Summary We formulate and implement a spectral element method (SEM) to simulate elastic wave propagation in an arbitrary anisotropic background with discrete anisotropic fractures. The approach uses a general linear-slip condition to incorporate the anisotropic fractures into SEM, which allows for discontinuities of displacement fields across the surfaces of fractures. We treat the extremely thin fractures as geometry interfaces instead of meshing them, thus reducing computational cost. The results obtained by the proposed method agree well with the reference solutions for both a single horizontal anisotropic planar fracture and a tilted fracture. Based on the numerical simulation, we analyze the effects of anisotropic fracture on the wavefields. We find that due to the presence of off-diagonal element in the anisotropic fracture stiffness matrix, the wavefields generated by the anisotropic fracture are different from the isotropic fracture. The method can also simulate the wavefields in the anisotropic background including the multiple fractures or the intersecting fractures.

中文翻译：

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具有离散各向异性裂缝的各向异性背景中弹性波传播的谱元建模

总结 我们制定并实施了谱元法 (SEM) 来模拟具有离散各向异性裂缝的任意各向异性背景中的弹性波传播。该方法使用一般线性滑移条件将各向异性裂缝纳入 SEM，这允许裂缝表面的位移场不连续。我们将极薄的裂缝视为几何界面而不是对其进行网格划分，从而降低计算成本。所提出的方法得到的结果与单个水平各向异性平面裂缝和倾斜裂缝的参考解决方案很好地吻合。在数值模拟的基础上，分析了各向异性裂缝对波场的影响。我们发现，由于各向异性断裂刚度矩阵中存在非对角元素，各向异性裂缝产生的波场不同于各向同性裂缝。该方法还可以模拟多向裂缝或交叉裂缝等各向异性背景下的波场。