• 论文 •

### 基于有限元方法的频率域弹性波全波形反演

1. 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;数学科学学院, 中国科学院大学, 北京 100049
• 收稿日期:2019-11-11 出版日期:2020-12-15 发布日期:2020-12-15
• 基金资助:

国家自然科学基金（11471328，51739007）资助.

Zhang Wensheng, Zhang Lina. ELASTIC WAVE FULL-WAVEFORM INVERSION BASED ON THE FINITE-ELEMENT METHOD IN THE FREQUENCY DOMAIN[J]. Journal on Numerica Methods and Computer Applications, 2020, 41(4): 315-336.

### ELASTIC WAVE FULL-WAVEFORM INVERSION BASED ON THE FINITE-ELEMENT METHOD IN THE FREQUENCY DOMAIN

Zhang Wensheng, Zhang Lina

1. LSEC, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China;School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
• Received:2019-11-11 Online:2020-12-15 Published:2020-12-15

In this paper, the frequency domain full-waveform inversion for the elastic wave equations based on the finite-element method is studied and developed intensively. Firstly, the finite-element forward method for the elastic wave equations in the frequency domain is expounded in detail. It includes the full discrete finite-element schemes on the rectangle element, the perfectly matched layer (PML) absorbing boundary conditions and the source treatment in the finite-element computations. The numerical computations of forward modelling are also accomplished. Secondly, we derive the full-waveform inversion formulae and the corresponding discrete schemes in detail based on the rectangle element. Moreover, the preconditioned steepest descent method and the regularization method are applied. Finally, the parallel numerical computations of full-waveform inversion for a homogeneous model and the international benchmark Overthrust model are completed. In the inversion, the density is assumed to be known and the compressional wave velocity and the shear wave velocity are obtained through the inversion results of Lame parameters. The inversion is based on the frequency multiscale strategy and is carried out from low frequency to high frequency step by step. Good inversion results are obtained including the inversion for the noisy data. Numerical computations show the correctness and effectiveness of the method, schemes and algorithms presented in this paper.

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