Sparse Regularization Least-Squares Reverse Time Migration Based on the Krylov Subspace Method

doi:10.3390/rs17050847

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Sparse Regularization Least-Squares Reverse Time Migration Based on the Krylov Subspace Method

2025-02-27

DOI：10.3390/rs17050847

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Abstract

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Least-squares reverse time migration (LSRTM) is an advanced seismic imaging technique that reconstructs subsurface models by minimizing the residuals between simulated and observed data. Mathematically, the LSRTM inversion of the sub-surface reflectivity is a large-scale, highly ill-posed sparse inverse problem, where conventional inversion methods typically lead to poor imaging quality. In this study, we propose a regularized LSRTM method based on the flexible Krylov subspace inversion framework. Through the strategy of the Krylov subspace projection, a basis set for the projection solution is generated, and then the inversion of a large ill-posed problem is expressed as the small matrix optimization problem. With flexible preconditioning, the proposed method could solve the sparse regularization LSRTM, like with the Tikhonov regularization style. Sparse penalization solution is implemented by decomposing it into a set of Tikhonov penalization problems with iterative reweighted norm, and then the flexible Golub-Kahan process is employed to solve the regularization problem in a low-dimensional subspace, thereby finally obtaining a sparse projection solution. Numerical tests on the Valley model and the Salt model validate that the LSRTM based on Krylov subspace method can effectively address the sparse inversion problem of subsurface reflectivity and produce higher-quality imaging results.

Keywords:

computational geophysics

least-squares migration

reverse time migration

flexible Krylov subspace method