Compressed-sensing application - Pre-stack kirchhoff migration

Abstract
Least-squares migration is a linearized form of waveform inversion that aims to enhance the spatial resolution of the subsurface reflectivity distribution and reduce the migration artifacts due to limited recording aperture, coarse sampling of sources and receivers, and low subsurface illumination. Least-squares migration, however, due to the nature of its minimization process, tends to produce smoothed and dispersed versions of the reflectivity of the subsurface. Assuming that the subsurface reflectivity distribution is sparse, we propose the addition of a non-quadratic L1-norm penalty term on the model space in the objective function. This aims to preserve the sparse nature of the subsurface reflectivity series and enhance resolution. We further use a compressed-sensing algorithm to solve the linear system, which utilizes the sparsity assumption to produce highly resolved migrated images. Thus, the Kirchhoff migration implementation is formulated as a Basis Pursuit denoise (BPDN) problem to obtain the sparse reflectivity model. Applications on synthetic data show that reflectivity models obtained using this compressed-sensing algorithm are highly accurate with optimal resolution.

Citation
Aldawood, A., Hoteit, I., & Alkhalifah, T. (2013). Compressed-sensing Application - Pre-stack Kirchhoff Migration. London 2013, 75th Eage Conference En Exhibition Incorporating SPE Europec. doi:10.3997/2214-4609.20130612

Publisher
EAGE Publications

Journal
London 2013, 75th eage conference en exhibition incorporating SPE Europec

Conference/Event Name
75th European Association of Geoscientists and Engineers Conference and Exhibition 2013 Incorporating SPE EUROPEC 2013: Changing Frontiers

DOI
10.3997/2214-4609.20130612

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