Elastic full waveform inversion based on equivalent staggered grid FDM and inter-parameter trade-off mitigation

Li, Qingyang; Wu, Guochen

doi:10.1007/s11600-022-00867-8

Artykuł - szczegóły

Tytuł artykułu

Elastic full waveform inversion based on equivalent staggered grid FDM and inter-parameter trade-off mitigation

Autorzy

Li Qingyang , Wu Guochen

Wybrane pełne teksty z tego czasopisma

https://www.springer.com/journal/11600

Identyfikatory

DOI

10.1007/s11600-022-00867-8

Warianty tytułu

Języki publikacji

Abstrakty

Elastic full waveform inversion (EFWI) has increasingly been applied in seismic exploration as computer performance improves. EFWI significantly improves calculation efficiency, but requires very large computer storage space and suffers interparameter trade-off and local minima problems. Preconditioning the gradients based on elastic wave mode decomposition can effectively mitigate inter-parameter trade-offs, but the decomposition-based scheme may further increase the memory usage, which limits EFWI application. The equivalent staggered grid (ESG) scheme in acoustic medium requires less memory usage and generates results numerically equivalent to those using the standard staggered grid (SSG) scheme. In this paper, we extend the ESG scheme to second-order elastic wave equations in terms of velocity, producing results numerically equivalent to the SSG ones based on first-order velocity–stress wave equations while reducing memory usage by 45% compared with the SSG scheme. We then apply the ESG scheme to EFWI and derive the formula of the preconditioned gradient of the S-wave velocity. Finally, three numerical examples demonstrate that applying the ESG scheme to decomposition-based EFWI can significantly reduce computer memory usage and mitigate the trade-offs between the P- and S-wave velocities.

Słowa kluczowe

elastic wave equation full waveform inversion wave-mode decomposition trade-off equivalent staggered grid

równanie fali sprężystej pełna inwersja przebiegu rozkład falowy kompromis

Wydawca

Instytut Geofizyki PAN
Springer

Czasopismo

Acta Geophysica

Rocznik

2022

Tom

Vol. 70, no 6

Strony

2555--2579

Opis fizyczny

Bibliogr. 71 poz.

Twórcy

autor

Li Qingyang

liqingyanggeo@foxmail.com

China University of Petroleum Huadong - Qingdao Campus, Qingdao 266555, China

https://orcid.org/0000-0003-2620-1321

autor

Wu Guochen

guochenwu_wgc@163.com

China University of Petroleum Huadong - Qingdao Campus, Qingdao 266555, China

Bibliografia

1. Berenger J (1994) A perfectly matched layer for the absorption of electromagnetic waves. J Comput Phys 114(2):185–200. https://doi.org/10.1006/jcph.1994.1159
2. Brossier R, Operto S, Virieux J (2009) Seismic imaging of complex onshore structures by 2D elastic frequency-domain full-waveform inversion. Geophysics 74(6):WCC105–WCC118. https://doi.org/10.1190/1.3215771
3. Bunks C, Saleck FM, Zaleski S, Chavent G (1995) Multiscale seismic waveform inversion. Geophysics 60(5):1457–1473. https://doi.org/10.1190/1.1443880
4. Carcione JM (2007) Wave fields in real media: wave propagation in anisotropic, anelastic, porous and electromagnetic media. Elsevier, Amsterdam
5. Cerjan C, Kosloff D, Kosloff R, Reshef M (1985) A nonreflecting boundary condition for discrete acoustic and elastic wave equations. Geophysics 50:705–708. https://doi.org/10.1190/1.1441945
6. Chi BX, Dong LG, Liu YZ (2015) Correlation-based reflection full-waveform inversion. Geophysics 80(4):R189–R202. https://doi.org/10.1190/geo2014-0345.1
7. Clayton R, Engquist B (1977) Absorbing boundary conditions for acoustic and elastic wave equations. Bull Seismol Soc Am 67(6):1529–1540
8. Collino F, Tsogka C (2001) Application of the perfectly matched absorbing layer model to the linear elastodynamic problem in anisotropic heterogeneous media. Geophysics 66(1):294–307. https://doi.org/10.1190/1.1444908
9. Crase E, Wideman C, Noble M, Tarantola A (1992) Nonlinear elastic waveform inversion of land seismic reflection data. J Geophys Res 97:4685–4703. https://doi.org/10.1029/90jb00832
10. De Basabe JD, Sen MK (2015) A comparison of finite-difference and spectral-element methods for elastic wave propagation in media with a fluid-solid interface. Geophys J Int 200(1):278–298. https://doi.org/10.1093/gji/ggu389
11. Di Bartolo L, Dors C, Mansur W (2012) A new family of finite-difference schemes to solve the heterogeneous acoustic wave equation. Geophysics 77(5):T187–T199. https://doi.org/10.1190/geo2011-0345.1
12. Du Q, Zhu Y, Ba J (2012) Polarity reversal correction for elastic reverse time migration. Geophysics 77(2):S31–S41. https://doi.org/10.1190/geo2011-0348.1
13. Du Q, Zhang M, Chen X, Gong X, Guo C (2014) True-amplitude wavefield separation using staggered-grid interpolation in the wavenumber domain. Appl Geophys 11:437–446. https://doi.org/10.1007/s11770-014-0458-9
14. Engquist B, Froese B (2014) Application of the Wasserstein metric to seismic signals. Commun Math Sci 9:79–88
15. Fichtner A, Trampert J (2011) Hessian kernels of seismic data functionals based upon adjoint techniques. Geophys J Int 185(2):775–798. https://doi.org/10.1111/j.1365-246X.2011.04966.x
16. Fletcher R, Reeves CM (1964) Function minimization by conjugate gradients. Comput J 7:149–154. https://doi.org/10.1093/comjnl/7.2.149
17. Forgues E, Lambaré G (1997) Parameterization study for acoustic and elastic ray + born inversion. J Seism Explor 6:253–278
18. Gu B, Li Z, Ma X, Liang G (2015) Multi-component elastic reverse time migration based on the P- and S-wave separated velocity–stress equations. J Appl Geophys 112:62–78. https://doi.org/10.1016/j.jappgeo.2014.11.008
19. Gu B, Li Z, Li Z, Yang P, Xu W, Han J (2017) Elastic least-squares reverse time migration with hybrid l1/l2 misfit function. Geophysics 82(3):S271–S291. https://doi.org/10.1190/geo2016-0235.1
20. Gu B, Han J, Ren Z, Li Z (2019) 2D least-squares elastic reverse time migration of multicomponent seismic data. Geophysics 84(6):S523–S538. https://doi.org/10.1190/geo2018-0720.1
21. Jeong W, Lee H, Min D (2012) Full waveform inversion strategy for density in the frequency domain. Geophys J Int 188(3):1221–1242. https://doi.org/10.1111/j.1365-246X.2011.05314.x
22. Kelly KR, Ward RW, Treitel S, Alford RM (1976) Synthetic seismograms: a finite-difference approach. Geophysics 41:2–27. https://doi.org/10.1190/1.1440605
23. Köhn D, De Nil D, Kurzmann A, Przebindowska A, Bohlen T (2012) On the influence of model parametrization in elastic full waveform tomography. Geophys J Int 191(1):325–345. https://doi.org/10.1111/j.1365-246X.2012.05633.x
24. Komatitsch D, Martin R (2007) An unsplit convolutional perfectly matched layer improved at grazing incidence for the seismic wave equation. Geophysics 72(5):SM155–SM167. https://doi.org/10.1190/1.2757586
25. Lailly P (1983) The seismic inverse problem as a sequence of before stack migrations. In: Conference on inverse scattering, theory and application. SIAM, expanded abstracts, pp 206–220
26. Levander AR (1988) Fourth-order finite-difference P-SV seismograms. Geophysics 53:1425–1436. https://doi.org/10.1190/1.1442422
27. Levander AR (1989) Finite-difference forward modeling in seismology. Van Nostrand Reinhold, New York, pp 410–430
28. Li Y, Demanet L (2015) Phase and amplitude tracking for seismic event separation. Geophysics 80(6):WD59–WD72. https://doi.org/10.1190/geo2015-0075.1
29. Li Y, Demanet L (2016) Full-waveform inversion with extrapolated low-frequency data. Geophysics 81(6):R339–R348. https://doi.org/10.1190/geo2016-0038.1
30. Li Q, Wu G (2019) 2D multi-parameter waveform inversion of land reflection seismic data obtained from the particle-motion response from the vertical geophone. Acta Geophys 68(2):377–388. https://doi.org/10.1007/s11600-020-00403-6
31. Liu Y, Sen M (2010) A hybrid scheme for absorbing edge reflections in numerical modeling of wave propagation. Geophysics 75(2):A1–A6. https://doi.org/10.1190/1.3295447
32. Luo Y, Schuster G (1991) Wave-equation traveltime inversion. Geophysics 56(5):645–653. https://doi.org/10.1190/1.1443081
33. Luo YY, Ma Y, Wu H. Liu, Cao L (2016) Full-traveltime inversion. Geophysics 81(5):R261–R274. https://doi.org/10.1190/geo2015-0353.1
34. Madariaga R (1976) Dynamics of an expanding circular fault. Bull Seismol Soc Am 66(3):639–666. https://doi.org/10.1007/BF02246368
35. Marfurt K (1984) Accuracy of finite-difference and finite-element modeling of the scalar and elastic wave equations. Geophysics 49:533–549. https://doi.org/10.1190/1.1441689
36. Martin G, Wiley R, Marfurt K (2006) Marmousi2: An elastic upgrade for Marmousi. Lead Edge 25:156. https://doi.org/10.1190/1.2172306
37. Métivier L, Brossier R, Mrigot Q, Oudet E, 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://doi.org/10.1093/gji/ggw014
38. Moczo P, Kristek J, Gális M (2014) The finite-difference modelling of earthquake motions: waves and ruptures. Cambridge University Press, Cambridge
39. Mora P (1987) Nonlinear two-dimensional elastic inversion of multioffset seismic data. Geophysics 52(9):1211–1228. https://doi.org/10.1190/1.1442384
40. Nolet G (2008) A breviary of seismic tomography. Cambridge University Press, Cambridge
41. Pan W, Innanen KA, Margrave GF, Fehler MC, Fang X, Li J (2016) Estimation of elastic constants for HTI media using Gauss–Newton and full-Newton multiparameter full-waveform inversion. Geophysics 81(5):R275–R291. https://doi.org/10.1190/geo2015-0594.1
42. Pan W, Innanen KA, Liao W (2017) Accelerating Hessian-free Gauss–Newton full-waveform inversion via l-BFGS preconditioned conjugate-gradient algorithm. Geophysics 82(2):R49–R64. https://doi.org/10.1190/geo2015-0595.1
43. Pan W, Innanen KA, Yu G, Li J (2019) Interparameter trade-off quantification for isotropic–elastic full-waveform inversion with various model parameterizations. Geophysics 84(2):R185–R206. https://doi.org/10.1190/geo2017-0832.1
44. Plessix RE (2006) A review of the adjoint-state method for computing the gradient of a functional with geophysical applications. Geophys J Int 167:495–503. https://doi.org/10.1111/j.1365-246X.2006.02978.x
45. Plessix RE, Solano CAP (2015) Modified surface boundary conditions for elastic waveform inversion of low-frequency wide-angle active land seismic data. Geophys J Int 201:1324–1334. https://doi.org/10.1093/gji/ggv087
46. Pratt RG, Shin C, Hick GJ (1988) 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
47. Raknes EB, Arntsen B, Weibull W (2015) Three-dimensional elastic full waveform inversion using seismic data from the Sleipner area. Geophys J Int 202(3):1877–1894. https://doi.org/10.1093/gji/ggv258
48. Ren Z, Liu Y (2016) A hierarchical elastic full-waveform inversion scheme based on wavefield separation and the multistep-length approach. Geophysics 81(3):R99–R123. https://doi.org/10.1190/geo2015-0431.1
49. Ren Z, Li Z, Gu B (2019) Elastic reflection waveform inversion based on the decomposition of sensitivity kernels. Geophysics 84(2):R235–R250. https://doi.org/10.1190/geo2018-0220.1
50. Sears T, Singh S, Barton P (2008) Elastic full waveform inversion of multi-component OBC seismic data. Geophys Prospect 56(6):843–862. https://doi.org/10.1111/j.1365-2478.2008.00692.x
51. Shipp RM, Singh SC (2002) Two-dimensional full wavefield inversion of wide-aperture marine seismic streamer data. Geophys J Int 151(2):325–344. https://doi.org/10.1046/j.1365-246X.2002.01645.x
52. Sirgue L, Pratt RG (2004) Efficient waveform inversion and imaging: a strategy for selecting temporal frequencies. Geophysics 69(1):231–248. https://doi.org/10.1190/1.1649391
53. Sun B, Alkhalifah T (2019) The application of an optimal transport to a preconditioned data matching function for robust waveform inversion. Geophysics 84(6):R923–R945. https://doi.org/10.1190/geo2018-0413.1
54. Tarantola A (1984) Inversion of seismic reflection data in the acoustic approximation. Geophysics 49(10):1259–1266. https://doi.org/10.1190/1.1441754
55. Tarantola A (1986) A strategy for nonlinear elastic inversion of seismic reflection data. Geophysics 51(10):1893–1903. https://doi.org/10.1190/1.1442046
56. Vigh D, Jiao K, Watts D, Sun D (2014) Elastic full-waveform inversion application using multicomponent measurements of seismic data collection. Geophysics 79(2):R63–R77. https://doi.org/10.1190/geo2013-0055.1
57. Virieux J (1986) P-SV wave propagation in heterogeneous media: velocity–stress finite-difference method. Geophysics 51:889–901. https://doi.org/10.1190/1.1442147
58. Virieux J, Operto S (2009) An overview of full-waveform inversion in exploration geophysics. Geophysics 74(6):WCC1–WCC26. https://doi.org/10.1190/1.3238367
59. Wang TF, Cheng JB (2015) Elastic wave mode decoupling for full waveform inversion. 85th annual international meeting. SEG, expanded abstracts, pp 1461–1466
60. Wang T, Cheng J (2017) Elastic full waveform inversion based on mode decomposition: the approach and mechanism. Geophys J Int 209(2):606–622. https://doi.org/10.1093/gji/ggx038
61. Wang J, Zhou H, Tian YK, Zhang HJ (2012) A new scheme for elastic full waveform inversion based on velocity-stress wave equations in time domain. 82nd annual international meeting, SEG, expanded abstracts. https://doi.org/10.1190/segam2012-0561.1
62. Wang TJ, Cheng Q. Guo, Wang C (2018a) Elastic wave-equation-based reflection kernel analysis and traveltime inversion using wave mode decomposition. Geophys J Int 215(1):450–470. https://doi.org/10.1093/gji/ggy291
63. Wang G, Wang S, Song J, Dong C, Zhang M (2018b) Elastic reflection traveltime inversion with decoupled wave equation. Geophysics 83(5):R463–R474. https://doi.org/10.1190/geo2017-0631.1
64. Warner M, Guasch L (2016) Adaptive waveform inversion: theory. Geophysics 81(6):R429–R445. https://doi.org/10.1190/geo2015-0387.1
65. Wu R, Aki K (1985) Scattering characteristics of elastic waves by an elastic heterogeneity. Geophysics 50:582–595. https://doi.org/10.1190/1.1441934
66. Wu R, Luo J, Wu B (2014) Seismic envelope inversion and modulation signal model. Geophysics 79(3):WA13–WA24. https://doi.org/10.1190/geo2013-0294.1
67. Xu S, Wang D, Chen F, Lambare G, Zhang Y (2012) Inversion on reflected seismic wave. 82nd annual international meeting, SEG, expanded abstracts. https://doi.org/10.1190/segam2012-1473.1
68. Yang Y, Engquist B (2018) Analysis of optimal transport and related misfit functions in full-waveform inversion. Geophysics 83(1):A7–A12. https://doi.org/10.1190/geo2017-0264.1
69. Yao G, Wu D (2017) Reflection full waveform inversion. Sci China Earth Sci 60(10):1783–1794. https://doi.org/10.1007/s11430-016-9091-9
70. Zhang Q, McMechan GA (2010) 2D and 3D elastic wavefield vector decomposition in the wavenumber domain for VTI media. Geophysics 75(3):D13–D26. https://doi.org/10.1190/1.3431045
71. Zhou H, Amundsen L, Zhang G (2012) Fundamental issues in full waveform inversion. 82nd annual international meeting, SEG, expanded abstracts. https://doi.org/10.1190/segam2012-0878.1

Uwagi

Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023).

Typ dokumentu

Bibliografia

Identyfikator YADDA

bwmeta1.element.baztech-f7090daf-ab1e-42cc-b52e-131a77edf71e