Bayesian 3-D Path Search and Its Applications to Focusing Seismic Data
The 3D-images studied here are essential to the analysis of cubes of seismic focalisation. In the detection of geological horizons, the improvement of migration techniques requires the construction of 3D “focal” paths. We start with blurred versions of (unknown) 3D-images consisting ideally of concentrated intensity spots which tend to lie on smooth isolated 3D-paths. The blur point-spread function is spatially dependent, roughly Gaussian in shape, and directly estimated on the blurred image. On the space of admissible paths, we describe the plausibility of a path by an energy function, using thus a 3D-Markov random field model. The adjustment of this Markov field model to the image data relies on an original interactive robust parameter localization approach.
Reconstruction of the original paths is based on a maximum (a posteriori) likelihood approach, implemented by a new variant of Besag’s ICM algorithm. Applications to actual 3D-seismic data are presented.
KeywordsSeismic Data Pointer Field Depth Migration Blur Kernel Seismic Trace
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- J.-P. Faye and J.-P. Jeannot–Prestack migration velocities from focusing depth analysis, 65th Annu. Int. Meet., Soc. Expl. Geophys., Expanded Abstract (1986), 38–440.Google Scholar
- J.F. Clearbout - Imaging the earth’s interior, Palo Alto, Blackwell Scientific Publications, Inc. (1985).Google Scholar
- Ph. Julien, Y. Vujasinovic and J.-J. Raoult–Depth continuous velocity analysis based on prestack migration, 58th Annu. Int. Meet., Soc. Expl. Geophys., Expanded Abstracts (1988), 437–441.Google Scholar
- B. Chalmond - PSF estimation for image deblurring, Comp. Graphics, Vision and Image Processing, July 1991.Google Scholar
- R. Azencott - Image analysis and Markov field, Proc. of Int. Conf. on Ind. Appl. Math. SIAM (1987).Google Scholar
- J. Besag - On the statistical analysis of dirty pictures, J.R. Statist. Soc. B-148 (1986).Google Scholar
- P. Bouthemy and P. Lalande–Detection and tracking of missing objects based on a statistical regularization method in space and time, Computer Vision–ECCV90, Lecture Notes in Computer Sciences, vol. 427, Springer-Verlag (1990), 307–314.Google Scholar
- J. Konrad and E. Dubois–A comparison of stochastic and deterministic solution methods in Bayesian estimation of 2-D motion, Computer Vision–ECCV90, Lecture Notes in Computer Sciences, vol. 427, Springer-Verlag (1990), 149–160.Google Scholar
- A. Possolo - Estimation of binary random Markov field, University of Washington, Technical report 77, Seattle (1986).Google Scholar
- N.R. Draper and H. Smith - Applied regression analysis, John-Wiley (1966).Google Scholar
- J.W. Wiggins - Attenuation of complex water-bottom multiples by waves-equation based prediction and subtraction, Geophysics, vol. 53 (1988), 1527.Google Scholar
- Ph. Julien and J.-J. Raoult - Adaptive subtraction of emulated multiples, 59th Annu. Int. Meet., Soc. Expl. Geophys., Expanded Abstracts, vol. II (1989), 1118.Google Scholar
- E. Denelle, Y. Dzard and J.-J. Raoult–Implementation of a 2D-prestack depth migration scheme on a CRAY-1S, 55th Annu. Int. Meet., Soc. Expl. Geophys., Expanded Abstracts (1985), 318–320.Google Scholar
- E. Denelle, Y. Dzard and J.-J. Raoult–2D-prestack depth migration in the (S-G-W) domain, 56th Annu. Int. Meet., Soc. Expl. Geophys., Expanded Abstracts (1986), 327–330.Google Scholar
- S.M. Doherty and J.F. Clearbout–Velocity analysis based on the wave equation, Stanford Exploration Project Rep. 1 (1984), 160–178.Google Scholar
- S. MacKay and K. Abma–Refining prestack depth-migration images without remigration, 59th Annu. Int. Meet., Soc. Expl. Geophys., Expanded Abstracts (1989), 1258–1261.Google Scholar
- Ph. Julien, M. Klein and T. Thomas–In quest of the base 59th Annu. Int. Meet., Soc. Expl. Geophys., Expanded Abstracts, vol. II (1989), 1275–1278.Google Scholar