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A Review of Seismic Full Waveform Inversion Based on Deep Learning

딥러닝 기반 탄성파 전파형 역산 연구 개관

  • Sukjoon, Pyun (Department of Energy Resources Engineering, Inha University) ;
  • Yunhui, Park (Korea Institute of Ocean Science and Technology)
  • 편석준 (인하대학교 에너지자원공학과) ;
  • 박윤희 (한국해양과학기술원)
  • Received : 2022.11.02
  • Accepted : 2022.11.28
  • Published : 2022.11.30

Abstract

Full waveform inversion (FWI) in the field of seismic data processing is an inversion technique that is used to estimate the velocity model of the subsurface for oil and gas exploration. Recently, deep learning (DL) technology has been increasingly used for seismic data processing, and its combination with FWI has attracted remarkable research efforts. For example, DL-based data processing techniques have been utilized for preprocessing input data for FWI, enabling the direct implementation of FWI through DL technology. DL-based FWI can be divided into the following methods: pure data-based, physics-based neural network, encoder-decoder, reparameterized FWI, and physics-informed neural network. In this review, we describe the theory and characteristics of the methods by systematizing them in the order of advancements. In the early days of DL-based FWI, the DL model predicted the velocity model by preparing a large training data set to adopt faithfully the basic principles of data science and apply a pure data-based prediction model. The current research trend is to supplement the shortcomings of the pure data-based approach using the loss function consisting of seismic data or physical information from the wave equation itself in deep neural networks. Based on these developments, DL-based FWI has evolved to not require a large amount of learning data, alleviating the cycle-skipping problem, which is an intrinsic limitation of FWI, and reducing computation times dramatically. The value of DL-based FWI is expected to increase continually in the processing of seismic data.

전파형 역산은 석유가스 탐사를 위한 탄성파 자료처리 분야에서 지층의 속도 모델을 추정하는데 사용되는 역산 기법이다. 최근 탄성파 자료처리에 딥러닝 기술의 활용이 급격하게 증가하고 있는데, 전파형 역산 기술도 마찬가지로 다양한 연구가 이루어지고 있다. 초기에는 머신러닝 기술을 활용한 자료처리 기법이 전파형 역산을 위한 입력자료의 전처리 목적으로 활용되는 수준이었으나, 딥러닝 기술을 통해 전파형 역산을 직접적으로 구현하는 연구가 등장하기 시작하였다. 딥러닝 기술을 활용한 전파형 역산은 순수 데이터 기반 접근법, 물리 기반 신경망 활용법, 인코더-디코더 구조 활용법, 신경망 재매개변수화를 이용한 구현법, 물리정보 기반 신경망 기법 등으로 구분할 수 있다. 이 논문에서는 딥러닝 기반 전파형 역산 기법을 발전 과정 순서로 체계화하여 각각의 접근법에 대한 이론과 특징을 설명하였다. 전파형 역산 기술에 딥러닝 기법을 도입한 초기에는 데이터 과학의 기본 원리에 충실하게 대량의 학습자료를 준비하고 순수 데이터 기반 예측 모델을 적용하여 속도 모델을 역산하는 연구로 시작하였다. 최근 연구 동향은 탄성파 자료의 잔차나 파동방정식 자체의 물리정보를 심층 신경망에 활용하여 순수 데이터 기반 접근법의 단점을 보완해 나가는 방향으로 진행되고 있다. 이러한 발전으로 대량의 학습자료가 필요하지 않고, 전파형 역산의 태생적 한계점인 주기 놓침 현상을 완화하며 계산 시간을 획기적으로 줄일 수 있는 딥러닝 기반 전파형 역산 기술이 등장하고 있다. 딥러닝 기술의 도입으로 전파형 역산 기술은 탄성파 자료처리 분야에서 가치가 더 높아질 것으로 생각된다.

Keywords

Acknowledgement

이 논문은 2022년도 정부(산업통상자원부)의 재원으로 한국에너지기술평가원의 지원을 받아 수행된 연구임(20226A10100030: 고성능 해양 CO2 모니터링 기술개발 & 20212010200020: CO2 지중저장 안전성 확보 기술개발).

References

  1. Adler, A., Araya-Polo, M., and Poggio, T., 2019, Deep recurrent architectures for seismic tomography, 81st Annual International Conference and Exhibition, EAGE, Extended Abstracts, 1-5. https://doi.org/10.3997/2214-4609.201901512
  2. Al-Chalabi, M., 1974, An analysis of stacking, RMS, average, and interval velocities over a horizontally layered ground, Geophys. Prospect., 22(3), 458-475. https://doi.org/10.1111/j.1365-2478.1974.tb00099.x
  3. Alkhalifah, T., Song, C., Waheed, U. B., and Hao, Q., 2020, Wavefield solutions from machine learned functions that approximately satisfy the wave equation, 81st Annual International Conference and Exhibition, EAGE, Extended Abstracts, 1-5. https://doi.org/10.3997/2214-4609.202010588
  4. Alterman, Z., and Karal, F. C., 1968, Propagation of elastic waves in layered media by finite difference methods, Bull. Seismol. Soc. Amer., 58, 367-398. https://www.semanticscholar.org/paper/Propagation-of-elastic-waves-in-layered-media-by-Alterman-Karal/fd2895fa7c8fb6221a0e1f25a2a7c1b175c7dc96
  5. Al-Yahya, K., 1989, Velocity analysis by iterative profile migration, Geophysics, 54(6), 718-729. https://doi.org/10.1190/1.1442699
  6. Araya-Polo, M., Jennings, J., Adler, A., and Dahlke, T., 2018, Deep-learning tomography, The Leading Edge, 37(1), 58-66. https://doi.org/10.1190/tle37010058.1
  7. Bengio, Y., Courville, A., & Vincent, P., 2013, Representation learning: A review and new perspectives. IEEE Trans. Pattern Anal. Mach. Intell., 35(8), 1798-1828. https://doi.org/10.1109/TPAMI.2013.50
  8. Biswas, R., Vassiliou, A., Stromberg, R., and Sen, M. K., 2018, Stacking velocity estimation using recurrent neural network, 68th Ann. Internat. Mtg., Soc. Expl. Geophys., Expanded Abstracts, 2241-2245. https://doi.org/10.1190/segam2018-2997208.1
  9. Bunks, C., Saleck, F. M., Zaleski, S., and Chavent, G., 1995, Multiscale seismic waveform inversion, Geophysics, 60(5), 1457-1473. https://doi.org/10.1190/1.1443880
  10. Chopra, S., and Castagna, J. P., 2014, AVO, Society of ExplorationGeophysicists. https://doi.org/10.1190/1.9781560803201.refs
  11. Crase, E., Pica, A., Noble, M., McDonald, J., and Tarantola, A., 1990, Robust elastic nonlinear waveform inversion: Application to real data, Geophysics, 55(5), 527-538. https://doi.org/10.1190/1.1442864
  12. Cybenko, G., 1989, Approximation by superpositions of a sigmoidal function, Math. Control Signal Syst., 2(4), 303-314. https://link.springer.com/article/10.1007/BF02551274
  13. De Souza, L., Desassis, N., Chauris, H., and Hachem, E., 2022, First Steps in the Application of Physics-Informed Neural Networks to Full Waveform Inversion, 83rd EAGE Annual Conference and Exhibition Workshop Programme, 1-5. https://doi.org/10.3997/2214-4609.202211045
  14. Dhara, A., and Sen, M. K., 2022, Physics-guided deep autoencoder to overcome the need for a starting model in full-waveform inversion, The Leading Edge, 41(6), 375-381. https://doi.org/10.1190/tle41060375.1
  15. Engquist, B., Froese, B. D., and Yang, Y., 2016, Optimal transport for seismic full waveform inversion, Commun. Math. Sci., 14, 2309-2330. https://doi.org/10.4310/CMS.2016.v14.n8.a9
  16. Esser, E., Guasch, L., van Leeuwen, T., Aravkin, A. Y., and Herrmann, F. J., 2018, Total variation regularization strategies in full-waveform inversion, SIAM J. Imaging Sci., 11, 376-406. https://doi.org/10.1137/17M111328X
  17. Fabien-Ouellet, G., and Sarkar, R., 2020, Seismic velocity estimation: A deep recurrent neural-network approach, Geophysics, 85(1), U21-U29. https://doi.org/10.1190/geo2018-0786.1
  18. Fang, J., Zhou, H., Elita Li, Y., Zhang, Q., Wang, L., Sun, P., and Zhang, J., 2020, Data-driven low-frequency signal recovery using deep-learning predictions in full-waveform inversion, Geophysics, 85(6), A37-A43. https://doi.org/10.1190/geo2020-0159.1
  19. 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 J. Sci. Comput., 38(5), S358-S384. https://doi.org/10.1137/15M1010117
  20. He, Q., and Wang, Y., 2021, Reparameterized full-waveform inversion using deep neural networks, Geophysics, 86(1), V1-V13. https://doi.org/10.1190/geo2019-0382.1
  21. Herrmann, F. J., Erlangga, Y., and Lin, T. T. Y., 2009, Compressive sensing applied to full-wave form inversion, 71st International Annual Conference and Exhibition, EAGE, Extended Abstracts, S016. https://slim.gatech.edu/content/compressive-sensing-applied-full-waveform-inversion
  22. Hicks, G. J., 2002, Arbitrary source and receiver positioning in finite-difference schemes using Kaiser windowed sinc functions, Geophysics, 67(1), 156-165. https://doi.org/10.1190/1.1451454
  23. Hornik, K., 1991, Approximation capabilities of multilayer feedforward networks, Neural Netw., 4(2), 251-257. https://doi.org/10.1016/0893-6080(91)90009-T
  24. Hornik, K., Stinchcombe, M., and White, H., 1989, Multilayer feedforward networks are universal approximators, Neural Netw., 2(5), 359-366. https://doi.org/10.1016/0893-6080(89)90020-8
  25. Huang, G., and Symes, W. W., 2015, Full waveform inversion via matched source extension, 85th Ann. Internat. Mtg., Soc. Expl. Geophys., Expanded Abstracts, 1320-1325. https://doi.org/10.1190/segam2015-5872566.1
  26. Huang, G., Nammour, R., and Symes, W., 2017, Full-waveform inversion via source-receiver extension, Geophysics, 82(3), R153-R171. https://doi.org/10.1190/geo2016-0301.1
  27. Huang, G., Symes, W. W., and Nammour, R., 2016, Matched source waveform inversion: Space-time extension, 86th Ann. Internat. Mtg., Soc. Expl. Geophys., Expanded Abstracts, 1426-1431. https://doi.org/10.1190/segam2016-13762051.1
  28. Hustedt, B., Operto, S., and Virieux, J., 2004, Mixed-grid and staggered-grid finite-difference methods for frequency-domain acoustic wave modelling, Geophys. J. Int., 157(3), 1269-1296. https://doi.org/10.1111/j.1365-246X.2004.02289.x
  29. Jo, J. H., and Ha, W., 2021, Case analysis of seismic velocity model building using deep neural networks, Geophys. and Geophys. Explor., 24(2), 53-66 (in Korean with English abstract). https://doi.org/10.7582/GGE.2021.24.2.53
  30. Karniadakis, G. E., Kevrekidis, I. G., Lu, L., Perdikaris, P., Wang, S., & Yang, L., 2021, Physics-informed machine learning. Nat. Rev. Phys., 3(6), 422-440. https://www.nature.com/articles/s42254-021-00314-5 https://doi.org/10.1038/s42254-021-00314-5
  31. Krizhevsky, A., Sutskever, I., and Hinton, G. E., 2017, ImageNet classification with deep convolutional neural networks, Commun. ACM, 60(6), 84-90. https://doi.org/10.1145/3065386
  32. Lailly, P., 1983, The seismic inverse problem as a sequence of before stack migrations, Conference on Inverse Scattering, Theory and Application, SIAM, Expanded Abstracts, 206-220. https://www.scirp.org/(S(351jmbntv-nsjt1aadkposzje))/reference/referencespapers.aspx?referenceid=3108101
  33. Lei, N., An, D., Guo, Y., Su, K., Liu, S., Luo, Z., Yau, S.-T., and Gu, X., 2020, A geometric understanding of deep learning, Engineering, 6(3), 361-374. https://doi.org/10.1016/j.eng.2019.09.010
  34. Leshno, M., Lin, V. Y., Pinkus, A., and Schocken, S., 1993, Multilayer feedforward networks with a nonpolynomial activation function can approximate any function, Neural netw., 6(6), 861-867. https://doi.org/10.1016/S0893-6080(05)80131-5
  35. Lewis, W., and Vigh, D., 2017, Deep learning prior models from seismic images for full-waveform inversion, 87th Ann. Internat. Mtg., Soc. Expl. Geophys., Expanded Abstracts, 1512-1517. https://doi.org/10.1190/segam2017-17627643.1
  36. Li, S., Liu, B., Ren, Y., Chen, Y., Yang, S., Wang, Y., and Jiang, P., 2020, Deep-Learning Inversion of Seismic Data, IEEE Trans. Geosci. Remote Sensing, 58(3), 2135-2149. https://doi.org/10.1109/TGRS.2019.2953473
  37. Liu, B., Yang, S., Ren, Y., Xu, X., Jiang, P., and Chen, Y., 2021, Deep-learning seismic full-waveform inversion for realistic structural modelsDL seismic FWI, Geophysics, 86(1), R31-R44. https://doi.org/10.1190/geo2019-0435.1
  38. Ma, Y., Ji, X., Fei, T. W., and Luo, Y., 2018, Automatic velocity picking with convolutional neural networks, 88th Ann. Internat. Mtg., Soc. Expl. Geophys., Expanded Abstracts, 2066-2070. https://doi.org/10.1190/segam2018-2987088.1
  39. Metivier, L., Brossier, R., Merigot, Q., Oudet, E., and Virieux, J., 2016, Measuring the misfit between seismograms using an optimal transport distance: Application to full waveform inversion, Geophys. J. Int., 205, 345-377. https://dx.doi.org/10.1093/gji/ggw014
  40. Mora, P., 1987, Nonlinear two-dimensional elastic inversion of multi offset seismic data, Geophysics, 52(9), 1211-1228. https://doi.org/10.1190/1.1442384
  41. Moseley, B., Markham, A., and Nissen-Meyer, T., 2018, Fast approximate simulation of seismic waves with deep learning, arXiv preprint arXiv:1807.06873. https://doi.org/10.48550/arXiv.1807.06873
  42. Mosser, L., Dubrule, O., and Blunt, M. J., 2020, Stochastic seismic waveform inversion using generative adversarial networks as a geological prior, Math Geosci., 52(1), 53-79. https://link.springer.com/article/10.1007/s11004-019-09832-6
  43. Oord, A. v. d., Dieleman, S., Zen, H., Simonyan, K., Vinyals, O., Graves, A., Kalchbrenner, N., Senior, A., and Kavukcuoglu, K., 2016, Wavenet: A generative model for raw audio, arXiv preprint arXiv:1609.03499. https://doi.org/10.48550/arXiv.1609.03499
  44. Operto, S., Virieux, J., Dessa, J. X., and Pascal, G., 2006, Crustal imaging from multifold ocean bottom seismometers data by frequency-domain fullwaveform tomography: Application to the eastern Nankai trough, J. Geophys. Res., 111, B09306. https://doi.org/10.1029/2005JB003835
  45. Ovcharenko, O., Kazei, V., Kalita, M., Peter, D., and Alkhalifah, T., 2019, Deep learning for low-frequency extrapolation from multioffset seismic data, Geophysics, 84(6), R989-R1001. https://doi.org/10.1190/geo2018-0884.1
  46. Park, M. J., and Sacchi, M. D., 2020, Automatic velocity analysis using convolutional neural network and transfer learning, Geophysics, 85(1), V33-V43. https://doi.org/10.1190/geo2018-0870.1
  47. Peters, B., and Herrmann, F. J., 2017, Constraints versus penalties for edge preserving full-waveform inversion: The Leading Edge, 36, 94-100. https://doi.org/10.1190/tle36010094.1
  48. Pica, A., Diet, J., and Tarantola, A., 1990, Nonlinear inversion of seismic reflection data in a laterally invariant medium, Geophysics, 55(3), 284-292. https://doi.org/10.1190/1.1442836
  49. Plessix, R.-E., 2006, A review of the adjoint-state method for computing the gradient of a functional with geophysical applications, Geophys. J. Int., 167(2), 495-503. https://doi.org/10.1111/j.1365-246X.2006.02978.x
  50. Plessix, R.-E., 2009, Three-dimensional frequency-domain fullwaveform inversion with an iterative solver, Geophysics, 74(6), WCC149-WCC157. https://doi.org/10.1190/1.3211198
  51. Pratt, R. G., 1999, Seismic waveform inversion in the frequency domain, Part 1: Theory and verification in a physical scale model, Geophysics, 64(3), 888-901. http://seisweb.usask.ca/classes/GEOL898/2020/WWW/Pratt_Geophysics1999.pdf https://doi.org/10.1190/1.1444597
  52. Pratt, R. G., Shin, C., and Hick, G., 1998, Gauss-Newton and full Newton methods in frequency-space seismic waveform inversion, Geophys. J. Int., 133(2), 341-362. https://doi.org/10.1046/j.1365-246X.1998.00498.x
  53. Raissi, M., Perdikaris, P., and Karniadakis, G. E., 2019, Physicsinformed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations, J. Comput. Phys., 378, 686-707. https://doi.org/10.1016/j.jcp.2018.10.045
  54. Rasht-Behesht, M., Huber, C., Shukla, K., and Karniadakis, G. E., 2022, Physics?Informed Neural Networks (PINNs) for Wave Propagation and Full Waveform Inversions, J. Geophys. Res.-Solid Earth, 127(5), e2021JB023120. https://doi.org/10.1029/2021JB023120
  55. Ren, Y., Xu, X., Yang, S., Nie, L., and Chen, Y., 2020, A physics-based neural-network way to perform seismic full waveform inversion, IEEE Access, 8, 112266-112277. https://doi.org/10.1109/ACCESS.2020.2997921
  56. Richardson, A., 2018a, Seismic full-waveform inversion using deep learning tools and techniques, arXiv preprint arXiv:1801.07232. https://doi.org/10.48550/arXiv.1801.07232
  57. Richardson, A., 2018b, Generative adversarial networks for model order reduction in seismic full-waveform inversion, arXiv preprint arXiv:1806.00828. https://doi.org/10.48550/arXiv.1806.00828
  58. Rickett, J., 2013, The variable projection method for waveform inversion with an unknown source function, Geophys. Prospect., 61(4), 874-881. https://doi.org/10.1111/1365-2478.12008
  59. Ronneberger, O., Fischer, P., and Brox, T., 2015, U-net: Convolutional networks for biomedical image segmentation, International Conference on Medical Image Computing and Computer-Assisted Intervention, 234-241. https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28
  60. Roth, G., and Tarantola, A., 1994, Neural networks and inversion of seismic data, J. Geophys. Res., 99(B4), 6753-6768. https://doi.org/10.1029/93JB01563
  61. Rouet, F.-H., Li, X. S., Ghysels, P., and Napov, A., 2016, A distributed-memory package for dense hierarchically semiseparable matrix computations using randomization, ACM Trans. Math. Softw., 42(4), 1-35. https://doi.org/10.1145/2930660
  62. Rumelhart, D. E., Hinton, G. E., and Williams, R. J., 1986, Learning representations by back-propagating errors, Nature, 323(6088), 533-536. https://www.nature.com/articles/323533a0 https://doi.org/10.1038/323533a0
  63. Shin, C., and Min, D.-J., 2006, Waveform inversion using a logarithmic wavefield, Geophysics, 71(3), R31-R42. https://sspace.snu.ac.kr/bitstream/10371/6107/1/Logarithm_inversion_2006_CSShin.pdf 10371/6107/1/Logarithm_inversion_2006_CSShin.pdf
  64. Shin, C., and Cha, Y. H., 2008, Waveform inversion in the Laplace domain, Geophys. J. Int., 173(3), 922-931. https://doi.org/10.1111/j.1365-246X.2008.03768.x
  65. Shin, C., and Ho Cha, Y., 2009, Waveform inversion in the Laplace-Fourier domain, Geophys. J. Int., 177(3), 1067-1079. https://doi.org/10.1111/j.1365-246X.2009.04102.x
  66. Shin, C., Pyun, S., and Bednar, J. B., 2007, Comparison of waveform inversion, Part 1: Conventional wavefield vs. logarithmic wavefield, Geophys. Prospect., 55, 449-464. https://scholar.google.co.kr/citations?user=9iBCrmcAAAAJ&hl=ko https://doi.org/10.1111/j.1365-2478.2007.00617.x
  67. Sirgue, L., and Pratt, R. G., 2004, Efficient waveform inversion and imaging: A strategy for selecting temporal frequencies, Geophysics, 69(1), 231-248. https://doi.org/10.1190/1.1649391
  68. Song, C., and Alkhalifah, T. A., 2022, Wavefield Reconstruction Inversion via Physics-Informed Neural Networks, IEEE Trans. Geosci. Remote Sensing, 60, 1-12. http://dx.doi.org/10.1109/tgrs.2021.3123122
  69. Stefani, J., 1995, Turning ray tomography, Geophysics, 60(6), 1917-1929. https://library.seg.org/toc/gpysa7/60/6 https://doi.org/10.1190/1.1443923
  70. Sun, H., and Demanet, L., 2020, Extrapolated full-waveform inversion with deep learning, Geophysics, 85(3), R275-R288. https://doi.org/10.1190/geo2019-0195.1
  71. Sun, J., Innanen, K. A., and Huang, C., 2021, Physics-guided deep learning for seismic inversion with hybrid training and uncertainty analysis, Geophysics, 86(3), R303-R317. https://doi.org/10.1190/geo2020-0312.1
  72. Sun, J., Niu, Z., Innanen, K. A., Li, J., and Trad, D. O., 2020, A theory-guided deep-learning formulation and optimization of seismic waveform inversion, Geophysics, 85(2), R87-R99. https://doi.org/10.1190/geo2019-0138.1
  73. Taner, M. T., and Koehler, F., 1969, Velocity spectra-digital computer derivation applications of velocity functions, Geophysics, 34(6), 859-881. https://doi.org/10.1190/1.1440058
  74. Tarantola, A., 1984, Inversion of seismic reflection data in the acoustic approximation, Geophysics, 49(8), 1259-1266. https://doi.org/10.1190/1.1441754
  75. van Leeuwen, T., and Herrmann, F. J., 2013, Mitigating local minima in full-waveform inversion by expanding the search space, Geophys. J. Int., 195(1), 661-667. doi: 10.1093/gji/ggt258
  76. van Leeuwen, T., and Herrmann, F. J., 2015, A penalty method for PDE-constrained optimization in inverse problems, Inverse Probl., 32(1), 015007. doi: 10.1088/0266-5611/32/1/015007
  77. Vantassel, J. P., Kumar, K., and Cox, B. R., 2022, Using convolutional neural networks to develop starting models for near-surface 2-D full waveform inversion, Geophys. J. Int., 231(1), 72-90. https://doi.org/10.1093/gji/ggac179
  78. Vigh, D., and Starr, E. W., 2008, 3D prestack plane-wave, fullwaveform inversion, Geophysics, 73(5), VE135-VE144. https://doi.org/10.1190/1.2952623
  79. Virieux, J., Brossier, R., Metivier, L., Operto, S., and Ribodetti, A., 2016, Direct and indirect inversions, J. Seismol., 20(4), 1107-1121. https://link.springer.com/article/10.1007/s10950-016-9587-3
  80. Wang, W., and Ma, J., 2019, VMB-Net: A deep learning network for velocity model building in a cross-well acquisition geometry, 89th Ann. Internat. Mtg., Soc. Expl. Geophys., Expanded Abstracts, 2569-2573. https://doi.org/10.1190/segam2019-3216078.1
  81. Wang, W., McMechan, G. A., Ma, J., and Xie, F., 2021, Automatic velocity picking from semblances with a new deep-learning regression strategy: Comparison with a classification approach, Geophysics, 86(2), U1-U13. https://doi.org/10.1190/geo2020-0423.1
  82. Wang, J., Xiao, Z., Liu, C., Zhao, D., and Yao, Z., 2019, Deep learning for picking seismic arrival times, J. Geophys. Res.-Solid Earth, 124(7), 6612-6624. https://doi.org/10.1029/2019JB017536
  83. Warner, M., and Guasch, L., 2014, Adaptive waveform inversion: Theory, 84th Ann. Internat. Mtg., Soc. Expl. Geophys., Expanded Abstracts, 1089-1093. https://doi.org/10.1190/segam2014-0371.1
  84. Warner, M., and Guasch, L., 2016, Adaptive waveform inversion: Theory, Geophysics, 81(6), R429-R445. https://doi.org/10.1190/geo2015-0387.1
  85. Warner, M., Stekl, I., and Umpleby, A., 2007, Full wavefield seismic tomography - Iterative forward modeling in 3D, 69th International Annual Conference and Exhibition, EAGE, Extended Abstracts, C025. https://doi.org/10.3997/2214-4609.201401526
  86. Woodward, M. J., Nichols, D., Zdraveva, O., Whitfield, P., and Johns, T., 2008, A decade of tomography: Geophysics, 73(5), VE5-VE11. https://doi.org/10.1190/1.2969907
  87. Wu, R. S., Luo, J., and Wu, B., 2014, Seismic envelope inversion and modulation signal model, Geophysics, 79(3), WA13-WA24. doi: 10.1190/GEO2013-0294.1
  88. Wu, Y., Lin, Y., and Zhou, Z., 2018, Inversionnet: Accurate and efficient seismic waveform inversion with convolutional neural networks, 88th Ann. Internat. Mtg., Soc. Expl. Geophys., Expanded Abstracts, 2096-2100. https://doi.org/10.1190/segam2018-2998603.1
  89. Wu, Y., and Lin, Y., 2019, InversionNet: An efficient and accurate data-driven full waveform inversion, IEEE Trans. Comput. Imaging, 6, 419-433. https://doi.org/10.1109/TCI.2019.2956866
  90. Wu, Y., and McMechan, G. A., 2019, Parametric convolutional neural network-domain full-waveform inversion, Geophysics, 84(6), R881-R896. https://doi.org/10.1190/geo2018-0224.1
  91. Yang, F., and Ma, J., 2019, Deep-learning inversion: A nextgeneration seismic velocity model building method, Geophysics, 84(4), R583-R599. https://doi.org/10.1190/geo2018-0249.1
  92. Yang, Y., Engquist, B., Sun, J., and Froese, B. D., 2016, Application of optimal transport and the quadratic Wasserstein metric to full-waveform inversion, arXiv preprint arXiv: 1612.05075. https://doi.org/10.48550/arXiv.1612.05075
  93. Yang, Y., Engquist, B., Sun, J., and Hamfeldt, B. F., 2018, Application of optimal transport and the quadratic Wasserstein metric to full-waveform inversion, Geophysics, 83(1), R43-R62. https://doi.org/10.1190/geo2016-0663.1
  94. Zhang, Z., and Lin, Y., 2020, Data-driven seismic waveform inversion: A study on the robustness and generalization, IEEE Trans. Geosci. Remote Sensing, 58(10), 6900-6913. https://doi.org/10.1109/TGRS.2020.2977635
  95. Zhu, W., Xu, K., Darve, E., Biondi, B., and Beroza, G. C., 2022, Integrating deep neural networks with full-waveform inversion: Reparameterization, regularization, and uncertainty quantification, Geophysics, 87(1), R93-R109. https://doi.org/10.1190/geo2020-0933.1