Large-scale Inversion of Magnetic Data Using Golub-Kahan Bidiagonalization with Truncated Generalized Cross Validation for Regularization Parameter Estimation

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VATANKHAH S.

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Journal: Journal of the Earth and Space Physics Year:2019 | Volume:44 | Issue:4 Page(s): 29-39

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Information Journal Paper

Title

Large-scale Inversion of Magnetic Data Using Golub-Kahan Bidiagonalization with Truncated Generalized Cross Validation for Regularization Parameter Estimation

Author(s)

VATANKHAH S. | | Issue Writer Certificate

Keywords

Magnetic surveyQ2

Sparse inversionQ3

Golub-Kahan bidiagonalizationQ3

Regularization parameter estimationQ3

Truncated generalized cross validationQ3

Abstract

In this paper a fast method for large-scale Sparse inversion of magnetic data is considered. The L1-norm stabilizer is used to generate models with sharp and distinct interfaces. To deal with the nonlinearity introduced by the L1-norm, a model-space iteratively reweighted least squares algorithm is used. The original model matrix is factorized using the Golub-Kahan bidiagonalization that projects the problem onto a Krylov subspace with a significantly reduced dimension. The model matrix of the projected system inherits the ill-conditioning of the original matrix, but the spectrum of the projected system accurately captures only a portion of the full spectrum. Equipped with the singular value decomposition of the projected system matrix, the solution of the projected problem is expressed using a filtered singular value expansion. This expansion depends on a regularization parameter which is determined using the method of Generalized Cross Validation (GCV), but here it is used for the truncated spectrum. This new technique, Truncated GCV (TGCV), is more effective compared with the standard GCV method. Numerical results using a synthetic example and real data demonstrate the efficiency of the presented algorithm.

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APA: Copy

VATANKHAH, S.. (2019). Large-scale Inversion of Magnetic Data Using Golub-Kahan Bidiagonalization with Truncated Generalized Cross Validation for Regularization Parameter Estimation. JOURNAL OF THE EARTH AND SPACE PHYSICS, 44(4), 29-39. SID. https://sid.ir/paper/80518/en

Vancouver: Copy

VATANKHAH S.. Large-scale Inversion of Magnetic Data Using Golub-Kahan Bidiagonalization with Truncated Generalized Cross Validation for Regularization Parameter Estimation. JOURNAL OF THE EARTH AND SPACE PHYSICS[Internet]. 2019;44(4):29-39. Available from: https://sid.ir/paper/80518/en

IEEE: Copy

S. VATANKHAH, “Large-scale Inversion of Magnetic Data Using Golub-Kahan Bidiagonalization with Truncated Generalized Cross Validation for Regularization Parameter Estimation,” JOURNAL OF THE EARTH AND SPACE PHYSICS, vol. 44, no. 4, pp. 29–39, 2019, [Online]. Available: https://sid.ir/paper/80518/en

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