Woodward, KR & Tierney, SR 2017, 'Seismic hazard estimation using databases with bimodal frequency–magnitude behaviour', in M Hudyma & Y Potvin (eds), UMT 2017: Proceedings of the First International Conference on Underground Mining Technology
, Australian Centre for Geomechanics, Perth, pp. 219-232, https://doi.org/10.36487/ACG_rep/1710_17_Woodward
Many underground mines experience seismic events associated with rock mass failure which can be of sufficient magnitude to pose a significant hazard to operations. Probabilistic seismic hazard assessments are typically performed assuming a Gutenberg–Richter distribution for the frequency–magnitude relation for which the parameters are obtained from a best fit to the data. This distribution assumes self-similar data above the magnitude of completeness but this is not always valid. The breakdown in self-similarity can occur when there are multiple superimposed seismic sources, or when there are artificial noise sources such as orepasses and underground crushers.
This paper introduces an alternative parametric technique to decompose a bimodal frequency–magnitude relation into two sub-distributions. The composite distribution method assumes that two separate distributions are underlying the observed frequency–magnitude behaviour. This assumption was tested with respect to a single Gutenberg–Richter model to describe frequency–magnitude behaviour. The hypercube optimisation algorithm was used to solve the parameters of the two superimposed distributions while minimising the residual sum of squares for the fit compared to the observed data.
The mXrap software was used to implement the method at multiple underground mines for specific volumes and for grid-based analysis. The results show that locally, the seismic hazard can be severely underestimated if a single Gutenberg–Richter model is assumed but this can be improved with the composite distribution method.
Keywords: seismic hazard, seismic sources, seismic noise, frequency–magnitude relation
Abiyev, R & Tunay, M 2015, ‘Optimization of high-dimensional functions through hypercube evaluation’, Computational Intelligence and Neuroscience, vol. 2015, pp. 1–11.
Amidzic, D 2001, ‘Energy-moment relation and its application’, in G Van Aswegen, R Durrheim & D Ortlepp (eds), Proceedings of Rockbursts and Seismicity in Mines (RaSiM5), South African Institute of Mining and Metallurgy, Johannesburg, pp. 509–513.
Del Pezzo, E, Esposito, A, Giudicepietro, F, Marinaro, M, Martini, M & Scarpetta, S 2003, ‘Discrimination of earthquakes and underwater explosions using neural networks’, Bulletin of the Seismological Society of America, vol. 93, no. 1, pp. 215–223.
Finnie, GJ 1999, ‘Using neural networks to discriminate between genuine and spurious seismic events in mines’, Pure and Applied Geophysics, vol. 154, pp. 41–56.
Ford, S & Walter, W 2010, ‘Aftershock characteristics as a means of discriminating explosions from earthquakes’, Bulletin of the Seismological Society of America, vol. 100, no. 1, pp. 364–376.
Gutenberg, B & Richter, CF 1944, ‘Frequency of earthquakes in California’, Bulletin of the Seismological Society of America, vol. 85, no. 5, pp. 1,571–1,579.
Hudyma, M 2008, Analysis and Interpretation of Clusters of Seismic Events in Mines, PhD thesis, The University of Western Australia, Perth.
Kijko, A 2011, ‘Seismic hazard’, in H Gupta (ed.), Encyclopedia of Solid Earth Geophysics, Springer, Dordrecht.
Kijko, A, Drzezla, B & Stankiewicz, T 1987, ‘Bimodal character of the distribution of extreme seismic events in Polish mines’, Acta Geophysica, vol. 35, pp. 157–166.
Kijko, A, Lasocki, S & Graham, G 2001, ‘Non-parametric seismic hazard in mines’, Pure and Applied Geophysics, vol. 158,
Kuyuk, H, Yildirim, E, Dogan, E & Horasan, G 2011, ‘An unsupervised learning algorithm: application to the discrimination of seismic events and quarry blasts in the vicinity of Istanbul’, Natural Hazards and Earth System Sciences, vol. 11, pp. 93–100.
Kwiatek, G, Plenkers, M, Nakatani, Y & Dresen, G 2010, ‘Frequency-magnitude characteristics down to Magnitude -4.4 for induced seismicity recorded at Mponeng Gold Mine, South Africa’, Bulletin of the Seismological Society of America, vol. 100, no. 3, pp. 1,165–1,173.
Lasocki, S 2001, ‘Quantitative evidences of complexity of magnitude distribution in mining-induced seismicity: Implications for hazard estimation’, in G Van Aswegen, R Durrheim & D Ortlepp (eds), Proceedings of Rockbursts and Seismicity in Mines (RaSiM5), South African Institute of Mining and Metallurgy, Johannesburg, pp. 543–550.
Lasocki, S 2005, ‘Probabilistic analysis of seismic hazard posed by mining induced events’, in M Hudyma & Y Potvin (eds), Proceedings of the Sixth International Symposium on Rockbursts in Mines: Controlling Seismic Risk, Australian Centre for Geomechanics, Perth, pp. 151–156.
Lasocki, S & Orlecka-Sikora, B 2006, ‘Seismic hazard assessment under complex source size distribution of mining-induced seismicity’, Tectonophysics, vol. 456, no. 2008, pp. 28–37.
Montibeller, G & Winterfeldt, DV 2015, ‘Cognitive and motivational biases in decision and risk analysis’, Risk Analysis, vol. 35, no. 7, pp. 1,230–1,251.
Morkel, IG & Wesseloo, J 2017, ‘The effect of sensor frequency range on the estimation of the current hazard state’, Proceedings of the Ninth International Symposium on Rockbursts and Seismicity in Mines (RaSiM9), University of Chile, Santiago.
Morkel, IG, Wesseloo, J & Harris, P 2015, ‘Highlighting and quantifying seismic data quality concerns’, in P Dight (ed.), Proceedings of the Ninth International Symposium on Field Measurements in Geomechanics, Australian Centre for Geomechanics, Perth, pp. 539–549.
Morrison, D, Swan, G & Scholz, C 1993, ‘Chaotic behaviour and mining-induced seismicity’, in R Young (ed.), Proceedings of the Third International Symposium on Rockbursts and Seismicity in Mines, A.A. Balkema, Rotterdam, pp. 233–237.
Orlecka-Sikora, B & Lasocki, S 2017, ‘Interval estimation of seismic hazard parameters’, Pure and Applied Geophysics, vol. 174, pp. 779–791.
Page, R 1968, ‘Aftershocks and microaftershocks of the great Alaska earthquake’, Bulletin of the Seismological Society of America, vol. 58, pp. 1,131–1,168.
Potvin, Y 2009, ‘Strategies and tactics to control seismic risks in mines’, Journal of The South African Institute of Mining and Metallurgy, vol. 109, no. 3, pp. 177–186.
Richardson, E & Jordan, TH 2002, ‘Seismicity in deep gold mines of South Africa: Implications for tectonic earthquakes’, Bulletin of the Seismological Society of America, vol. 92, no. 5, pp. 1,766–1,782.
Silverman, B 1986, Density Estimation for Statistics and Data Analysis, Chapman and Hall, London.
Taylor, S 1996, ‘Analysis of high-frequency Pg/Lg ratios from NTS explosions and western US earthquakes’, Bulletin of the Seismological Society of America, vol. 86, no. 4, pp. 1,042–1,053.
Wesseloo, J 2013, ‘Towards real-time probabilistic hazard assessment of the current hazard state for mines’, in A Malovichko & D Malovichko (eds), Proceedings of the Eighth International Symposium on Rockbursts and Seismicity in Mines (RaSiM8), Geological Survey of the Russian Academy of Sciences.
Wesseloo, J 2014, ‘Evaluation of the spatial variation of b-value’, Journal of The South African Institute of Mining and Metallurgy, vol. 114, October 2014, pp. 823–828.
Wesseloo, J, Woodward, K & Pereira, J 2014, ‘Grid-based analysis of seismic data’, Journal of The South African Institute of Mining and Metallurgy, vol. 114, October 2014, pp. 815–822.