Effects of vector attenuation on AVO of offshore reflections

Waves transmitted at the ocean bottom have the characteristic that, for any incidence angle, the attenuation vector is perpendicular to the ocean-bottom interface (assuming water a lossless medium). Such waves are called inhomogeneous; in this case, the inhomogeneity angle coincides with the propagation angle. The vector character of this transmitted pulse affects the amplitude variation with offset (AVO) response of deeper reflectors, The analysis of the reflection coefficient is performed for a shale (the ocean-bottom sediment) overlying a chalk, assuming no loss in the sea floor and loss with an incident homogeneous wave and an incident inhomogeneous wave. Beyond the elastic critical angle the differences are important, mainly for the incident homogeneous wave. These differences depend not only on the properties of the media but also on the inhomogeneity of the wave.