Computer algorithms for earthquake forecasting hypotheses

Abstract

Earthquakes are regarded as the realization of a point process modeled by a generalized Poisson distribution. No hypothesis is inferred on the physical model of such a process. The occurrence of a seismic event within an infinitesimal volume of the space of its characterizing parameters is supposed to be completely random, while the behaviour in a reasonably large volume of the same space may exhibit some average non-random features.
The description of seismicity as a point process in space, time and magnitude is suitable for the application of statistical tools for comparing the performance of different models. Here the Bayes theorem is introduced aiming to its application in computing the probability that a given model is true in light of the results of experimental observations. The use of the Bayes theorem requires the computation of the likelihood ratio for the two models to be compared. It follows that both the hypotheses are fully and quantitatively described.
In the application of the statistical algorithms to seismicity, the Gutenberg-Richter law is assumed to describe the magnitude distribution of all the earthquakes in a sample, with a constant b value.
The occurrence rate density of earthquakes in space and time is modeled as the sum of two terms, one representing the independent, or spontaneous, activity and the other representing the activity induced by previous earthquakes. The first term depends only on space and is modeled by a continuous function of the geometrical coordinates, obtained by smoothing the discrete distribution of the past instrumental seismicity. The second term depends on both space and time, and it is factorized in two terms that depend on the space distance according to an isotropic normal distribution) and on the time difference (according to the generalized Omori law), respectively, from the past earthquakes. Knowing the expected rate density, the likelihood of any realization of the process (actually represented by an earthquake catalog) can be computed straightforwardly.
This paper is concluded with a short outline of some...