Estimation of the waiting time distributions of earthquakes |
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| Authors: | S M J R Goel S K Malasi P S Moharir H R Wason K N Khattri V K Gaur |
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| Institution: | (1) Department of Earth Sciences, University of Roorkee, 247 667 Roorkee, India |
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| Abstract: | Whether the earthquake occurrences follow a Poisson process model is a widely debated issue. The Poisson process model has
great conceptual appeal and those who rejected it under pressure of empirical evidence have tried to restore it by trying
to identify main events and suppressing foreshocks and aftershocks. The approach here is to estimate the density functions
for the waiting times of the future earthquakes. For this purpose, the notion of Gram-Charlier series which is a standard
method for the estimation of density functions has been extended based on the orthogonality properties of certain polynomials
such as Laguerre and Legendre. It is argued that it is best to estimate density functions in the context of a particular null
hypothesis. Using the results of estimation a simple test has been designed to establish that earthquakes do not occur as
independent events, thus violating one of the postulates of a Poisson process model. Both methodological and utilitarian aspects
are dealt with. |
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| Keywords: | Gram-Charlier series earthquakes Hermite polynomials Laguerre polynomials Poisson process Polya process |
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