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 Q, 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.

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