| 一种时空域优化的高精度交错网格差分算子与正演模拟 |
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| 引用本文： | 雍鹏,黄建平,李振春,曲璐萍,李庆洋,袁茂林,关哲.一种时空域优化的高精度交错网格差分算子与正演模拟[J].地球物理学报,2016,59(11):4223-4233. |
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| 作者姓名： | 雍鹏 黄建平 李振春 曲璐萍 李庆洋 袁茂林 关哲 |
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| 作者单位： | 1. 中国石油大学(华东)地球科学与技术学院, 青岛 266580;
2. 中国石油大学(北京)地球物理与信息工程学院, 北京 102249;
3. 莱斯大学 地球科学学院, 美国德克萨斯州休斯顿 77005 |
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| 基金项目： | 大地测量与地球动力学国家重点实验室重点基金（SKLGED2015-5-2-EZ），国家973项目（2014CB239006，2011CB202402），国家自然科学基金（41104069，41274124）联合资助. |
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| 摘 要： | 如何有效压制数值频散是有限差分正演模拟研究中的关键问题之一.近年来,许多学者对二阶声波方程的差分算子开展了大量的优化工作,在压制频散方面取得不错的效果.一阶压强-速度方程广泛用于研究地震波在地下变密度模型中传播规律,目前针对一阶方程的优化工作大多只是在空间差分算子上展开.本文在前人研究的基础上,推导出一阶声波方程中压强场与偏振速度场之间的解析关系,据此在传统交错网格基础上给出一种高精度的显式时间递推格式,该递推格式将时间差分与空间差分算子结合在一起,并采用共轭梯度法得到精确时间递推匹配系数,实现时空差分算子的同时优化.在编程实现算法的基础上,通过频散分析与三个典型模型测试表明:本文方法能够较为有效地压制时间频散与空间频散,提高数值计算精度;同时对复杂模型也有很好适用性.
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| 关 键 词： | 数值频散 一阶压强-速度方程 优化差分算子 交错差分递推格式 共轭梯度法 |
| 收稿时间： | 2015-04-03 |
Optimized staggered-grid finite-difference method in time-space domain based on exact time evolution schemes |
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| YONG Peng,HUANG Jian-Ping,LI Zhen-Chun,QU Lu-Ping,LI Qing-Yang,YUAN Mao-Lin,GUAN Zhe.Optimized staggered-grid finite-difference method in time-space domain based on exact time evolution schemes[J].Chinese Journal of Geophysics,2016,59(11):4223-4233. |
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| Authors: | YONG Peng HUANG Jian-Ping LI Zhen-Chun QU Lu-Ping LI Qing-Yang YUAN Mao-Lin GUAN Zhe |
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| Institution: | 1. Department of Geophysics, School of Geosciences, China University of Petroleum, Qingdao 266555, China;
2. College of Geophysics and Information Engineering, China University of Petroleum, Beijing 102249, China;
3. Department of Earth Science, Rice University, Houston, TX 77005 |
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| Abstract: | Finite-difference (FD) methods have been widely applied to solving seismic wave equations due to high computational efficiency in seismic exploration. Meanwhile, grid dispersion is one of the key numerical problems when using FD schemes for modeling seismic wave propagation. Many optimized finite-difference schemes have been proposed. However, most of them focus on suppressing dispersion errors based on second-order acoustic wave equation. We develop a novel optimized Staggered Grid Finite-Difference (SGFD) method scheme for the variable density forward modeling based on first-order acoustic wave equation. We firstly derive exact time evolution solutions of acoustic particle velocity and pressure from coupled first-order wave-propagation equations. We then get a time difference scheme and space difference scheme based on staggered grids. Comparing with the response of time difference and spatial difference using analytical solution, evolution matching coefficient would be obtained by introducing least square approximation method. Considering the ill-conditioned property of the linear system, we adopt Conjugate Gradient Method to stably provide evolution matching coefficient. Finally, dispersion analysis and three typical model tests are carried out to verify the proposed algorithm. |
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| Keywords: | Numerical dispersion First-order acoustic wave equation Optimized finite-difference operators Staggered grid finite-difference schemes Conjugate gradient method |
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