A two-point, three-dimensional seismic ray tracing using genetic algorithms

Abstract

Ray tracing between two fixed points is a boundary value problem. An initial path connecting two points, the source and the receiver, is algorithmically perturbed until it converges to a solution giving a minimum travel-time path. In multi-pathing cases, it is quite possible for an algorithm to converge to a ray path with local minimum travel time. Furthermore, when the velocity structure has discontinuities, there is another serious problem, i.e., how to determine the correct intersection between the ray and the surface of discontinuity. In this paper, a new approach for two-point ray tracing is presented, which uses genetic algorithms (GAs) to overcome these problems. Since GAs are efficient global search techniques, the proposed method guarantees to find a global minimum travel-time path and also the correct intersections. A micro-GA implementation is adopted to further enhance computational efficiency. This approach is suitable for tracing the first arriving seismic waves through a 3-D heterogeneous medium with discontinuities. The method can also find the minimum time paths of later arrivals, such as reflected and refracted waves, by constraining the ray to hit a prescribed interface. The accuracy of the method is demonstrated on the numerical examples.