Effective poroelastic model for one-dimensional wave propagation

Abstract

An effective poroelastic model is proposed that describes seismic attenuation and dispersion in periodically layeredmedia. In this model, the layers represent mesoscopic-scale heterogeneities (larger than the grain and pore sizes but smaller than the wavelength) that can occur both in fluid and solid properties. The proposed effectivemedium is poroelastic, contrary to previously introduced models that lead to effective viscoelastic media. The novelty lies in the application of the pressure continuity boundary conditions instead of no-flow conditions at the outer edges of the elementary cell. The approach results in effective Biot elastic moduli and effective porosity that can be used to obtain responses of heterogeneous media in a computationally fast manner. The model is validated by the exact solution obtained with the use of Floquet’s theory. Predictions of the new effective poroelastic model are more accurate than the predictions of the corresponding effective viscoelastic model when the Biot critical frequency is of the same order as the frequency of excitation, and for materials with weak frame. This is the case for media such as weak sandstones, weakly consolidated and unconsolidated sandy sediments. The reason for the improved accuracy for materials with low Biot critical frequency is the inclusion of the Biot global flow mechanism which is not accounted for in the effective viscoelastic media. At frequencies significantly below the Biot critical frequency and for wellconsolidated porous rocks, the predictions of the new model are in agreement with previous solutions.