A Nearly Analytic Discrete Method for Acoustic and Elastic Wave Equations in Anisotropic Media

Abstract

We transform the seismic wave equations in 2D inhomogeneous aniso- tropic media into a system of first-order partial differential equations with respect to time t. Based on the transformed equations, a new nearly analytic discrete method (NADM) is developed in this article. Our method enables wave propagation to be simulated in two dimensions through generally anisotropic and heterogeneous mod- els. The space derivatives are calculated by using an interpolation approximation, while the time derivatives are replaced by a truncated Taylor expansion. Our analyses show that the error of the NADM is less than that of the conventional finite-difference method (FDM) and is about 1/60 to 1/100 of that of the FDM. We also demonstrate numerically that the stability of the NADM is higher than that of the FDM. The three- component seismic wave fields in two layered isotropic and transversely isotropic media (TIM) are simulated and compared with the conventional FDM. Again, we show from the three-component seismic wave fields that the NADM has higher ac- curacy, stronger stability, and less numerical dispersion, effectively suppressing the source noises as compared with the FDM.