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摘要
Seismic anisotropy exists extensively in the earth, wherea the TI medium is the most common anisotropic one. The conventional finite difference modeling (FDFDM) of 2D VTI media frequency-space domain with 9-point scheme can cause serious numerical dispersion because of its poor computational accuracy. The average-derivative optimal method (ADM) not only is suitable for equal and unequal directional sampling intervals, but also retains high precision. We introduce this idea into the qP wave equation of 2D VTI media to improve the computational accuracy. @@@ We firstly deal with the P-SV wave phase velocity dispersion equation for VTI media and derive the frequency-space domain qP wave equation for 2D VTI media following Alkhalifah's TI acoustic approximation theory. Then we propose a new kind of qP wave equation for 2D VTI media with a second-order 9-point FDFDM scheme based on ADM. Specifically, we represent the finite-difference approximations of the second-order centered spatial-derivative terms as the weighted average of 3 grid points in orthogonal directions and the acceleration term as the weighted average of all 9 grid points. Afterwards we use the least-square optimal method to resolve the optimized coefficients of the VTI media with the ADM 9-point scheme and perform numerical dispersion analysis towards this new scheme. The results show that the ADM 9-point scheme for VTI media can decrease the required number of grid points per wavelength from 12 to 3. 57 bounded by a phase velocity error range of 1%. Therefore this scheme significantly increases the computational accuracy of VTI media FDFDM compared to the VTI media conventional 9-point scheme. So the VTI media ADM 9-point scheme allows using a larger grid interval in the modeling and obviously improves the computational efficiency. Finally we derive the 2D VTI media ADM 9-point frequency-space domain with the perfectly matched layer (PML) wave equation and perform seismic wave modeling in the frequency-space domain. @@@ We use a complex BP2007 2D VTI ocean standard model to verify the validity and precision of the VTI media ADM 9-point scheme. As the VTI media conventional 9-point scheme is also suitable for unequal directional sampling intervals, we use this scheme for comparison. The horizontal sampling interval and the vertical sampling interval are 10 m and 4 m, respectively, so the ratio of the horizontal sampling interval to the vertical sampling interval comes to 2. 5. The VTI media parameters include P-wave velocity and Thomsen anisotropic parameter. The frequency-space domain wavefield characteristic of qP wave is very clear and depicts well from the 35 Hz monochromatic wavefield computed by the VTI media ADM 9-point scheme. The simulation result with this scheme is accurate while the result with VTI media conventional 9-point scheme exhibits errors due to numerical dispersion. The simulation results also demonstrate the VTI media ADM 9-point scheme is in good agreement with the high-precision time domain 12-order finite difference scheme for VTI media. It is worth mentioning that the frequency-space domain PML absorbing boundary condition eliminates the artificial boundary reflection very well. The numerical example proves the precision and validity of the VTI media ADM 9-point scheme. @@@ We propose a new VTI ADM 9-point scheme which obviously increases the computational precision of VTI FDFDM compared to the VTI media conventional 9-point scheme. We obtain the optimized coefficients by the least-square method and decrease the required grid points per wavelength from 12 to 3. 57. The numerical example demonstrates that the VTI ADM 9-point scheme can not only possess high computational precision and computational efficiency, but also possess applicability and flexibility. The VTI ADM 9-point scheme can be developed further and has many applications. Taking FWI for example, the VTI ADM 9-point scheme can be applied to the VTI FWI as a fast and accurate modeling engine.
- 出版日期2015-9
- 单位广州海洋地质调查局; 中国科学院大学; 中国科学院地质与地球物理研究所; 中国科学院地质与地球物理研究所兰州油气资源研究中心
