Seismic deconvolution by atomic decomposition: A parametric approach with sparseness constraints

Article type: Research Article

Authors: Herrmann, Felix J.

Affiliations: Department of Earth and Ocean Sciences, University of British Columbia, 6339 Stores Road, Vancouver, BL, Canada V6T 1Z4. Tel.: +1 604 822 8628; Fax: +1 604 822 6088; E-mail: fherrmann@eos.ubc.ca

Abstract: In this paper an alternative approach to the blind seismic deconvolution problem is presented that aims for two goals namely recovering the location and relative strength of seismic reflectors, possibly with super-localization, as well as obtaining detailed parametric characterizations for the reflectors. We hope to accomplish these goals by decomposing seismic data into a redundant dictionary of parameterized waveforms designed to closely match the properties of reflection events associated with sedimentary records. In particular, our method allows for highly intermittent non-Gaussian records yielding a reflectivity that can no longer be described by a stationary random process or by a spike train. Instead, we propose a reflector parameterization that not only recovers the reflector's location and relative strength but which also captures reflector attributes such as its local scaling, sharpness and instantaneous phase-delay. The first set of parameters delineates the stratigraphy whereas the second provides information on the lithology. As a consequence of the redundant parameterization, finding the matching waveforms from the dictionary involves the solution of an ill-posed problem. Two complementary sparseness-imposing methods Matching and Basis Pursuit are compared for our dictionary and applied to seismic data.

DOI: 10.3233/ICA-2005-12106

Journal: Integrated Computer-Aided Engineering, vol. 12, no. 1, pp. 69-90, 2005