# A Fast Ray-tracing Method for Locating Mining-induced Seismicity by Considering Underground Voids
## 5 Conclusions  
In this paper, we propose a new algorithm of ray tracing for the location of mining-induced seismicity considering underground voids. The triangular patch is used to describe the complicated void model. The accuracy of ray tracing is controlled by arranging the step length of nodes on the  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multicolumn{1}{c}{**Blasts**} & **B1** & **B2** & **B3** & **Mean** \\ \hline \multirow{3}{*}{Actual position} & x (m) & 31,412,506.50 & 31,412,516.92 & 31,412,514.32 & \\  & y (m) & 4,719,746.39 & 4,719,743.59 & 4,719,815.21 & \\  & z (m) & 146.68 & 119.19 & 134.94 & \\ Location & x (m) & 31,412,512.19 & 31,412,531.62 & 31,412,533.47 & \\ method with & y (m) & 4,719,758.60 & 4,719,726.15 & 4,719,802.70 & \\ constant & z (m) & 137.57 & 127.94 & 146.69 & \\ velocity & Location error & (m) & 16.26 & 24.44 & 25.72 & 22.14 \\  & x (m) & 31,412,509.44 & 31,412,511.35 & 31,412,521.42 & \\ Location & y (m) & 4,719,749.60 & 4,719,749.67 & 4,719,813.89 & \\ method based & z (m) & 143.57 & 122.49 & 136.74 & \\ on FMM & Location error & 5.35 & 8.87 & 7.44 & 7.22 \\  & (m) & 31,412,508.98 & 31,412,520.52 & 31,412,517.76 & \\ Location based & y (m) & 4,719,743.05 & 4,719,746.21 & 4,719,818.79 & \\ on the & z (m) & 149.03 & 114.29 & 131.16 & \\ proposed ray tracing & Location error & 4.78 & 6.62 & 6.24 & 5.88 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Location results of the controlled blast experiments.  
Figure 14: Distributions of voids and sensors in the Huangtupo Copper and Zinc Mine. P1, P2 are collection devices.  
edges of the model. A fast and accurate ray-tracing method is proposed based on [PERSON]'s principle and Dijkstra algorithm. We tested the effectiveness of the new method with models of single-void and multiple-voids and compared the new method with classic FMM and SPR. The results show that the accuracy and efficiency of the new method are higher than the classic ray-tracing method. The biggest advantage of our proposed method is that there is no need to divide the grid, and only a small number of nodes can be used to obtain high-precision ray paths. Finally, our method was applied to locate the pre-measured blasts in Huangtopo Copper and Zinc Mine. By integrating our proposed ray-tracing method, the mean location error is improved from 22.14 to 5.88 m compared with that using a constant velocity model, which indicates that our method is effective in the location of mining-induced seismicity.  
[PERSON] and [PERSON] participated in data analysis, participated in the design of the study and drafted the manuscript, carried out the statistical analyses; [PERSON] and [PERSON] collected field data; [PERSON] conceived of the study, designed the study, coordinated the study, and helped draft the manuscript. All authors have read and agreed to the published version of the manuscript.  
This research was funded by The National Key R&D Program of China (2017 YFC0602905) and the Fundamental Research Funds for the Central Universities of Central South University (2020 zzts194).  
The authors declare no conflict of interest.