An Efficient Immersed Free Surface Boundary Method for 3-D Scalar Seismic Waves Finite-Difference Modeling in Presence of Topography

The irregular surface topography has significant effects on seismic wave propagation, including introduction of free surface-related multiples, strong scattering, and distortion of the shapes of seismic events. Because of the high efficiency, the finite-difference (FD) time-domain (FDTD) method is the most widely used numerical approach to solve 3-D seismic wave equations. However, FDTD at a uniform rectangular mesh could suffer from strong spurious diffractions, due to the stair-step grid approximation to irregular surfaces. To resolve this problem, we immerse the irregular surfaces into fractional nodes under a uniform rectangular mesh and impose the free surface boundary condition along the normal direction of the surface. The implementation process of the free surface boundary condition in the presence of irregular surfaces can be viewed as a generalization of the traditional mirror image method designed for a planar free surface. The developed FD scheme with the immersed boundary method (IBM), denoted as IBM-FD, needs to update the wavefields at a small number of ghost nodes, implicitly. We adopt Seidel iterations plus a third-degree Lagrange polynomial interpolation to realize this purpose. Compared with the FD scheme without IBM, the IBM-FD scheme only increases the computational cost slightly, due to the cost to determine the ghost nodes and update the wavefields at the ghost nodes. We present 3-D scalar wavefield simulation examples with irregular surface topography to confirm the accuracy and stability of IBM-FD.