A parameter-modified method for implementing surface topography in elastic-wave finite-difference modeling

Abstract

Accurate seismic modeling with a realistic topography plays an essential role in onshore seismic migration and inversion. The finite-difference (FD) method is one of the most popular numerical tools for seismic modeling. But implementing the free surface on topography using the FD method is nontrivial. We have developed a stable and efficient parameter-modified (PM) method for modeling elastic-wave propagation in the presence of complex topography. This method is based on a standard staggered-grid scheme, and the stress-free condition is implemented on the rugged surface by modifying the redefined medium parameters at the discrete topography boundary points. This numerical treatment for topography needs to be performed only once before the wave simulation. In this way, we avoid the tedious handling of wavefield variables in every time step, and this boundary treatment can be integrated easily into existing staggered-grid FD modeling codes. A series of numerical tests in two dimensions and three dimensions indicate that with a spatial sampling of 15 grid points per minimum wavelength, our method is good enough to eliminate staircase diffractions and produces more accurate results than those obtained by some other staggered-grid-based numerical approaches. Numerical experiments on some more complex models also demonstrate the feasibility of our method in handling topography with strong variation and Poisson’s ratio discontinuity. In addition, this PM method can be used in a discontinuous-grid scheme in which only the regions near the irregular topography need to be oversampled, which is very important for improving its efficiency in real applications.