Determination of the Earthquake Hypocenter: A Challenge for the Differential Evolution Algorithm

Abstract

Determination of the earthquake hypocenter represents a basic problem routinely solved in seismology. The problem belongs to the class of simpler problems in geophysics, but it is still difficult to solve. The dimension of the model space is low (three coordinates of the hypocenter plus origin time, resulting in four parameters to be searched for), but the forward problem exhibits a case-to-case-dependent degree of nonlinearity. The standard solution is based on minimizing the time residuals (differences between observed and computed arrivals of seismic waves) in the common L2 norm. We have compiled a set of 56 synthetic earthquake hypocenter location tasks, which was submitted to three different optimizers for solution: (i) Powell’s method, (ii) the downhill simplex algorithm and (iii) the differential evolution (DE) algorithm. Each localization process listed was performed two times using exact and approximate forward modeling. Our analysis has shown that the DE algorithm has worked with 100 % reliability, while other optimizing algorithms have often failed. The accuracy achieved by using the DE algorithm was at least the same or better than that achieved by competing algorithms. The only minor disadvantage of the DE algorithm is a higher computational effort needed to reach the solution.