Source wavefield reconstruction based on a new finite-difference stencil and infinity norm
BAO Qianzong1,2, DAI Xue1, LIANG Xue3
1. Department of Geological Engineering, School of Geological Engineering and Geomatics, Chang'an University, Xi'an, Shaanxi 710054, China; 2. National Engineering Research Center of Offshore Oil and Gas Exploration, Beijing 100028, China; 3. BGP Inc., CNPC, Zhuozhou, Hebei 072750, China
Abstract:The adjoint-state method is widely used in migration imaging and full waveform inversion. The image or gradient of the model can be obtained by the interaction between source and adjoint wavefields. The two wavefields, however, propagate in forward and backward time directions, respectively, and cannot be accessed at the same time. To avoid the storage of the source wavefield, we can use boundary wavefields to reconstruct the source wavefield in the backward time direction, but the existing reconstruction methods still cannot balance the requirements of accuracy and storage. Hence, this paper develops a new staggered-grid finitedifference (FD) source wavefield reconstruction method. The method stores the N-layer wavefields and a linear combination of (M-N)-layer wavefields in the boundary area to reconstruct the internal source wavefield, where M denotes the length parameter of the FD operator, and 0 ≤N≤M. On the basis of the new FD stencil, we derive the dispersion relation, construct an infinite-norm-type objective function, and optimize the reconstruction coefficients by the Remez exchange algorithm. Moreover, we analyze the accuracy and stability of the proposed method and apply it to acoustic reverse time migration and elastic full waveform inversion. Numerical results reveal that the new method can obtain sufficiently accurate reconstructed wavefields, migration profiles, and inversion results, and its memory usage is only (N+1)/M of that of the traditional method.
包乾宗, 戴雪, 梁雪. 一种基于新差分模板和无穷范数的震源波场重建方法[J]. 石油地球物理勘探, 2022, 57(6): 1384-1394.
BAO Qianzong, DAI Xue, LIANG Xue. Source wavefield reconstruction based on a new finite-difference stencil and infinity norm. Oil Geophysical Prospecting, 2022, 57(6): 1384-1394.
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