An intelligent method is presented for locating a microseismic source based on the particle swarm optimization (PSO) concept. It eliminates microseismic source locating errors caused by the inaccurate velocity model of the earth medium. The method uses, as the target of PSO, a global minimum of the sum of squared discrepancies between differences of modeled arrival times and differences of measured arrival times. The discrepancies are calculated for all pairs of detectors of a seismic monitoring system. Then, the adaptive PSO algorithm is applied to locate the microseismic source and obtain optimal value of the P-wave velocity. The PSO algorithm adjusts inertia weight, accelerating constants, the maximum flight velocity of particles, and other parameters to avoid the PSO algorithm trapping by local optima during the solution process. The origin time of the microseismic event is estimated by minimizing the sum of squared discrepancies between the modeled arrival times and the measured arrival times. This sum is calculated using the obtained estimates of the microseismic source coordinates and P-wave velocity. The effectiveness of the PSO algorithm was verified through inversion of a theoretical model and two analyses of actual data from mine blasts in different locations. Compared with the classic least squares method (LSM), the PSO algorithm displays faster convergence and higher accuracy of microseismic source location. Moreover, there is no need to measure the microseismic wave velocity in advance: the PSO algorithm eliminates the adverse effects caused by error in the P-wave velocity when locating a microseismic source using traditional methods.
Microseismic monitoring technology can be used for effectively locating rock ruptures caused by rock burst, coal and gas outbursts, water inrush, and other coal mine disasters. In recent years it was also used in early warning systems (Li et al., 2016; Pastén et al., 2015; Jia et al., 2015). The spatial coordinates of monitoring stations and the arrival times of the first seismic wave are used to determine the coordinates of the microseismic source, origin time, and other attributes. The accuracy of microseismic source location has been an important research topic in microseismic monitoring technology for a long time.
Current microseismic source location methods mostly come from seismology. Now they are widely used in microseismic monitoring (Sun et al., 2016; Xue et al., 2015; Anikiev et al., 2014; Dong and Li, 2013). The earthquake source location method, based on time-difference principles, was proposed (Geiger, 1912). Based on this work, Lienert et al. (1986) developed an improved algorithm called HYPOCENTER. Since then, Nelson and Vidale (1990) presented the Quake3D method for 3-D velocity modeling. Lomax et al. (2000, 2001) worked out a nonlinear mode for locating global earthquakes in 3-D media and developed NonLinLoc software. Waldhauser and Ellsworth (2000) presented an earthquake location algorithm based on a double difference and developed HypoDD software. After occurrence of characteristics of the coal mine overburden, namely layers and abscission zones, Gong et al. (2012) proposed a microseismic detecting algorithm for the isotropic velocity model along the mine length; the algorithm decreases source location errors. Dong et al. (2017) proposed mathematical algorithms of microseismic source location where there is no need to predict velocity in advance. The algorithms overcome location errors caused by errors of velocity measurement inherent in traditional location methods. Lin et al. (2010) analyzed the characteristics of the linear location method and Geiger method and proposed a joint method to address the problem of low precision in estimation of source coordinates inherent in the linear location method. Feng et al. (2015) proposed stratified methods for microseismic source location based on particle swarm optimization to obtain correlations among the source position, origin time, and microseismic propagation speed for a non-unique solution.
In conclusion we note that the microseismic source location accuracy is influenced by many factors, such as the location method, the layout of the microseismic network, the velocity model, and the accuracy of the arrival-time measurement (Dong and Li, 2013). Among these, the key factor influencing the stability of the location algorithm and the location accuracy is precision of the velocity model (Prange et al., 2015; Li et al., 2014; Usher et al., 2013). In this paper, an adaptive particle swarm optimization algorithm is proposed for microseismic source location, which is based on average flying velocity of the particles. It uses, as the particle swarm optimization (PSO) target function, the least squares sum of measured arrival-time differences for all pairs of seismic sensors and uses the PSO algorithm to identify the source coordinates and microseismic wave velocity. Then, the origin time of the microseismic event is calculated according to the source location just determined and the wave velocity. Parameters of the PSO algorithm, such as the inertia weight, the acceleration constants, and the flight velocities of particles, are adaptively adjusted to avoid the algorithm failure caused by the improper selection of these parameters. Careful dynamic adjusting of the PSO parameters improves the robustness of the PSO algorithm, reduces the number of iterations, and improves estimation of the microseismic source coordinates and the seismic wave velocity.
Suppose that there are
According to time-difference location principles, the equation for
calculation of the source origin time
Source location based on the time-difference principle is a multi-extremum nonlinear problem. The most popular method is the classical method proposed by Geiger (1912) and various improvements thereafter. This kind of method is a solution method in the linear category. According to Taylor's formula, the nonlinear problem is transformed into a linear problem, and then different strategies are adopted to solve the linear equation system. In many cases, such as those of a second order or more, this will appear. Problems such as in appropriate omitting of terms, unreasonable selection of initial values, and trapping solutions into local minima will occur (Lee and Stewart, 1981). The particle swarm optimization (PSO) method is simple to operate and easy to use, and it is easy to get the global optimal solution for multi-extremum nonlinear problems. Therefore, the improved PSO method is introduced to solve the above problems.
The PSO is an evolutionary computation technique developed by Eberhart and
Kennedy (1995). It is an evolutionary algorithm similar to a simulated
annealing optimization algorithm for a problem of iterative improvement of a
candidate for the solution with regards to a given measure of quality. PSO is
an intelligent computational algorithm for analyzing the dynamic behavior of
a swarm of particles. In comparison with other similar algorithms, PSO has
such advantages as simple implementation, high accuracy, and fast
convergence. It has been successfully applied in the field of optimization
in recent years (Fong et al., 2016; Renaudineau et al., 2015; Sudheeret al.,
2014). The basic PSO principles are as follows: PSO randomly initializes a
set of particles in the solution space. Each particle flies through the
solution space with a certain speed by following the current optimum
particle, and the optimal solution is found through the search in successive
generations. In each generation, the particles update themselves by tracking
two types of extreme values: local optimums and global optimums. The first
extreme values are the optimal values for every particle itself in a set of
positions of this particle in the sequence of generations that already exist.
They are denoted as
Equation (2) concerns a nonlinear optimization problem with multiple
local extrema. The PSO algorithm was developed for solving such problems
and can be applied to search for the optimal value in four-dimensional
solution space composed of (
Flow chart for the microseismic source location algorithm based on adaptive particle swarm optimization.
The procedure for the source location parameter evaluation based on the PSO algorithm is described as follows.
The parameter values for the PSO algorithm are the keys to influencing the algorithm performance and efficiency. This paper proposes guiding principles for adjusting parameters of the PSO algorithm based on the practical approach for solving for the seismic source parameters.
Generally, optimization problems are divided into local and global problems.
The former consists of looking for the minimum in a finite area of function
value space; the latter is for finding the minimum in the whole area of function
value space. As early as 1998, Shi and Eberhart (1998) found that when the
value of inertia weight
In order to enhance the exploring competence of the PSO algorithm, the
population average velocity should be maintained to be rather high at the initial
stages of evolution, while in the late stage of evolution a smaller
population average velocity should be maintained in order to strengthen the
development capabilities of the algorithm. We assume that evolution of the
average particle flying velocity with changing number of generations
We will call
Set the initial inertia weight to
Substitution of
Gao and Liao noted that the position
However, if
The selection and analysis of the maximum flight velocity of particles
should proceed as follows: if
For the simulation, eight sensors comprising a microseismic localization
system are located on the eight vertices of a cube. Four microseismic
sources,
Coordinates of sensors and microseismic sources.
The locations of geophones and microseismic sources.
It is assumed that the velocity of wave propagation (
Suppose a microseismic velocity of
Travel time of a microseismic wave.
Comparison of the LSM and PSO algorithms.
Note: “–” means that the value cannot be obtained directly. The calculated value from the PSO is the average value obtained after running the PSO algorithm 20 times.
Based on the results shown in Table 3, the LSM algorithm has different
convergent results for different initial values. When the initial value is
far from the true value, the required calculation accuracy
Comparisons of the errors in the microseismic source location parameters obtained using the LSM and PSO algorithms are shown in Fig. 3, and the comparison of iterations between the two algorithms is shown in Fig. 4.
Comparisons of the errors in the source location parameters between
the LSM and PSO algorithms.
The selection of initial values for parameters in the LSM algorithm is comparatively complex, so the basic principle of parameter selection is to approach the desired value as near as possible. The selection of different initial values for parameters in the LSM algorithm has a greater influence on the accuracy of the solution location compared to PSO and results in a large difference in the number of iterations between the two methods. The improved PSO algorithm only needs to provide a value range for the initial parameters. Then, it automatically selects parameter values to iterate, and the algorithm runs for a maximum number of 3000 iterations. As is shown in Table 3, Fig. 3, and Fig. 4, compared with the LSM algorithm, the PSO algorithm not only improves the computational accuracy of the desired value of microseismic source parameters but also increases the computational efficiency and determines the microseismic source's real time location.
The following is a discussion of some special conditions. (1) Since source
Because rock bursts occur frequently at a mine in central China, a Paladin
24-bit, multi-channel microseismic monitoring system of ESG Solutions in
Canada was installed. In total, 18 seismic detection devices were installed
in different positions at the mine: 9 seismic detection devices were
installed at the
Geophone coordinates and travel time from the burst point.
Schematic diagram of the relative position of the 10 geophones and the two burst points.
The experiment was carried out on the advanced roadway of the coal mine working face. The diameter of the borehole is 42 mm, the depth of the borehole is 1.2 m, and the length of the filled explosive is one-fourth of the borehole depth. We approximate the blasting point to a spherical blasting point without considering the error caused by the assumption. Based on the data presented in Table 4, the PSO algorithm and LSM algorithm were used to solve for the seismic source location parameters and origin time. A comparison of the error is shown in Table 5.
Error comparison for the LSM algorithm and PSO algorithm.
According to Table 5, the accuracy of the LSM algorithm is relatively poor.
Its average deviation in the
The simulation example and blasting experiment discussed above clearly demonstrate that the PSO optimization algorithm is better than the LSM when solving for the microseismic positioning parameters and the seismic origin time. The algorithm has high positioning accuracy and fast convergence speed, and it is easy to set the initial parameters. This is because the adaptive PSO algorithm is more accurate in fitting the relationship between each coordinate for the seismic detection equipment and the time difference. It can dynamically adjust the velocity value in an iterative process until the value approximates the optimal average velocity, which can account for the nonlinear relationship between each coordinate of the seismic detection equipment and the time difference and can greatly reduce the impact of the velocity error on the positioning precision.
In order to further verify the effectiveness of the proposed method, the
experiments in Sect. 4.1 are compared and analyzed under different wave
velocities. The comparative analysis steps are as follows. (1) Use the PSO
method and the LSM to locate the microseismic source when using real velocity
(i.e., error floating at 0 %). (2) Because it is difficult to measure real
wave velocity in practical engineering, small errors of 1 %, 3 %,
and 5 % are given to the PSO method and LSM; in other words,
when the wave velocity is 5.544, 5.432, and 5.320 m ms
Comparison of locating errors between PSO method and LSM at different wave velocities.
As we can be seen from Fig. 7, the LSM will cause large errors in the
location system under the disturbance of different wave velocities. The
maximum error is up to 25 m (except for the seismic source
An adaptive PSO optimization method is proposed based on the average
population velocity in order to solve for location parameters of the seismic
source in a location model. This method takes the minimum residual sum of
squares between the time-difference regression values and the time-difference measured values for two seismic detection devices, and the PSO
algorithm is designed to solve for the seismic source coordinates and the
equivalent wave velocity and then solve for the seismic source origin time. Combined with the actual need to solve for seismic source parameters,
the model constraints of inertia weight, accelerating constants, the maximum
flight velocity of particles, and other parameters are discussed in order to
improve the optimization capacity of the PSO algorithm and avoid being
trapped in a local optimum. Comparative analysis shows that when solving for the seismic source
location parameters, compared with the classic least squares method, the
adaptive PSO algorithm has high positioning accuracy and fast convergence,
and it is easy to set the initial parameter values.
Data and results of calculations are available by e-mail request.
HMS designed the study, performed the research, analyzed data, and wrote the paper. JZY performed the analysis with constructive discussions. XLZ helped performed the data analyzes. BGW contributed to the collection and analysis of the data. RSJ contributed to refining the ideas, carrying out additional analyses, and finalizing this paper.
The authors declare that they have no conflict of interest.
The authors wish to thank the two anonymous reviewers and editor for their suggestions for improving the paper. They are also grateful for collaborative funding support from the Key Research and Development Program of Shandong Province (grant nos. 2017GSF20115 and 2018GGX109013), the Natural Science Foundation of Shandong Province (grant no. ZR2018MEE008), and the project of the Shandong Province High Educational Science and Technology Program (grant no. J18KA307).
This research has been supported by the Key Research and Development Program of Shandong Province (grant nos. 2017GSF20115 and 2018GGX109013), the Natural Science Foundation of Shandong Province (grant no. ZR2018MEE008), and the project of the Shandong Province High Educational Science and Technology Program (grant no. J18KA307).
This paper was edited by Luciano Telesca and reviewed by two anonymous referees.