ESTIMATION OF THE PARAMETERS IN THE MODIFIED OMORI FORMULA FOR AFTERSHOCK FREQUENCIES BY THE MAXIMUM LIKELIHOOD PROCEDURE

Abstract

This paper proposes the maximum likelihood method to estimate the parameters of the modified Omori formula for aftershock sequences directly based on a time series of aftershocks. The likelihood function is derived by assuming that the aftershocks are distributed according to a certain non-stationary Poisson process. This method incidentally provides the asymptotic error distribution of the estimates. Statistical comparison of the characteristic parameters between two aftershock sequences, parameter estimation in case of the existence of the secondary aftershocks and other related problems are also discussed. As illustrative examples of calculations, some aftershock data are analyzed.