We have used the spectral-element method (SEM) to simulate 3D acoustic wavefields in the fluid-filled borehole embedded in fractured media. The fractures are characterized by the linear-slip model (LSM), which is incorporated into the surface integral of the SEM weak form, avoiding meshing individual fractures, thus reducing the degrees of freedom of the fractures compared with meshing each fracture directly. For the fracture-free case, we validate SEM through the comparison with the real-axis integration method for monopole and dipole sources. For the case with a fracture, we compare the SEM-LSM solutions with the reference numerical solutions of a thin-layer model using the finite-difference method. Good agreement is achieved between the results from our method and the reference finite-difference solutions. We find that the acoustic wavefields excited by a dipole source are more sensitive to the fractures than those by a monopole source. To show the ability of the approach to handle complex problems, we simulate the cases with a tilted fracture and multiple fractures. Based on the simulated results, we investigate the influence of the fracture parameters (e.g., stiffness, tilt angle, azimuth, thickness, number, and spatial intervals of fractures) on the scattered wavefields. We find that the tilt angle has an obvious influence on the scattered waveforms and amplitudes. The results also demonstrate that the wavefields are quite sensitive to the number of fractures. The magnitudes of the horizontal components’ transmitted wavefields decrease linearly with the number of fractures. Through analyzing the synthetic data in the time and frequency domains, we discuss how to evaluate the properties of fractures intersected by a borehole.

中文翻译：

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谱元法与线性滑移模型相结合的裂缝介质井眼声波场模拟

我们使用谱元法 (SEM) 来模拟嵌入在裂缝介质中的充满流体的钻孔中的 3D 声波场。裂缝采用线性滑移模型（LSM）进行表征，将其纳入SEM弱形式的表面积分，避免对单个裂缝进行网格剖分，与直接对每个裂缝进行网格剖分相比，降低了裂缝的自由度。对于无裂缝的情况，我们通过与单极和偶极源的实轴积分方法的比较来验证 SEM。对于断裂的情况，我们使用有限差分方法将 SEM-LSM 解与薄层模型的参考数值解进行比较。我们的方法的结果与参考有限差分解决方案之间取得了良好的一致性。我们发现偶极源激发的声波场比单极源激发的声波场对裂缝更敏感。为了展示该方法处理复杂问题的能力，我们模拟了倾斜裂缝和多个裂缝的情况。基于模拟结果，我们研究了裂缝参数（例如，刚度、倾角、方位角、裂缝的厚度、数量和空间间隔）对散射波场的影响。我们发现倾斜角对散射波形和幅度有明显的影响。结果还表明，波场对裂缝的数量非常敏感。水平分量透射波场的大小随裂缝数量呈线性下降。通过分析时域和频域的合成数据，