A hybrid explicit-implicit staggered-grid finite-difference scheme for the first-order acoustic wave-equation modeling

Implicit staggered-grid finite-difference (ISGFD) methods are widely used for the first-order acoustic wave-equation modeling. The identical ISGFD operator is commonly used for all of the first-order spatial derivatives in the first-order acoustic wave-equation. In this paper, we propose a hybrid explicit-implicit SGFD (HEI-SGFD) scheme which could simultaneously preserve the wave-equation simulation accuracy and increase the wave-equation simulation speed. We use a second-order explicit SGFD (ESGFD) operator for half of the first-order spatial derivatives in the first-order acoustic wave-equation. At the same time, we use the ISGFD operator with added points in the diagonal direction for the other first-order spatial derivatives in the first-order acoustic wave-equation. The proposed HEI-SGFD scheme nearly doubles the wave-equation simulation speed compared to the ISGFD schemes. In essence, the proposed HEI-SGFD scheme is equivalent to the second-order FD scheme with ordinary grid format. We then determine the HEI-SGFD coefficients in the time-space domain by minimizing the phase velocity error using the least-squares method. Finally, the effectiveness of the proposed method is demonstrated by a dispersion analysis and numerical simulations.