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The Insidious Effects of Fine-scale Heterogeneity in Reflection Seismology

Friday, October 21, 2005 - 10:20am - 11:10am
EE/CS 3-180
Patrick Lailly (Institut Français du Pétrole)
Joint work with Florence Delprat-Jannaud.

Geophysicists are quite aware of the important troubles that can be met when
the seismic data are contaminated by multiple reflections. The situation
they have in mind is the one where multiple reflections are generated by
isolated interfaces associated with high impedance contrasts. We here study
a more insidious effect of multiple scattering, namely the one associated
with fine scale heterogeneity.
Our numerical experiments show that the effect of such multiple scattering
can be far from negligible. As a consequence, it can lead standard imaging
techniques (based on high-frequency analysis for wave propagation) to
complete failure. The parameters that control the importance of the
phenomenon are the depth of the target and the heterogeneity of the
overburden. The dynamic theory of homogenization, unfortunately available
only in 1D, allows us to better understand the role of the seismic frequency
band: the multiple scattering phenomenon is all the more important as we
deal with high frequencies. This leads to an interesting consequence: we can
take advantage of a super-resolution phenomenon; namely, in situations where
multiple scattering is important, we can expect a higher resolution than the
one given by the classical Rayleigh criterion.

References
Delprat-Jannaud, F. and Lailly, P., 2004. The insidious effects of
fine-scale heterogeneity in reflection seismology. Journal of Seismic
Exploration, 13: 39-84.
Bamberger, A., Chavent, B. and Lailly, P., 1979. About the stability of the
inverse problem in the 1D wave equation, application to the interpretation
of seismic profiles, Journal of Applied Mathematics and Optimization, 5:
1-47.
MSC Code: 
35L05
Keywords: