| 基于新的差分结构的时-空域高阶有限差分波动方程数值模拟方法 |
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| 引用本文： | 张保庆,周辉,陈汉明,盛善波.基于新的差分结构的时-空域高阶有限差分波动方程数值模拟方法[J].地球物理学报,2016,59(5):1804-1814. |
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| 作者姓名： | 张保庆 周辉 陈汉明 盛善波 |
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| 作者单位： | 1. 油气资源与探测国家重点实验室, CNPC物探重点实验室, 中国石油大学(北京), 北京 102249;2. 东方地球物理公司研究院大港分院, 天津大港 300280;3. 中国石油天然气勘探开发公司, 北京 100034 |
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| 基金项目： | 国家重点基础研究发展计划(973计划)(2013CB228603),国家自然科学基金(41174119)和中石油物探新方法新技术研究(2014A-3609)联合资助. |
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| 摘 要： | 传统的高阶有限差分波动方程数值模拟方法采用高阶差分算子近似空间偏导数,能有效抑制空间频散.然而,传统的有限差分法仅采用二阶差分算子近似时间偏导数,这使得地震波场沿时间外推的精度较低.当采用较大的时间采样间隔,传统的有限差分法模拟波场会出现明显的时间频散,甚至不稳定.本文基于新的差分结构和中心网格剖分,发展了一种空间任意偶数阶精度、时间四阶和六阶精度的时空域有限差分方法.基于对离散后的频散关系进行泰勒展开,本文推导了时空域高阶有限差分算子的差分系数.相速度分析表明时间四阶、六阶精度的差分方法能显著地减小传统时间二阶精度差分方法的时间频散.在相同的精度下与传统差分法比较,本文发展的时间四阶、六阶有限差分方法的计算效率比传统方法高.均匀和非匀均介质中的波场数值模拟实验进一步证实本文研究的时空高阶有限差分方法的优越性.
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| 关 键 词： | 波动方程 时空域 高阶有限差分 数值模拟 |
| 收稿时间： | 2015-08-04 |
Time-space domain high-order finite-difference methods for seismic wave numerical simulation based on new stencils |
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| ZHANG Bao-Qing,ZHOU Hui,CHEN Han-Ming,SHENG Shan-Bo.Time-space domain high-order finite-difference methods for seismic wave numerical simulation based on new stencils[J].Chinese Journal of Geophysics,2016,59(5):1804-1814. |
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| Authors: | ZHANG Bao-Qing ZHOU Hui CHEN Han-Ming SHENG Shan-Bo |
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| Institution: | 1. State Key Laboratory of Petroleum Resources and Prospecting, CNPC Key Lab of Geophysical Exploration, China University of Petroleum, Beijing 102249, China;2. Dagang Branch of GRI, BGP Inc., CNPC, Tianjin Dagang 300280, China;3. China National Oil & Gas Exploration and Development Corporation, Beijing 100034, China |
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| Abstract: | The traditional finite-difference (FD) seismic wave simulation scheme adopts high-order FD operators to discretize the spatial derivatives, and the second-order FD operator to discretize the temporal derivative. Therefore, the traditional high-order FD method only achieves high-order accuracy in space, but exhibits low-order accuracy in time. When a relatively large time step is applied, the traditional FD method suffers from visible temporal dispersion and even instability. This paper develops new time-space domain high-order FD methods that attain arbitrary even-order accuracy in space, fourth- and sixth-order accuracy in time. The new FD methods are developed based on new FD stencils and a centered-grid. The FD coefficients are determined from the discrete dispersion relation using the Taylor-series expansion (TE) approach. Dispersion analysis indicates that our temporal fourth- and sixth-order FD methods improve the accuracy of the traditional temporal second-order FD method significantly. Computational cost analysis demonstrates that our temporal high-order FD methods are more efficient than the traditional temporal second-order method. Numerical simulation of seismic waves in homogeneous and heterogeneous media further validates the effectiveness of our high-order FD methods. |
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| Keywords: | Seismic wave equation Time-space domain High-order finite-difference Numerical simulation |
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