Elastic wave modeling with free surfaces: Stability of long simulations

Abstract

Three‐dimensional (3D) elastic wave propagation modeling in the velocity‐stress formulation using finite differences (FDs) have been investigated for a homogeneous medium covered by a representative, relatively steep surface topography consisting of a 1D square root function. This scenario using various numerical implementations is explored. The behavior with regard to stability of long simulations is expected to be indicative of each numerical implementation's robustness for other types of topographies/media. Employing various combinations of the FD order was found only to change the time of the first incidence of instability. On the other hand, nonequidistant grids in the horizontal and vertical directions are found to be extremely useful for long‐term stability of 3D wave propagation modeling with our free‐surface boundary condition for single‐valued topographies. In particular dz ≥ (3/2) dx is found completely stable for all tested vP/vSratios. Such relationships of using dz > dx are also favorable for more accurate Rayleigh‐wave modeling. Setting the density equal to 1/10 of its interior value at one layer only at the surface is another simple means of achieving stability.