1887

Abstract

Summary

In this paper, a new, robust and resistant, inversion based 2D Fourier transformation is presented where the spectrum is discretized by series expansion (S-IRLS-FT). The series expansion coefficients as model parameters are given by the solution of the inverse problem. Since it is advantageous to use squared-integrable, full, orthogonal and normed basis functions, Hermite-functions are chosen as basis functions of the inversion based Fourier transformation. Taking advantage of the beneficial properties of Hermite polynomials, that they are the eigenfunctions of the inverse Fourier transformation, the elements of the Jacobian matrix can be calculated fast and easily, without integration. The procedure can be robustified using Iteratively Reweighted Least Squares (IRLS) method with Steiner weights. The advantage of the Steiner weights is that the scale parameters ( 2) can be determined from the statistic of the measured data set in an inner iteration process. Thus, a very effective robust and resistant inversion procedure can be defined. Its applicability using magnetic data calculated above a square and “L”-shape object is proved.

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/content/papers/10.3997/2214-4609.201600633
2016-05-31
2020-07-13
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References

  1. Dobróka, M., Szegedi, H., Somogyi Molnár, J. Szűcs, P.
    [2015] On the Reduced Noise Sensitivity of a New Fourier Transformation Algorithm. Mathematical Geosciences. 47:(6) 679–697.
    [Google Scholar]
  2. Gyulai, Á., Szabó, N. P.
    [2014] Series expansion based geoelectric inversion methodology used for geo-enveronmental investigations. Frontiers in Geosciences2:(1) 11–17.
    [Google Scholar]
  3. Kunaratnam, K.
    [1981] Simplified expressions for the magnetic anomalies due to vertical rectangular prisms. Geophysical Prospecting29. 883–890.
    [Google Scholar]
  4. Pethő, G., Turai, E., Szabó, N.P., Németh, N., Baracza, M.K., Bulla, D., Kormos, K.
    [2014] Geophysical Exploration of a Complex Metavolcanic Environment. Near Surface Geoscience 2014. Athen, Greece.
    [Google Scholar]
  5. Steiner, F.
    [1997] Optimum methods in statistics. Akadémiai Kiadó, Budapest.
    [Google Scholar]
  6. Szabó, N. P.
    [2011] Shale volume estimation based on the factor analysis of well-logging data. Acta Geophysica59:(5) 935–953.
    [Google Scholar]
  7. Szegedi, H., Dobróka, M.
    [2014] On the use of Steiner’s weights in inversion-based Fourier transformation - robustification of a previously published algorithm. Acta Geodaetica et Geophysica, 49/1, 95–104, DOI 10.1007/s40328‑014‑0041‑0.
    https://doi.org/10.1007/s40328-014-0041-0 [Google Scholar]
  8. Turai, E.
    [2011] Data processing method developments using tau-transformation of time domain IP data (II) - Interpretation results of field measured data. Acta Geodaetica et Geophysica46(4), 391– 400.
    [Google Scholar]
  9. Vaidyanathan, P. P.
    [2008] Eigenfunctions of the Fourier transform. IETE Journal of Education, 49(2), 51–58.
    [Google Scholar]
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