Calculation of focal loci for earthquake location in complex media
复杂介质地震定位中震源轨迹的计算

Focal loci are often required in earthquake location.However,it is extremely difficult to analytically express them when the earthquake lies in a complex model.Therefore,the calculation of focal loci is usually limited to simple media.In this paper,we present a method for calculating focal loci in complex media by means of a minimum traveltime tree algorithm for ray tracing.The focal loci are constrained with observed arrival time differences at seismic stations so that the problem of origin time is evaded.From all the model nodes,we select a small part with smaller absolute residuals between observed and calculated traveltime differences(or double- differences)as reference points of the focal locus.The reference point with minimum double difference is assigned as an initial point.The ray paths from the initial point to the other selected reference points in the double-difference field actually represent the focal locus,which are traced with a minimum traveltime tree algorithm.When the obtained focal locus is rather rough due to the excessive amount of selected reference points,it can be improved by removing some ray paths to the reference points that there are less rays going through.Additionally,the stop condition of the minimum traveltime tree algorithm is modified to reduce computational time.The results of numerical tests including velocity perturbations and noisy arrival data in a laterally heterogeneous model indicate that the presented method is feasible.