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

Two Types of Multiple Solutions for Microseismic Source Location Based on Arrival-Time-Difference Approach

The arrival-time-difference approach is the dominant source location approach used in the microseismic source location area. Multiple solutions problem is one of the major concerns in microseismic source location, which is closely related to the microseismic network. This paper categorizes the multiple solutions into two types based on the origin times when using the arrival-time-difference approach. Type I multiple solutions are those which have the same origin time; type II multiple solutions are those with different origin times. The sufficient and necessary conditions to produce type I multiple solutions are that all sensors are located in a straight line for two-dimensional cases and on a plane for three-dimensional cases. The sufficient and necessary conditions to produce type II multiple solutions are that all sensors are located on a hyperbola for two-dimensional cases and on a hyperboloid for three-dimensional cases. Furthermore, the proofs indicate that type I multiple solutions are preventable, while a microseismic network consisting of the minimum number of sensors can never be free of type II multiple solutions. It means, besides the minimum number of sensors, at least one more sensor which is not on this hyperbola or hyperboloid is needed to uniquely determine a source. The results from field tests and applications indicate that when the sensors of a network lie on a hyperbola, the type II multiple solutions may not be the necessary outcome under the influence of errors in real data. However, the accuracy of the microseismic source location is affected significantly by this kind of networks. The results also show that not only the multiple solutions problem can be avoided effectively, but more importantly, the accuracy of the source location will be greatly improved by the optimization of network based on the characteristics of the microseismic network and field conditions. © 2014 Springer Science+Business Media Dordrecht

A Nonlinear Microseismic Source Location Method Based on Simplex Method and Its Residual Analysis

Source location is one of the most valuable features of the microseismic technique due to its ability to delineate the unstable areas. In this paper, the precise formulas of the station residual and event residual are derived for the L1 norm statistical standard and the L2 norm statistical standard based on the residual analysis. Then, the error space for microseismic source location is proposed and analyzed. Based on the above research, a nonlinear microseismic source location method using the Simplex method is developed. This new method can search the microseismic source directly in the error space through four deformations of the simplex figures, and it is able to make use of both P-wave and S-wave velocities. Finally, the performance of the Simplex microseismic source location method is tested and verified by laboratory experiments. Test results show that the Simplex microseismic source location method can improve the accuracy and stability of the source location greatly when P-wave and S-wave velocities are involved simultaneously and correctly. The results also demonstrate that the L1 norm statistical standard always provides more accurate and reliable solutions than the L2 norm statistical standard when there are some major but isolated errors in the input data. However, none of the optimization methods are able to function when the errors in the input data are systematic and extreme, which indicates that an early detection and correction of these errors is of primary importance for microseismic source location