Effect of fluid on Thomsen’s parameters in weakly anisotropic media

Abstract

Predicting seismic velocities in fluid-saturated rocks is commonly done using Gassmann equations. For anisotropic media, these equations are expressed in terms of stiffness or compliance tensors. To gain a more intuitive understanding on the impact of fluid on anisotropy, we express Gassmann equations in terms of Thomsen’s anisotropy parameters. Using the derived expressions for anisotropy parameters of fluid-saturated media, we analyse the effect of fluid on two anisotropy patterns, the one caused by aligned fractures embedded in an isotropic porous background and the stress-induced anisotropy pattern. By deriving an approximation of the anellipticity parameter ƞ, we show that if the dry medium is elliptical, the saturated medium is also elliptical but only if the porosity is sufficiently large. This result can provide a way of differentiating between stress- and fracture-induced anisotropy.