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

Area of Science:

• Computational Seismology
• Numerical Methods in Geophysics
• Wave Propagation Modeling

Background:

• Implicit staggered-grid finite-difference (SGFD) methods are standard for first-order acoustic wave-equation modeling.
• Current methods often use identical implicit SGFD operators for all spatial derivatives, potentially limiting simulation speed.

Purpose of the Study:

• To introduce a hybrid explicit implicit SGFD (HEI-SGFD) scheme for acoustic wave-equation modeling.
• To enhance simulation speed without compromising accuracy.
• To investigate the effectiveness of the HEI-SGFD scheme through numerical analysis.

Main Methods:

• Developed a hybrid scheme combining second-order explicit SGFD operators for half the spatial derivatives and implicit SGFD operators (with diagonal points) for the other half.
• Determined HEI-SGFD coefficients in the time-space domain by minimizing phase velocity error using least-squares.
• Validated the method through dispersion analysis and numerical simulations.

Main Results:

• The proposed HEI-SGFD scheme achieves nearly double the simulation speed compared to conventional implicit SGFD methods.
• The HEI-SGFD scheme demonstrates equivalence to a second-order finite-difference scheme on an ordinary grid.
• Dispersion analysis and numerical simulations confirm the method's effectiveness and accuracy preservation.

Conclusions:

• The HEI-SGFD scheme offers a significant improvement in computational efficiency for acoustic wave-equation modeling.
• This hybrid approach successfully balances simulation speed and accuracy, providing a valuable alternative for geophysical modeling.
• The method's performance is robust, as evidenced by rigorous numerical testing.