Research on the non-double-couple (NDC) components in an earthquake is important for characterizing true source processes. The moment-tensor (MT) source model is commonly used to study NDC earthquakes. However, MT inversions are still challenging when earthquakes have small magnitudes, especially microearthquakes. The general-dislocation (GD) model specifies the focal mechanism as a shear-tensile slip on a fault plane; thus, GD inversion is better constrained than MT inversion. We focus on GD model-based waveform forward modeling and its application to microseismic source inversions. We expand the generalized reflection-transmission matrix method to synthesize waveforms based on the GD model and fully describe a GD source with five parameters: the scalar seismic moment (which defines the magnitude) and the strike, dip, rake, and slope angles (which define the fault geometry). We compare the GD, MT, and double-couple models and introduce the differences in their characterization and wave synthesis theories. We have developed a GD model-based microseismic focal mechanism inversion method that requires calculating only four angles under hybrid constraints. Two sets of solutions correspond to the same seismograms in a GD model-based inversion. These two solutions have the same scalar seismic moment and slope angle but different strike, dip, and rake angles, and we have derived formulas for mapping from one solution to the other. Synthetic and field surface microseismic data sets are used to test our GD model-based modeling and inversion methods. According to our study, the GD model is effective in microseismic focal mechanism inversion. By developing specific wave synthesis and inversion methods for the GD model, we offer a novel perspective to study this model and the NDC mechanisms for hydraulic fracturing-induced microearthquakes.

中文翻译：

---

一般位错源模型及其在微震震源机制反演中的应用

研究地震中的非双偶 (NDC) 分量对于表征真实震源过程非常重要。矩张量 (MT) 震源模型通常用于研究 NDC 地震。然而，当地震规模较小时，尤其是微地震，MT 反演仍然具有挑战性。广义位错 (GD) 模型将震源机制指定为断层面上的剪切-拉伸滑动；因此，GD 反演比 MT 反演受到更好的约束。我们专注于基于 GD 模型的波形正演建模及其在微震震源反演中的应用。我们扩展了广义反射-透射矩阵方法以基于 GD 模型合成波形，并使用五个参数完整描述 GD 源：标量地震矩（定义震级）和走向、倾角、倾斜度、和倾斜角（定义断层几何形状）。我们比较了 GD、MT 和双偶模型，并介绍了它们在表征和波浪合成理论方面的差异。我们开发了一种基于 GD 模型的微震震源机制反演方法，该方法只需要在混合约束下计算四个角度。在基于 GD 模型的反演中，两组解对应于相同的地震图。这两个解具有相同的标量地震矩和斜角，但走向、倾角和前角不同，我们推导出了从一个解到另一个解的映射公式。合成和现场表面微震数据集用于测试我们基于 GD 模型的建模和反演方法。根据我们的研究，GD模型在微震震源机制反演中是有效的。