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为改进全波形反演受初始模型限制而使反演陷入局部极小值的问题，提高反演计算效率，有效重构地下地质体边界，引入全变差正则化方法，通过将解投影到一个受全变差范数约束的凸集上。首先对初始速度进行反演，然后依次放宽全变差范数约束，每次模型迭代时均满足全变差范数约束，逐步得到速度扰动。并应用Marmousi模型对提出的方法进行实验，通过与常规全波形反演对比，得出该方法计算效率提升5.3%左右，反演精度大幅提高，能够有效重构地质体不连续界面。数值模拟表明：全变差约束方法能够有效降低反演对初始模型的依赖程度，提高反演精度，降低周波跳跃风险，收敛效果好。
Abstract：To improve the problem that full waveform inversion gets trapped in local minima due to the limitation of the initial model, enhance the computational efficiency of inversion, and effectively reconstruct the boundaries of underground geological bodies, this paper introduces the total variation regularization method. By projecting the solution onto a convex set constrained by the total variation norm, the initial velocity model is first inverted under a strict total variation constraint, and then the total variation norm constraint is gradually relaxed. Each model iteration satisfies the corresponding total variation norm constraint, allowing the velocity perturbation to be gradually obtained. This paper applies the Marmousi model to test the proposed method. Compared with the conventional full waveform inversion, the results show an approximately 5.3% improvement in inversion accuracy, effectively reconstructing the discontinuous interfaces of geological bodies. Numerical simulations show that the total variation constraint method can effectively reduce the dependence of inversion results on the initial model, improve the inversion accuracy, lower the risk of cycle skipping, and achieve a robust convergence effect.
[1] Tarantola A.Inversion of seismic reflection data in the acoustic approximation[J].Geophysics,1984,49(8):1 259-1 266.
[2] Tang Y X.Target-oriented wave-equation least-squares migration/inversion with phase-encoded Hessian[J].Geophysics,2009,74(6):WCA95-WCA107.
[3] Operto S,Gholami Y,Prieux V,et al.A guided tour of multiparameter full-waveform inversion with multicomponent data:From theory to practice[J].The Leading Edge,2013,32(9):1 040-1 054.
[4] van Leeuwen T,Herrmann F J.Mitigating local minima in full-waveform inversion by expanding the search space[J].Geophysical Journal International,2013,195(1):661-667.
[5] Aghamiry H S,Gholami A,Operto S.et al.Accurate and efficient data-assimilated wavefield reconstruction in the time domain[J].Geophysics,2020,85(2):A7-A12.
[6] Aghamiry H S,Gholami A,Operto S.Improving full-waveform inversion by wavefield reconstruction with the alternating direction method of multipliers[J].Geophysics,2019,84(1):R125-R148.
[7] Nocedal J,Wright S J.Numerical optimization[M].2006,2nd ed.Springer.
[8] da Silva N V,Yao G.Wavefield reconstruction inversion with a multiplicative cost function[J].Inverse Problems,2018,34(1):015004.
[9] Fu L,Symes W W.A discrepancy-based penalty method for extended waveform inversion[J].Geophysics,2017,82(5):R287-R298.
[10] Aghamiry H S,Gholami A,Operto S.Implementing bound constraints and total-variation regularization in extended full-waveform inversion with the alternating direction method of multiplier:Application to large contrast media[J].Geophysical Journal International,2019,218(2):855-872.
[11] Goldstein T,Osher S.The split bregman method for L1-regularized problems[J].SIAM Journal on Imaging Sciences,2009,2(2):323-343.
[12] Rudin L I,Osher S,Fatemi E.Nonlinear total variation based noise removal algorithms[J].Physica D:Nonlinear Phenomena,1992,60(1-4):259-268.
[13] Aghamiry H S,Gholami A,Operto S.Compound regularization of full-waveform inversion for imaging piecewise media[J].IEEE Transactions on Geoscience and Remote Sensing,2020,58(2):1 192-1 204.
[14] Askan A,Akcelik V,Bielak J,et al.Full waveform inversion for seismic velocity and anelastic losses in heterogeneous structures[J].Bulletin of the Seismological Society of America,2007,97(6):1 990-2 008.
[15] Kazei V V,Kalita M,Alkhalifah T.Salt-body inversion with minimum gradient support and Sobolev space norm regularizations[C]//79th EAGE Conference and Exhibition 2017,2017:1-5.
[16] Gholami A,Siahkoohi H R.Regularization of linear and non-linear geophysical ill-posed problems with joint sparsity constraints[J].Geophysical Journal International,2010,180(2):871-882.
[17] Loris I,Verhoeven C.Iterative algorithms for total variation-like reconstructions in seismic tomography[J].GEM-International Journal on Geomathematics,2012,3(2):179-208.
[18] Gholami A,Aghamiry H S,Abbasi M.Constrained nonlinear amplitude variation with offset inversion using Zoeppritz equations[J].Geophysics,2018,83(3):R245-R255.
[19] Anagaw A Y.Total variation and adjoint state methods for seismic wavefield imaging[D].Alberta:Physics Department of University of Alberta,2009.
[20] Anagaw A Y,Sacchi M D.Edge-preserving seismic imaging using the total variation method[J].Journal of Geophysics and Engineering,2012,9(2):138-146.
[21] Brandsberg-Dahl S,Chemingui N,Valenciano A,et al.FWI for model updates in large-contrast media[J].The Leading Edge,2017,36(1):81-87.
[22] Peters B,Herrmann F J.Constraints versus penalties for edge-preserving full-waveform inversion[J].The Leading Edge,2017,36(1):94-100.
[23] Esser E,Guasch L,van Leeuwen T,et al.Total variation regularization strategies in full-waveform inversion[J].SIAM Journal on Imaging Sciences,2018,11(1):376-406.
[24] Herrmann F J,Hanlon I,Kumar R,et al.Frugal full-waveform inversion:From theory to a practical algorithm[J].The Leading Edge,2013,32(9):1 082-1 092.
[25] Bertsekas D P.Nonlinear programming[J].Journal of the Operational Research Society,1997,48(3):334-334.
[26] Esser E,Zhang X Q,Chan T F.A general framework for a class of first order primal-dual algorithms for convex optimization in imaging science[J].SIAM Journal on Imaging Sciences,2010,3(4):1 015-1 046.
[27] 田锦瑞，张昭，亚东菊，等.基于贪心算法的地震数据采集特殊观测系统程序设计及应用[J].工程地球物理学报，2023,20(1):105-113.Tian J R,Zhang Z,Ya D J,et al.Design and application of special observation system design program for seismic data acquisition based on greedy algorithm[J].Chinese Journal of Engineering Geophysics,2023,20(1):105-113.
[28] 李江.煤田高密度三维地震勘探数据采集高效资料整理方法[J].工程地球物理学报，2021,18(4):416-420.Li J.High efficiency method for high density 3D seismic data acquisition in coal field[J].Chinese Journal of Engineering Geophysics,2021,18(4):416-420.
[29] 杨化军.基于全变差正则化约束的早至波波形反演[D].青岛：中国石油大学(华东),2021.Yang H J.Early-arrival waveform inversion based on total variation regularization constraint[D].Qingdao:China University of Petroleum (Huadong),2021.
基本信息:
中图分类号:P631.4
引用信息:
[1]杨化军,杨柳辉,孙旭东,等.基于全变差正则化约束的波场重建反演[J].工程地球物理学报,2026,23(01):139-146.
基金信息:
中国石油科技重大专项项目(编号:ZD2019-183-003); 甘肃省自然科学基金项目(编号:202004-M05)
2026-01-30
2026-01-30