Full waveform inversion for a long-wavelength velocity model using a regenerated wavefield based on the SWEET method
In full waveform inversion (FWI), long-wavelength velocity models are essential for accurately estimating subsurface physical parameters. However, building long-wavelength velocity models with low-frequency components is challenging due to mechanical limitations in seismic data acquisition. We propose a novel FWI method that utilizes a regenerated wavefield derived from the Suppressed Wave Equation Estimation of Traveltime (SWEET) algorithm. The regenerated wavefield in our approach was obtained by convolving the arbitrary source wavelet with a Green’s function, which is represented by the first-arrival traveltime and amplitude extracted from the SWEET algorithm. Our approach can build long-wavelength velocity models, provided that a low-frequency wavelet is used. Furthermore, the potential for multi-scale inversion was demonstrated by gradually increasing the frequency of the source wavelet, leading to the acquisition of high-resolution models. In numerical examples, our proposed algorithm was validated using both synthetic and field data sets. We also assessed the noise sensitivity of the proposed method, confirming its applicability in practical scenarios. These results demonstrate that the proposed method is a robust and versatile tool for constructing long-wavelength and high-resolution velocity models from band-limited seismic data.
- Lailly P, Bednar J. The Seismic Inverse Problem as a Sequence of Before-Stack Migrations. In: Proceedings SIAM Conference Inverse Scattering; 1983. p. 206-220.
- Tarantola A. Inversion of seismic reflection data in the acoustic approximation. Geophysics. 1984;49(8):1259-1266. doi: 10.1190/1.1441754
- Virieux J, Operto S. An overview of full-waveform inversion in exploration geophysics. Geophysics. 2009;74(6):WCC1- WCC26. doi: 10.1190/1.3238367
- Mora P. Inversion = migration + tomography. Geophysics. 1989;54(12):1575-1586. doi: 10.1190/1.1442625
- Bunks C, Saleck FM, Zaleski S, Chavent G. Multiscale seismic waveform inversion. Geophysics. 1995;60(5):1457-1473. doi: 10.1190/1.1443880
- Pratt RG, Shin C, Hicks GJ. Gauss-newton and full newton methods in frequency-space seismic waveform inversion. Geophys J Int. 1998;133(2):341-362. doi: 10.1046/j.1365-246X.1998.00498.x
- Gauthier O, Virieux J, Tarantola A. Two-dimensional nonlinear inversion of seismic waveforms: Numerical results. Geophysics. 1986;51(7):1387-1403. doi: 10.1190/1.1442188
- Zelt CA, Smith RB. Seismic traveltime inversion for 2-D crustal velocity structure. Geophys J Int. 1992;108(1):16-34. doi: 10.1111/j.1365-246X.1992.tb00836.x
- Zhang J, Ten Brink US, Toksöz MN. Nonlinear refraction and reflection travel time tomography. J Geophys Res Solid Earth. 1998;103(B12):29743-29757. doi: 10.1029/98JB01981
- Woodward MJ, Nichols D, Zdraveva O, Whitfield P, Johns T. A decade of tomography. Geophysics. 2008;73(5):VE5-VE11. doi: 10.1190/1.2969907
- Brenders AJ, Pratt RG. Full waveform tomography for lithospheric imaging: Results from a blind test in a realistic crustal model. Geophys J Int. 2007;168(1):133-151. doi: 10.1111/j.1365-246X.2006.03156.x
- Brenders AJ, Pratt RG, Kamei R, Charles S. Waveform Tomography-Marine vs Land: Targets, Challenges and Opportunities. In: 72nd EAGE Conference and Exhibition- Workshops and Fieldtrips; 2010. p. 162.
- Ravaut C, Operto S, Improta L, Virieux J, Herrero A, Dell’Aversana P. Multiscale imaging of complex structures from multifold wide-aperture seismic data by frequency-domain full-waveform tomography: Application to a thrust belt. Geophys J Int. 2004;159(3):1032-1056. doi: 10.1111/j.1365-246X.2004.02442.x
- Operto S, Virieux J, Dessa JX, Pascal G. Crustal seismic imaging from multifold ocean-bottom seismometer data by frequency-domain full-waveform tomography: Application to the eastern Nankai Trough. J Geophys Res Solid Earth. 2006;111(B9):B09306.doi: 10.1029/2005JB003835
- Bording RP, Gersztenkorn A, Lines LR, Scales JA, Treitel S. Applications of seismic travel-time tomography. Geophys J Int. 1987;90(2):285-303. doi: 10.1111/j.1365-246X.1987.tb00728.x
- Moser TJ. Shortest path calculation of seismic rays. Geophysics. 1991;56(1):59-67. doi: 10.1190/1.1442958
- Rawlinson N, Sambridge M. Seismic traveltime tomography of the crust and lithosphere. Adv Geophys. 2003;46:81-199. doi: 10.1016/S0065-2687(03)46002-0
- Leung S, Qian J. An adjoint-state method for three-dimensional transmission traveltime tomography using first arrivals. Commun Math Sci. 2006;4:249-266. doi: 10.4310/CMS.2006.v4.n1.a10
- Liu Y, Wu Z, Geng Z. First-arrival phase-traveltime tomography. In: SEG 2017 Workshop: Full-Waveform Inversion and Beyond. United States: SEG; 2017. p. 83-86.
- Shin C, Cha YH. Waveform inversion in the Laplace domain. Geophys J Int. 2008;173(3):922-931. doi: 10.1111/j.1365-246X.2008.03768.x
- Ha W, Pyun S, Yoo J, Shin C. Acoustic full-waveform inversion of synthetic land and marine data in the Laplace domain. Geophys Prospect. 2010;58(6):1033-1047. doi: 10.1111/j.1365-2478.2010.00884.x
- Bozdağ E, Trampert J, Tromp J. Misfit functions for full-waveform inversion based on instantaneous phase and envelope measurements. Geophys J Int. 2011;185(2):845-870. doi: 10.1111/j.1365-246X.2011.04970.x
- Wu R, Luo J, Wu B. Seismic envelope inversion and modulation-signal model. Geophysics. 2014;79(3):WA13-WA24. doi: 10.1190/geo2013-0294.1
- Xiong K, Lumley D, Zhou W. Improved seismic-envelope full-waveform inversion. Geophysics. 2023;88(4):R421-R437. doi: 10.1190/geo2022-0444.1
- Xu S, Wang D, Chen F, Lambaré G, Zhang Y. Inversion on reflected seismic wave. In: SEG Annual International Meeting, Expanded Abstracts. United States: SEG; 2012. p. 1-7. doi: 10.1190/segam2012-1473.1
- Zhou H, Amundsen L, Zhang G. Fundamental issues in full-waveform inversion. In: SEG Annual International Meeting, Expanded Abstracts. United States: SEG; 2012. p. 1-5. doi: 10.1190/segam2012-0878.1
- Berkhout AJ. Combining full wavefield migration and full-waveform inversion: A glance into the future of seismic imaging. Geophysics. 2012;77(2):S43-S50.doi: 10.1190/geo2011-0148.1
- Dong S, Dong X, Zhang R, Cong Z, Zhong T, Wang H. Global-feature-fusion and multiscale network for low-frequency extrapolation. IEEE Trans Geosci Remote Sens. 2024;62:1-14. doi: 10.1109/TGRS.2024.3408949
- Operto S, Gholami A, Aghamiry H, Guo G, Beller S. Extending the search space of full-waveform inversion beyond the single-scattering born approximation: A tutorial review. Geophysics. 2023;88(6):R671-R702. doi: 10.1190/geo2022-0758.1
- Métivier L, Brossier R, Mérigot Q, Oudet E, Virieux J. Measuring the misfit between seismograms using an optimal-transport distance: Application to full-waveform inversion. Geophys J Int. 2016;205(1):345-377. doi: 10.1093/gji/ggw014
- Van Leeuwen T, Herrmann FJ. Mitigating local minima in full-waveform inversion by expanding the search space. Geophys J Int. 2013;195(1):661-667. doi: 10.1093/gji/ggt258
- Dong X, Yuan Z, Lin J, Dong S, Tong X, Li Y. PreAdaptFWI: Pretrained-Based Adaptive Residual Learning for full-Waveform Inversion without Dataset Dependency. [Preprint]; 2025. doi: 10.48550/arXiv.2502.11913
- Muller AP, Costa JC, Bom CR, et al. Deep pre-trained FWI: Where supervised learning meets physics-informed neural networks. Geophys J Int. 2023;235(1):119-134. doi: 10.1093/gji/ggad215
- Cheng S, Wang Y, Zhang Q, Harsuko R, Alkhalifah T. A self-supervised learning framework for seismic low-frequency extrapolation. J Geophys Res Mach Learn Comput. 2024;1(3):e2024JH000157. doi: 10.1029/2024JH000157
- Wu RS, Toksöz MN. Diffraction tomography and multisource holography applied to seismic imaging. Geophysics. 1987;52(1):11-25. doi: 10.1190/1.1442237
- Shin C, Min DJ, Lim HY, et al. Traveltime and amplitude calculations using the damped-wave solution. Geophysics. 2002;67(5):1637-1647. doi: 10.1190/1.1512811
- Shin C, Min DJ. Waveform inversion using a logarithmic wavefield. Geophysics. 2006;71(3):R31-R42. doi: 10.1190/1.2194523
- Shin C, Jang S, Min DJ. Improved amplitude preservation for prestack depth migration by inverse scattering theory. Geophys Prospect. 2001;49(5):592-606. doi: 10.1046/j.1365-2478.2001.00279.x
- Boonyasiriwat C, Valasek P, Routh P, Zhu X. Application of multiscale waveform tomography for high-resolution velocity estimation in complex geologic environments: Canadian Foothills synthetic-data example. Lead Edge. 2009;28(4):454-456. doi: 10.1190/1.3112764
- Pasalic D, McGarry R. Convolutional perfectly matched layer for isotropic and anisotropic acoustic wave equations. In: SEG International Exposition and Annual Meeting. United States: SEG; 2010. doi: 10.1190/1.3513453
- Aminzadeh F, Burkhard N, Nicoletis L, Rocca F, Wyatt K. SEG/EAEG 3-D modeling project: Second update. Lead Edge. 1994;13(9):949-952. doi: 10.1190/1.1437054
- Symes WW. A differential semblance criterion for inversion of multioffset seismic reflection data. J Geophys Res. 1993;98(B2):2061-2073. doi: 10.1029/92JB01304
- Prucha ML, Biondi BL, Symes WW. Angle-domain common-image gathers by wave-equation migration. In: SEG Technical Program Expanded Abstracts. United States: SEG; 1999. p. 824-827. doi: 10.1190/1.1821156
- Xu S, Chauris H, Lambaré G, Noble M. Common-angle migration: A strategy for imaging complex media. Geophysics. 2001;66(6):1877-1894. doi: 10.1190/1.1487131
- Zhou H, Gray SH, Young J, Pham D, Zhang Y. Tomographic residual curvature analysis: The process and its components. In: SEG Technical Program Expanded Abstracts. United States: SEG; 2003. p. 666-669. doi: 10.1190/1.1818018
- Sava PC, Fomel S. Angle-domain common-image gathers by wavefield-continuation methods. Geophysics. 2003;68(3):1065-1074. doi: 10.1190/1.1581078
- Valenciano AA, Biondi B. Wave-equation angle-domain Hessian. In: 68th EAGE Conference and Exhibition Incorporating SPE EUROPEC. 2006. p. 2. doi: 10.3997/2214-4609.201402166
- Chauris H, Lameloise CA, Donno D. Migration velocity analysis with reflected and transmitted waves. In: 75th EAGE Conference and Exhibition Incorporating SPE EUROPEC. 2013. p. 348. doi: 10.3997/2214-4609.20130936
- Kalita M, Alkhalifah T. Common-image gathers using the excitation-amplitude imaging condition. Geophysics. 2016;81(4):S261-S269. doi: 10.1190/geo2015-0413.1
