019 ergs and in the years 1934 and 1950 the 
maximum energy exceeding 1024 ergs was released. The average an-
nual energy released by shallow earthquakes is 2.58 x 1023 ergs and 
for the intermediate earthquakes 1.57 x 1022 ergs respectively; the 
annual total release being 2.74 x 1023 ergs. There are only eight 
years in which the energy release was more than the average energy 
release per year. The ratio of the average energy release in shallow 
and intermediate earthquakes is 10.5:1. Gutenberg and Richter (5) 
have shown that ratio for the shallow intermediate and deep earth-
quakes is 31:4:1. 

Each plotted points in figures 3 and 4 represents cumulative 
energy released by earthquakes since the beginning of 1910 until the 



S T A T I S T I C S OF I N D I A N E A R T H Q U A K E S - F R E Q U E N C Y E N E R G Y E T C . ()1 

T I M E IN Y E A R S 
Fig. 3 - Cumulative sum of annual energy plotted against time for the same 
period of figs 1, 2. The figure is a plot of shallow earthquakes. 

end of 1909, for a period of 60 years. The points are bounded in bet-
ween parallel straight lines of which the upper line, in fig. 3 is express-
ed for shallow earthquakes. 

5 X = (3.56 t + 2.56) 1023 ergs [6] 



66 R . K . S. C I I O U I I A N - V . K . S H R I V A S T A V A 

where 2-Es is cumulative energy for shallow earthquakes, and for in-
termediate earthquakes 

S-Bi = (2.23 t + 0.85) IO22 ergs [7] 

where is the cumulative sum of energy for intermediate earth-
quakes. 

In equations [6] and [7] t is counted from 1910. The distance 
between the two parallel lines in fig. 3 corresponds to about 2 x 1024 

ergs which is very close to the energy of the largest conceivable earth-
quakes. Similarly in fig. 4 the distance between the two parallel lines 
corresponds to 1.81 x 1023 ergs which is very close to the largest in-
termediate shocks observed in the past 60 years. 

0 ' -i- —I - i - ! , 
1910 1930 1950 1970 

T I M E IN Y E A R S 

Fig. 4 - See the caption of fig. 3. The plot is for intermediate earthquakes. 



S T A T I S T I C S OF I N D I A N E A R T H Q U A K E S - F R E Q U E N C Y E N E R G Y E T C . ()1 

The slope in equations [6] and [7] gives approximately the rate 
of accumulation of energy in the crust and in the upper mantle upto 
a depth of about 300 km, respectively. 

Similar study carried out by Tsuboi (9) shows that the rate of 
accumulation of energy in Japan is 2.24 x 1023 ergs per year and this 
rate of energy accumulation is 2.5 times higher than the rate of ac-
cumulation arrived at here which, after normalising in area, comes 
to 0.89 x 1023 ergs per year. These interpretation of secular seismic 
energy release is quite in line with the observations of Bath and 
Duda (2). The rate of energy accumulation for shallow and intermedia-
te earthquakes is always greater than the average energy release 
in these shocks and at the most they may be equal. 

Distribution of number of earthquakes having M > 5.3 with 
depth is shown below in TABLE 2. 

Depth range in kms. 0-50 50-100 100-150 150-200 200-250 250-300 

Number of shocks. 279 51 35 39 76 1 

The distribution of earthquakes does show a maximum at a depth 
of 200-250 kms which is in agreement with Bitsema's (8) second maxi-
mum and also agrees with Gutenberg-Richter's minimum in the 
depth range of 250-300 kms. 

5 . - C O N C L U S I O N S 

1) Frequency-magnitude and energy-magnitude distribution of 
shallow and intermediate earthquakes shown in figures 1 and 2 show 
logarithmic dependence of N and E on M and relation between N 
and E may be written in the form N (E) = G.E. -<w«>-1 

2) Secular studies of energy release clearly show that the average 
energy release is in general less than rate of accumulation of energy. 
I t also follows from figures 3 and 4 that the maximum size of concei-
vable shallow earthquake is M ~ 8.6 and of intermediate earthquake 
is M ~ 7.6. 

3) Distribution of number of earthquakes with depth shows a 
maxima at a depth of 200 to 250 kms and a minima in the depth 
range of 250 to 300 kms. 



66 
R . K . S. C I I O U I I A N - V . K . S H R I V A S T A V A 

A c k n o w l e d g e m e n t s 

The authors are grateful to Profs. J. Singh, H . S. Rathor, E . K . 
Yerma for discussions from time to time and for providing all the 
facilities to carry out the present work. 

R E F E R E N C E S 

(') BATH M., 1958. - The energies of seismic body waves and surface waves. 
"Contributions in Geophysics in hon. of B. Gutenberg", 1-16. 

(-) BA'rn M. and DUDA S. J., 1964. — Earthquake volume, fault plane area, 
seismic energy, strain, deformation and related quantities. " A n n . di 
Geofis.", X V I I , 353-368. 

(3) CIIOUIIAN R. K . S. and DAS U. C., 1971. - Preliminary report on Global 
seismicity, frequency energy distribution of earthquakes. " P u r e and 
Applied Geophysics", 89, 98-108. 

(4) CIIOUIIAN R. K . S., 1970. - On the frequency magnitude relation 
Log N = a — bM. " P u r e Appl. Geophys.", 81, 119-123. 

( 6 ) GUTENBERG B . a n d RICHTER C. F . , 1954. - Seismicity of the Earth and 
associated phenomena. "Princeton University Press". 

(8) GUTENBERG B. and RICIITER C. P., 1956. - Magnitude and Energy of 
earthquakes, " A n n . di Geofis.", I X , 1-15. 

(7) PAGE R., 1968. - Aftershocks and microaftershocks of the great Alaskan 
earthquake of 1964. "Bull. Seis. Soc. A m . " , 58, 1131-1168. 

(8) RITSEMA A . R., 1954. - A statistical study of seismicity of the Earth. 
"Meteorol. and Geopliys. Serv. Indonesia", 46, 41-46. 

(°) TSUBOI C., 1964. - Time rate of energy release by earthquakes in and near 
Japan. " J l . Pliys. E a r t h " , 12, 25-36. 

(10) UTSU T., 1961. — A statistical study on the occurrence of aftershocks. 
"Geophys. Mag.", 30, 521-605.