| Summary: | A strategy for relocating earthquakes in a catalog is presented. The strategy is based on the argument that the distribution of the earthquake events in a catalog is reasonable a priori information for earthquake relocation in that region. This argument can be implemented using the method of maximum likelihood for arrival time data inversion, where the a priori probability distribution of the event locations is defined as the sum of the probability densities of all events in the catalog. This a priori distribution is then added to the standard misfit criterion in earthquake location to form the likelihood function. The probability density of an event in the catalog is described by a Gaussian probability density. The a priori probability distribution is, therefore, defined as the normalized sum of the Gaussian probability densities of all events in the catalog, excluding the event being relocated. For a linear problem, the likelihood function can be approximated by the joint probability density of the a priori distribution and the distribution of an unconstrained location due to the misfit alone. After relocating the events according to the maximum of the likelihood function, a modified distribution of events is generated. This distribution should be more densely clustered than before in general since the events are moved towards the maximum of the posterior distribution. The a priori distribution is updated and the process is iterated. The strategy is applied to the aftershock sequence in southwest Iceland after a pair of earthquakes on 29th May 2008. The relocated events reveal the fault systems in that area. Three synthetic data sets are used to test the general behaviour of the strategy. It is observed that the synthetic data give significantly different behaviour from the real data.
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