1887
Volume 61 Number 6
  • E-ISSN: 1365-2478

Abstract

ABSTRACT

We introduce a new structural constraint for joint inversion with an application to regional scale seismic traveltimes and magnetotelluric data. We call the constraint ‘directed’ as it takes into account information on the sign of cross‐correlation between the gradients of reconstructed parameters. With special treatment of singularities, arising from vanishing gradients and linearization, this constraint demonstrates some properties of an edge‐preserving stabilizer – it provides blocky models with coincident discontinuities. We develop an algorithm for 2D pixel‐based joint inversion, including the proposed structural constraint as a penalty term of the objective function; additional stabilizing terms are total variation of seismic slowness and Levenberg–Marquardt damping. The resulting regularized Gauss–Newton scheme is numerically stable and demonstrates relatively fast convergence both in data misfits and in the structural similarity measure. This is shown by a numerical study of the algorithm on a simplified regional model of the Earth's crust. The considered model has a blocky structure with a positive correlation between P‐wave velocity and electrical resistivity; it represents a faulted basement overlain by sediments embedding an allochthonous salt dome. The developed joint inversion improves both velocity and resistivity reconstruction relative to separate inversions. In comparison with the cross‐gradients constraint the considered structural constraint firstly fixes the sign of correlation between the gradients of the parameters, thus reducing uncertainty in the model recovery and secondly due to its stabilizing properties it limits the amount of additional regularization, which results in sharper reconstructed models.

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2013-08-20
2024-03-28
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References

  1. BerdichevskyM.N. and DmitrievV.I.2008. Models and Methods of Magnetotellurics. Springer.
    [Google Scholar]
  2. CarcioneJ.M. and UrsinB.2007. Cross‐property relations between electrical conductivity and the seismic velocity of rocks. Geophysics72(5), E193–E204.
    [Google Scholar]
  3. De StefanoM., AndreasiF.G., ReS., VirgilioM. and SnyderF.F.2011. Multiple‐domain, simultaneous joint inversion of geophysical data with application to subsalt imaging. Geophysics76(3), R69–R80.
    [Google Scholar]
  4. GallardoL.A. and MejuM.A.2003. Characterization of heterogeneous near‐surface materials by joint 2D inversion of dc resistivity and seismic data. Geophysical Research Letters30(13), 1658.
    [Google Scholar]
  5. GallardoL.A. and MejuM.A.2011. Structure‐coupled multiphysics imaging in geophysical sciences. Reviews of Geophysics49.
    [Google Scholar]
  6. HabashyT.M. and AbubakarA.2004. A general framework for constraint minimization for the inversion of electro‐magnetic measurements. Progress in Electromagnetics Research46, 265–312.
    [Google Scholar]
  7. HaberE. and OldenburgD.1997. Joint inversion: a structural approach. Inverse Problems13, 63–77.
    [Google Scholar]
  8. HaberE. and ModersitzkiJ.2006. Intensity gradient based registration and fusion of multi‐modal images. Medical Image Computing and Computer‐Assisted Intervention ‐ MICCAI 2006. Lecture Notes in Computer Science4191, 726–733.
    [Google Scholar]
  9. HeinckeB., JegenM. and HobbsR.2006. Joint inversion of MT, gravity and seismic data applied to sub‐basalt imaging. 76th Annual International Meeting, SEG, Expanded Abstracts, 784–789.
  10. HuW., AbubakarA. and HabashyT.M.2009. Joint electromagnetic and seismic inversion using structural constraints. Geophysics74(6), R99–R109.
    [Google Scholar]
  11. MolodtsovD.M., KashtanB.M. and RoslovY.V.2011. Joint inversion of seismic and magnetotelluric data with structural constraint based on dot product of image gradients. 81st Annual International Meeting, SEG, Expanded Abstracts, 740–744.
  12. NewmanG.M., GasperikovaE., HoverstenG.M. and WannamakerP.E.2008. Three‐dimensional magnetotelluric characterization of the Coso geothermal field. Geothermics37(4), 369–399.
    [Google Scholar]
  13. PortniaguineO. and ZhdanovM.S.1999. Focusing geophysical inversion images. Geophysics64, 874–887.
    [Google Scholar]
  14. RodiW.L.1976. A technique for improving the accuracy of FE solutions for MT data. Geophysical Journal of the Royal Astronomical Society44, 483–506.
    [Google Scholar]
  15. RudinL., OsherS. and FatemiE.1992. Nonlinear total variation based noise removal algorithms. Physica D60, 259–268.
    [Google Scholar]
  16. TikhonovA.N. and ArseninV.Y.1977. Solutions of ill‐posed problems. Winston, Washington, DC.
    [Google Scholar]
  17. TroyanV.N. and HayakawaM.2002. Inverse geophysical problems. TerraPub, Tokyo, p. 289.
    [Google Scholar]
  18. TroyanV.N. and KiselevY.V.2010. Statistical methods of geophysical data processing. World Scientific, p. 436.
    [Google Scholar]
  19. VogelC.R.2002. Computational methods for inverse problems. SIAM, p. 183.
    [Google Scholar]
  20. VsemirnovaE.A. and RoslovYu.V.2004. Raytracing on irregular mesh. V International Conference “Problems of Geocosmos”, St.Petersburg, Book of abstracts, p. 68.
  21. WannamakerP.E., StodtJ.A. and RijoL.A.1987. Stable finite element solution for two‐dimensional magnetotelluric modeling. Geophysical Journal of the Royal Astronomical Society88(1), 277–296.
    [Google Scholar]
  22. ZhdanovM.S.2002. Geophysical inverse theory and regularization problems. Elsevier.
    [Google Scholar]
  23. ZhdanovM.S., GribenkoA. and WilsonG.2012. Generalized joint inversion of multimodal geophysical data using Gramian constraints. Geophysical Research Letters39(9), L09301.
    [Google Scholar]
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  • Article Type: Research Article
Keyword(s): Electromagnetics; Inverse problem; Rays; Resistivity; Tomography

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