Full-waveform inversion of elastic waves in variable grids based on variable difference coefficients
ZHANG Hongjing1,2, HE Huili3, SUN Wenbo4,5, SUN Pengyuan3, LI Honghui3, ZHOU Hui6,7,8
1. State Key Laboratory of Nuclear Resources and Environment, East China University of Technology, Nanchang, Jiangxi 330013, China; 2. School of Geophysics and Measurement-Control Technology, East China University of Technology, Nanchang, Jiangxi 330013, China; 3. Geophysical Exploration Technology Research Center, BGP Inc, CNPC, Zhuozhou, Hebei 072751, China; 4. Exploration and Development Research Institute of CNOOC Research Institute Co., Ltd, Beijing 100028, China; 5. National Engineering Research Center of Offshore Oil and Gas Exploration, Beijing 100028, China; 6. National Key Laboratory of Petroleum Resources and Engineering, China University of Petroleum (Beijing), Beijing 102249, China; 7. CNPC Key Laboratory of Geophysical Exploration, China University of Petroleum (Beijing), Beijing 102249, China; 8. College of Geophysics, China University of Petroleum (Beijing), Beijing 102249, China
Abstract：Full-waveform inversion fully utilizes all the information of seismic wave propagation, including amplitude, phase, and travel time, which can obtain inversion results with higher resolution and accuracy compared with travel time tomography. When the velocity in the shallow layer of the medium is low, fine grids are usually used to sample the low-velocity layer, so as to ensure the accuracy of forward modeling. However, subdividing the entire model into finer grids will increase computational complexity and storage requirements, and oversampling will occur in the high-velocity regions of the model. These problems are further amplified in the process of full-waveform inversion. To address these issues, this study introduced a finite difference forward modeling method of the elastic wave equation in variable grids based on variable difference coefficients. Firstly, the difference coefficient of variable grid wave field simulation was derived based on Taylor expansion, and the variable grid wave field simulation was realized. Secondly, the forward modeling method of variable difference coefficients was applied to the forward modeling, residual backpropagation, and wave field reconstruction of the full-waveform inversion, and the full-waveform inversion of elastic waves in variable grids based on the variable difference coefficient was realized. In the full-waveform inversion, the multi-scale inversion strategy and the conventional conjugate gradient method were used for the iterative solution. The fine grids were used to divide shallow low-velocity layers, and coarser grids were used to divide the middle and deep layers with high velocity, which ensured the accuracy of inversion for the shallow layers while avoiding oversampling in the middle and deep layers. The inversion results of the model data demonstrate that the full-waveform inversion in variable grids based on variable difference coefficients can effectively characterize the low-velocity anomalies compared with full-waveform inversion in uniform coarse grids. The test of noisy data shows that the proposed full-waveform inversion method has strong noise resistance.
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