Time-space domain scalar wave modeling by a novel hybrid staggered-grid finite-difference method with high temporal and spatial accuracies

Staggered-grid finite-difference (SFD) scheme is favored in wave equation simulation due to its superior accuracy and stability to center-grid finite-difference (CFD) scheme. However, for the scalar wave equation (SWE) modeling, the conventional SFD (CSFD) scheme only reaches second-order accuracy in space and time for the discrete SWE; the recently developed modified SFD (MSFD) scheme improves the accuracy to (2N)th-order (N < 4) but is costly because the MSFD scheme is coined by adding many extra grid points to the CSFD scheme. To tackle these issues, we develop a cost-effective hybrid SFD (HSFD) scheme, which combines the features of the CSFD and MSFD schemes; we prove that the new HSFD scheme can simultaneously reach (2N)th-order accuracy in space and time for the discrete wave equation. In addition, to deal with the optimization difficulties due to the nonlinear dispersion relation of the SFD schemes, we propose a two-step linear optimization method to improve the accuracy of the new HSFD scheme. The analyses on dispersion, stability properties and numerical simulation examples demonstrate that the new HSFD scheme owns better accuracy and stability than the CSFD scheme. Computational cost analysis shows that the HSFD scheme can be more efficient than the MSFD scheme because it only requires half the additional grid points. (C) 2022 Elsevier Inc. All rights reserved.

Automated summary

The staggered-grid finite-difference (SFD) scheme is favored for wave equation simulation due to its accuracy and stability. However, the conventional SFD scheme only achieves second-order accuracy. To improve the accuracy, a cost-effective hybrid SFD (HSFD) scheme is proposed, combining the features of CSFD and MSFD schemes. An optimization method is also introduced to deal with the nonlinear dispersion relation. Analysis shows that the new HSFD scheme has better accuracy and stability, with lower computational cost compared to the MSFD scheme.