A theoretical study of correlation between scaled energy and earthquake magnitude based on two source displacement models

The correlation of the scaled energy, e = E-s/M-0, versus earthquake magnitude, M-s, is studied based on two models: (1) Model 1 based on the use of the time function of the average displacements, with a omega(-2) source spectrum, across a fault plane; and (2) Model 2 based on the use of the time function of the average displacements, with a omega(-3) source spectrum, across a fault plane. For the second model, there are two cases: (a) As tau = T, where tau is the rise time and T the rupture time, lg(e) similar to -M-s; and (b) As tau << T, lg(e) similar to -(1/2) Ms. The second model leads to a negative value of e. This means that Model 2 cannot work for studying the present problem. The results obtained from Model 1 suggest that the source model is a factor, yet not a unique one, in controlling the correlation of e<^> versus M-s.