Influence of the Interface Fresnel zone on the reflectedP-wave amplitude modelling

Abstract

SUMMARY The aim of the paper is to emphasize the importance of accounting for the Fresnel volume and for the Interface Fresnel zone (IFZ) for calculating the amplitude of the P wave emanating from a point source and recorded at a receiver after its specular reflection on a smooth homogeneous interface between elastic media. For this purpose, by considering the problem of interest as a problem of diffraction by the IFZ, that is, the physically relevant part of the interface which actually affects the reflected wavefield, we have developed a method which combines the Angular Spectrum Approach (ASA) with the IFZ concept to get the 3-D analytical solution. The variation in the reflected P-wave amplitude evaluated with the ASA, as a function of the incidence angle, is compared with the plane wave (PW) reflection coefficient and with the exact solution provided by the 3-D code OASES, for one solid/solid configuration and two dominant frequencies of the source. For subcritical incidence angles the geometrical spreading compensation is mostly quite sufficient to reduce the point-source amplitudes to the PW amplitudes. On the contrary, for specific regions of incidence angles for which the geometrical spreading compensation is not sufficient anymore, that is, near the critical region and in the post-critical domain, the ASA combined with the IFZ concept yields better results than the PW theory whatever the dominant frequency of the source, which suggests that the additional application of the IFZ concept is necessary to obtain the reflected P-wave amplitude. Nevertheless, as the ASA combined with the IFZ has been used only for evaluating the contribution of the reflected wavefield at the receiver, its predictions fail when the interference between the reflected wave and the head wave becomes predominant.