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Mathematical Problems in Engineering
Volume 2015 (2015), Article ID 427153, 11 pages
Research Article

A Seismic Blind Deconvolution Algorithm Based on Bayesian Compressive Sensing

1School of Electrical Engineering & Automation, Tianjin University, Tianjin 300072, China
2Department of Disaster Prevention Equipment, Institute of Disaster Prevention, Beijing 101601, China

Received 19 March 2015; Accepted 20 April 2015

Academic Editor: Wanquan Liu

Copyright © 2015 Yanqin Li and Guoshan Zhang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Compressive sensing in seismic signal processing is a construction of the unknown reflectivity sequence from the incoherent measurements of the seismic records. Blind seismic deconvolution is the recovery of reflectivity sequence from the seismic records, when the seismic wavelet is unknown. In this paper, a seismic blind deconvolution algorithm based on Bayesian compressive sensing is proposed. The proposed algorithm combines compressive sensing and blind seismic deconvolution to get the reflectivity sequence and the unknown seismic wavelet through the compressive sensing measurements of the seismic records. Hierarchical Bayesian model and optimization method are used to estimate the unknown reflectivity sequence, the seismic wavelet, and the unknown parameters (hyperparameters). The estimated result by the proposed algorithm shows the better agreement with the real value on both simulation and field-data experiments.