Inversion of electromagnetic induction data, including VLF, is generally realized using smooth inversion methods. The smoothness of the recovered models and the regularization of the ill-conditioned problem is ensured with smoothing matrices. Smoothing matrices are simple linear derivative matrices penalizing the resistivity differences between adjacent cells. Since these matrices are linear operators, they are calculated once at the beginning of the inversion process. Considering its structure, smoothing matrices can be considered similar to low-pass Gaussian filters. Similarly, it’s possible to define a non-linear smoothing operator based on rank order filtering. We have defined a non-linear smoothing constraint based on these filters and penalized the differences from the cells corresponding to the desired rank value. Since the defined constraint is non-linear it is re-calculated as the model parameters change. The defined constraint is tested on synthetic data and its results are compared to the results obtained with a traditional smoothing matrix. Accordingly, the defined non-linear rank order smoothing constraint can provide relatively focused, amplified structures, and can increase blockiness.


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  1. Ataman, E., Aatre, V., & Wong, K.
    [1981] Some statistical properties of median filters. IEEE Transactions on Acoustics, Speech, and Signal Processing, 29(5), 1073–1075. doi: 10.1109/TASSP.1981.1163659
    https://doi.org/10.1109/TASSP.1981.1163659 [Google Scholar]
  2. Auken, E., and ChristiansenA. V.
    [2004] Layered and laterally constrained 2D inversion of resistivity data. Geophysics, 69, 752–761. doi: 10.1190/1.1759461
    https://doi.org/10.1190/1.1759461 [Google Scholar]
  3. Baranwal, V. C., Franke, A., Börner, R. U., & Spitzer, K.
    [2011] Unstructured grid based 2-D inversion of VLF data for models including topography. Journal of Applied Geophysics, 75(2), 363–372. doi: 10.1016/j.jappgeo.2011.07.011
    https://doi.org/10.1016/j.jappgeo.2011.07.011 [Google Scholar]
  4. Candansayar, M. E.
    [2008] Two-dimensional inversion of magnetotelluric data with consecutive use of conjugate gradient and least-squares solution with singular value decomposition algorithms. Geophysical Prospecting, 56(1), 141–157. doi: 10.1111/j.1365‑2478.2007.00668.x
    https://doi.org/10.1111/j.1365-2478.2007.00668.x [Google Scholar]
  5. Constable, S. C., Parker, R. L., & Constable, C. G.
    [1987] Occam’s inversion: A practical algorithm for generating smooth models from electromagnetic sounding data. Geophysics, 52(3), 289–300. doi: 10.1190/1.1442303
    https://doi.org/10.1190/1.1442303 [Google Scholar]
  6. de Groot-Hedlin, C., & Constable, S.
    [1990] Occam’s inversion to generate smooth, two-dimensional models from magnetotelluric data. Geophysics, 55(12), 1613–1624. doi: 10.1190/1.1442813
    https://doi.org/10.1190/1.1442813 [Google Scholar]
  7. Gürer, A., Bayrak, M., Gürer, Ö.F.
    [2009] A VLF survey using current gathering phenomena for tracing buried faults of Fethiye—Burdur Fault Zone, Turkey. Journal of Applied Geophysics, 68, 437–447. doi: 10.1016/j.jappgeo.2009.03.011
    https://doi.org/10.1016/j.jappgeo.2009.03.011 [Google Scholar]
  8. Olesen, O., Henkel, H., Lile, O.B., Mauring, E., Ronning, J.S.
    [1992] Geophysical inverstigations of the Stuoragurra postglacial fault, Finnmark, northern Norway. Journal of Applied Geophysics, 29, 95–118. doi: 10.1016/0926‑9851(92)90001‑2
    https://doi.org/10.1016/0926-9851(92)90001-2 [Google Scholar]
  9. Portniaguine, O., & Zhdanov, M. S.
    [1999] Focusing geophysical inversion images. Geophysics, 64(3), 874–887. doi: 10.1190/1.1444596
    https://doi.org/10.1190/1.1444596 [Google Scholar]
  10. Smith, T., Hoversten, M., Gasperikova, E., & Morrison, F.
    [1999] Sharp boundary inversion of 2D magnetotelluric data. Geophysical Prospecting, 47(4), 469–486. doi: 10.1046/j.1365‑2478.1999.00145.x
    https://doi.org/10.1046/j.1365-2478.1999.00145.x [Google Scholar]
  11. Siripunvaraporn, W., & Egbert, G.
    [2000] An efficient data-subspace inversion method for 2-D magnetotelluric data. Geophysics, 65(3), 791–803. doi: 10.1190/1.1444778
    https://doi.org/10.1190/1.1444778 [Google Scholar]
  12. Uchida, T.
    [1993] Smooth 2-D inversion for magnetotelluric data based on statistical criterion ABIC. Journal of geomagnetism and geoelectricity, 45(9), 841–858. doi: 10.5636/jgg.45.841
    https://doi.org/10.5636/jgg.45.841 [Google Scholar]

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