A Generalized 2.5-D Time-Domain Seismic Wave Equation to Accommodate Various Elastic Media and Boundary Conditions

The 2.5-D seismic wave numerical simulation method employs point sources from 2-D geological models, enabling the calculation of point source wavefields at pseudo-2-D computational cost. We present herein a generalized 2.5-D first-order time-domain governing equation to model seismic wave propagation in different (acoustic, elastic isotropic, and anisotropic) media, then derive different formulae that incorporate topographic free-surface and fluid–solid interfaces. Furthermore, by assigning different model parameters from point to point, accommodating different boundary conditions, and applying the finite difference approach, we achieve the numerical simulation of seismic wave propagation with just one computer program. Comparisons with 3-D analytic and numerical solutions obtained using different full-space homogeneous models (acoustic, elastic isotropic, and anisotropic) verify the correctness of the 2.5-D method. Comparison of the results with a 3-D pseudospectral method show that the proposed 2.5-D method can simulate seismic wave propagation in various media with different boundary conditions. In addition, unlike the problems encountered when using 2-D numerical solutions for real 3-D applications, the 2.5-D method can be employed directly as a forward modeling method in seismic reverse-time migration and an efficient wavefield conversion tool between practical point source data and artificial line source data for 2-D seismic full waveform inversion.