Amplitude variation with offset/angle of incidence inversion has been playing a key role in hydrocarbon detection and reservoir characterization. Traditionally, it has been limited to elastic even viscoelastic cases. We investigated the reflectivity in diffusive-viscous media. Our study demonstrated that the magnitude of the reflection coefficients in such a media is not only related to the incident angle and the parameters of the medium but also strongly depends on the frequency. We first demonstrated the validity of diffusive-viscous wave equation, proposed empirically, based on the continuum equations and basic laws of physics. Then, we investigated the frequency-dependent phase velocity and the quality factor [Formula: see text], whose impacts typically increase toward high frequencies, and we studied the magnitude and phase of the reflection coefficient at an interface between two diffusive-viscous media. A general equation of the reflection coefficients was also obtained for a stack of arbitrary number of plane layers in such media. Finally, we computed synthetic vertical seismic profile seismograms using the reflectivity method for a model consisting of five fluid-saturated layers to demonstrate that the diffusive and viscous terms in diffusive-viscous theory have a big impact on the synthetic seismograms, and stronger attenuation is observed in the layer having larger attenuation parameters.
Frequency-dependent reflections in elastic diffusive-viscous media