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.

Bulletin of Seismological Society of America