Fast and accurate 3-D ray tracing using bilinear traveltime interpolation and the wave front group marching

Abstract

P>We propose a new ray tracing technique in a 3-D heterogeneous isotropic media based on bilinear traveltime interpolation and the wave front group marching. In this technique, the media is discretized into a series of rectangular cells. There are two steps to be carried out: one is a forward step where wave front expansion is evolved from sources to whole computational domain and the subsequent one is a backward step where ray paths are calculated for any source-receiver configuration as desired. In the forward step, we derive a closed-form expression to calculate traveltime at an arbitrary point in a cell using a bilinear interpolation of the known traveltimes on the cell's surface. Then the group marching method (GMM), a fast wave front advancing method, is applied to expand the wave front from the source to all girds. In the backward step, ray paths starting from receivers are traced by finding the intersection points of potential ray propagation vectors with the surfaces of relevant cells. In this step, the same TI scheme is used to compute the candidate intersection points on all surfaces of each relevant cell. In this process, the point with the minimum traveltime is selected as a ray point from which the similar step is continued until sources. A number of numerical experiments demonstrate that our 3-D ray tracing technique is able to achieve very accurate computation of traveltimes and ray paths and meanwhile take much less computer time in comparison with the existing popular ones like the finite-difference-based GMM method, which is combined with the maximum gradient ray tracing, and the shortest path method.