Earthquake location — genetic algorithms for teleseisms

Abstract

The location of earthquakes requires the estimation of the spatial and temporal components of the hypocentre. This can be achieved by a direct minimisation of a measure of the misfit between observed and calculated travel times, and also slownesses and azimuths if array data are available. An efficient means of carrying out this optimisation procedure is to make use of genetic algorithms. This technique is based on the use of many estimates of the hypocentre location at once and the properties of the cluster of estimated locations in four dimensions are exploited in the course of the optimisation process. Each estimate of the hypocentral location is represented on a local discrete grid by a bit-string and successive iterations generate new bit-strings (and hence location estimates) by operations based on biological analogues. These operations are the replication of the best-fitting bit-strings, the cross-over of information between pairs of bit-strings and the mutation of individual bits in a string. The non-local character of the information on the misfit function carried in the cloud of hypocentral estimates is usually sufficient to prevent the location being trapped in local minima of the misfit surface. Convergence to the global misfit minimum can be achieved with a very limited sampling of the original spatial and temporal grid. No derivatives of the seismic phase information are required and so the technique is easily generalised to three-dimensional velocity models, and can be used with any suitable measure of the quality of an earthquake location by the choice of the misfit criterion between observed and calculated quantities.