SUMMARY The microseismic events can often be characterized by a complex non-double couple source mechanism. Recent laboratory studies recording the acoustic emission during rock deformation help connecting the components of the seismic moment tensor with the failure process. In this complementary contribution, we offer a mathematical model which can further clarify these connections. We derive the seismic moment tensor based on classical continuum mechanics and plasticity theory. The moment tensor density can be represented by the product of elastic stiffness tensor and the plastic strain tensor. This representation of seismic sources has several useful properties: (i) it accounts for incipient faulting as a microseismicity source mechanism, (ii) it does not require a pre-defined fracture geometry, (iii) it accounts for both shear and volumetric source mechanisms, (iv) it is valid for general heterogeneous and anisotropic rocks and (v) it is consistent with elasto-plastic geomechanical simulators. We illustrate the new approach using 2-D numerical examples of seismicity associated with cylindrical openings, analogous to wellbore, tunnel or fluid-rich conduit and provide a simple analytic expression of the moment density tensor. We compare our simulation results with previously published data from laboratory and field experiments. We consider four special cases corresponding to ‘dry’ elastically homogeneous and elastically heterogeneous isotropic rocks, ‘dry’ transversely isotropic rocks and ‘wet’ isotropic rocks. The model highlights theoretical links between stress state, geomechanical parameters and conventional representations of the moment tensor such as Hudson source type parameters.

中文翻译：

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微震和声发射的弹塑性源模型

总结 微震事件通常可以通过复杂的非双偶震源机制来表征。最近的实验室研究记录了岩石变形过程中的声发射，有助于将地震矩张量的分量与破坏过程联系起来。在这个互补的贡献中，我们提供了一个数学模型，可以进一步阐明这些联系。我们根据经典连续介质力学和塑性理论推导出地震矩张量。力矩张量密度可以用弹性刚度张量和塑性应变张量的乘积来表示。地震源的这种表示具有几个有用的特性：（i）它将初期断层解释为微震源机制，（ii）它不需要预定义的裂缝几何形状，(iii) 它考虑了剪切源机制和体积源机制，(iv) 它适用于一般的非均质和各向异性岩石，并且 (v) 它与弹塑性地质力学模拟器一致。我们使用与圆柱形开口相关的地震活动的二维数值示例来说明新方法，类似于井筒、隧道或富含流体的管道，并提供矩密度张量的简单解析表达式。我们将我们的模拟结果与之前发布的实验室和现场实验数据进行比较。我们考虑四种特殊情况，分别对应于“干”弹性均质和弹性非均质各向同性岩石、“干”横向各向同性岩石和“湿”各向同性岩石。该模型突出了应力状态之间的理论联系，