The Interface Fresnel Zone revisited
Résumé
We determine the part of reflectors which actually affects the reflected wavefield, which is of particular interest for the characterization of the interfaces from physical and seismic viewpoints, and for seismic resolution. We reformulate the concepts of Fresnel volumes (FV) and Interface Fresnel zones (IFZ), by accounting for all possible rays defining the isochrone for the source-receiver pair and the specular reflected wave. In the case of a plane homogeneous interface, the results obtained with our reformulation (in particular, the size of the IFZ) are identical to previous published works. Nevertheless, with the help of the lens formula of geometrical optics, we propose a correction to the classical expression for the depth penetration of the FV across the interface in the transmission medium, which can result in a depth penetration 50% greater than the classical one. Additionally, we determine a region above the interface in the incidence medium, which is also involved in the wave reflection. Finally, we propose a new definition for the minimal volume of integration and homogenization of properties above and beyond the interface, which is necessary to the evaluation of an effective reflectivity of interfaces with lateral change in physical and geometrical properties.
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