Abstract
As an alternative to traditional parametric approaches, we suggest nonparametric methods for analyzing temporal data on earthquake occurrences. In particular, the kernel method for estimating the hazard function and the intensity function are presented. One novelty of our approaches is that we take into account the possible dependence of the data to estimate the distribution of time intervals between earthquakes, which has not been considered in most statistics studies on seismicity. Kernel estimation of hazard function has been used to study the occurrence process of cluster centers (main shocks). Kernel intensity estimation, on the other hand, has helped to describe the occurrence process of cluster members (aftershocks). Similar studies in two geographic areas of Spain (Granada and Galicia) have been carried out to illustrate the estimation methods suggested.
Highlights
The problem of searching for stochastic models to describe the sequence of occurrence times of earthquakes from some geographic region is of great interest to seismologists
Other more recent models include the trigger models (Lomnitz and Nava, 1983), the Epidemic-Type Aftershock Sequence (ETAS) model (Ogata, 1988), whose extensions can be seen in Ogata (1998), or refinements of Hawkes’ (1971) self-exciting point process model, which describes spatial-temporal patterns in a catalog
The objective of our analysis is to show two statistical tools which could help to describe the whole cycle of seismic activity in a region without imposing predetermined conditions on this activity
Summary
The problem of searching for stochastic models to describe the sequence of occurrence times of earthquakes from some geographic region is of great interest to seismologists. Udias and Rice (1975) propose the gamma distribution to describe the series of time intervals between consecutive shocks These authors deal with hazard and intensity functions. These methods do not require formulation of structural models, so they are not affected by the deficiencies noted above They involve several different approaches to nonparametric estimation of the hazard and intensity functions of point processes that evolve with time. This enables us to split up and analyze the occurrence of temporal processes of earthquakes within a region without constraining them to having predetermined properties.
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