To reduce the ill-posedness of seismic full waveform inversion,a common method is to introduce prior information to regularize the inversion problem.Traditional regularization methods still face challenges even when they contain multiple prior information.This study proposed an extended full waveform inversion formula,which includes the convex set constraints on models.Specifically,this study showed how to constrain the total variation of the slowness square while forcing the constraint to keep it within a physical reality range.To verify the applicability of the algorithm proposed in this study,numerical experiments on simple models and international standard geological models were carried out.The results show that the introduction of total variation regularization can improve the reconstruction of high-speed disturbances under smooth background models.
姚含, 徐海. 基于梯度投影法的全变差正则化全波形反演[J]. 物探与化探, 2022, 46(4): 977-981.
YAO Han, XU Hai. Total variation regularized full waveform inversion based on gradient projection method. Geophysical and Geochemical Exploration, 2022, 46(4): 977-981.
Virieux J, Operto S. An overview of full-waveform inversion in exploration geophysics[J]. Geophysics, 2009, 74(6):WCC1-WCC26.
doi: 10.1190/1.3238367
[2]
Andrew P V, Malcolm S. Elastic versus acoustic inversion for marine surveys[J]. Geophysical Journal International, 2018, 215(1):1003-1021.
doi: 10.1093/gji/ggy303
[3]
Lailly P. The seismic inverse problem as a sequence of before-stack migrations[C]// Conference on Inverse Scattering: Theory and Applications,Expanded Abstracts, 1983:206-220.
[4]
Tarantola A. Inversion of seismic reflection data in the acoustic approximation[J]. Geophysics, 1984, 49(8):1259-1266.
doi: 10.1190/1.1441754
[5]
Mora P, Wu Z. Elastic versus acoustic inversion for marine surveys[J]. Geophysical Journal International, 2018, 214(1):596-622.
doi: 10.1093/gji/ggy166
[6]
Lin Y Z, Huang L J. Acoustic and elastic-waveform inversion using a modified total-variation regularization scheme[J]. Geophysical Journal International, 2015, 200:489-502.
doi: 10.1093/gji/ggu393
[7]
Du Z, Liu D, Wu G, et al. A high-order total-variation regularisation method for full-waveform inversion[J]. Journal of Geophysics and Engineering, 2021, 18(2): 241-252.
doi: 10.1093/jge/gxab010
[8]
Rudin L, Osher S, Fatemi E. Nonlinear total variation based noise removal algorithms[J]. Physica D:Nonlinear Phenomena, 1992, 60:259-268.
doi: 10.1016/0167-2789(92)90242-F
[9]
Chung E T, Chan T F, Tai X C. Electrical impedance tomography using level set representation and total variational regularization[J]. Journal of Computational Physics, 2005, 205:357-372.
doi: 10.1016/j.jcp.2004.11.022
Gong C M. Application of variational principle in seismic data denoising[J]. Computer & Digital Engineering, 2014, 42(7):1271-1274.
[12]
Anagaw A Y. Total variation and adjoint stat methods for seismic wavefield imaging[M]. Alberta: Physics Department of University of Alberta, 2009.
[13]
Anagaw A Y, Sacchi M D. Edge-preserving seismic imaging using the total variation method[J]. Joutnal of Geophysics and Engineering, 2012, 9(2):138-146.
Lu X T, Han L G, Zhang P, et al. Direct migration method of multi-source blended data based on total variation[J]. Chinese Journal of Geophysics, 2015, 58(9):3335-3345.
[15]
Esser E, Guasch L, Leeuwen T V, et al. Total variation regularization strategies in full-waveform inversion[J]. SIAM Journal on Imaging sciences, 2018, 11(1):376-406.
doi: 10.1137/17M111328X
[16]
Birgin E G, Martínez J M, Raydan M. Nonmonotone spectral projected gradient methods on convex sets[J]. SIAM Journal on Control and Optimization, 2000, 10(4):1196-1211.
[17]
Bertsekas D P. Nonlinear programming:2nd edition[M]. Belmont: Athena Scientific, 1999.
[18]
van Leeuwen T, Herrmann F J. Mitigating local minima in full-waveform inversion by expanding the search space[J]. Geophysical Journal International, 2013, 195:661-667.
doi: 10.1093/gji/ggt258