Amplitude and phase changes for reflected and transmitted waves from a curved interface in anisotropic media

Abstract

It is well known that seismic data that have been recorded in complex geological environments must be compensated for geometrical spreading before AVO/AVA (amplitude-versus-offset/amplitude-versus-angle) analysis, in order to avoid erroneous imaging interpretation. By investigating analytically both the effect of the geometrical spreading and the effect of the reflector curvature on amplitude and phase changes for reflected and transmitted waves between anisotropic media, using ray theory, we show that these data should be compensated for interface effects as well. In order to gain insight more specifically in the focusing effect of the interface, the special case of homogeneous isotropic media separated by a curved interface of syncline type is discussed and compared to the case of a plane interface. 3-D numerical simulations of wave reflection from curved interfaces using a spectral element method validate our analytical derivations. In particular, numerical seismograms obtained at a vertical receiver array highlight that the effect of interface curvature on the reflected events is much more pronounced in a restricted area associated with the existence of caustics, which is consistent with our analytical predictions. Moreover, comparisons between the numerical and the analytical results confirm the fact that using plane-wave reflection coefficients without correction for the interface effect may lead to wrong interpretation of AVA/AVO analysis.