3D Nearly Analytic Central Difference Method for Computation of Sensitivity Kernels of Wave-Equation-Based Seismic Tomography

We propose a numerical method to perform forward-modeling and sensitivity kernel computation in wave-equation-based seismic tomography. This method is an extension of the 2D nearly analytic central difference (NACD) method for solving the 3D acoustic wave equation. The 3D NACD method has fourth-order accuracies both in time and space with only a three-point stencil in each axis direction. Theoretical properties such as the stability criterion and the numerical dispersion relation were analyzed in detail. Relative to the fourth-order Lax-Wendroff correction method and the fourth-order staggered-grid finite-difference method, the 3D NACD method exhibits better performance in suppressing numerical dispersion. This was numerically confirmed by simulation of seismic-wave propagation in different models. Additionally, the 3D NACD method explicitly calculates the spatial gradients of the propagating wavefield, allowing a direct route to sensitivity kernel calculation. Using this method, waveform kernels and travel-time kernels for direct arrival, single reflected phase, multiple reflected phase, and headwave are computed in a crust-over-mantle model. Numerical examples reveal that sensitivity kernel computation based on solving the full-wave equation can accurately capture the interactions between wavefields and the Earth's interior heterogeneous structures, and hence generate high-accuracy sensitivity kernels for the subsequent tomographic inversion. Overall, the proposed method showed good performances for both forward-modeling and sensitivity kernel calculation. This suggests that the 3D NACD method could serve as an efficient and accurate forwarding-modeling tool for wave-equation-based seismic tomography.