An energy-based approach to estimate seismic attenuation due to wave-induced fluid flow in heterogeneous poroelastic media

Abstract

Wave-induced fluid flow (WIFF) due to the presence of mesoscopic heterogeneities is considered as one of the main seismic attenuation mechanisms in the shallower parts of the Earth's crust. For this reason, several models have been developed to quantify seismic attenuation in the presence of heterogeneities of varying complexity, ranging from periodically layered media to rocks containing fractures and highly irregular distributions of fluid patches. Most of these models are based on Biot's theory of poroelasticity and make use of the assumption that the upscaled counterpart of a heterogeneous poroelastic medium can be represented by a homogeneous viscoelastic solid. Under this dynamic-equivalent viscoelastic medium (DEVM) assumption, attenuation is quantified in terms of the ratio of the imaginary and real parts of a frequency-dependent, complex-valued viscoelastic modulus. Laboratory measurements on fluid-saturated rock samples also rely on this DEVM assumption when inferring attenuation from the phase shift between the applied stress and the resulting strain. However, whether it is correct to use an effective viscoelastic medium to represent the attenuation arising from WIFF at mesoscopic scales in heterogeneous poroelastic media remains largely unexplored. In this work, we present an alternative approach to estimate seismic attenuation due to WIFF. It is fully rooted in the framework of poroelasticity and is based on the quantification of the dissipated power and stored strain energy resulting from numerical oscillatory relaxation tests. We employ this methodology to compare different definitions of the inverse quality factor for a set of pertinent scenarios, including patchy saturation and fractured rocks. This numerical analysis allows us to verify the correctness of the DEVM assumption in the presence of different kinds of heterogeneities. The proposed methodology has the key advantage of providing the local contributions of energy dissipation to the overall seismic attenuation, information that is not available when attenuation is retrieved from methods based on the DEVM assumption. Using the local attenuation contributions we provide further insights into the WIFF mechanism for randomly distributed fluid patches and explore the accumulation of energy dissipation in the vicinity of fractures.