Some reflections on reflectors and wave amplitudes
Résumé
The paper describes the refl ector 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 aff ects the refl ected 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 diff raction by the IFZ which is the physically relevant part of the interface which actually aff ects the refl ected wavefi eld 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 refl ected P-wave amplitude evaluated with the ASA, as a function of the incidence angle, is fi nally compared with the plane-wave refl ection coeffi cient, and with the exact solution obtained with the 3D code OASES. Below but close to the critical angle, the prediction of our approximation better fi ts the exact solution than the plane-wave refl ection coefficient, which emphasizes the importance of accounting for the IFZ in amplitude calculations even for a very simple elastic model.
Origine : Fichiers éditeurs autorisés sur une archive ouverte