Acoustic VTI modeling with a time-space domain dispersion-relation-based finite-difference scheme

Abstract

The finite-difference (FD) method is widely used in numerical modeling of wave equations. Conventional FD stencils for space derivatives are usually designed in the space domain. When they are used to solve wave equations, it is difficult to satisfy the dispersion relations exactly. We have designed a spatial FD stencil based on a time-space domain dispersion relation to simulate wave propagation in an acoustic vertically transversely isotropic (VTI) medium. Two-dimensional dispersion analysis and numerical modeling demonstrate that this stencil has greater precision than one used in a conventional FD, when the same number of grid points is used in the calculation of the spatial derivatives. Thus, the spatial FD stencil based on time-space domain dispersion relation can be used to replace a conventional one such that we can achieve greater accuracy with almost no increase in computational cost.