LAUSR

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.