Hypocenter determination in strongly heterogeneous Earth models using the shortest path method

Abstract

The shortest path method [Moser, 1991] for the calculation of seismic ray paths and travel times along them can be applied directly in the hypocenter location method proposed by Tarantola and Valette [1982]. It uses the analogy between seismic rays in the Earth and shortest paths in networks to construct first arrival times from one point to all other points of a three‐dimensional grid simultaneously in a fast, robust way, in Earth models of arbitrary complexity. Doing this for all stations of a seismic array, one can find the hypocenter location by minimizing the difference between the observed and the calculated travel times at the stations over the three‐dimensional grid. The concept of probability density functions allows then for a fully nonlinear examination of the uncertainties in the hypocenter location, due to uncertainties in the travel time data, numerical errors in the calculated travel times and, to a limited extent, incomplete knowledge about the Earth model. The result is a three‐dimensional contour map of regions of equal confidence for the earthquake location. The method becomes especially attractive when more than one event recorded by the same array is studied, because the calculation of the travel times, which is relatively the most time consuming operation, has to be done only once. The method is applied on the location of an event that occurred on January 18, 1989, in Israel.