This article is cited in 7 papers

Sparse optimization methods for seismic wavefields recovery

Y. F. Wang

Key Laboratory of Petroleum Resources Research, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing, P. R. China

Abstract: Due to the influence of variations in landform, geophysical data acquisition is usually sub-sampled. Reconstruction of the seismic wavefield from sub-sampled data is an ill-posed inverse problem. It usually requires some regularization techniques to tackle the ill-posedness and provide a stable approximation to the true solution. In this paper, we consider the wavefield reconstruction problem as a compressive sensing problem. We solve the problem by constructing different kinds of regularization models and study sparse optimization methods for solving the regularization model. The $l_p$-$l_q$ model with $p=2$ and $q=0,1$ is fully studied. The projected gradient descent method, linear programming method and an $l_1$-norm constrained trust region method are developed to solve the compressive sensing problem. Numerical results demonstrate that the developed approaches are robust in solving the ill-posed compressive sensing problem and can greatly improve the quality of wavefield recovery.

Keywords: seismic inversion, optimization, sparsity, regularization.

UDC: 517.983.54

Received: 10.05.2011

Language: English

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