The Influence Mechanism and Optimization of the Sensor Network on the MS/AE Source Location

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.