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A hybrid explicit implicit staggered grid finite-difference scheme for the first-order acoustic wave equation
Wenquan Liang1, Yanfei Wang2, Jingjie Cao3
1College of Resource Engineering, Longyan University, Longyan, 364000, People's Republic of China.
Abstract:
Implicit staggered-grid finite-difference (SGFD) methods are widely used for the first-order acoustic wave-equation modeling. The identical implicit SGFD 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 operator for half of the first-order spatial derivatives in the first-order acoustic wave-equation. At the same time, we use the implicit SGFD 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 implicit SGFD 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 dispersion analysis and numerical simulations.
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