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Transport and Localization of Elastic Waves in Two‐Dimensional Fractured Media: Consequences on Scattering Attenuation
Author(s) -
Lei Qinghua,
Sornette Didier
Publication year - 2021
Publication title -
journal of geophysical research: solid earth
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.983
H-Index - 232
eISSN - 2169-9356
pISSN - 2169-9313
DOI - 10.1029/2020jb021178
Subject(s) - attenuation , scattering , physics , fracture (geology) , discontinuity (linguistics) , wavenumber , mechanics , dimensionless quantity , computational physics , geometry , mathematical analysis , optics , geology , mathematics , geotechnical engineering
Abstract We 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 ῶ c (≈5), waves are in the extended mode, either propagating (for small ῶ ) or diffusing by multiple scattering (for intermediate ῶ ); as ῶ exceeds ῶ c , 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 < ῶ c and almost frequency independence when ῶ > ῶ c . Furthermore, when ῶ < ῶ c , the wavefield exhibits a weak dependence on fracture network geometry, whereas when ῶ > ῶ c , the fracture network connectivity has an important impact on the wavefield such that strong attenuation occurs in well‐connected fracture systems.