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A clustering model for earthquake occurrences

DEPARTMENT OF EARTH AND PLANETARY SCIENCES MASSACHUSETTS INSTITUTE OF TECHNOLOGY, CAMBRIDGE, MASSACHUSETTS 02139

Abstract

A statistical analysis of the time occurrence of the earthquakes listed in the USCGS catalog was performed. Except for the deep earthquakes, goodness of fit tests have rejected the simple Poisson process as a model of earthquake occurrences at a very low significance level. It was inferred that another parameter related to the Poisson index of dispersion is required to describe earthquake occurrences. Attempts to fit the distribution of the number of days with n earthquakes with standard two-parameter distributions like the lognormal and the distribution were not very successful. The data were tested with respect to the generalized Poisson process, a model in which there are finite probabilities for more than one event occurring at the same time instant. It was deduced that the distribution of the number of earthquakes generated in an aftershock sequence is reasonably approximated by an inverse power law distribution with exponent E being between 2.5 and 4.0. Good fits were obtained with respect to the generalized Poisson distribution, and regional variations in the parameter E could be detected.

Estimates of the autocovariance function and power spectra failed to detect definite periodicities of earthquake occurrences in the range of 2 to 256 days. Positive correlations of earthquake activity were observed for time intervals as long as 10 days.

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