Through the study of microseismic focal mechanisms, information such as fracture orientation, event magnitude, and in situ stress status can be quantitatively obtained, thus providing a reliable basis for unconventional oil and gas exploration. Most source inversion methods assume that the medium is isotropic. However, hydraulic fracturing is usually conducted in sedimentary rocks, which often exhibit strong anisotropy. Neglecting this anisotropy may cause errors in focal mechanism inversion results. We have developed a microseismic focal mechanism inversion method that considers velocity anisotropy in a vertically transverse isotropic medium. To generate synthetic data, we adopt the moment-tensor model to represent microearthquake sources. We use a staggered-grid finite-difference method to calculate synthetic seismograms in anisotropic media. We perform seismic moment-tensor (SMT) inversion with only P-waves by matching the synthetic and observed waveforms. The synthetic and field data sets are used to test the inversion method. For the field data set, we investigate the inversion stability using randomly selected partial data sets in the calculation. We pay special attention to analyze the sensitivity of the inversion. We test and evaluate the impact of noise in the data and errors in the model parameters ($V_{\mathrm{P}0}$, $\epsilon$, and $\delta$) on the SMT inversion using synthetic data sets. The results indicate that, for a surface acquisition system, our method can tolerate moderate noise in the data and deviations in the anisotropy parameters can cause errors in the SMT inversion, especially for dip-slip events and the inverted percentages of non-double-couple (DC) components. According to our study, including anisotropy in the model is important to obtain reliable non-DC components of moment tensors for hydraulic fracturing-induced microearthquakes.

中文翻译：

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垂直横观各向同性介质中的微地震矩张量反演及敏感性分析

通过对微震震源机制的研究，可以定量获得裂缝方向，事件幅度和原地应力状态等信息，为非常规油气勘探提供了可靠的依据。大多数源反演方法都假定介质是各向同性的。但是，水力压裂通常在沉积岩中进行，沉积岩通常表现出强烈的各向异性。忽略这种各向异性可能会导致震源机制反演结果出错。我们已经开发了一种微地震震源机制反演方法，该方法考虑了垂直横向各向同性介质中的速度各向异性。为了生成综合数据，我们采用矩张量模型来表示微震源。我们使用交错网格有限差分法来计算各向异性介质中的合成地震图。通过匹配合成波形和观察到的波形，我们仅用P波进行地震矩张量（SMT）反演。综合和现场数据集用于测试反演方法。对于现场数据集，我们在计算中使用随机选择的部分数据集来研究反演稳定性。我们特别注意分析反演的敏感性。我们测试并评估数据中噪声和模型参数误差的影响（$V_{\mathrm{P}0}$， $\epsilon$和 $\delta$）使用合成数据集进行SMT反演。结果表明，对于表面采集系统，我们的方法可以容忍数据中的适度噪声，并且各向异性参数的偏差会导致SMT反演中的误差，特别是对于倾滑事件和非双偶数的反演百分比而言（DC）组件。根据我们的研究，在模型中包括各向异性对于获得水力压裂引起的微地震的力矩张量的可靠非DC分量很重要。