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Abstract

We present a Bayesian approach to solve the problem of simultaneous inversion for optimal hypocentre parameters and 1-D velocity models as well as station corrections for a given set of local earthquakes utilizing a hierarchical, transdimensional Markov chain Monte Carlo (McMC) algorithm. The simultaneous inversion is necessary because of the velocity–hypocentre coupling inherent to the problem. Tests with synthetic arrival time data indicate an excellent performance of the approach, at the same time benefiting from all the advantages related to the McMC algorithm. These advantages are that only minimum prior knowledge is used (i.e. regarding starting focal coordinates, initial velocity model, which are set to random initial values), no regularization parameters (e.g. damping) have to be selected, and the parametrization of the velocity model (i.e. model nodes/layers) is automatically set and adjusted according to the quality of the data, that is noise level. By minimizing the amount of pre-inversion assumptions, which are regularly not available at the required precision or often only available after very careful and time-consuming assessment, the inversion results are therefore almost exclusively data-driven. On output, we obtain a suite of well fitting models which can statistically be analysed and provide direct estimates of the posterior uncertainties of the models. Tests with real arrival time data from a temporary local network deployed in South-Central Chile in 2004 and 2005 show a very good agreement with the results obtained with a conventional inversion method.