Seismic ray tracing in models with complex surface topography using linear traveltime interpolation on a hybrid grid
Jianguo Sun, Zhangqing Sun, Fuxing Han · 2013
If the earth's surface has a complex geometry, the implementation of the grid method for solving the eikonal equation will become difficult. In fact, in this case we must first solve the following six problems, namely (1) how to describe the curved earth's surface, (2) how to divide the surface into discrete pieces, (3) how to describe the medium directly near the surface, (4) how to divide the medium directly near the surface into discrete elements, (5) how to compute the local traveltime, and (6) how to capture and to propagate the local wavefront near the curved earth's surface or interface. Previously, for solving the problems (1) to (5), we used a second order upwind finite difference scheme that uses nonuniform grid spacing in the regions near the earth's surface or the interface (Sun et al., 2011). For solving the problem (6), we modified the fast marching method (FMM) based on the narrow band technique by introducing new point types, namely the surface point, the point above the surface, the interface point, and the point under the interface (Sun et al., 2011). Here, for solving the problems listed above we present a method that uses a hybrid grid and that combines the linear interpolation method and the FMM. Specifically, the surface is approximated by broken lines (2D cases) and the medium directly near the surface is divided by an irregular grid that is composed of rectangular and triangular grid elements. For the local travetime computation and the local wavefront propagation, we use the linear interpolation method and the modified FMM, respectively. Furthermore, for constructing rays from the computed traveltimes, we search the point from which a ray comes from in reversed direction, i.e., from the bottom of the model to the top. Numerical results show that the method presented here not only can flexibly approximate the traveltimes, but also can give accurate ray trajectories in the models with strong heterogeneities.