Penghong Fan This email address is being protected from spambots. You need JavaScript enabled to view it.^1,2,3, Baisheng Nie This email address is being protected from spambots. You need JavaScript enabled to view it.^2,3, Tao Yang⁴

¹ Shanxi Institute of Technology, Department of Mining Engineering, 045000, Shanxi, China.
² China University of Mining & Technology (Beijing), School of Emergency Management and Safety Engineering, 100083, Beijing, China.
³ China University of Mining & Technology (Beijing), State Key Laboratory of Coal Resources and Safe Mining, 100083, Beijing, China.
⁴ North China Institute of Science and Technology, School of Safety Engineering, 065201, Hebei, China.

REFERENCES

1. [1] Gibowicz, S.J. and Kijko, A., An Introduction to Mining Seismology.Academic Press, San Diego (1994).
2. [2] Young, R.P. and Collins, D.S., "Seismic studies of rock fracture at the Underground Research Laboratory, Canada," Int. J. Rock Mech. Min. Sci, Vol. 38, No. 6, pp. 787-799 (2001).
3. [3] Mondal, D., Roy, P.N.S. and Kumar, M., "Monitoring the strata behavior in the Destressed Zone of a shallow Indian longwall panel with hard sandstone cover using Mine-Microseismicity and Borehole Televiewer data," Eng. Geol., Vol. 271, pp. 105593 (2020). doi: https://doi.org/10.1016/j.enggeo.2020.105593
4. [4] Li, N., Huang, B., Zhang, X., et al., "Characteristics of microseismic waveforms induced by hydraulic fracturing in coal seam for coal rock dynamic disasters prevention," Safety Science, Vol. 115,  pp. 188-198 (2019). doi: https://doi.org/10.1016/j.ssci.2019.01.024
5. [5] Yuan-hui, L., Gang, L., Shi-da, X., et al., "The spatial-temporal evolution law of microseismic activities in the failure process of deep rock masses," Journal of Applied Geophysics, Vol. 154, pp. 1-10 (2018). doi: https://doi.org/10.1016/j.jappgeo.2018.04.024
6. [6] Leake, M.R., Conrad, W.J., Westman, E.C., et al., "Microseismic monitoring and analysis of induced seismicity source mechanisms in a retreating room and pillar coal mine in the Eastern United States," Underground Space, Vol. 2, No. 2, pp. 115-124 (2017). doi: https://doi.org/10.1016/j.undsp.2017.05.002
7. [7] Cook, N.G.W., Hoek, E., Pretorius, J.P.G., et al., "Rock mechanics applied to the study of rockburst," J. South. Afr. Inst. Min. Metall, Vol. 66, No. 10, pp. 436-528 (1966).
8. [8] Sepehri, M., Apel, D.B., Adeeb, S., et al., "Evaluation of mining-induced energy and rockburst prediction at a diamond mine in Canada using a full 3D elastoplastic finite element model,"Eng.Geol.,Vol.266,pp.105457(2020).doi: ttps://doi.org/10.1016/j.enggeo.2019.105457
9. [9] Fujii, Y., Ishijima, Y. and Deguchi, G., "Prediction of coal face rockbursts and microseismicity in deep longwall coal mining," Int. J. Rock Mech. Min. Sci, Vol. 34, No. 1, pp. 85-96 (1997). doi: http://dx.doi.org/10.1016/S1365-1609(97)80035-4
10. [10] Mendeeki, A.J., Seismie monitoring in mines.Chapman Hall, London, (1997).
11. [11] Senfaute, G., Chambon, C., Bigarré, P., et al., "Spatial Distribution of Mining Tremors and the Relationship to Rockburst Hazard," Pure appl. Geophys, Vol. 150, No. 3, pp. 451-459 (1997). doi: 10.1007/s000240050087
12. [12] Krystyna, S., "Characteristics of seismic activity of the Upper Silesian Coal Basin in Poland," Geophys. J. Int, Vol. 168, No. 2, pp. 757-768 (2007). doi: 10.1111/j.1365-246X.2006.03227.x
13. [13] Cesca, S., Sen, A.T. and Dahm, T., "Seismicity monitoring by cluster analysis of moment tensors," Geophys. J. Int., Vol. 196, No. 3, pp. 1813-1826 (2013). doi: 10.1093/gji/ggt492
14. [14] Sen, A.T., Cesca, S., Bischoff, M., et al., "Automated full moment tensor inversion of coal mining-induced seismicity," Geophys. J. Int, Vol. 195, No. 2, pp. 1267-1281 (2013). doi: 10.1093/gji/ggt300
15. [15] Zhang, M.W., Shimada, H., Sasaoka, T., et al., "Seismic energy distribution and hazard assessment in underground coal mines using statistical energy analysis," Int. J. Rock Mech. Min. Sci, Vol. 64, No. pp. 192-200 (2013). doi: 10.1016/j.ijrmms.2013.09.001
16. [16] Liu, F., Ma, T., Tang, C.a., et al., "Prediction of rockburst in tunnels at the Jinping II hydropower station using microseismic monitoring technique," Tunnelling and Underground Space Technology, Vol. 81, pp. 480-493 (2018). doi: https://doi.org/10.1016/j.tust.2018.08.010
17. [17] Mondal, D. and Roy, P.N.S., "Fractal and seismic b-value study during dynamic roof displacements (roof fall and surface blasting) for enhancing safety in the longwall coal mines," Eng. Geol., Vol. 253, pp. 184-204 (2019). doi: https://doi.org/10.1016/j.enggeo.2019.03.018
18. [18] Ma, C., Li, T. and Zhang, H., "Microseismic and precursor analysis of high-stress hazards in tunnels: A case comparison of rockburst and fall of ground," Eng. Geol., Vol. 265, pp. 105435 (2020). doi: https://doi.org/10.1016/j.enggeo.2019.105435
19. [19] Kinscher, J., Bernard, P., Contrucci, I., et al., "Location of microseismic swarms induced by salt solution mining," Geophys. J. Int, Vol. 200, No. 1, pp. 337-362 (2015). doi: 10.1093/gji/ggu396
20. [20] Falconer, K.J., Fractal Geometry : Mathematical Foundations and Applications.Wiley, New York, (1990).
21. [21] Mandelbrot, B.B., The Fractal Geometry of Nature.W. H. Freeman and Company, New York, (1982).
22. [22] Hirata, T. and Imoto, M., "Multifractal analysis of spatial distribution of microearthquakes in the Kanto region," Geophys. J. Int, Vol. 107 No. 1, pp. 155-162 (1991).
23. [23] Molchan, G. and Kronrod, T., "The fractal description of seismicity," Geophys. J. Int, Vol. 179, No. 3, pp. 1787-1799 (2009). doi: 10.1111/j.1365-246X.2009.04380.x
24. [24] Nampally, S., Padhy, S. and Dimri, V.P., "Characterizing spatial heterogeneity based on the b-value and fractal analyses of the 2015 Nepal earthquake sequence," Tectonophysics, Vol. 722, pp. 154-162 (2018). doi: https://doi.org/10.1016/j.tecto.2017.11.004
25. [25] De Rubeis, V., Dimitriu, P., Papadimitriou, E., et al., "Recurrent patterns in the spatial behaviour of Italian seismicity revealed by the fractal approach," Geophys. Res. Lett, Vol. 20, No. 18, pp. 1911-1914 (1993).
26. [26] Hayat, U., Barkat, A., Ali, A., et al., "Fractal analysis of shallow and intermediate-depth seismicity of Hindu Kush," Chaos, Solitons & Fractals, Vol. 128, pp. 71-82 (2019). doi: https://doi.org/10.1016/j.chaos.2019.07.029
27. [27] Xie, H.P., Introduction to Fractal-Rock Mechanics.Science Press, Beijing, (1997).
28. [28] Wu, X.Z., Liu, X.X., Liang, Z.Z., et al., "Experimental study of fractal dimension of AE serials of different rocks under uniaxial compression," Rock Soil Mech, Vol. 33, No. 12, pp. 3561-3569 (2012).
29. [29] Qiu, X., Xu, J., Xiao, S., et al., "Acoustic emission parameters and waveforms characteristics of fracture failure process of asphalt mixtures," Construction and Building Materials, Vol. 215, pp.135-147(2019).doi: https://doi.org/10.1016/j.conbuildmat.2019.04.150
30. [30] Xue, R., Liang, Z., Xu, N., et al., "Rockburst prediction and stability analysis of the access tunnel in the main powerhouse of a hydropower station based on microseismic monitoring," International Journal of Rock Mechanics and Mining Sciences, Vol. 126, pp. 104174 (2020). doi: https://doi.org/10.1016/j.ijrmms.2019.104174
31. [31] Li, D., Wang, E., Kong, X., et al., "Mechanical behaviors and acoustic emission fractal characteristics of coal specimens with a pre-existing flaw of various inclinations under uniaxial compression," International Journal of Rock Mechanics and Mining Sciences, Vol. 116, pp. 38-51 (2019). doi: https://doi.org/10.1016/j.ijrmms.2019.03.022
32. [32] Liu, S., Li, X., Li, Z., et al., "Energy distribution and fractal characterization of acoustic emission (AE) during coal deformation and fracturing," Measurement, Vol. 136, pp. 122-131 (2019). doi: https://doi.org/10.1016/j.measurement.2018.12.049
33. [33] Feng, X.T., Yu, Y., Feng, G.L., et al., "Fractal behaviour of the microseismic energy associated with immediate rockbursts in deep, hard rock tunnels," Tunn. Undergr. Space Technol, Vol. 51, pp. 98-107 (2016). doi: 10.1016/j.tust.2015.10.002
34. [34] Zhu, H. and Ji, C.C., Fractal Theory and its Applications.Science Press, Beijing, (2010).
35. [35] Fraser, A.M. and Swinney, H.L., "Independent coordinates for strange attractors from mutual information," Phys. Rev. A Gen Phys, Vol. 33, No. 2, pp. 1134-1140 (1986).
36. [36] Grassberger, P. and Procaccia, I., "Characterization of Strange Attractors," Phys. Rev. Lett, Vol. 50, No. 5, pp. 346-349 (1983).
37. [37] Albano, A.M., Muench, J. and Schwartz, C., "Singular-value decomposition and the Grassberger-Procaccia algorithm," Phys. Rev. A Gen Phys, Vol. 38, No. 6, pp. 3017-3026 (1988).
38. [38] Huang, J. and Turcotte, D.L., "Are earthquakes an example of deterministic chaos," Geophys. Res. Lett, Vol. 17, No. 3, pp. 223-226 (1990).
39. [39] Kiyashchenko, D., Smirnova, N., Troyan, V., et al., "Seismic hazard precursory evolution: fractal and multifractal aspects," Phys. Chem. Earth, Vol. 29, No. 4-9, pp. 367-378 (2004).
40. [40] Lei, X., Nishizawa, O. and Kusunose, K., "Band-limited heterogeneous fractal structure of earthquakes and acoustic-emission events," Geophys. J. Int, Vol. 115, No. 1, pp. 79-84 (1993). doi: 10.1111/j.1365-246X.1993.tb05589.x
41. [41] Pasten, D., Estay, R., Comte, D., et al., "Multifractal analysis in mining microseismicity and its application to seismic hazard in mine," Int. J. Rock Mech. Min. Sci, Vol. 78, pp. 74-78 (2015). doi: 10.1016/j.ijrmms.2015.04.020
42. [42] Kong, X.G., Wang, E.Y., Hu, S.B., et al., "Fractal characteristics and acoustic emission of coal containing methane in triaxial compression failure," J. Appl. Geophys, Vol. 124, pp. 139-147 (2016). doi: 10.1016/j.jappgeo.2015.11.018
43. [43] Xie, H.P. and Pariseau, W.G., "Fractal character and mechanism of rock bursts," Int. J. Rock Mech. Min. Sci, Vol. 30, No. 4, pp. 343-350 (1993). doi: http://dx.doi.org/10.1016/0148-9062(93)91718-X