1887
Volume 18, Issue 6
  • ISSN: 1569-4445
  • E-ISSN: 1873-0604

Abstract

ABSTRACT

A novel traveltime tomographic approach is applied to anisotropic media, limited to 2D geometry at present. A general anisotropic Eikonal solver based on a discontinuous Galerkin method is combined with an efficient adjoint formulation for multiparameter least‐squares inversion. This new approach is tested considering synthetic crosshole ground‐penetrating radar data. The configuration of the ground‐penetrating radar survey is inspired by a real experiment done on layered carbonate media disturbed by the presence of a deep gallery, which induces a localized high‐electromagnetic contrast. This made it possible to define a well‐adapted general workflow in this context. We notably show that, under the elliptical anisotropic assumption, the parametrization based on vertical and horizontal velocities provides less biased results than those obtained by considering the vertical velocity and the relevant Thomsen parameter . The initial vertical and horizontal velocity models are identical and built from an isotropic inversion. The presence of the high‐contrast gallery generates a weak diffraction pattern, which is taken into account in our tomography approach. It also creates potential artefacts due to the model discretization, which are mitigated by a model regularization term within the definition of the misfit function. This general workflow is then applied to the real experiment dataset. The vertical and horizontal velocity images provide similar structures as those previously obtained by isotropic full waveform inversion, complemented by an image of a rather weak elliptical anisotropy.

Loading

Article metrics loading...

/content/journals/10.1002/nsg.12116
2020-11-16
2024-04-26
Loading full text...

Full text loading...

References

  1. Alkhalifah, T. and Plessix, R. (2014) A recipe for practical full‐waveform inversion in anisotropic media: an analytical parameter resolution study. Geophysics, 79(3), R91–R101.
    [Google Scholar]
  2. Asnaashari, A., Brossier, R., Garambois, S., Audebert, F., Thore, P. and Virieux, J. (2013) Regularized seismic full waveform inversion with prior model information. Geophysics, 78(2), R25–R36.
    [Google Scholar]
  3. Berryman, J.G. (1989) Weighted least‐squares criteria for seismic traveltime tomography. IEEE Transactions on Geoscience and Remote Sensing, 27(3), 302–309.
    [Google Scholar]
  4. Bouaziz, I. (2015) Etude d'une carotte de la plateforme urgonienne du vaucluse: Approches sédimentologie, pétrophysique et numérique. Master's Thesis, Université de Pau et des Pays de l'Adour, Pau.
  5. Carcione, J. and Cavallini, F. (1995) On the acoustic‐electromagnetic analogy. Wave Motion, 21, 149–162.
    [Google Scholar]
  6. Cerveny, V. (1985) Ray synthetic seismograms for complex two‐dimensional and three‐dimensional structures. Journal of Geophysics, 58(2), 26.
    [Google Scholar]
  7. Cheng, Y. and Wang, Z. (2014) A new discontinuous Galerkin finite element method for directly solving the Hamilton–Jacobi equations. Journal of Computational Physics, 268, 134–153.
    [Google Scholar]
  8. Crandall, M.G. and Lions, P.L. (1983) Viscosity solutions of Hamilton–Jacobi equations. Transactions of the American Mathematical Society, 277(1), 1–42.
    [Google Scholar]
  9. Dafflon, B., Irving, J. and Barrash, W. (2011) Inversion of multiple intersecting high‐resolution crosshole GPR profiles for hydrological characterization at the Boise Hydrogeophysical Research Site. Journal of Applied Geophysics, 73(4), 305–314.
    [Google Scholar]
  10. Gholami, Y., Brossier, R., Operto, S., Ribodetti, A. and Virieux, J. (2013) Which parametrization is suitable for acoustic VTI full waveform inversion? art 1: sensitivity and trade‐off analysis. Geophysics, 78(2), R81–R105.
    [Google Scholar]
  11. Giroux, B. and Gloaguen, E. (2012) Geostatistical traveltime tomography in elliptically anisotropic media. Geophysical Prospecting, 60(6), 1133–1149.
    [Google Scholar]
  12. Gloaguen, E., Marcotte, D., Chouteau, M. and Perroud, H. (2005) Borehole radar velocity inversion using cokriging and cosimulation. Journal of Applied Geophysics, 57, 242–259.
    [Google Scholar]
  13. Hale, D. (2007) Local dip filtering with directional laplacians. Centre for Wave Phenomena, Colorado School of Mines. Technical report.
    [Google Scholar]
  14. Hanafy, S. and Al Hagrey, S. (2005) Ground‐penetrating radar tomography for soil‐moisture heterogeneity. Geophysics, 71(1), K9–K18.
    [Google Scholar]
  15. Hunziker, J., Laloy, E. and Linde, N. (2017) Inference of multi‐gaussian relative permittivity fields by probabilistic inversion of crosshole ground‐penetrating radar data. Geophysics, 82(5), H25–H40.
    [Google Scholar]
  16. Ikelle, L.T. (2012) On elastic‐electromagnetic mathematical equivalences. Geophysical Journal International, 189(3), 1771–1780.
    [Google Scholar]
  17. Irving, J., Knoll, M. and Knight, R. (2007) Improving crosshole radar velocity tomograms: a new approach to incorporating high‐angle traveltime data. Geophysics, 72(4).
    [Google Scholar]
  18. Le Bouteiller, P. (2018) Eulerian approach of Hamilton–Jacobi equation with a discontinuous Galerkin method in heterogeneous anisotropic medium: Application to seismic imaging. PhD thesis, University Grenoble Alpes.
    [Google Scholar]
  19. Le Bouteiller, P., Benjemaa, M., Métivier, L. and Virieux, J. (2018) An accurate discontinuous Galerkin method for solving point–source Eikonal equation in 2‐D heterogeneous anisotropic media. Geophysical Journal International, 212(3), 1498–1522.
    [Google Scholar]
  20. Le Bouteiller, P., Benjemaa, M., Métivier, L. and Virieux, J. (2019) A discontinuous galerkin fast‐sweeping Eikonal solver for fast and accurate traveltime computation in 3D tilted anisotropic media. Geophysics, 84(2), C107–C118.
    [Google Scholar]
  21. Leung, S. and Qian, J. (2006) An adjoint state method for three‐dimensional transmission traveltime tomography using first‐arrivals. Communications in Mathematical Sciences, 4(1), 249–266.
    [Google Scholar]
  22. Métivier, L. and Brossier, R. (2016) The seiscope optimization toolbox: a large‐scale nonlinear optimization library based on reverse communication. Geophysics, 81(2), F11–F25.
    [Google Scholar]
  23. Nocedal, J. (1980) Updating quasi‐Newton matrices with limited storage. Mathematics of Computation, 35(151), 773–782.
    [Google Scholar]
  24. Operto, S., Virieux, J., Ribodetti, A. and Anderson, J.E. (2009) Finite‐difference frequency‐domain modeling of visco‐acoustic wave propagation in two‐dimensional TTI media. Geophysics, 74(5), T75–T95.
    [Google Scholar]
  25. Paige, C.C. and Saunders, M.A. (1982) ALGORITHM 583 LSQR: sparse linear equations and least squares problems. ACM Transactions on Mathematical Software, 8(2), 195–209.
    [Google Scholar]
  26. Pinard, H., Garambois, S., Métivier, L., Dietrich, M., Sénéchal, G. and Rousset, D. (2016) Full‐waveform inversion of gpr data acquired between boreholes in Rustrel carbonates. In: Coulié, K., Micolau, G. and Febvre, P. (Eds.) E3S Web of Conferences: Inter‐Disciplinary Underground Science & Technology (i‐DUST 2016), Avignon, France, Vol. 12.
    [Google Scholar]
  27. Plessix, R.E. (2006) A review of the adjoint‐state method for computing the gradient of a functional with geophysical applications. Geophysical Journal International, 167(2), 495–503.
    [Google Scholar]
  28. Podvin, P. and Lecomte, I. (1991) Finite difference computation of traveltimes in very contrasted velocity model: a massively parallel approach and its associated tools. Geophysical Journal International, 105, 271–284.
    [Google Scholar]
  29. Taillandier, C., Noble, M., Chauris, H. and Calandra, H. (2009) First‐arrival travel time tomography based on the adjoint state method. Geophysics, 74(6), WCB1–WCB10.
    [Google Scholar]
  30. Tavakoli, B., Operto, S., Ribodetti, A. and Virieux, J. (2019) Matrix‐free anisotropic slope tomography: theory and application. Geophysics, 84(1), R35–R57.
    [Google Scholar]
  31. Thomsen, L.A. (1986) Weak elastic anisotropy. Geophysics, 51, 1954–1966.
    [Google Scholar]
  32. Tikhonov, A. and Arsenin, V. (1977) Solution of Ill‐Posed Problems. Winston, Washington, DC.
    [Google Scholar]
  33. Trinh, P.T., Brossier, R., Métivier, L., Virieux, J. and Wellington, P. (2017) Bessel smoothing filter for spectral element mesh. Geophysical Journal International, 209(3), 1489–1512.
    [Google Scholar]
  34. Vasco, D.W., PetersonJr., J.E. and Lee, K.H. (1997) Ground‐penetrating radar velocity tomography in heterogeneous and anisotropic media. Geophysics, 62(6), 1758–1773.
    [Google Scholar]
  35. Waheed, U.B., Flagg, G. and Yarman, C.E. (2016) First‐arrival traveltime tomography for anisotropic media using the adjoint‐state method. Geophysics, 81(4), R147–R155.
    [Google Scholar]
  36. Wellington, P., Brossier, R., Hamitou, O., Trinh, P. and Virieux, J. (2017) Efficient anisotropic dip filtering via inverse correlation functions. Geophysics, 82(4), A31–A35.
    [Google Scholar]
http://instance.metastore.ingenta.com/content/journals/10.1002/nsg.12116
Loading
/content/journals/10.1002/nsg.12116
Loading

Data & Media loading...

  • Article Type: Research Article
Keyword(s): Anisotropy; Multiparameter; Tomography; Traveltime; Velocity

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