An average-derivative based second-order staggered-grid finite-difference scheme for 3D frequency-domain elastic wave modeling

In this paper, we develop an average-derivative based second-order staggered-grid finite-difference (ADSSFD) scheme for performing 3D frequency-domain elastic wave modeling. The ADSSFD scheme applies the idea of average derivative to discretize the first-order derivative of the stress tensors and combines the anti-lumped mass strategy to obtain a set of optimal finite-difference (FD) coefficients. We combine the Levenberg-Marquardt method with simulated annealing to minimize the misfit between the normalized phase velocity and one, ensuring the solution avoids local minima. Dispersion analysis indicates that when the upper limit of the phase velocity error is set to 1%, the ADSSFD scheme can reduce the minimum number of grid points per shear wavelength to 3.6. Numerical experiments indicate that under the same numerical setting, the ADSSFD scheme exhibits higher accuracy than the classic fourth-order staggered-grid FD (FSFD) scheme and the compact second-order staggered-grid FD scheme. In addition, we find the feasibility of using the ADSSFD scheme to perform simulations in the 3D overthrust model. We use a parallel iteration solver to solve the large sparse linear system obtained after the discretization. Because the condition number of the matrix in the ADSSFD scheme is smaller than that of the FSFD scheme, the ADSSFD scheme is cheaper to run.