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 ῶ
plays a crucial role in governing wave transport. 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, 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 ῶ 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.