DEVELOPMENT OF MODELS FOR RATING SEISMIC ACTIVITIES USING RADIATED ENERGY OF EARTHQUAKES

ABSTRACT

Seismic activity evaluation is usually carried out using the Gutenberg-Richter’s (G-R) relation. This relation is defective because it does not include area of the region involved, thereby making a small but active region to be underrated. Secondly it gives the rate of seismicity of a region in terms of the total number, N, of earthquakes irrespective of magnitudes. This makes regions with few but great earthquakes to be underestimated since energy due to magnitude m is proportional to 10m. Therefore the method does not justifiably compare seismic activities of two or more regions. Assessment of seismic activities of regions in terms of radiated energy of earthquakes will make comparison reliable because each earthquake magnitude will be converted to its equivalent energy. The aim of this work was to develop models for rating seismic activities in terms of radiated energy of earthquakes.

Considering an arbitrary region of area A where N earthquakes have occurred over a

period T, total radiated energy per unit area per unit time was defined as

Ei TA ; where

 

Ei is the energy radiated by the ith earthquake. The Ei

 

was expressed in terms of earthquake

 

moment magnitude, mi, as

 

E = 10(1.5mi +11.8)

 

using Bath equation to yield the first model Á1 . A

second model,

 

Á2 , was developed by dividing T into equal sub-periods, and substituting for

m in the G-R relation. Fifty-year (1956 - 2005) earthquake data for 10 regions in the world seismic zones were obtained from the Catalogue of Advanced National Seismic System (ANSS), U.S.A. The regions were Mediterranean (Rg1), Southern Africa (Rg2), West Europe (Rg3), West Pacific (Rg4), South Australia (Rg5), Southwest Pacific (Rg6), West of South America (Rg7), West of North America (Rg8), Arctic (Rg9) and Japan (Rg10). Different magnitude types of the data were converted to moment magnitudes using empirical relations of Geller and Kanamori. The G-R relation and the developed models were applied to each region.

The developed models were

1 5 101.5a j / bj

Á1 =

 

 1  k

50 i=1

 

10(1.5mi +11.8)

 

 

A

 

and

 

Á2 =

 

å

j =1

 

 

1/ bj

j

 

´ 1011.8

 

where k is the total number of earthquakes in a region; aj and bj are

G-R constants for the jth sub-period. The average values of G-R constant, a, obtained for regions 1 to 10 were 6.20, 5.06, 3.37, 4.44, 4.56, 5.19, 3.52, 3.95, 6.20, and 3.72. Thus, the

G-R rated the regions as Rg3 < Rg7 < Rg10 < Rg8 < Rg4 < Rg6 < Rg5< Rg2 < Rg9< Rg1.

11 -2  -1

The respective values of Á1 and Á  for regions 1 to 10 in 10 J km yr  were 1.37 and 6.29;

0.08 and 2.07; 0.40 and 3.15; 0.81 and 6.21; 0.65 and 5.16; 0.72 and 5.39; 0.53 and 4.15; 0.22

and 3.04; 0.22 and 3.05; 3.76 and 8.36. Both models rated the regions as Rg2<Rg8<Rg9<Rg3<Rg7<Rg5<Rg6<Rg4<Rg1<Rg10.

The two models gave a more reliable seismic activity rating than Gutenberg-Richter’s relation. The first Model is suitable for all categories of magnitude spread including those for which Gutenberg-Richter’s constants are indeterminate while the second model will not be applicable when Gutenberg-Richter’s constants are indeterminate.

Keywords: Seismic activities, Gutenberg-Richter’s relation, Earthquakes, Radiated

energy.

Word Count: 487.