In this paper, we propose a new method for two-dimensional (2-D) magnetotelluric (MT) inversion based on the curvelet transform. Unlike the conventional inversion methods that apply constraints on the model in the space-domain, the method presented in this paper is based on the sparse constraint by the curvelet transform, and we directly invert the curvelet coefficients instead of the model conductivities in the space-domain. The curvelet transform is a multiscale sparse scheme that transforms the model parameters into the curvelet coefficients at multiple scales. The basis function of the curvelet transform is the “wedge base” that satisfies the anisotropic scale relationship (width∝length2) and has the characteristic of arbitrary directivity. Thus, it has the capability to “optimally” represent the edge of the target objects. To achieve a sparse constraint, we use L1-norm of the curvelet coefficients for the inversion. This can help extract the features of target objects more sparsely and get high-resolution inversion results. We compare the results of our curvelet-based inversion with those based on the traditional L1-norm and L2-norm inversions. The experiments with theoretical data demonstrate that the sparse constraint inversion based on the curvelet transform can better reveal the boundaries of target objects.


Article metrics loading...

Loading full text...

Full text loading...


  1. Candès, E. and Donoho, D.
    [2002] New tight frames of curvelets and optimal representations of objects with piecewise-C2 singularities. Comm. on Pure and Appl. Math., 57, 219–266.
    [Google Scholar]
  2. Candès, E., Demanet, L., Donoho, D. and Ying, L.
    [2006] Fast Discrete Curvelet Transforms. Multiscale Model. Simul., 5(3), 861–899.
    [Google Scholar]
  3. Ekblom, H.
    [1987] The L1-estimate as limiting case of an Lp-or Huber-estimate, in Statistical Data Analysis based on the L1-Norm and Related Methods, ed. Doge Y., pp. 109–116. Elsevier Science Publ. Co., Inc.
    [Google Scholar]
  4. Farquharson, C.G.
    [2008] Constructing piecewise-constant models in multidimensional minimum-structure inversions. Geophysics, 73(1), K1–K9.
    [Google Scholar]
  5. Liu, Y.H., Farquharson, C.G., Yin, C.C. and Baranwal, V. C.
    [2018] Wavelet-based 3-D inversion for frequency-domain airborne EM data. Geophys. J. Int., 213(1), 1–15.
    [Google Scholar]

Data & Media loading...

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