The study of the influence of rock fabric and porefluid distribution on the seismic wavefield is important for the prediction and detection of reservoir properties such as lithology and fluid saturation. Wave-induced local fluid flow (WILFF), which is affected by local heterogeneities of the pore structure and fluid saturation, is believed to be the main mechanism to explain the measured attenuation levels at different frequency bands. These two types of heterogeneity affect seismic waves as a combined WILFF process. In this work, we consider a double porosity system, each part with a different compressibility and patchy saturation, and derive the wave equations from Hamilton’s principle. A plane-wave analysis yields the properties of the classical P-wave and those of the four slow waves. The examples show that patchy fluid saturation dominates the peak frequency of the relaxation mechanism. The relation between seismic anelasticity (velocity dispersion and attenuation) and saturation depends on frequency
and on the geometrical features of the two heterogeneities. The proposed theory constitutes the comprehensive description for wave propagation process through reservoirs rocks of shallow Earth and porous media in general, to estimate fluid content and distribution.