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Scattering Attenuation of Elastic Waves in Fractured Media
  • Qinghua Lei,
  • Didier Sornette
Qinghua Lei
ETH Zürich

Corresponding Author:[email protected]

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Didier Sornette
ETH Zürich
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Abstract

We present numerical simulations of elastic wave propagation, scattering and attenuation in two-dimensional fractured media. Natural fracture systems following a power law length scaling are modeled by the discrete fracture network approach for the geometrical representation of fracture distributions and the displacement discontinuity method for the mechanical computation of fracture-wave interactions. The model is validated against analytical solutions for wave reflection, transmission and scattering by single fractures, after which we apply it to solve the spatiotemporal wavefield evolution in various synthetic fracture networks. We find that the dimensionless angular frequency plays a crucial role in governing wave transport. When is smaller than the critical frequency c (≈ 5), waves are in the extended mode, either propagating (for small ) or diffusing by multiple scattering (for intermediate ); as exceeds c, the wave energy becomes 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 obeying a two-branch power law dependence, showing significant frequency dependence when ῶ < ῶc and almost frequency independence when ῶ > ῶc. In addition, 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 wave behavior such that strong attenuation occurs in well-connected fracture systems.