Finite-difference Modeling of High-frequency Rayleigh waves

The finite-difference (FD) method described here is specially developed to model high-frequency Rayleigh-wave propagation in near-surface mediums. Although many FD programs existed for earthquake research and oil exploration, none has been developed to model high-frequency Rayleigh-wave propagation in near-surface elastic mediums when the source and all receivers are on the free-surface. The scheme described here uses the second-order staggered grid, based on a set of first-order differential equations. Special implementations of combined elastic and acoustic free-surface conditions were developed, which were originally derived from surface wave propagation in a transversely isotropic medium. A combination of one-way sponge filtering and anisotropic filtering methods was used to minimize Rayleigh-wave reflections from artificial boundaries. Numerical stability was achieved by using a small spatial grid size and time step. This new FD method was tested and proved satisfactory using dispersion analysis of Rayleigh waves in a homogenous and layered half-space. The present study provides a practical tool for improving the confidence and uniqueness of deriving 2D interpretation of high-frequency Rayleigh-wave data, and makes successful in the first phase to 2D inversion.