Abstract
We study the wave anelasticity (attenuation and velocity dispersion) of a periodic set of three flat porous layers saturated by two immiscible fluids. The fluids are very dissimilar in properties, namely gas, oil, and water, and, at most, three layers are required to study the problem from a general point of view. The sequence behaves as viscoelastic and transversely isotropic (VTI) at wavelengths much longer than the spatial period. Wave propagation causes fluid flow and slow P modes, inducing anelasticity. The fluids are characterized by capillary forces and relative permeabilities, which allow for the existence of two slow modes and the presence of dissipation, respectively. The methodology to study the physics is based on a finite-element uspcaling approach to compute the complex and frequency-dependent stiffnesses of the effective VTI medium. The results of the experiments indicate that there is higher dissipation and anisotropy compared to the widely used model based on an effective fluid that ignores the effects of surface tension (capillarity) and viscous flow interference between the two fluid phases.