| 一种全局优化的隐式交错网格有限差分算法及其在弹性波数值模拟中的应用 |
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| 引用本文： | 王洋,刘洪,张衡,王之洋,唐祥德.一种全局优化的隐式交错网格有限差分算法及其在弹性波数值模拟中的应用[J].地球物理学报,2015,58(7):2508-2524. |
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| 作者姓名： | 王洋 刘洪 张衡 王之洋 唐祥德 |
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| 作者单位： | 1. 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;2. 中国科学院大学, 北京 100049;3. 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 |
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| 基金项目： | 国家高技术研究发展计划(863计划)项目(2012AA061202),国家油气重大专项(2011ZX05008-006-50),国家油气重大专项(2011ZX05003-003),国家科技重大专项(2011ZX05023-005-002)联合资助. |
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| 摘 要： | 在数值模拟中,隐式有限差分具有较高的精度和稳定性.然而,传统隐式有限差分算法大多由于需要求解大型矩阵方程而存在计算效率偏低的局限性.本文针对一阶速度-应力弹性波方程,构建了一种优化隐式交错网格有限差分格式,然后将改进格式由时间-空间域转换为时间-波数域,利用二范数原理建立目标函数,再利用模拟退火法求取优化系数.通过对均匀模型以及复杂介质模型进行一阶速度-应力弹性波方程数值模拟所得单炮记录、波场快照分析表明:这种优化隐式交错网格差分算法与传统的几种显式和隐式交错网格有限差分算法相比不但降低了计算量,而且能有效的压制网格频散,使弹性波数值模拟的精度得到有效的提高.
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| 关 键 词： | 隐式有限差分 数值模拟 交错网格 弹性波方程 模拟退火 |
| 收稿时间： | 2014-06-11 |
A global optimized implicit staggered-grid finite-difference scheme for elastic wave modeling |
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| WANG Yang,LIU Hong,ZHANG Heng,WANG Zhi-Yang,TANG Xiang-De.A global optimized implicit staggered-grid finite-difference scheme for elastic wave modeling[J].Chinese Journal of Geophysics,2015,58(7):2508-2524. |
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| Authors: | WANG Yang LIU Hong ZHANG Heng WANG Zhi-Yang TANG Xiang-De |
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| Institution: | 1. Key Laboratory of Petroleum Resources Research, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing 100029, China;2. University of Chinese Academy of Sciences, Beijing 100049, China;3. MLR Key Laboratory of Marine Mineral Resources, Guangzhou Marine Geological Survey, Guangzhou 510075, China |
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| Abstract: | The advanced algorithms, such as reverse time migration (RTM) and full waveform inversion (FWI), require iterative calculation of the wave field. Its wave propagation part is highly sensitive to computational accuracy and stability. Therefore, how to find a way to obtain a finite-difference scheme that can consider the both aspects is absolutely critical. Here we propose a global optimized implicit staggered-grid finite-difference scheme that inherits the merit of high stability from the implicit finite-difference scheme and improves the computational efficiency remarkably.The conventional implicit finite-difference operators generally have to obtain the high accuracy solutions from the inversion of either pentadiagonal or more diagonals matrices using the LU decomposition method, which greatly reduce the computation efficiency. Therefore, we first perform a global optimized implicit staggered-grid finite-difference (OISFD) scheme for first-order derivatives, which only needs to solve twice tridiagonal matrix inversion using the chasing method. In this way, it avoids the requirement of solving the large-scale matrix equation. Then we transform the new scheme from the time-space domain into the time-wavenumber domain, and develop the objective function by means of the two-norm theory. Different from traditional global optimized methods, we select the simulated annealing algorithm to get the optimized coefficients. And finally, after introducing the coefficients to the operator we establish the global optimized implicit staggered-grid finite-difference scheme.We use independent tests to show that for same size matrix inversion, the average CPU time of the chasing method occupies 0.0019~0.0058 times that of the LU decomposition method. And this comparison becomes the theoretical basis of improving the computational efficiency. From the accuracy curves of approximation between the conventional explicit staggered-grid finite-difference method (ESFDM) and implicit staggered-grid finite-difference method (ISFDM), we can indicate that the OISFD operators have wider frequency coverage and smaller accuracy error fluctuation than those of the conventional ESFD operators and ISFD operators when using the same order spatial difference operator. In order to demonstrate the effect in elastic wave modeling, we perform first-order velocity-stress elastic wave equation numerical simulations on a homogeneous model and the modified Sigsbee2A model. The resulting shot records and wave field snapshots indicate that the OISFDM is more effective in suppressing the numerical dispersion, which is fully consistent with the theoretical accuracy curve comparison. What's more, the least CPU time cost in numerical simulation further confirms that the OISFD scheme reduces calculating amount while keeping high accuracy numerical simulation performance.We have presented an implicit optimized scheme with any order of accuracy for calculating first spatial derivatives on a staggered-grid. The operator is designed by fitting the response in the wavenumber domain using the simulated annealing algorithm. The method is based on applying optimized operators to each of the spatial coordinates in elastic wave equation. It could utilize smaller stencils to achieve more accurate results than the corresponding explicit operator without adding significantly higher computational cost to conventional implicit finite-difference methods. The dispersion relation analysis and the numerical results demonstrate that the OISFD operators can achieve higher accuracy compared with those using the conventional ESFD operators and ISFD operators. This means we can greatly save the memory and computational cost required when using our optimized OISFD methods. |
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| Keywords: | Implicit finite-difference Numerical simulations Staggered-grid Elastic wave equation Simulated annealing algorithm |
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