Zhangqing Sun

Joint 3D traveltime calculation based on fast marching method and wavefront construction

Abstract3D traveltime calculation is widely used in seismic exploration technologies such as seismic migration and tomography. The fast marching method (FMM) is useful for calculating 3D traveltime and has proven to be efficient and stable. However, it has low calculation accuracy near the source, which thus gives it low overall accuracy. This paper proposes a joint traveltime calculation method to solve this problem. The method firstly employs the wavefront construction method (WFC), which has a higher calculation accuracy than FMM in calculating traveltime in the small area near the source, and secondly adopts FMM to calculate traveltime for the remaining grid nodes. Due to the increase in calculation precision of grid nodes near the source, this new algorithm is shown to have good calculation precision while maintaining the high calculation efficiency of FMM, which is employed in most of the computational area. Results are verified using various numerical models.

Wavefront construction using a two‐dimensional cubic convolution interpolation

Wavefront construction is a method used for fast seismic ray tracing. An essential process in the method is the interpolation of traveltimes from an irregular grid to a regular grid. Usually, this interpolation is realized by using bilinear interpolation. However, bilinear interpolation cannot give continuous derivatives across the grid element used for realizing interpolation. Therefore, it is not adequate for ray tracing in complex media with certain smoothness, because for computing rays traveltime derivatives should be continuous everywhere in the smoothed model. To have an interpolation scheme that meets the requirements for solving ray tracing system numerically, we introduce a two-dimensional cubic convolution interpolation. It is found that the twodimensional cubic convolution interpolation is efficient and accurate in comparison to bilinear interpolation. Also, it is found that the difference between the ray families respectively computed by the two-dimensional cubic convolution interpolation and by bilinear interpolation is large when the velocity change in the model used is strong. This leads to the conclusion that for obtaining correct ray trajectories in the complex velocity model, an interpolation formula with a smoothness order higher than that of bilinear interpolation formula is necessary.

A finite difference scheme for solving the eikonal equation including surface topography

Summary To imaging the subsurface structure directly from the earth’s surface with arbitrary relief, we present a finite difference (FD) scheme that uses nonuniform grid spacing in the region near the curved surface and that adapts the fast marching method (FMM) for treating the grid irregularity caused by the surface relief. Specifically, for adapting FMM we introduce new point types, namely the surface point, the point above the surface, the interface point, and the point under the interface. For adapting the upwind FD formula used in the original FMM, the grid spacing in the conventionally used rectangular grid is replaced by the vertical distance between the surface point and the grid point under consideration. Numerical results show that the scheme presented here can treat the irregular region problem caused by the curved earth’s surface with effectiveness and flexibility.