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Proceedings Paper

Multifractional splines: application to seismic imaging
Author(s): Felix J. Herrmann
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Paper 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.

Paper Details

Date Published: 13 November 2003
PDF: 19 pages
Proc. SPIE 5207, Wavelets: Applications in Signal and Image Processing X, (13 November 2003); doi: 10.1117/12.505275
Show Author Affiliations
Felix J. Herrmann, Univ. of British Columbia (Canada)

Published in SPIE Proceedings Vol. 5207:
Wavelets: Applications in Signal and Image Processing X
Michael A. Unser; Akram Aldroubi; Andrew F. Laine, Editor(s)

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