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.

中文翻译：

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二维断裂介质中弹性波的传输和定位：散射衰减的后果

我们提出了二维断裂介质中弹性波传输的数值模拟。天然裂缝系统遵循幂律长度标度，由离散裂缝网络方法建模，用于几何表示裂缝分布，位移不连续方法用于机械计算裂缝波相互作用。该模型针对单个裂缝的波反射、传输和散射的解析解进行了验证，然后应用于求解合成裂缝网络中的波场演化。我们发现无量纲角频率ῶ  =  ωZ / κ在控制波传输中起着至关重要的作用，其中ω、Z和κ分别是角频率、地震阻抗和断裂刚度。当ῶ小于临界频率ῶ _c (≈5) 时，波处于扩展模式，要么传播（对于小ῶ），要么通过多次散射扩散（对于中间ῶ）；作为ῶ超过ῶ _Ç，波被截留，在进入任一安德森本地化制度（KL *≈1）中公连接断裂系统或弱本地化制度（KL *> 1）在难溶性连接断裂系统，其中ķ是入射波数和l* 是平均自由程长度。因此，逆质量因子Q ^-1与ῶ遵循两分支幂律相关性成比例，当ῶ < ῶ _c时显示出显着的频率依赖性，而当ῶ  >  ῶ _c时几乎与频率无关。此外，当ῶ  < ῶ _{c 时}，波场表现出对裂缝网络几何形状的弱依赖性，而当ῶ  >  ῶ _{c 时}，裂缝网络连通性对波场有重要影响，使得在连接良好的裂缝系统中发生强衰减。