Some Reflections on Reflectors and Wave Amplitudes

The paper describes the reflector from a seismic viewpoint, and investigates the imprint of such a description on the wave reflection process. More specifically, the spatial region in the vicinity of the interface which actually affects the reflected wavefield is determined using the Fresnel volume and the Interface Fresnel zone (IFZ) concepts. This region is represented by a volume of integration of properties above and below the interface whose maximum lateral extent corresponds to the lateral extent of the IFZ, and whose maximum vertical extent corresponds to a thickness we evaluate accurately and which can be greater than the seismic wavelengths. Considering this description of a reflector, we then calculate 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 two elastic media. As the problem under consideration can be viewed as a problem of diffraction by the IFZ which is the physically relevant part of the interface which actually affects the reflected wavefield in this simple case, we then apply the Angular Spectrum Approach (ASA) combined with the IFZ concept to get the 3D analytical solution. The variation in the reflected P-wave amplitude evaluated with the ASA, as a function of the incidence angle, is finally compared with the plane-wave reflection coefficient, and with the exact solution obtained with the 3D code OASES. Below but close to the critical angle, the prediction of our approximation better fits the exact solution than the plane-wave reflection coefficient, which emphasizes the importance of accounting for the IFZ in amplitude calculations even for a very simple elastic model.