1887
Volume 54, Issue 4
  • ISSN: 0812-3985
  • E-ISSN: 1834-7533

Abstract

Rayleigh and body waves are both solutions of the same propagation equation, but correspond to different wavenumber regions and boundary conditions, so their interaction with the elastic parameters (Vp, Vs and density) provides independent constraints during inversion. We develop and illustrate concurrent, elastic, full-waveform inversion of P and S body- and Rayleigh-waves using interleaved envelope- and waveform-based misfit functions, in a gradually-increasing frequency, multi-scale, inversion strategy. A wavelet and its envelope have different effective bandwidths, spectral shapes, and provide complementary frequency and wavenumber weighting in concurrent inversion. Because of the greater depth extent sampled by the exponentially decaying tail of a Rayleigh wave, compared to a body waveform, the depth extent of the model required to support both body and surface waves in concurrent inversion is defined by the Rayleigh waves. Correlation coefficients provide quantitative measures of the contributions of the data subsets to the fits of the solutions. For both smooth and constant starting models, concurrent interleaved inversion gives smaller data misfits than the envelope-only and waveform-only solutions. Treating the whole wavefield as a single data set means that it is not necessary to separate, or even to identify, different types of body and surface waves.

© 2023 Australian Society of Exploration Geophysicists
Loading

Article metrics loading...

/content/journals/10.1080/08123985.2022.2158806
2023-07-04
2026-01-18

  • From This Site

    /content/journals/10.1080/08123985.2022.2158806
    dcterms_title,dcterms_subject,pub_keyword
    -contentType:Journal -contentType:Contributor -contentType:Concept -contentType:Institution
    10
    5
Loading full text...

Full text loading...

References

  1. Aravkin, A.Y., T.van Leeuwen, H.Calandra, and F.J.Herrmann. 2012. Source estimation for frequency-domain FWI with robust penalties. In 74th annual international conference and exhibition, P018. EAGE, Extended Abstracts.
  2. Ben-Menahem, A., and D.G.Harkrider. 1964. Radiation patterns of seismic surface waves from buried dipolar point sources in a flat stratified earth. Journal of Geophysical Research69 (12): 2605–2620.
     [Google Scholar]
  3. Ben-Menahem, A., and S.J.Singh. 2012. Seismic waves and sources. New York, NY: Springer.
  4. Boiero, D., and L.V.Socco. 2010. Retrieving lateral variations from surface wave dispersion curves. Geophysical Prospecting58 (6): 977–996. https://doi.org/10.1111/j.1365‑2478.2010.00877.x
     https://doi.org/https://doi.org/10.1111/j.1365-2478.2010.00877.x [Google Scholar]
  5. Borisov, D., F.Gao, P.Williamson, and J.Tromp. 2020. Application of 2D full-waveform inversion on exploration land data. Geophysics85 (2): R75–R86. https://doi.org/10.1190/geo2019‑0082.1
     https://doi.org/https://doi.org/10.1190/geo2019-0082.1 [Google Scholar]
  6. Borisov, D., R.Modrak, F.Gao, and J.Tromp. 2018. 3D elastic full-waveform inversion of surface waves in the presence of irregular topography using an envelope-based misfit function. Geophysics83 (1): R1–R11. https://doi.org/10.1190/2017‑0081.1
     https://doi.org/https://doi.org/10.1190/2017-0081.1 [Google Scholar]
  7. Bozdaǧ, E., J.Trampert, and J.Tromp. 2011. Misfit functions for full waveform inversion based on instantaneous phase and envelope measurements. Geophysical Journal International185 (2): 845–870. https://doi.org/10.1111/j.1365‑246X.2011.04970.x
     https://doi.org/https://doi.org/10.1111/j.1365-246X.2011.04970.x [Google Scholar]
  8. Carcione, J.M.2007. Wavefield in real media: Wave propagation in anisotropic, anelastic, porous and electromagnetic media. Amsterdam: Elsevier.
  9. Chi, B., L.Dong, and Y.Liu. 2014. Full waveform inversion method using envelope objective function without low frequency data. Journal of Applied Geophysics109: 36–46. http://www.sciencedirect.com/science/article/pii/S0926985114002031
     [Google Scholar]
  10. Choi, Y., and T.Alkhalifah. 2018. Time-domain full-waveform inversion of exponentially damped wavefield using the deconvolution-based objective function. Geophysics83 (2): R77–R88. https://doi.org/10.1190/geo2017‑0057.1
     https://doi.org/https://doi.org/10.1190/geo2017-0057.1 [Google Scholar]
  11. Gao, L., Y.Pan, and T.Bohlen. 2020. 2-D multiparameter viscoelastic shallow-seismic full-waveform inversion: reconstruction tests and first field-data application. Geophysical Journal International222 (1): 560–571.
     [Google Scholar]
  12. Gao, L., Y.Pan, A.Rieder, and T.Bohlen. 2021. Multiparameter viscoelastic full-waveform inversion of shallow-seismic surface waves with a pre-conditioned truncated newton method. Geophysical Journal International227 (3): 2044–2057. https://doi.org/10.1093/gji/ggab311
     https://doi.org/https://doi.org/10.1093/gji/ggab311 [Google Scholar]
  13. Hayashi, K., and H.Suzuki. 2004. CMP cross-correlation analysis of multi-channel surface-wave data. Exploration Geophysics35 (1): 7–1. https://library.seg.org/doi/abs/10.1071/EG04007
     https://doi.org/10.1071/EG04007 [Google Scholar]
  14. Hu, Y., R.-S.Wu, X.Huang, Y.Long, Y.Xu, and L.-G.Han. 2022. Phase-amplitude-based polarized direct envelope inversion in the time-frequency domain. Geophysics87 (3): R245–R260.
     [Google Scholar]
  15. Huang, X., K.S.Eikrem, M.Jakobsen, and G.Nævdal. 2020. Bayesian full-waveform inversion in anisotropic elastic media using the iterated extended kalman filter. Geophysics85 (4): C125–C139.
     [Google Scholar]
  16. Komatitsch, D., Q.Liu, J.Tromp, P.Süss, C.W.Stidham, and J.H.Shaw. 2004. Simulations of ground motion in the Los Angeles basin based upon the spectral-element method. Bulletin of the Seismological Society of America94 (1): 187–206.
     [Google Scholar]
  17. Koo, N.-H., C.Shin, D.-J.Min, K.-P.Park, and H.-Y.Lee. 2011. Source estimation and direct wave reconstruction in laplace-domain waveform inversion for deep-sea seismic data. Geophysical Journal International187: 861–870. https://doi.org/10.1111/j.1365‑246X.2011.05141.x
     https://doi.org/https://doi.org/10.1111/j.1365-246X.2011.05141.x [Google Scholar]
  18. Lee, K.H., and H.J.Kim. 2003. Source-independent full-waveform inversion of seismic data. Geophysics68 (6): 2010–2015. https://doi.org/10.1190/1.1635054
     https://doi.org/https://doi.org/10.1190/1.1635054 [Google Scholar]
  19. Li, J., G.Dutta, and G.Schuster. 2017a. Wave-equation qs inversion of skeletonized surface waves. Geophysical Journal International209 (2): 979–991. https://doi.org/10.1093/gji/ggx051
     https://doi.org/https://doi.org/10.1093/gji/ggx051 [Google Scholar]
  20. Li, J., Z.Feng, and G.Schuster. 2017b. Wave-equation dispersion inversion. Geophysical Journal International208 (3): 1567–1578. https://doi.org/10.1093/gji/ggw465
     https://doi.org/https://doi.org/10.1093/gji/ggw465 [Google Scholar]
  21. Li, J., and G.Schuster. 2016. Skeletonized wave equation of surface wave dispersion inversion. In SEG technical program expanded abstracts 2016, 3630–3635. https://library.seg.org/doi/abs/10.1190/segam2016‑13770057.1.
     https://doi.org/10.1190/segam2016-13770057.1
  22. Liner, C.2012. Elements of seismic dispersion: A somewhat practical guide to frequency-dependent phenomena. Society of Exploration Geophysicists 15. https://library.seg.org/doi/abs/10.1190/1.9781560802952.
     https://doi.org/10.1190/1.9781560802952 [Google Scholar]
  23. Liu, Q., D.Peter, and C.Tape. 2019. Square-root variable metric based elastic full-waveform inversion – part 1: theory and validation. Geophysical Journal International218 (2): 1121–1135. https://doi.org/10.1093/gji/ggz188
     https://doi.org/https://doi.org/10.1093/gji/ggz188 [Google Scholar]
  24. Lucca, E., G.Festa, and A.Emolo. 2012. Kinematic inversion of strong-motion data using a gaussian parameterization for the slip: application to the 2008 iwate–Miyagi, Japan, earthquake. Bulletin of the Seismological Society of America102 (6): 2685–2703. https://doi.org/10.1785/0120110292
     https://doi.org/https://doi.org/10.1785/0120110292 [Google Scholar]
  25. Masoni, I., J.-L.Boelle, R.Brossier, and J.Virieux. 2016. Layer stripping fwi for surface waves. In SEG technical program expanded abstracts 2016, 1369–1373. https://library.seg.org/doi/abs/10.1190/segam2016‑13859781.1.
     https://doi.org/10.1190/segam2016-13859781.1
  26. Masoni, I., R.Brossier, J.L.Boelle, and J.Virieux. 2014. Robust full waveform inversion of surface waves. In SEG technical program expanded abstracts 2014, 1126–1130. https://library.seg.org/doi/abs/10.1190/segam2014‑1077.1.
     https://doi.org/10.1190/segam2014-1077.1
  27. Masoni, I., R.Brossier, J.Virieux, and J.L.Boelle. 2013. Alternative misfit functions for FWI applied to surface waves. In 75th annual international conference and exhibition, EAGE, Extended Abstracts, P10 13.
  28. Modrak, R.T., D.Borisov, M.Lefebvre, and J.Tromp. 2018. Seisflows – flexible waveform inversion software. Computers & Geosciences115: 88–95. http://www.sciencedirect.com/science/article/pii/S0098300417300316
     [Google Scholar]
  29. Modrak, R., and J.Tromp. 2016. Seismic waveform inversion best practices: regional, global and exploration test cases. Geophysical Journal International206 (3): 1864–1889. https://doi.org/10.1093/gji/ggw202
     https://doi.org/https://doi.org/10.1093/gji/ggw202 [Google Scholar]
  30. Mora, P.1989. Inversion = migration + tomography. Geophysics54 (12): 1575–1586. https://doi.org/10.1190/1.1442625
     https://doi.org/https://doi.org/10.1190/1.1442625 [Google Scholar]
  31. Nazarian, S., and K.H.Stokoe. 1984. In situ determination of elastic moduli of soil deposits and pavement systems by spectral-analysis-of-surface-waves method. University Microfilms. https://books.google.com/books?id=jpvNnQEACAAJ.
  32. Nguyen, B.D., and G.A.McMechan. 2015. Five ways to avoid storing source wavefield snapshots in 2D elastic prestack reverse time migration. Geophysics80 (1): S1–S18. https://doi.org/10.1190/geo2014‑0014.1
     https://doi.org/https://doi.org/10.1190/geo2014-0014.1 [Google Scholar]
  33. Nocedal, J., and S.J.Wright. 2006. Numerical optimization. New York, NY: Springer.
  34. Operto, S., Y.Gholami, V.Prieux, A.Ribodetti, R.Brossier, L.Metivier, and J.Virieux. 2013. A guided tour of multiparameter full-waveform inversion with multicomponent data. From Theory to Practice: The Leading Edge32 (9): 1040–1054. https://doi.org/10.1190/tle32091040.1
     https://doi.org/https://doi.org/10.1190/tle32091040.1 [Google Scholar]
  35. Pan, W., Y.Geng, and K.A.Innanen. 2018. Interparameter trade-off quantification and reduction in isotropic-elastic full-waveform inversion. synthetic Experiments and Hussar Land Data Set Application: Geophysical Journal International213 (2): 1305–1333. https://doi.org/10.1093/gji/ggy037
     https://doi.org/https://doi.org/10.1093/gji/ggy037 [Google Scholar]
  36. Pan, W., K.A.Innanen, Y.Geng, and J.Li. 2019. Interparameter trade-off quantification for isotropic-elastic full-waveform inversion with various model parameterizations. Geophysics84 (2): R185–R206. https://doi.org/10.1190/geo2017‑0832.1
     https://doi.org/https://doi.org/10.1190/geo2017-0832.1 [Google Scholar]
  37. Pan, Y., J.Xia, Y.Xu, L.Gao, and Z.Xu. 2016. Love-wave waveform inversion in time domain for shallow shear-wave velocity. Geophysics81 (1): R1–R14. https://doi.org/10.1190/geo2014‑0225.1
     https://doi.org/https://doi.org/10.1190/geo2014-0225.1 [Google Scholar]
  38. Pérez Solano, C.A., D.Donno, and H.Chauris. 2014. Alternative waveform inversion for surface wave analysis in 2-D media. Geophysical Journal International198 (3): 1359–1372. https://doi.org/10.1093/gji/ggu211
     https://doi.org/https://doi.org/10.1093/gji/ggu211 [Google Scholar]
  39. Prieux, V., R.Brossier, S.Operto, and J.Virieux. 2013a. Multiparameter full waveform inversion of multicomponent ocean-bottom-cable data from the valhall field. part 1: imaging compressional wave speed, density and attenuation. Geophysical Journal International194 (3): 1640–1664. https://doi.org/10.1093/gji/ggt177
     https://doi.org/https://doi.org/10.1093/gji/ggt177 [Google Scholar]
  40. Prieux, V., R.Brossier, S.Operto, and J.Virieux. 2013b. Multiparameter full waveform inversion of multicomponent ocean-bottom-cable data from the valhall field. part 2: imaging compressive-wave and shear-wave velocities. Geophysical Journal International194 (3): 1665–1681. https://doi.org/10.1093/gji/ggt178
     https://doi.org/https://doi.org/10.1093/gji/ggt178 [Google Scholar]
  41. Robertsson, J.O.A., J.O.Blanch, and W.W.Symes. 1994. Viscoelastic finite-difference modeling. Geophysics59 (9): 1444–1456. https://doi.org/10.1190/1.1443701
     https://doi.org/https://doi.org/10.1190/1.1443701 [Google Scholar]
  42. Romdhane, A., G.Grandjean, R.Brossier, F.Rejiba, S.Operto, and J.Virieux. 2011. Shallow-structure characterization by 2D elastic full-waveform inversion. Geophysics76 (3): R81–R93.
     [Google Scholar]
  43. Shi, J., M.D.Hoop, F.Faucher, and H.Calandra. 2016. Elastic full-waveform inversion with surface and body waves. In SEG technical program expanded abstracts 2016, 1120–1124. https://library.seg.org/doi/abs/10.1190/segam2016‑13961828.1.
     https://doi.org/10.1190/segam2016-13961828.1
  44. Shin, C., and Y.H.Cha. 2009. Waveform inversion in the laplace – Fourier domain. Geophysical Journal International177 (3): 1067–1079. https://onlinelibrary.wiley.com/doi/abs/10.1111/j.1365‑246X.2009.04102.x.
     https://doi.org/10.1111/j.1365-246X.2009.04102.x [Google Scholar]
  45. Socco, L.V., S.Foti, and D.Boiero. 2010. Surface-wave analysis for building near-surface velocity models – established approaches and new perspectives. Geophysics75 (5): 75A83–75A102.
     [Google Scholar]
  46. Socco, L.V., and C.Strobbia. 2004. Surface-wave method for near-surface characterization: A tutorial. Near Surface Geophysics2 (4): 165–185.
     [Google Scholar]
  47. Sun, D., K.Jiao, X.Cheng, D.Vigh, and R.Coates. 2014. Source wavelet estimation in full waveform inversion. In SEG technical program expanded abstracts 2014, 1184–1188. https://library.seg.org/doi/abs/10.1190/segam2014‑1632.1.
     https://doi.org/10.1190/segam2014-1632.1
  48. Sun, R., and G.A.McMechan. 1991. Full-wavefield inversion of wide-aperture SH and love wave data. Geophysical Journal International106 (1): 67–75. https://doi.org/10.1111/j.1365‑246X.1991.tb04601.x
     https://doi.org/https://doi.org/10.1111/j.1365-246X.1991.tb04601.x [Google Scholar]
  49. Tang, C., and G.A.McMechan. 2017. From classical reflectivity-to-velocity inversion to full-waveform inversion using phase-modified and deconvolved reverse time migration images. Geophysics82 (1): S31–S49. https://doi.org/10.1190/geo2016‑0033.1
     https://doi.org/https://doi.org/10.1190/geo2016-0033.1 [Google Scholar]
  50. Teyssandier, B., and J.J.Sallas. 2019. The shape of things to come–Development and testing of a new marine vibrator source. The Leading Edge38 (9): 680–690. https://doi.org/10.1190/tle38090680.1
     https://doi.org/https://doi.org/10.1190/tle38090680.1 [Google Scholar]
  51. Tiwari, U.K., and G.A.McMechan. 2007. Effects of incomplete parameterization on full-wavefield viscoelastic seismic data for petrophysical reservoir properties. Geophysics72 (3): O9–O17.
     [Google Scholar]
  52. Tromp, J., D.Komatitsch, and Q.Liu. 2008. Spectral-element and adjoint methods in seismology. Communications in Computational Physics3 (1): 1–32.
     [Google Scholar]
  53. Tromp, J., C.Tape, and Q.Liu. 2005. Seismic tomography, adjoint methods, time reversal and banana-doughnut kernels. Geophysical Journal International160 (1): 195–216.
     [Google Scholar]
  54. Virieux, J., and S.Operto. 2009. An overview of full-waveform inversion in exploration geophysics. Geophysics74 (6): WCC1–WCC26.
     [Google Scholar]
  55. Wu, R., and K.Aki. 1985. Scattering characteristics of elastic waves by an elastic heterogeneity. Geophysics50 (4): 582–595.
     [Google Scholar]
  56. Wu, R.-S., J.Luo, and B.Wu. 2014. Seismic envelope inversion and modulation signal model. Geophysics79 (3): WA13–WA24. https://doi.org/10.1190/geo2013‑0294.1
     https://doi.org/https://doi.org/10.1190/geo2013-0294.1 [Google Scholar]
  57. Xia, J., R.D.Miller, and C.B.Park. 1999. Estimation of near-surface shear-wave velocity by inversion of Rayleigh waves. Geophysics64 (3): 691–700. https://doi.org/10.1190/1.1444578
     https://doi.org/https://doi.org/10.1190/1.1444578 [Google Scholar]
  58. Xu, T., G.A.McMechan, and R.Sun. 1995. 3-D prestack full-wavefield inversion. Geophysics60 (6): 1805–18. https://doi.org/10.1190/1.1443913
     https://doi.org/https://doi.org/10.1190/1.1443913 [Google Scholar]
  59. Yuan, Y.O., F.J.Simons, and E.Bozdağ. 2015. Multiscale adjoint waveform tomography for surface and body waves. Geophysics80 (5): R281–R302.
     [Google Scholar]
  60. Zhang, Z., and T.Alkhalifah. 2018. Wave-equation rayleigh wave inversion using fundamental and higher modes. In SEG technical program expanded abstracts 2018, 2511–2515. https://library.seg.org/doi/abs/10.1190/segam2018‑2989655.1.
     https://doi.org/10.1190/segam2018-2989655.1
  61. Zhang, Z., T.Alkhalifah, E.Z.Naeini, and B.Sun. 2018. Multiparameter elastic full waveform inversion with facies-based constraints. Geophysical Journal International213 (3): 2112–2127. https://doi.org/10.1093/gji/ggy113
     https://doi.org/https://doi.org/10.1093/gji/ggy113 [Google Scholar]
  62. Zhang, Z., Y.Liu, and G.Schuster. 2015. Wave equation inversion of skeletonized surfacewaves. In SEG technical program expanded abstracts 2015, 2391–2395. https://library.seg.org/doi/abs/10.1190/segam2015‑5805253.1.
     https://doi.org/10.1190/segam2015-5805253.1
  63. Zhang, Z., G.Schuster, Y.Liu, S.M.Hanafy, and J.Li. 2016. Wave equation dispersion inversion using a difference approximation to the dispersion-curve misfit gradient. Journal of Applied Geophysics133: 9–15. http://www.sciencedirect.com/science/article/pii/S092698511630204X
     [Google Scholar]
/content/journals/10.1080/08123985.2022.2158806
Loading
Concurrent elastic inversion of Rayleigh and body waves with interleaved envelope-based and waveform-based misfit functions
Exploration Geophysics 54, 416 (2023); https://doi.org/10.1080/08123985.2022.2158806
/content/journals/10.1080/08123985.2022.2158806
/content/journals/10.1080/08123985.2022.2158806
Loading

Data & Media loading...

  • Article Type: Research Article
Keyword(s): Full waveform inversion; near surface; Rayleigh waves

Most Cited This Month Most Cited RSS feed

This is a required field
Please enter a valid email address
Approval was a Success
Invalid data
An Error Occurred
Approval was partially successful, following selected items could not be processed due to error