Seismic attenuation of double‐porosity media derived from numerical relaxation experiments

Abstract

Heterogeneous porous media such as hydrocarbon reservoir rocks are effectively described as anisotropic viscoelastic solids. They show characteristic velocity dispersion and attenuation of seismic waves within a broad frequency band, and an explanation for this observation is the mechanism of waveinduced pore fluid flow. Layered porous media show effective VTI behaviour and highand low-frequency limits of the stiffness tensor are known. In addition to that, various theoretical models quantify dispersion and attenuation of normal incident P-waves. Similar models of shear wave attenuation are not known, nor do general theories exist to predict wave-induced fluid flow effects in media with a more complex distribution medium heterogeneities. In this work we show that by using finite-element relaxation experiments, the total frequencydependent complex stiffness tensor can be derived. From the stiffness tensor, velocity dispersion and attenuation are derived. We apply our approach to the case of layered media and to that of an ellipsoidal poroelastic inclusion, but in principle it is applicable for any internal medium geometry. Our results confirm that in layered media, P-waves an SV -waves show comparable amounts of attenuation, while horizontally polarised SH-waves propagate dispersion-free. In the case of a 3-D ellipsoidal inclusion, all three wave modes show significant attenuation, and the characteristic frequency-dependence of the effect is governed by the spatio-temporal scale of the pore pressure relaxation.