| 基于平均导数优化方法的VTI介质频率空间域正演 |
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| 引用本文： | 张衡,刘洪,唐祥德,王洋,张宝金.基于平均导数优化方法的VTI介质频率空间域正演[J].地球物理学报,2015,58(9):3306-3316. |
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| 作者姓名： | 张衡 刘洪 唐祥德 王洋 张宝金 |
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| 作者单位： | 1. 国土资源部海底矿产资源重点实验室, 广州海洋地质调查局, 广州 510075;
2. 中国科学院地质与地球物理研究所, 中国科学院油气资源研究重点实验室, 北京 100029;
3. 中国科学院大学, 北京 100049 |
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| 基金项目： | 国家油气重大专项(2011ZX05003-003),国家自然科学基金(41176056)和国家高技术研究发展计划(863计划)主题项目(2012AA061202)联合资助. |
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| 摘 要： | 本文提出了一种新的基于平均导数优化方法(average-derivative optimal method,简称ADM)的二维VTI介质qP波波动方程频率空间域二阶9点格式,这种新算法将二维VTI介质qP波波动方程中中心空间导数项的差分近似表示为正交方向上3个网格点的加权平均形式.通过最小二乘优化方法求取空间导数项和加速度项的加权优化系数从而使数值频散达到极小化,每个波长所需要的网格点数在1%的误差范围内仅为3.57个网格点数,而VTI介质常规9点差分格式在相同的误差范围内则需要约12个网格点数,新方法的计算精度明显提高.复杂BP2007 2D VTI海洋标准模型数值模拟结果也验证了本文VTI介质9点ADM算法的有效性和准确性.
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| 关 键 词： | VTI介质 平均导数优化方法 频率空间域 |
| 收稿时间： | 2014-11-25 |
Forward modeling of VTI media in the frequency-space domain based on an average-derivative optimal method |
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| ZHANG Heng,LIU Hong,TANG Xiang-De,WANG Yang,ZHANG Bao-Jin.Forward modeling of VTI media in the frequency-space domain based on an average-derivative optimal method[J].Chinese Journal of Geophysics,2015,58(9):3306-3316. |
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| Authors: | ZHANG Heng LIU Hong TANG Xiang-De WANG Yang ZHANG Bao-Jin |
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| Institution: | 1. MLR Key Laboratory of Marine Mineral Resources, Guangzhou Marine Geological Survey, Guangzhou 510075, China;
2. Key Laboratory of Petroleum Resources Research, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing 100029, China;
3. University of Chinese Academy of Sciences, Beijing 100049, China |
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| Abstract: | Seismic anisotropy exists extensively in the earth, whereas 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. |
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| Keywords: | VTI media Average-derivative optimal method Frequency-space domain |
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