Numerical approach for analysis of surface wave field in the vicinity of caustics

Due to lateral heterogeneity of upper part of the Earth surface waves paths deviate from great circle arcs that result in appearance of caustics at the hemisphere opposite to the epicenter. The caustics have a shape of cusps, and they may superpose. Asymptotic approach for analysis of the wave field in the vicinity of such caustics is reduced to calculation of the Pearcey integral, whose parameters are determined through the eikonals of three superposed waves. Calculation of surface wave field on the basis of the asymptotic approach has some drawbacks and cannot be applied to superposition of caustics. We propose a numerical approach for calculation of the field using the Green formula. It is reduced to calculation of an integral with oscillating integrand. A method for suppression of oscillation of the integral is outlined. For a simple model asymptotic and numerical approaches are in a good agreement. Some examples of calculation for different shape of caustics on spherical surface are given.