none 10.1190/geo2021-0794.1 Society of Exploration Geophysicists Society of Exploration Geophysicists 186 141940520 5981 2025121211460408100 10.1190 2025-12-12T16:46:11Z 2022-10-31T13:09:54Z 20 Geophysics 0016-8033 1942-2156 01 01 2023 88 1 Jiashun Yao Imperial College London 1 , Centre for Reservoir Geophysics, Resource Geophysics Academy, London SW7 2BP, UK. j.yao14@imperial.ac.uk http://orcid.org/0000-0001-8623-3224 Michael Warner Imperial College London 1 , Centre for Reservoir Geophysics, Resource Geophysics Academy, London SW7 2BP, UK. m.warner@imperial.ac.uk http://orcid.org/0000-0002-1858-218X Yanghua Wang Imperial College London 1 , Centre for Reservoir Geophysics, Resource Geophysics Academy, London SW7 2BP, UK. yanghua.wang@imperial.ac.uk (corresponding author) http://orcid.org/0000-0002-1044-4348 ABSTRACT The anisotropic full-waveform inversion (FWI) is a seismic inverse problem for multiple parameters, which aims to simultaneously reconstruct the vertical velocity and the anisotropic parameters of the earth’s subsurface. This multiparameter inverse problem suffers from two issues. First, the objective function of the data fitting is less sensitive to the anisotropic parameters. Second, the crosstalk effect among the different parameters worsens the model update in the iterative inversion. We have developed a method that statistically regularizes the anisotropic FWI using Wasserstein adversarial networks, by penalizing the Wasserstein distance between the distribution of the current model parameters and that of the parameters at the borehole locations. The regularizer can mitigate the issues of anisotropic FWI with multiple parameters and therefore it also can be applied to other inverse problems with multiple parameters. 01 05 2023 01 01 2023 10 31 2022 R95 R103 Resource Geophysics Academy 1 10.1190/crossmark-policy library.seg.org true 2021-12-08 2022-09-15 2022-09-25 2023-01-05 Resource Geophysics Academy 10.1190/geo2021-0794.1 https://pubs.geoscienceworld.org/geophysics/article/88/1/R95/619744/Regularization-of-anisotropic-full-waveform https://pubs.geoscienceworld.org/seg/geophysics/article-pdf/88/1/R95/5777551/geo-2021-0794.1.pdf https://pubs.geoscienceworld.org/seg/geophysics/article-pdf/88/1/R95/5777551/geo-2021-0794.1.pdf https://pubs.geoscienceworld.org/geophysics/article/88/1/r95/619744/regularization-of-anisotropic-full-waveform 0016-8033 Geophysics Aragao 85 2 R101 2020 10.1190/geo2019-0285.1 Elastic full-waveform inversion with probabilistic petrophysical model constraints Arjovsky M. Chintala S. Bottou L. , 2017, Wasserstein generative adversarial networks: International Conference on Machine Learning, 214–223. 0016-8033 Geophysics Asnaashari 78 2 R25 2013 10.1190/geo2012-0104.1 Regularized seismic full waveform inversion with prior model information The Leading Edge Bakulin 29 1450 2010 10.1190/1.3525359 Anisotropic model building with wells and horizons: Gulf of Mexico case study comparing different approaches 10.1190/segam2014-0546.1 Baumstein A. , 2014, Extended subspace method for attenuation of crosstalk in multiparameter full wavefield inversion: 84th Annual International Meeting, SEG, Expanded Abstracts, 1121–1125, doi: http://dx.doi.org/10.1190/segam2014-0546.1. 10.3997/2214-4609.201412904 Baumstein A. , 2015, Borehole-constrained multi-parameter full waveform inversion: 77th Annual International Conference and Exhibition, EAGE, Extended Abstracts, doi: http://dx.doi.org/10.3997/2214-4609.201412904. 1053-5888 IEEE Signal Processing Magazine Creswell 35 53 2018 10.1109/MSP.2017.2765202 Generative adversarial networks: An overview 0016-8033 Geophysics da Silva 81 4 U25 2016 10.1190/geo2015-0349.1 A new parameter set for anisotropic multiparameter full-waveform inversion and application to a North Sea data set 10.1190/segam2015-5921944.1 Debens H. A. Warner M. Umpleby A. Silva N. V. D. , 2015, Global anisotropic 3D FWI: 85th Annual International Meeting, SEG, Expanded Abstracts, 1193–1197, doi: http://dx.doi.org/10.1190/segam2015-5921944.1. 0033-4553 Pure and Applied Geophysics Gao 175 4321 2018 10.1007/s00024-018-1904-z Waveform tomography of two-dimensional three-component seismic data for HTI anisotropic media 0016-8033 Geophysics Gholami 78 2 R107 2013 10.1190/geo2012-0203.1 Which parameterization is suitable for acoustic vertical transverse isotropic full waveform inversion? Part 2: Synthetic and real data case studies from Valhall 0016-8033 Geophysics Gholami 78 2 R81 2013 10.1190/geo2012-0204.1 Which parameterization is suitable for acoustic vertical transverse isotropic full waveform inversion? Part 1: Sensitivity and trade-off analysis Goodfellow I. Pouget-Abadie J. Mirza M. Xu B. Warde-Farley D. Ozair S. Courville A. Bengio Y. , 2014, Generative adversarial nets: Advances in Neural Information Processing Systems. Gulrajani 2017 Improved training of Wasserstein GANs 0956-540X Geophysical Journal International Kazei 213 963 2018 10.1093/gji/ggy034 Waveform inversion for orthorhombic anisotropy with P waves: Feasibility and resolution 0956-540X Geophysical Journal International Li 226 1322 2021 10.1093/gji/ggab162 Deep-learning assisted regularized elastic full waveform inversion using the velocity distribution information from wells Mathematical Geosciences Mosser 52 53 2020 10.1007/s11004-019-09832-6 Stochastic seismic waveform inversion using generative adversarial networks as a geological prior The Leading Edge Operto 32 1040 2013 10.1190/tle32091040.1 A guided tour of multiparameter full-waveform inversion with multicomponent data: From theory to practice 0956-540X Geophysical Journal International Podgornova 214 200 2018 10.1093/gji/ggy116 Resolution of VTI anisotropy with elastic full-waveform inversion: Theory and basic numerical examples 0956-540X Geophysical Journal International Prieux 187 1495 2011 10.1111/j.1365-246X.2011.05209.x On the footprint of anisotropy on isotropic full waveform inversion: The Valhall case study 0016-8033 Geophysics Rusmanugroho 82 3 R135 2017 10.1190/geo2016-0025.1 Anisotropic full-waveform inversion with tilt-angle recovery 0016-8025 Geophysical Prospecting Singh 69 1650 2021 10.1111/1365-2478.13139 Facies-based full-waveform inversion for anisotropic media: A North Sea case study Optimal transport: Old and new Villani 2009 10.1007/978-3-540-71050-9 0016-8033 Geophysics Virieux 74 6 WCC1 2009 10.1190/1.3238367 An overview of full-waveform inversion in exploration geophysics 0016-8033 Geophysics Wang 78 5 WC51 2013 10.1190/geo2012-0394.1 Multiparameter TTI tomography of P-wave reflection and VSP data 0016-8033 Geophysics Wang 64 182 1999 10.1190/1.1444514 Simultaneous inversion for model geometry and elastic parameters Seismic inversion: Theory and applications Wang 2016 10.1002/9781119258032 0016-8033 Geophysics Warner 78 2 R59 2013 10.1190/geo2012-0338.1 Anisotropic 3D full-waveform inversion 0016-8033 Geophysics Zhang 85 4 WA137 2020 10.1190/geo2019-0340.1 High-resolution reservoir characterization using deep learning-aided elastic full-waveform inversion: The North Sea field data example Journal of Geophysics and Engineering Zhou 19 750 2022 10.1093/jge/gxac048 An efficient symplectic stereo-modeling method for seismic inversion by using deep learning technique