Multifractional splines: application to seismic imaging

TitleMultifractional splines: application to seismic imaging
Publication TypeConference
Year of Publication2003
AuthorsFelix J. Herrmann
Secondary AuthorsMichael A. Unser, Akram Aldroubi, Andrew F. Laine
Conference NameProceedings of SPIE Technical Conference on Wavelets: Applications in Signal and Image Processing X
Volume5207
Page240-258
OrganizationSPIE
KeywordsPresentation, SLIM
Abstract

Seismic imaging commits itself to locating singularities in the elastic properties of the Earth’s subsurface. Using the high-frequency ray-Born approximation for scattering from non-intersecting smooth interfaces, seismic data can be represented by a generalized Radon transform mapping the singularities in the medium to seismic data. Even though seismic data are bandwidth limited, signatures of the singularities in the medium carry through this transform and its inverse and this mapping property presents us with the possibility to develop new imaging techniques that preserve and characterize the singularities from incomplete, bandwidth-limited and noisy data. In this paper we propose a non-adaptive Curvelet/Contourlet technique to image and preserve the singularities and a data-adaptive Matching Pursuit method to characterize these imaged singularities by Multi-fractional Splines. This first technique borrows from the ideas within the Wavelet-Vaguelette/Quasi-SVD approach. We use the almost diagonalization of the scattering operator to approximately compensate for (i) the coloring of the noise and hence facilitate estimation; (ii) the normal operator itself. Results of applying these techniques to seismic imaging are encouraging although many open fundamental questions remain.

Presentation

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