3D numerical simulation of frequency-domain elastic wave equation with a compact second-order scheme

Finite-difference frequency-domain (FDFD) modeling has gained popularity in recent years. However, its main drawback lies in the need to solve large sparse linear systems, which is computationally expensive, especially for 3D elastic wave simulations. The existing elastic wave optimal schemes improve the simulation accuracy at the cost of using large-sized stencils or high-order finite-difference (FD) operators, and most of them only consider equal grid spacing and solid media. To address these issues, we have proposed a compact second-order scheme for simulating 3D elastic wave propagation. Starting from the second-order FD discretization of the first-order velocity-stress expression, the compact discrete scheme of the second-order elastic wave equation is obtained by using a parsimonious staggered-grid strategy to eliminate the stress variables. In this way, the scheme preserves the ability to handle high-contrast velocity and liquid-solid media, and has a more compact and sparse impedance matrix than existing schemes, which helps save computational costs. We also use an antilumped mass strategy to further improve the modeling accuracy. Dispersion analysis indicates that our compact second-order scheme has better accuracy than the classic second-order scheme, and even better accuracy than the average derivative 27-point scheme at large Poisson's ratio. Compared with the existing 3D elastic wave schemes, the compact second-order scheme has advantages in computational cost for the same grid. Finally, we employ these schemes to implement 3D numerical simulations, validating the effectiveness of our proposed scheme. •Discretization of the second-order elastic wave equation based on a parsimonious staggered-grid strategy.•Our compact scheme allows for arbitrary grid-spacing ratios and liquid-solid media.•Optimization coefficients depend only on grid-spacing ratios.•Our compact scheme has computational cost advantages over existing 3D elastic wave schemes for the same grid.•The new scheme is superior to all existing optimal 27-point schemes for large Poisson's ratios.