An introduction to the mathematical theory of inverse problems
An introduction to the mathematical theory of inverse problems
Iterative methods for solving linear systems
Iterative methods for solving linear systems
On the nonmonotone line search
Journal of Optimization Theory and Applications
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
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The core problem in seismic exploration is to invert the subsurface reflectivity from the surface recorded seismic data. However, most of the seismic inverse problems are ill-posed by nature. To overcome the ill-posedness, different regularized least squares methods are introduced in the literature. In this paper, we developed a preconditioning non-monotone gradient method, proved it converges with R-superlinear rate and applied it to seismic deconvolution and imaging. Numerical examples demonstrate that the method is efficient. It helps to improve the resolution of the seismic inversions.