A theoretical study of correlation between scaled energy and earthquake magnitude based on two sourc

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The correlation of the scaled energy,e?=Es/M0,versus earthquake magnitude,Ms,is studied based on two models:(1)Model 1 based on the use of the time function of the average displacements,with a x-2source spectrum,across a fault plane;and(2)Model 2 based on the use of the time function of the average displacements,with a x-3source spectrum,across a fault plane.For the second model,there are two cases:(a)As s*T,where s is the rise time and T the rupture time,lg(e?)*-Ms;and(b)As s T,lg(e?)*-(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 Ms. The correlation of the scaled energy, e = Es / M0, versus earthquake magnitude, Ms, is studied based on two models: (1) Model 1 based on the use of the time function of the average displacements, with a x-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 x-3 source spectrum, across a fault plane. For the second model, there are two cases: (a ) As s * T, where s is the rise time and T rupture time, lg (e?) * - Ms; and (b) As s T, lg (e?) * - second model leads to a negative value of e? .This means that Model 2 can not 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? or Ms.
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