1887
Volume 66, Issue 4
  • E-ISSN: 1365-2478

Abstract

ABSTRACT

We present a 2D inversion scheme for magnetotelluric data, where the conductivity structure is parameterised with different wavelet functions that are collected in a wavelet‐based dictionary. The inversion model estimate is regularised in terms of wavelet coefficient sparsity following the compressive sensing approach. However, when the model is expressed on the basis of a single wavelet family only, the geometrical appearance of model features reflects the shape of the wavelet functions. Combining two or more wavelet families in a dictionary provides greater flexibility to represent the model structure, permitting, for example, the simultaneous occurrence of smooth and sharp anomalies within the same model. We show that the application of the sparsity regularisation scheme with wavelet dictionaries provides the user with a number of different model classes that may explain the data to the same extent. For a real data example from the Dead Sea Transform, we show that the use of such a scheme can be beneficial to evaluate the geometries of conductivity anomalies and to understand the effect of regularisation on the model estimate.

Loading

Article metrics loading...

/content/journals/10.1111/1365-2478.12605
2018-01-18
2020-06-02
Loading full text...

Full text loading...

References

  1. BedrosianP., MaercklinN., WeckmannU., BartovY., RybergT. and RitterO.2007. Lithology‐derived structure classification from the joint interpretation of magnetotelluric and seismic models. Geophysical Journal International170(2), 737–748.
    [Google Scholar]
  2. CharletyJ., VoroninS., NoletG., LorisI., SimonsF.J., SiglochK.et al. 2013. Global seismic tomography with sparsity constraints: comparison with smoothing and damping regularization. Journal of Geophysical Research118(9), 4887–4899.
    [Google Scholar]
  3. ConstableS.C., ParkerR.L. and ConstableC.G.1987. Occam's inversion: A practical algorithm for generating smooth models from electromagnetic sounding data. Geophysics52(3), 289–300.
    [Google Scholar]
  4. DaubechiesI.1992. Ten lectures on Wavelets . Society for Industrial and Applied Mathematics (SIAM).
  5. DaubechiesI., DefriseM. and De MolC.2004. An iterative thresholding algorithm for linear inverse problems with a sparsity constraint. Communications on Pure and Applied Mathematics57(11), 1413–1457.
    [Google Scholar]
  6. deGroot‐HedlinC. and ConstableS.1990. Occam's inversion to generate smooth, two‐dimensional models from magnetotelluric data. Geophysics55(12), 1613–1624.
    [Google Scholar]
  7. DonohoD.L.2006. Compressed sensing. IEEE Transactions on Information Theory52(4), 1289–1306.
    [Google Scholar]
  8. GholamiA. and SiahkoohiH.2010. Regularization of linear and non‐linear geophysical ill‐posed problems with joint sparsity constraints. Geophysical Journal International180(2), 871–882.
    [Google Scholar]
  9. HerrmannF.J.2010. Randomized sampling and sparsity: getting more information from fewer samples. Geophysics75(6), WB173–WB187.
    [Google Scholar]
  10. HerrmannF.J. and LiX.2012. Efficient least‐squares imaging with sparsity promotion and compressive sensing. Geophysical Prospecting60, 696–712.
    [Google Scholar]
  11. LeeS.K., KimH.J., SongY. and LeeC.‐K.2009. MT2DInvMatlab—A program in Matlab and Fortran for two‐dimensional magnetotelluric inversion. Computers & Geosciences35(8), 1722–1734.
    [Google Scholar]
  12. LiX., EsserE. and HerrmannF.J.2016. Modified Gauss–Newton full‐waveform inversion explained—Why sparsity‐promoting updates do matter. Geophysics81(3), R125–R138.
    [Google Scholar]
  13. LorisI., NoletG., DaubechiesI. and DahlenF.2007. Tomographic inversion using L1‐norm regularization of wavelet coefficients. Geophysical Journal International170(1), 359–370.
    [Google Scholar]
  14. MaercklinN., BedrosianP., HaberlandC., RitterO., RybergT., WeberM. and WeckmannU.2005. Characterizing a large shear‐zone with seismic and magnetotelluric methods: the case of the Dead Sea Transform. Geophysical Research Letters32(15).
    [Google Scholar]
  15. MallatS.1999. A Wavelet Tour of Signal Processing, Academic Press.
    [Google Scholar]
  16. NittingerC.G. and BeckenM.2016. Inversion of magnetotelluric data in a sparse model domain. Geophysical Journal International206(2), 1398–1409.
    [Google Scholar]
  17. RitterO., RybergT., WeckmannU., Homann‐RotheA., AbueladasA. and GarfunkelZ.2003. Geophysical images of the Dead Sea Transform in Jordan reveal an impermeable barrier for fluid flow. Geophysical Research Letters30, 1741.
    [Google Scholar]
  18. RodiW. and MackieR.L.2001. Nonlinear conjugate gradients algorithm for 2‐D magnetotelluric inversion. Geophysics66(1), 174–187.
    [Google Scholar]
  19. Rosas‐CarbajalM., LindeN. and KalscheuerT.2012. Focused time‐lapse inversion of radio and audio magnetotelluric data. Journal of Applied Geophysics84, 29–38.
    [Google Scholar]
  20. SelesnickI.W., BaraniukR.G. and KingsburyN.C.2005. The dual‐tree complex wavelet transform. IEEE Signal Processing Magazine22(6), 123–151.
    [Google Scholar]
  21. SiripunvarapornW. and EgbertG.2000. An efficient data‐subspace inversion for two‐dimensional magnetotelluric data. Geophysics65, 791–803.
    [Google Scholar]
  22. ZhdanovM. and TolstayaE.2004. Minimum support nonlinear parametrization in the solution of a 3D magnetotelluric inverse problem. Inverse Problems20(3), 937.
    [Google Scholar]
  23. ZhuL., LiuE. and McClellanJ.H.2017.Sparse‐promoting full‐waveform inversion based on online orthonormal dictionary learning. Geophysics82(2), R87–R107.
    [Google Scholar]
http://instance.metastore.ingenta.com/content/journals/10.1111/1365-2478.12605
Loading
/content/journals/10.1111/1365-2478.12605
Loading

Data & Media loading...

  • Article Type: Research Article
Keyword(s): Electromagnetics , Imaging , Inverse problem and Inversion
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