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Modern Physics 2022
混合全变差正则化的全波形反演
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Abstract:
全波形反演(FWI)是一个高度非线性和不适定的数学物理反问题。全变差(TV)正则化方法具有保持解的不连续的性质，然而其对具有一定倾斜角度(如分段线性)的区域会呈现阶梯状伪影。二阶TV (TV2)正则化方法可以减弱阶梯现象，同时很好地保留反演的边缘信息。但二阶TV正则化方法与传统TV正则化相比，其需要更多的计算量。因此，本文基于TV和TV2正则化方法，提出了混合的全变差正则化方法(HTV)。基于Marmousi2模型和Sigsbee模型进行数值实验，数值结果表明相对于TV和TV2正则化方法，HTV正则化方法在反演精度方面具有较好的计算表现。
Full waveform inversion (FWI) is a highly nonlinear and ill-posed mathematical physics inverse problem. Total variation (TV) regularization method has the property of preserving the discontinuity of the solution. However, it leads to the stair-casing artifacts for regions with certain skew angles (e.g., piecewise linearity). The second-order TV (TV2) regularization method can attenuate the staircase phenomenon while preserving the edge information of the inversion resolution well. However, compared with the conventional TV regularization method, the TV2 regularization method requires large computation costs. Therefore, we combine the advantages of TV and TV2 regularization and propose a hybrid regularization (HTV) method. Numerical experiments based on the Marmousi2 model and the Sigsbee model are conducted, and the numerical results show that the HTV regularization method has better computational performance in terms of inversion accuracy compared with the TV and TV2 regularization methods.
| [1] | Tarantola, A. and Valette, B. (1982) Generalized Nonlinear Inverse Problems Solved Using the Least Squares Criterion. Reviews of Geophysics, 20, 219-232. https://doi.org/10.1029/RG020i002p00219 |
| [2] | Tarantola, A. (1984) Inver-sion of Seismic Reflection Data in the Acoustic Approximation. Geophysics, 49, 1259-1266.
https://doi.org/10.1190/1.1441754 |
| [3] | Tikhonov, A.N. (1963) Regularization of Incorrectly Posed Problems. So-viet Mathematics Doklady, 4, 1624-1627. |
| [4] | Aghamiry, H.S., Gholami, A. and Operto, S. (2019) Compound Regu-larization of Full-Waveform Inversion for Imaging Piecewise Media. IEEE Transactions on Geoscience and Remote Sensing, 58, 1192-1204.
https://doi.org/10.1109/TGRS.2019.2944464 |
| [5] | Anagaw, A.Y. and Sacchi, M.D. (2011) Full Waveform Inver-sion with Total Variation Regularization. Recovery-CSPG CSEG CWLS Convention 2011, Alberta, 9-11 May 2011, 1-4. |
| [6] | Royden, H.L. and Fitzpatrick, P. (1988) Real Analysis. Vol. 32, Macmillan, New York. |
| [7] | Aghamiry, H.S., Gholami, A. and Operto, S. (2019) Implementing Bound Constraints and Total-Variation Regularization in Extended Full-Waveform Inversion with the Alternating Direction Method of Multiplier: Application to Large Contrast Media. Geophysical Journal International, 218, 855-872. https://doi.org/10.1093/gji/ggz189 |
| [8] | Li, J., Bai, L. and Liu, H. (2021) Numerical Verification of Full Waveform Inversion for the Chang’E-5 Lunar Regolith Penetrating Array Radar. IEEE Transactions on Geoscience and Remote Sensing, 60, 1-10.
https://doi.org/10.1109/TGRS.2021.3098104 |
| [9] | Anagaw, A.Y. and Sacchi, M.D. (2012) Edge-Preserving Seismic Imaging Using the Total Variation Method. Journal of Geophysics and Engineering, 9, 138-146. https://doi.org/10.1088/1742-2132/9/2/138 |
| [10] | Anagaw, A. and Sacchi, M.D. (2022) A Regularization by De-noising (RED) Scheme for 3-D FWI Model Updates in Large-Contrast Media. Geophysical Journal International, 229, 814-827. https://doi.org/10.1093/gji/ggab505 |
| [11] | Du, Z., Liu, D., Wu, G., Cai, J., Yu, X. and Hu, G. (2021) A High-Order Total-Variation Regularisation Method for Full-Waveform Inversion. Journal of Geophysics and Engineer-ing, 18, 241-252. https://doi.org/10.1093/jge/gxab010 |
| [12] | Steidl, G. (2006) A Note on the Dual Treatment of Higher-Order Regularization Functionals. Computing, 76, 135-148.
https://doi.org/10.1007/s00607-005-0129-z |
| [13] | Bredies, K. and Holler, M. (2020) Higher-Order Total Variation Approaches and Generalisations. Inverse Problems, 36, Article ID: 123001. https://doi.org/10.1088/1361-6420/ab8f80 |
| [14] | Lv, X.G., Song, Y.Z., Wang, S.X. and Le, J. (2013) Image Resto-ration with a High-Order Total Variation Minimization Method. Applied Mathematical Modelling, 37, 8210-8224. https://doi.org/10.1016/j.apm.2013.03.028 |
| [15] | Yuan, J., Schn？rr, C. and Steidl, G. (2009) Total-Variation Based Piecewise Affine Regularization. International Conference on Scale Space and Variational Methods in Computer Vision, Voss, 1-5 June 2009, 552-564.
https://doi.org/10.1007/978-3-642-02256-2_46 |
| [16] | Hager, W.W. and Zhang, H. (2013) The Limited Memory Conjugate Gradient Method. SIAM Journal on Optimization, 23, 2150-2168. https://doi.org/10.1137/120898097 |
| [17] | He, Q. and Wang, Y. (2020) Inexact Newton-Type Methods Based on Lanczos Orthonormal Method and Application for Full Waveform Inversion. Inverse Problems, 36, Article ID: 115007. https://doi.org/10.1088/1361-6420/abb8ea |
| [18] | Yan, X., He, Q. and Wang, Y. (2022) Truncated Trust Region Method for Nonlinear Inverse Problems and Application in Full-Waveform Inversion. Journal of Computational and Applied Mathematics, 404, Article ID: 113896.
https://doi.org/10.1016/j.cam.2021.113896 |
| [19] | Hustedt, B., Operto, S. and Virieux, J. (2004) Mixed-Grid and Staggered-Grid Finite-Difference Methods for Frequency-Domain Acoustic Wave Modelling. Geophysical Journal In-ternational, 157, 1269-1296.
https://doi.org/10.1111/j.1365-246X.2004.02289.x |
| [20] | Berenger, J.P. (1994) A Perfectly Matched Layer for the Absorption of Electromagnetic Waves. Journal of Computational Physics, 114, 185-200. https://doi.org/10.1006/jcph.1994.1159 |
| [21] | Ghysels, P., Li, X.S., Rouet, F.H., Williams, S. and Napov, A. (2016) An Efficient Multicore Implementation of a Novel HSS-Structured Multifrontal Solver Using Randomized Sampling. SIAM Journal on Scientific Computing, 38, S358-S384.
https://doi.org/10.1137/15M1010117 |
| [22] | Yoo, J.C. and Ahn, C.W. (2012) Image Matching Using Peak Sig-nal-to-Noise Ratio-Based Occlusion Detection. IET image processing, 6, 483-495. https://doi.org/10.1049/iet-ipr.2011.0025 |
