Multi-valued reflection arrival tracking via an extremal solution of the summed ray field

Abstract

In heterogeneous media involving large velocity contrasts and/or strongly curved interfaces, the seismic wavefronts may self-intersect, implying that the rays follow multi-paths between source and receiver. In order to simulate such multi-valued reflection arrivals, we present here an algorithm to trace the various events. We refer to this as an extremal solution based on the summed ray field, one emanating from the source to the reflecting interface and the other from the receiver to the reflecting interface. Two popular grid-based algorithms, the fast marching method and the irregular shortest path method, are used in the ray tracing process. The steps involved in the extremal solution method are: (1) conduct downwind ray tracing from both the source and receiver to the reflecting interfaces and record the traveltimes and the raypaths at each sampled point along the interface, and then sum up the traveltime value at each sampled point on the interface to form a stacked 'traveltime-distance' curve along the interface (or subsurface interface for 3D case); (2) solve for the extremal values of this stacked 'traveltime-distance' curve (or subsurface interface), to obtain the locations of the extremal points which are the actual reflection points; (3) link the raypaths and the traveltimes from the source to those reflection points, and then to the receiver, by which the multi-valued reflected arrivals are successfully traced. This algorithm has a simple principle, high accuracy and easy adaptation for complex media. Several numerical simulations and an angular error analysis indicate that it is a feasible, accurate and efficient way to track the multi-valued reflected arrivals. © 2012 Sinopec Geophysical Research Institute.