### EARTHQUAKE FORECAST BY TIME-DEPENDENT HAZARD MODELS

#### Abstract

This presentation outlines methodological aspects of earthquake forecasting. The recurring debates concerning predictability of earthquakes clearly show how this problem is centred on the difficulty of systematically testing the numerous methodologies that in the years have been proposed and sustained by the supporters of prediction. This difficulty starts, sometimes, from the lack of a quantitative and rigorous definition of the concerned precursor, and other times from the lack of continuous observations, upon which statistical analyses could be based. After an introduction concerning the definition of earthquake precursors, the way how to validate forecast hypotheses and the cost associated to their operational application, I give two examples of time-dependent hazard models, for long-term and short-term earthquake forecasts respectively. Considering the long-term forecast modelling, the effect of stress change due to previous historical earthquakes on the probability of occurrence of future earthquakes on neighbouring faults is taken into account. Following a standard methodology developed a couple of decades ago, the probability of occurrence in the next 50 years for a characteristic earthquake on known seismogenic structures can be estimated by a time-dependent renewal model. Then, a physical model for the Coulomb stress change caused by previous earthquakes on these structures is applied. The influence of this stress change on the occurrence rate of characteristic earthquakes is computed taking into account the permanent perturbation (clock advance). The method so developed is applied to the computation of earthquake hazard of the main seismogenic structures recognized in the Southern Apennines region, for which both historical and paleoseismological data are available. A popular short-term time dependent hazard forecast model is the epidemic model. In this model earthquakes are regarded as the realization of a stochastic point process, and their magnitude distribution is described by the Gutenberg-Richter law with a constant b-value. The occurrence rate density is computed by the sum of two terms, one representing the independent, or spontaneous activity, and the other representing the activity induced by previous earthquakes. While the first term depends only on space, the second one is factored into three terms that respectively include the magnitude, time and location of the past earthquakes. An example of application of the epidemic model to the 2009 L’Aquila seismic series is shown.

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