数值计算与计算机应用
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数值计算与计算机应用  2017, Vol. 38 Issue (3): 167-196    DOI:
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频率域声波方程全波形反演
张文生, 庄源
中国科学院数学与系统科学研究院, LSEC, 计算数学与科学工程计算研究所, 北京 100190
FULL-WAVEFORM INVERSION BASED ON THE ACOUSTIC WAVE EQUATION IN THE FREQUENCY DOMAIN
Zhang Wensheng, Zhuang Yuan
LSEC, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China
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摘要 全波形反演是一种利用地表或井中观测到的波场来推测地下物性参数的高精度成像方法.本文研究了频率域声波方程全波形反演的数值方法.正演用带PML边界条件的九点差分格式求解.反演是一个极小化模拟数据与观测数据之间残量的优化迭代过程,文中比较了多种数值优化方法,包括最速下降法、共轭梯度法、LBFGS方法、高斯牛顿法以及预条件方法.反演从低频到高频逐级进行,且前一个频率的反演结果作为下一个频率反演的初值,该策略有效克服了反演发散或收敛到局部极小值的情况.文中详细描述了正反演方法,并对一个简单模型和两个国际标准模型(即Marmousi模型和Overthrust模型)进行了MPI并行反演计算,结果表明牛顿方法和预条件方法能较精确地对复杂构造模型进行反演成像.
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关键词波动方程   频率域   全波形反演   预条件   最速下降法   共轭梯度法   LBFGS方法   高斯牛顿法   Marmousi模型   Overthrust模型     
Abstract: The full-waveform inversion is a high accurate imaging method which deduces physical parameters by using the wavefield observed on surface or in cross well. In this paper, we investigate the numerical methods of the frequency-domain full-waveform inversion. The forward problem is solved by the 9-point difference scheme with PML absorbing boundary conditions. The inversion is an optimization iterative process to minimize the residual between the synthetic data and the observed data. Several numerical optimization methods are compared in detail in this paper. They include the steepest descent method, the conjugate gradient method, the LBFGS method, the Gauss-Newton method and the preconditioned methods. The inversion is implemented from low frequency to high frequency successively. Furthermore, the inversion result of present frequency is used as the initial model for the inversion of the next frequency. This strategy overcomes the difficulty that the inversion falls into the local minimum or may be divergence. The forward and inverse methods are described detailly in this paper. Numerical computations based on MPI parallelization for a simple mode and two international benchmark models called Marmousi model and Overthrust model are completed. The computational results show that the Newton-type method and the preconditioned methods can yield very high accurate inversion results for complicated models.
Key wordswave equation   frequency domain   full-waveform inversion   preconditioner   steepest descent method   conjugate gradient method   LBFGS   Gauss-Newton method   Marmousi model   Overthrust model   
收稿日期: 2016-07-24;
基金资助:

国家自然科学基金(11471328)资助项目.

引用本文:   
. 频率域声波方程全波形反演[J]. 数值计算与计算机应用, 2017, 38(3): 167-196.
. FULL-WAVEFORM INVERSION BASED ON THE ACOUSTIC WAVE EQUATION IN THE FREQUENCY DOMAIN[J]. Journal of Numerical Methods and Computer Applicat, 2017, 38(3): 167-196.
 
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