Abstract
The assessment of the temporal characteristics of seismicity is fundamental to understanding and quantifying the seismic hazard associated with mining, the effectiveness of strategies and tactics used to manage seismic hazard, and the relationship between seismicity and changes to the mining environment. This article aims to improve the accuracy and precision in which the temporal dimension of seismic responses can be quantified and delineated. We present a review and discussion on the occurrence of time-dependent mining seismicity with a specific focus on temporal modelling and the modified Omori law (MOL). This forms the basis for the development of a simple weighted metric that allows for the consistent temporal delineation and quantification of a seismic response. The optimisation of this metric allows for the selection of the most appropriate modelling interval given the temporal attributes of time-dependent mining seismicity. We evaluate the performance weighted metric for the modelling of a synthetic seismic dataset. This assessment shows that seismic responses can be quantified and delineated by the MOL, with reasonable accuracy and precision, when the modelling is optimised by evaluating the weighted MLE metric. Furthermore, this assessment highlights that decreased weighted MLE metric performance can be expected if there is a lack of contrast between the temporal characteristics of events associated with different processes.
Similar content being viewed by others
References
Akaike, H. (1974). A new look at the statistical model identification. IEEE Transactions on Automatic Control, 19, 716–723.
Anderson, T. W., & Darling, D. A. (1954). A test of goodness of fit. American Statistical Association, 49, 765–769.
Bohnenstiehl, D. R., Tolstoy, M., Dziak, R. P., Fox, C. G., & Smith, D. K. (2002). Aftershock sequences in the mid-ocean ridge environment: an analysis using hydroacoustic data. Tectonophysics, 354, 49–70.
Cho, N. F., Tiampo, K. F., Mckinnon, S. D., Vallejos, J. A., Klein, W., & Dominguez, R. (2010). A simple metric to quantify seismicity clustering. Nonlinear Processes in Geophysics, 17, 293–302.
Davis, S. D., & Frohlich, C. (1991). Single-link cluster analysis of earthquake aftershocks: Decay laws and regional variations. Geophysical Research: Solid Earth (1978–2012), 96, 6335–6350.
Dieterich, J. (1994). A constitutive law for rate of earthquake production and its application to earthquake clustering. Geophysical Research: Solid Earth (1978–2012), 99, 2601–2618.
Enescu, B., Mori, J., Miyazawa, M., & Kano, Y. (2009). Omori–Utsu law C-values associated with recent moderate earthquakes in Japan. Bulletin of the Seismological Society of America, 99, 884–891.
Eremenko, V. A., Eremenko, A. A., Rasheva, S. V., & Turuntaev, S. B. (2009). Blasting and the man-made seismicity in the Tashtagol mining area. Mining Science, 45, 468–474.
Gasperini, P., & Lolli, B. (2006). Correlation between the parameters of the aftershock rate equation: Implications for the forecasting of future sequences. Physics of the Earth and Planetary Interiors, 156, 41–58.
Gasperini, P., & Lolli, B. (2009). An empirical comparison among aftershock decay models. Physics of the Earth and Planetary Interiors, 175, 183–193.
Gibowicz, S. J., & Lasocki, S. (2001). Seismicity induced by mining: Ten years later. Advances in Geophysics, 44, 39–181.
Gross, S. J., & Kisslinger, C. (1994). Tests of models of aftershock rate decay. Bulletin of the Seismological Society of America, 84, 1571–1579.
Helmstetter, A., Kagan, Y. Y., & Jackson, D. D. (2005). Importance of small earthquakes for stress transfers and earthquake triggering. Geophysical Research: Solid Earth (1978–2012), 110, 1–13.
Helmstetter, A., & Sornette, D. (2002). Subcritical and supercritical regimes in epidemic models of earthquake aftershocks. Geophysical Research: Solid Earth (1978–2012), 107, 1–21.
Hills, P.B., & Penney, A.R. (2008). Management of seismicity at the Beaconsfield Gold Mine, Tasmania. Proceedings in 10th underground operators’ conference (pp. 157–170). Launceston, Tasmania, Australia: Australasian Institute of Mining and Metallurgy.
Hudyma, M., Heal, D., & Mikula, P. (2003). Seismic monitoring in mines—Old technology—New applications. Proc. in 1st Australasian ground control in mining conference (pp. 201–218). Sydney, Australia: UNSW School of Mining Engineering.
Hudyma, M., & Potvin, Y. (2010). An engineering approach to seismic risk management in hardrock mines. Rock Mechanics and Rock Engineering, 43, 891–906.
Kagan, Y. Y. (2004). Short-term properties of earthquake catalogs and models of earthquake source. Bulletin of the Seismological Society of America, 94, 1207–1228.
Kagan, Y.Y. (2006). Why does theoretical physics fail to explain and predict earthquake occurrence? In P. Bhattacharyya & B.K. Chakrabarti (Eds.), Modelling critical and catastrophic phenomena in geoscience: a statistical physics approach (pp. 303–359). Berlin: Springer.
Kagan, Y. Y., & Jackson, D. D. (1991). Long-term earthquake clustering. Geophysical Journal International, 104, 117–133.
Kagan, Y. Y., & Knopoff, L. (1981). Stochastic synthesis of earthquake catalogs. Geophysical Research: Solid Earth (1978–2012), 86, 2853–2862.
Kagan, Y. Y., & Knopoff, L. (1987). Statistical short-term earthquake prediction. Science, 236, 1563–1567.
Kgarume, T., Spottiswoode, S., & Durrheim, R. (2010a). Statistical properties of mine tremor aftershocks. Pure and Applied Geophysics, 167, 107–117.
Kgarume, T.E., Spottiswoode, S.M., & Durrheim, R.J. (2010b). Deterministic properties of mine tremor aftershocks. In: Proceedings in 5th international seminar on deep and high stress mining (pp. 227–237). Santiago, Chile: Australian Centre for Geomechanics.
Kisslinger, C. (1993). The stretched exponential function as an alternative model for aftershock decay rate. Geophysical Research: Solid Earth (1978–2012), 98, 1913–1921.
Kisslinger, C., & Jones, L. M. (1991). Properties of aftershock sequences in Southern California. Geophysical Research: Solid Earth (1978–2012), 96, 11947–11958.
Klein, F. W., Wright, T., & Nakata, J. (2006). Aftershock decay, productivity, and stress rates in hawaii: indicators of temperature and stress from magma sources. Geophysical Research: Solid Earth (1978–2012), 111, B07307.
Kwiatek, G. (2004). A search for sequences of mining-induced seismic events at the Rudna Copper Mine in Poland. Acta Geophysica Polonica, 52, 155–171.
Lewis, P. A. W. (1961). Distribution of the Anderson-Darling statistic. The Annals of Mathematical Statistics, 32, 1118–1124.
Lolli, B., Boschi, E., & Gasperini, P. (2009). A comparative analysis of different models of aftershock rate decay by maximum likelihood estimation of simulated sequences. Geophysical Research: Solid Earth (1978–2012), 114, B01305.
Malek, F. & Leslie, I.S. (2006). Using seismic data for rockburst re-entry protocol at Inco’s Copper Cliff North Mine. Proc. in 41st U.S. symposium on rock mechanics. Golden, USA: American Rock Mechanics Association.
Mendecki, A. (2005). Persistence of seismic rock mass response to mining. Proceedings in 6th International Symposium on Rockburst and Seismicity in Mines (pp. 97–105). Perth, Australia.
Mendecki, A. J., & Lynch, R. A. (2004). Gap601a: Experimental and theoretical investigations of fundamental processes in mining induced fracturing and rock instability close to excavations. Johannesburg: ISS International Limited.
Molchan, G. M., & Dmitrieva, O. E. (1992). Aftershock identification—Methods and new approaches. Geophysical Journal International, 109, 501–516.
Naoi, M., Nakatani, M., Yabe, Y., Kwiatek, G., Igarashi, T., & Plenkers, K. (2011). Twenty thousand aftershocks of a very small (M 2) earthquake and their relation to the mainshock rupture and geological structures. Bulletin of the Seismological Society of America, 101, 2399–2407.
Narteau, C., Shebalin, P., & Holschneider, M. (2002). Temporal limits of the power law aftershock decay rate. Geophysical Research: Solid Earth (1978–2012), 107, ESE-12.
Nyffenegger, P., & Frohlich, C. (1998). Recommendations for determining P values for aftershock sequences and catalogs. Bulletin of the Seismological Society of America, 88, 1144–1154.
Nyffenegger, P., & Frohlich, C. (2000). Aftershock occurrence rate decay properties for intermediate and deep earthquake sequences. Geophysical Research Letters, 27, 1215–1218.
Ogata, Y. (1983). Estimation of the parameters in the modified Omori formula for aftershock frequencies by the maximum likelihood procedure. Physics of the Earth, 31, 115–124.
Ogata, Y. (1988). Statistical models for earthquake occurrences and residual analysis for point processes. American Statistical Association, 83, 9–27.
Omori, F. (1894a). On after-shocks. Seismological Journal of Japan, 19, 71–80.
Omori, F. (1894b). On the after-shocks of earthquakes (Vol. 7, pp. 111–200). Tokyo: College of Science, On the after-shocks of earthquakes.
Phillips, W. S., Pearson, D. C., Edwards, C. L., & Stump, W. B. (1997). Microseismicity Induced by a Controlled. Mine collapse at White Pine, Michigan. International Journal of Rock Mechanics and Mining Sciences, 34, 246.
Plenkers, K., Kwiatek, G., Nakatani, M., & Dresen, G. (2010). Observation of seismic events with frequencies F > 25 Khz at Mponeng deep gold mine, South Africa. Seismological Research Letters, 81, 467–479.
Potvin, Y. (2009). Strategies and tactics to control seismic risks in mines. Journal of the South African Institute of Mining and Metallurgy, 109, 177–186.
Reasenberg, P. (1985). Second-order moment of Central California Seismicity, 1969–1982. Geophysical Research: Solid Earth (1978–2012), 90, 5479–5495.
Reasenberg, P. A., & Jones, L. M. (1989). Earthquake hazard after a mainshock in California. Science, 243, 1173–1176.
Saichev, A., & Sornette, D. (2007). Power law distributions of seismic rates. Tectonophysics, 431, 7–13.
Spottiswoode, S.M. (2000). Aftershocks and foreshocks of mine seismic events. Proc. in 3rd international workshop on the application of geophysics to rock and soil engineering (p. 82). Melbourne, Australia: ISRM.
Tiampo, K. F., & Shcherbakov, R. (2012). Seismicity-based earthquake forecasting techniques: Ten years of progress. Tectonophysics, 522–523, 89–121.
Utsu, T. (1957). Magnitude of earthquakes and occurrence of their aftershocks (Vol. 2, pp. 35–45). Japan: Seismological Society of Japan.
Utsu, T. (1961). A statistical study of the occurrence of aftershocks. Geophysical Magazine, 30, 521–605.
Utsu, T. (2002). Statistical features of seismicity. International Geophysics Series, 81, 719–732.
Utsu, T., Ogata, Y., & Matsu’ura, R. S. (1995). The centenary of the Omori formula for a decay law of aftershock activity. Physics of the Earth, 43, 1–33.
Vallejos, J. A., & Mckinnon, S. D. (2010a). Omori’s law applied to mining-induced seismicity and re-entry protocol development. Pure and Applied Geophysics, 167, 91–106.
Vallejos, J.A., & Mckinnon, S.D. (2010b). Temporal evolution of aftershock sequences for re-entry protocol development in seismically active mines. Proceedings in 5th international seminar on deep and high stress mining (pp. 199–214). Santiago, Chile: Australian Centre for Geomechanics.
Vallejos, J. A., & Mckinnon, S. D. (2011). Correlations between mining and seismicity for re-entry protocol development. International Journal of Rock Mechanics and Mining Sciences, 48, 616–625.
Woodward, K. (2015). Identification and delineation of mining induced seismic responses. PhD, University of Western Australia.
Woodward, K., & Wesseloo, J. (2015). Observed spatial and temporal behaviour of seismic rock mass response to blasting. South African Institute of Mining and Metallurgy, 15, 1045–1056.
Acknowledgements
A special thanks is due to Paul Harris for assisting in the programming of these analysis techniques. This research is part of Phase 5 of the ACG’s Mine Seismicity and Rockburst Risk Management project, sponsored by the following organisations: Barrick Gold of Australia, BHP Billiton Nickel West, BHP Billiton Olympic Dam, Independence Group (Lightning Nickel), LKAB Sweden, Perilya Limited (Broken Hill Mine), Vale Inc. Canada, Agnico-Eagle Canada, Gold Fields St Ives Gold Operations, Hecla USA, Kirkland Lake Gold, MMG Golden Grove, Newcrest Cadia Valley Operations, Newmont Asia Pacific, Xstrata Copper (Kidd Mine), Xstrata Nickel Rim, and the Minerals and Energy Research Institute of Western Australia.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Woodward, K., Wesseloo, J. & Potvin, Y. Temporal Delineation and Quantification of Short Term Clustered Mining Seismicity. Pure Appl. Geophys. 174, 2581–2599 (2017). https://doi.org/10.1007/s00024-017-1570-6
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00024-017-1570-6