The Insidious Effects of Fine-scale Heterogeneity in Reflection Seismology

October 21, 2005
  • Wave equation
  • 35L05
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.