Transport and Localization of Elastic Waves in Two‐Dimensional Fractured Media: Consequences on Scattering Attenuation

Abstract

AbstractWe present numerical simulations of elastic wave transport in two‐dimensional fractured media. Natural fracture systems, following a power‐law length scaling, are modeled by the discrete fracture network approach for geometrically representing fracture distributions and the displacement discontinuity method for mechanically computing fracture‐wave interactions. The model is validated against analytical solutions for wave reflection, transmission, and scattering by single fractures, and then applied to solve the wavefield evolution in synthetic fracture networks. We find that the dimensionless angular frequency ῶ = ωZ/κ plays a crucial role in governing wave transport, where ω, Z, and κ are the angular frequency, seismic impedance, and fracture stiffness, respectively. When ῶ is smaller than the critical frequency ῶc (≈5), waves are in the extended mode, either propagating (for small ῶ) or diffusing by multiple scattering (for intermediate ῶ); as ῶ exceeds ῶc, waves become trapped, entering either the Anderson localization regime (kl* ≈ 1) in well‐connected fracture systems or the weak localization regime (kl* > 1) in poorly‐connected fracture systems, where k is the incident wavenumber and l* is the mean free path length. Consequently, the inverse quality factor Q−1 scales with ῶ obeying a two‐branch power‐law dependence, showing significant frequency dependence when ῶ < ῶc and almost frequency independence when ῶ > ῶc. Furthermore, when ῶ < ῶc, the wavefield exhibits a weak dependence on fracture network geometry, whereas when ῶ > ῶc, the fracture network connectivity has an important impact on the wavefield such that strong attenuation occurs in well‐connected fracture systems.