University of Tehran Press Journal of the Earth and Space Physics 2538-371X 44 4 2018 12 22 Large-scale Inversion of Magnetic Data Using Golub-Kahan Bidiagonalization with Truncated Generalized Cross Validation for Regularization Parameter Estimation Large-scale Inversion of Magnetic Data Using Golub-Kahan Bidiagonalization with Truncated Generalized Cross Validation for Regularization Parameter Estimation 29 39 65881 10.22059/jesphys.2018.247879.1006954 FA Saeed Vatankhah Assistant Professor, Department of Earth Physics, Institute of Geophysics, University of Tehran, Iran Journal Article 2017 12 20 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 non-linearity 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. 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 non-linearity 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. https://jesphys.ut.ac.ir/article_65881_6379712cc0856924f302337e3f0a59a9.pdf