The sensor network layout is a key factor affecting the accuracy and stability of the microseismic/acoustic source (MS/AE) location. Based on the arrival-time-difference principle, the hyperbolic/hyperboloidal governing equations for the source location are derived. The nonuniformity geometrical characteristics of hyperbolic/hyperboloidal field for the source location are obtained. The sensor network does not induce any location errors; it only affects the source location accuracy by amplifying the existing errors in the input data during the source location process. Also, this amplication effect of the input data errors is characterized by nonuniformity because of the nonuniformity of the hyperbolic/hyperboloidal field. Furthermore, two basic effects, the geometrical spreading and the directional control, of the sensor network are investigated, and the three-dimensional space quantitative models of these two effects are established, respectively. The influence of the wave velocity error and arrival time error on the source location accuracy is analytically compared, and the propagation characteristics of these two types of errors during the source location process are revealed. The concepts of critical arrival-time difference and critical hyperbola/hyperboloid are proposed. Based on these two concepts, the monitoring area can be divided into two regions where the source location accuracy is controlled by the velocity error and the arrival time error, respectively. The concept of direction angle of paired sensors is proposed, and the relationship between the source location and the layout of four typical paired sensors is studied. Finally, the principles of sensor network optimization are determined.

中文翻译：

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传感器网络对MS / AE源位置的影响机理与优化

传感器网络布局是影响微地震/声源（MS / AE）位置的准确性和稳定性的关键因素。基于到达时间差原理，推导了源位置的双曲/双曲面控制方程。获得了双曲线/双曲面场对于源位置的非均匀几何特性。传感器网络不会引起任何位置错误；它只会通过在源定位过程中放大输入数据中的现有错误来影响源定位精度。而且，由于双曲/双曲面场的不均匀性，所以输入数据错误的这种放大效应的特征在于不均匀性。此外，还研究了传感器网络的两个基本影响，即几何扩展和方向控制，建立了这两种效应的三维空间定量模型。分析了波速误差和到达时间误差对震源定位精度的影响，揭示了这两种类型的误差在震源定位过程中的传播特征。提出了临界到达时间差和临界双曲线/双曲面的概念。基于这两个概念，可以将监视区域划分为两个区域，其中源位置精度分别由速度误差和到达时间误差控制。提出了成对传感器方向角的概念，研究了四种典型成对传感器的源位置与布局之间的关系。最后，