A Stochastic Time and Space Model for Earthquakes

A stochastic model for earthquake occurrence focusing on the spatio-temporal interactions between earthquakes is discussed. The model is a marked point process model in which each earthquake is represented as a marked point in space and time. The marks are given by the magnitudes of the earthquakes but other observed properties of the earthquakes, such as information on the fault lines, can straightforwardly be included. The parameters of the model is estimated based on Bayesian updating of priors, using empirical data to derive posterior distributions. In the model we discuss the spatial and temporal dependencies between foreand aftershocks. In addition the effect of strain build-up and subsequent release following an earthquake is discussed. An algorithm for simulating earthquakes from the model is presented along with simulation results for the region of Southern California. With an improved set of simulations the ambition of the model is to make more precise predictions on the occurrence of earthquakes. The prediction results may give clues as to whether such predictions of earthquakes is at all possible.