1887

Abstract

Summary

Gravity inverse problem, like other geophysical data inversion, is an ill posed problem that could be solved using Tikhonov regularization. The regularization parameter is one of the effective parameters for obtaining optimal model in inversion of the potential field data similar inversion of other geophysical data. In other word, the regularization parameter has been important parameter for more stability and convergence in inverse modeling. This parameter is experimentally estimated in the most of the inversion method. There are different approaches for automatic estimation of regularization parameter in 3D inversion.

In this paper the modified Generalized Cross Validation (GCV) as a new method was used for estimating the regularization parameter in three-dimensional (3-D) inversion of gravity data. However, we used the conjugate gradient (CG) algorithm for computation of model parameters

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/content/papers/10.3997/2214-4609.201801463
2018-06-11
2024-04-20
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References

  1. Farquharson, CG., Oldenburg, D.W.
    , 2004. A comparison of automatic techniques for estimating the regularization parameter in non-linear inverse problems. Geophys. J. Int.156, 411–425.
    [Google Scholar]
  2. Hansen, P.C.
    , 1997Rank-deficient and discrete ill-posed problems: numerical aspects of linear inversion, SIAM, Philadelphia.
    [Google Scholar]
  3. Li, Y., & Oldenburg, D. W.
    , 2003. Fast inversion of large-scale magnetic data using wavelet transforms and a logarithmic barrier method. Geophysical Journal International, 152(2), 251–265.
    [Google Scholar]
  4. Morozov, V. A.
    , 1966. On the solution of functional equations by the method of regularization, Sov. Math. Dokl., 7, 414–417.
    [Google Scholar]
  5. Marquardt, D. W.
    , 1970. Generalized inverses, ridge regression, biased linear estimation, and nonlinear estimation, Technometrics, 12 (3), 591–612.
    [Google Scholar]
  6. Mead, J. L. & Renaut, R. A.
    , 2009. A Newton root-finding algorithm for estimating the regularization parameter for solving ill-conditioned least squares problems, Inverse Problems, 25, 025002.
    [Google Scholar]
  7. Renaut, R. A., Hnetynkov´a, I. & Mead, J. L.
    , 2010. Regularization parameter estimation for large scale Tikhonov regularization using a priori information, Computational Statistics and Data Analysis54(12), 3430–3445.
    [Google Scholar]
  8. Tikhonov, A. N., and Arsenin, V. Y.
    , 1977, Solution of ill-posed Problems: V. H. Winston and Sons.
    [Google Scholar]
  9. Vatankhah, S., Ardestani, V.E., Renaut, R.A.
    , 2014a. Automatic estimation of the regularization parameter in 2d focusing gravity inversion: application of the method to the Safo manganese mine in the northwest of Iran. J. Geophys. Eng.11, 045001.
    [Google Scholar]
  10. Vatankhah, S., Renaut, R. A. & Ardestani, V. E.
    , 2014b. Regularization parameter estimation for underdetermined problems by the χ2 principle with application to 2D focusing gravity inversion, Inverse Problems, 30, 085002.
    [Google Scholar]
  11. Wahba, G.
    , 1977. Practical approximate solutions to linear operator equations when the data are noisy. SIAM Journal on Numerical Analysis, 14(4), 651–667.
    [Google Scholar]
  12. , 1990. Spline Models for Observational Data, vol. 59. SIAM, Philadelphia.
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