Earthquake hypocenter location using genetic algorithms

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Abstract
A new method for hypocenter location is proposed introducing some recent developments in global optimization techniques. The approach is based on the use of genetic algorithms to minimize some misfit criteria of the data. The method does not use derivative information and therefore does not require the calculation of partial derivatives of travel times of particular phases with respect to hypocentral parameters. The method is completely independent of details of the forward modeling. The only requirement is that the misfit function can be evaluated. Consequently one may use robust error statistics, any type of velocity model (including laterally heterogeneous 3-D models), and combine any type of data that can be modeled (e.g., arrival times and waveforms) without any modification of the algorithm. The new approach is extremely efficient and is superior to previous techniques that share its advantages, in the sense that it can rapidly locate near optimal solutions without an exhaustive search of the parameter space. It achieves this by using an analogy with biological evolution to concentrate sampling in the more favorable regions of parameter space, while improving upon a group of hypocenters simultaneously. Initially, the population of hypocenters is generated randomly and at each subsequent iteration three stochastic processes are applied. The first, “reproduction”, imposes a survival of the fittest criterion to select a new population of hypocenters; the second, “crossover”, produces an efficient exchange of information between the surviving hypocenters; the third, “mutation”, introduces a purely random element that maintains diversity in the new population. Together these steps mimic an evolutionary process, allowing the algorithm to rapidly assimilate and exploit the information, gained from the group as a whole, to find better data fitting hypocenters. The algorithm is illustrated with some synthetic examples using an actual local earthquake network. It is demonstrated how the initially random cloud of hypocenters quickly shrinks and concentrates sampling near the global minimum. Some simple new improvements to the basic algorithm are proposed to assist in avoiding local minima.

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