Abstract
The perfectly matched layer (PML) boundary condition has been proven to be effective for attenuating reflections from model boundaries during wavefield simulation. As such, it has been widely used in time-domain finite-difference wavefield simulations. The conventional PML has poor performance for near grazing incident waves and low-frequency reflections. To overcome these limitations, a more complex frequency-shifted stretch (CSF) function is introduced, which is known as the CFS-PML boundary condition and can be implemented in the time domain by a recursive convolution technique (CPML). When implementing the PML technique to second-order wave equations, all the existing methods involve adding auxiliary terms and rewriting the wave equations into new second-order partial differential equations that can be simulated by the finite-difference scheme, which may affect the efficiency of numerical simulation. In this paper, we propose a relatively simple and efficient approach to implement CPML for the second-order equation system, which solves the original wave equations numerically in the stretched coordinate. The spatial derivatives in the stretched coordinate are computed by adding a correction term to the regular derivatives. Once the first-order spatial derivatives are computed, we computed the second-order spatial derivatives in a similar way; therefore, we refer to the method as two-step CPML (TS-CPML). We apply the method to the second-order acoustic wave equation and a coupled second-order pseudo-acoustic TTI wave equation. Our simulations indicate that amplitudes of reflected waves are only about half of those computed with the traditional CPML method, suggesting that the proposed approach has computational advantages and therefore can be widely used for forwarding modeling and seismic imaging.
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Acknowledgements
We thank Drs. Yang ZHAO and Gang YAO at the China University of Petroleum at Beijing for helpful discussion. We also thank the associate editor and two anonymous reviewers for their constructive and thoughtful comments and suggestions, which have significantly improved the quality of this paper. This work was supported by the National Natural Science Foundation of China (Grant No. 41630209).
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Fang, X., Niu, F. An unsplit complex frequency-shifted perfectly matched layer for second-order acoustic wave equations. Sci. China Earth Sci. 64, 992–1004 (2021). https://doi.org/10.1007/s11430-021-9784-7
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DOI: https://doi.org/10.1007/s11430-021-9784-7