Joint solution of seismicity parameters for seismic source zones through simulation

A key issue in seismic hazard modelling is determining seismicity parameters for each source zone in a given model. The three main parameters are the activity rate, the b-value (slope of the Gutenberg-Richter magnitude-frequency curve), and the maximum magnitude. Procedures for estimating these vary from study to study; in recent years the application of maximum likelihood methods, with or without priors, seems to be the most favoured approach. A new approach is presented here, based on Monte Carlo methods, which solves for all three parameters simultaneously. The conceptual basis is as follows: there exists some \"true\" set of values for a, b and Mmax that governs the long-term occurrence of earthquakes in a zone. Take three values for a, b and Mmax at random and use them to generate a synthetic earthquake catalogue, subject to the same historical constraints as the real catalogue. Is the resulting synthetic catalogue similar to the real one? If so, the a, b and Mmax values are credible. If not, try again. If one repeats the exercise a very large number of times, one easily builds up a weighted distribution of credible values for a, b and Mmax that can be converted directly into a logic tree structure. The method is entirely data-driven, and imposes no preconceived assumptions on the shape of the uncertainty distribution. Also the method tests implicitly whether the Gutenberg-Richter model itself is credible for that data set. If it turns out to be the case that no values for a, b and Mmax can provide a good approximation to the observed data, then a different seismicity model is called for.