Abstract
The staggered-grid finite-difference (SGFD) method has been widely used in seismic forward modeling. The precision of the forward modeling results directly affects the results of the subsequent seismic inversion and migration. Numerical dispersion is one of the problems in this method. The window function method can reduce dispersion by replacing the finite-difference operators with window operators, obtained by truncating the spatial convolution series of the pseudospectral method. Although the window operators have high precision in the low-wavenumber domain, their precision decreases rapidly in the high-wavenumber domain. We develop a least squares optimization method to enhance the precision of operators obtained by the window function method. We transform the SGFD problem into a least squares problem and find the best solution iteratively. The window operator is chosen as the initial value and the optimized domain is set by the error threshold. The conjugate gradient method is also adopted to increase the stability of the solution. Approximation error analysis and numerical simulation results suggest that the proposed method increases the precision of the window function operators and decreases the numerical dispersion.
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Acknowledgments
The authors wish to thank all the reviewers and editors. We also give thanks to Seismic Wave Propagation and Imaging (SWPI) for supports.
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This work was jointly supported by the NSF (No. 41720104006), the Strategic Priority Research Program of the Chinese Academy of Sciences (A) (No. XDA14010303), the National Oil and Gas Project (Nos. 2016ZX05002-005-007HZ and 2016ZX05014-001-008HZ), the Shandong Innovation Project (No. 2017CXGC1602), and the Qingdao Innovation Project (Nos. 16-5-1-40-jch and 17CX05011).
Ren Ying-Jun is a graduate student at China University of Petroleum (East China). His research interests are seismic forward modeling and full-waveform inversion.
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Ren, YJ., Huang, JP., Yong, P. et al. Optimized staggered-grid finite-difference operators using window functions. Appl. Geophys. 15, 253–260 (2018). https://doi.org/10.1007/s11770-018-0668-7
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DOI: https://doi.org/10.1007/s11770-018-0668-7