Optimized staggered-grid finite-difference operators using window functions
Ren Ying-Jun1,2, Huang Jian-Ping1,2, Yong Peng1,2,3, Liu Meng-Li1,2, Cui Chao1,2, and Yang Ming-Wei1,2
1. School of Geosciences, China University of Petroleum, Qingdao 266580, China.
2. Qingdao National Laboratory for Marine Science and Technology, Qingdao 266071, China.
3. Department of Mathematics and Statistics, University of Calgary, Calgary, Alberta T2N 1N4, Canada.
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.
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).
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