Anti-dispersion finite difference simulation and reverse-time migration for wave equations
Zhang Zhiyu1, Tan Xianbo1, Huang Luyao1, Liu Liansheng2
1. School of Automation, Xi'an University of Technology, Xi'an, Shaanxi 710048, China;
2. Panimaging Software Development Limited, Beijing 100096, China
Abstract:Numerical dispersion is the most prominent problem in solving wave equations by the finite difference method, which seriously affects the wave field modeling and decreases the resolution of wave field in the simulation process. Usually refined computational grids or high order difference operators are used to solve this problem. But all these approaches increase the computational complexity. In this work we propose a new finite-difference model. Firstly by adding a dispersion correction term to the conventional finite-difference equations, the finite-difference based wave equation method is constructed to weaken the numerical dispersion. Secondly by analyzing the relation between phase velocity/group velocity and the dispersion, the optimal parameters of the correction terms in the second and fourth order finite-difference scheme are derived. When the optimal values are chosen for correction parameters, the corresponding dispersion curves show that the dispersion error is minimum while the phase velocity has the best match with group velocity. The numerical simulation and reverse-time migration results suggest that the proposed algorithm has an obvious suppression on numerical dispersion, and the performance of the second order finite-difference in the new method is equivalent to or even better than the conventional fourth order finite-difference, but the computational cost is about the same as that of conventional second order finite-difference. Additionally, the anti-dispersion finite-difference scheme has a better imaging result and higher accuracy than the conventional method with the same order in reverse time migration.
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