Abstract
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.
Highlights
It is generally accepted today that rock emits seismic signals when it is stressed and/or deformed. e microseismic (MS)/ acoustic emission (AE) technique refers to a geophysical monitoring technology that studies the internal structure and stability, fracture mechanism, and morphology of rock mass by using the seismic signals
A high accuracy source location is the first step in studies of the MS/AE technique. e factors that influence the source location accuracy may be divided into two types: input data errors and systematic bias [4, 5]. e source location accuracy is definitely affected if there are errors in the input data such as the velocity model and the arrival time. e influence of the systematic error is mainly caused by the sensor network layout
It is generally known that the AE/MS source location accuracy is mainly affected by the sensors coordinates and network layouts, wave velocity model, arrival time, and source location methods
Summary
It is generally accepted today that rock emits seismic signals when it is stressed and/or deformed. e microseismic (MS)/ acoustic emission (AE) technique refers to a geophysical monitoring technology that studies the internal structure and stability, fracture mechanism, and morphology of rock mass by using the seismic signals. Erefore, based on the space geometry theory and arrival-timedifference principle, we first demonstrated that why and how the sensor network has such an important influence on the MS/AE source location. Based on the source location-governing equation, the source is always located somewhere on one of the hyperbolas whose value of the real axis is equal to 2aij v|tj − ti| It means that the shape and position of a hyperbola that contains the source is affected by the parameters of arrival time and wave velocity. The hyperbolic field associated with sensor network is nonuniform, and the density of hyperbolas varies from point to point in the hyperbolic field It makes the source location accuracy heavily dependent on the relative position of the true source and the sensor network layout. The effect of this amplification is not uniform, and this nonuniform amplification effect is due to the nonuniformity of the hyperbolic field. e results indicate that the location error is highly dependent on the position of the true source relative to the sensor network layout
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