In underground mines, episodes of sudden inelastic deformation in the rockmass are often induced by mining and are therefore localized near the excavations. The seismic radiation associated with such deformation can be described by a point seismic source using a volume integral of the stress‐free strain (or incremental plastic strain)—expression (1) in the Theory section. This conventional description is valid if seismic waveforms are modeled or inverted using the elastodynamic Green’s function, which takes the presence of nearby excavation(s) into account. If the adopted Green’s function does not model these excavations, then the conventional expressions for a point source need to be adjusted by adding a term that depends on the displacement at the surface of the excavations (equations 2). Alternatively, a Kirchhoff‐type representation can be used, in which the parameters of the point source are expressed using increments of displacement and traction over the surface covering both the volume of inelastic deformation and nearby excavation(s) (equations 3). Numerical simulations demonstrate that the suggested expressions provide a very different result to the conventional expressions for the case of inelastic deformation in a volume adjacent to an excavation. The utilization of the suggested expressions results in a change in the type of mechanisms from explosive to implosive and significantly affects other characteristics of the modeled sources (moment magnitude and orientation of principal axes). Typically, seismic waveforms recorded by monitoring systems in underground mines are processed using an elastodynamic Green’s function that does not take medium‐sized excavations (e.g., tunnels and stopes) into account. Therefore, the results of such processing need to be interpreted using the suggested expressions: adjusted conventional (equations 2) or Kirchhoff‐type (equations 3).

中文翻译：

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地下矿山震源描述：理论

在地下矿山中，岩体中突然的非弹性变形的发生通常是由采矿引起的，因此，局部分布在开挖附近。与这种变形相关的地震辐射可以通过点震源使用“理论”部分中的无应力应变（或增量塑性应变）的体积积分表达式（1）来描述。如果使用弹性动力格林函数对地震波形进行建模或反演，则该常规说明是有效的，该函数考虑了附近挖掘的存在。如果采用的格林函数未对这些基坑进行建模，则需要通过添加一个依赖于基坑表面位移的项来调整点源的常规表达式（方程式2）。或者，可以使用Kirchhoff型表示法，其中点源的参数使用覆盖非弹性变形量和附近开挖量的方程（等式3）在地面上的位移和牵引力增量表示。数值模拟表明，对于与基坑相邻的空间中发生非弹性变形的情况，建议的表达式与传统表达式提供了截然不同的结果。建议表达式的使用导致爆炸类型到爆炸性机制的类型发生变化，并显着影响建模源的其他特征（矩量级和主轴方向）。通常，地下矿井中监控系统记录的地震波形是使用弹性动力学格林函数处理的，该函数不考虑中型开挖（例如隧道和采场）。因此，需要使用建议的表达式来解释此类处理的结果：调整后的常规表达式（公式2）或Kirchhoff型表达式（公式3）。