3D acoustic and elastic VTI modeling with optimal finite-difference schemes and hybrid absorbing boundary conditions

The coefficients of the conventional finite-difference (FD) stencil are commonly determined by the Taylor-series expansion method (TEM), which can produce major numerical dispersion errors at large wavenumbers. To solve this problem, we develop a novel optimal explicit FD method (FDM) for the second-order spatial derivative. We first combine the TEM and multiple sampling to the spatial dispersion relation, and then construct an intuitive and effective objective function using the maximum-norm method (MNM) and solve it by the Remez iteration algorithm (RIA). The maximum-norm (MN)-based FDM is adopted to solve the 3D acoustic and elastic vertical transversely isotropic (VTI) wave equations. Moreover, we extend the 2D hybrid absorbing boundary conditions (HABCs) to 3D acoustic and elastic VTI media, and improve the absorbing effectiveness through reasonably adjusting wavefield velocities in the absorption areas based on anisotropy properties. To improve computational efficiency for a 3D case, we utilize graphic processing unit (GPU) instead of traditional central processing unit (CPU) architecture. Numerical accuracy analyses indicate that the optimal scheme has better tolerance to the numerical dispersion at large wavenumbers than the conventional TEM. Numerical modeling experiments for 3D homogeneous and modified Hess VTI models demonstrate that the proposed schemes have greater accuracy and efficiency than the conventional schemes and achieve significant absorbing effects.