Lasocki, S 2008, 'Some Unique Statistical Properties of the Seismic Process in Mines', in Y Potvin, J Carter, A Dyskin & R Jeffrey (eds), Proceedings of the First Southern Hemisphere International Rock Mechanics Symposium
, Australian Centre for Geomechanics, Perth, pp. 667-678.
From a statistical point of view, a series of seismic events is seen as the n-element sample from a stochastic process. If this process is stationary and memoryless then the complete information on the parameters of seismic events is preserved in the joint probability distribution functions of the parameters. In common practice the joint probability description is replaced with marginal distributions of a particular parameter. Such an approach through the marginal distributions splits the seismic process into a number of respective processes of the parameters of seismic events. The parameters can either be measurable, for example, the occurrence time, epicenter coordinates, focal depth, magnitude etc., or derived, for example, inter-event time, inter-event distance, maximum magnitude etc. Each of these parameter processes can be studied separately.
This paper reviews recent investigations into the statistical properties of the parameter series of seismic events from mines. Because the seismic process in mines is controlled by complex and changeable anthropogenic factors it is not surprising that the differences in statistical properties between mining-induced seismicity (MIS) and natural seismicity are substantial. Unlike tectonic seismicity, which is permanent in both space and time, MIS is transient and forms time-space zones or clusters that correlate in space and time with mining works. The event occurrence process in mines is not Poissonian. It is time-dependent and, at best, can be regarded as quasi-stationary. Information on non-stationarity is stored mainly in smaller and more frequent events. The event magnitude processes in MIS is also time-dependent. Consequently, the Gutenberg b-value, the return period and other hazard parameters vary in time. Furthermore, for the majority of mining event parameterisations, their stochastic features cannot be ignored. The interval estimation of autocorrelation function used to study short-term interrelations, and the Hurst rescaled-range analysis applied to investigate long-term clustering, show that the occurrence process, the magnitude process and likely the event location process, have memory of both the long- and the short-type. Inter-event times, inter-event distances and magnitudes are internally interrelated. One of the possible ways for these interactions among mining-induced seismic events is the static Coulomb stress transfer. The subsequent events tend to locate within the areas of increased Coulomb stress due to previous events. Finally, the magnitude distribution of mining seismic events is complex and often multi-modal. Populations of magnitudes consist of at least two components. The magnitude distribution cannot be accurately approximated with the Gutenberg–Richter model.
The unique features of the MIS process presented: time-dependence, memory, inter-relations, multi-modality etc., show that the process is complex. This complexity complicates the practice of the statistical analysis of mining seismic data. On the other hand, however, the non-stationarity and inter-relations mean that the mining seismic event generation process is intrinsically predictable.
Chinnery, M.A. (1963) The state of stress changes that accompany strike-slip faulting, Bulletin of the Seismological Society of America, Vol. 53, 921–932.
Du Toit, C. and Mendecki, A.J. (2007) Examples of time distribution of seismic events in mines, Our Changing Planet. Proceedings IUGG XXIV General Assembly Perugia, Italy 2007, Published on website:
, Abstract 6609.
Efron, B. and Tibshirani, R.J. (1998) An Introduction to the Bootstrap, Chapman and Hall, London.
Feustel, A.J. (1997) Temporal-spatial b-values and observed relationships to structurally controlled ground falls in an open-stope mine, Proceedings of the 4th International Symposium on Rockburst and Seismicity in Mines, Gibowicz, S.J. and Lasocki, S. (editors), Balkema, Netherlands, pp. 191–195.
Gardner, J.K., and Knopoff, L. (1974) Is the sequence of earthquakes in southern California, with aftershocks removed, Poissonian Bulletin of the Seismological Society of America, Vol. 64, pp. 1363–1367.
Gibowicz, S.J. and Lasocki, S. (2001) Seismicity induced by mining: Ten years later. Advances in Geophysics, Vol. 44, pp. 39–181.
Gomberg, J., Belardinelli, M.E., Cocco, M. and Reasenberg, P. (2005) Time-dependent earthquake probabilities, Journal of Geophysical Research. Vol. 110, B05S04,
Gumbel, E.J. (1958) Statistics of Extremes, Columbia University Press, New York.
Hurst, H.E. (1951) Long-term storage capacity of reservoirs, Transactions of the American Society of Civil Engineers, 116 p.
Kagan, Y.Y. (1999) Universality of seismic moment-frequency relation, Pure and Applied Geophysics, Vol. 155, pp. 537–573.
Kijko, A. (1997) Keynote lecture: Seismic hazard assessment in mines, Proceedings of the 4th International Symposium on Rockburst and Seismicity in Mines, Gibowicz, S.J. and Lasocki, S. (editors), Balkema, Netherlands, pp. 247–256.
Kijko, A., Drzęźla, B. and Stankiewicz, T. (1987) Bimodal character of the distribution of extreme seismic events in Polish mines, Acta Geophysica Polonica, Vol. 35, pp. 157–166.
Kijko, A., Lasocki, S. and Graham, G. (2001) Nonparametric seismic hazard analysis in mines,. Pure and Applied Geophysics, Vol. 158, pp. 1655–1676.
King, G.C.P. and Cocco, M. (2001) Fault interaction by elastic stress changes: new clues from earthquake sequences, Advances in Geophysics, Vol. 44, pp. 1–38.
Lasocki, S. (1992) Non-Poissonian structure of mining-induced seismicity, Acta Montana, Vol. 84, pp. 51–57.
Lasocki, S. (1993) Statistical prediction of strong mining tremors, Acta Geophysica Polonica, Vol 41, pp. 197–234.
Lasocki, S. (2001) Quantitative evidences of complexity of magnitude distribution in mining-induced seismicity: implications for hazard evaluation. Rockburst and Seismicity in Mine: Dynamic Rock Mass Response to Mining, G. van Aswegen, R.J. Durrheim and W.D. Ortlepp (editors.), SAIMM S27, Johannesburg, pp. 543–550.
Lasocki, S. (2005) Probabilistic analysis of seismic hazard posed by mining induced events, Controlling Seismic Risk, Proceedings Sixth International Symposium on Rockburst and Seismicity in Mines 9–11 March, Australia, Y. Potvin and M. Hudyma (editors), Australian Centre for Geomechanics, Perth, pp. 151–156.
Lasocki, S. and Orlecka-Sikora, B. (2008) Seismic hazard assessment under complex source size distribution of mining-induced seismicity. Tectonophysics in Press,
Lomnitz, C. (1974) Global Tectonics and Earthquake Risk, Elsevier Scientific Publishing Company, New York.
McGarr, A. and Simpson, D. (1997) A broad look at induced and triggered seismicity, Rockburst and Seismicity in Mines, S.J. Gibowicz and S. Lasocki (editors), Balkema, Rotterdam, pp. 385–396.
Orlecka-Sikora, B. and Lasocki, S. (2002) Clustered structure of seismicity from the Legnica-Glogow copper district, Publications of the Institute of Geophysics Polish Academy of Sciences, Vol. M-24 502 (340), pp. 105–119 (in Polish with English abstract).
Orlecka-Sikora, B. and Lasocki, S. (2005) Nonparametric characterization of mining induced seismic sources, Controlling Seismic Risk, Proceedings Sixth International Symposium on Rockburst and Seismicity in Mines 9–11 March, Australia, Y. Potvin and M. Hudyma (editors), Australian Centre for Geomechanics, Nedlands, pp. 555–560.
Orlecka-Sikora, B., Papadimitriou, E. and Kwiatek, G. (2008) Study of the interaction among mining induced seismic events in the Legnica-Glogow Copper District, Poland, Acta Geophysica (submitted).
Reasenberg, P.A. and Simpson, R.W. (1992) Response of regional seismicity to the static stress change produced by the Loma Prieta earthquake, Science, Vol. 255, pp. 1687–1690.
Richardson, E. and Jordan, T.H. (2002) Seismicity in deep gold mines of South Africa: Implications for tectonic earthquakes, Bulletin of the Seismological Society of America, Vol. 92, pp. 1766–1782.
Silverman, B.W. (1986) Density Estimation For Statistics And Data Analysis. Monographs on Statistics and Applied Probability, Chapman and Hall, London.
Smith, S.W. and Van de Lindt, W. (1969) Strain adjustments associated with earthquakes in Southern California, Bulletin of the Seismological Society of America, Vol. 59, pp. 1569–1589.
Steacy, S., Gomberg, J. and Cocco, M. (2005), Introduction to special section: Stress transfer, earthquake triggering, and time-dependent seismic hazard, Journal of Geophysical Research, Vol. 110, B05S01,
Stein, R.S. and Lisowski, M. (1983) The 1979 Homestead Valley earthquake sequence, California: Control of aftershocks and postseismic deformation, Journal of Geophysical Research, Vol. 88, pp. 6477–6490.
Subbaramu, K.R., Rao, B.S.S., Krishnamurthy, R. and Srinivasan, C. (1989) Seismic investigations of rockbursts in the Kolar Gold Fields, Proceedings 4th Conference on Acoustic Emission/Microseismic Activity in Geologic Structures and Materials, Penn State University, H.R. Hardy, Jr. (editor), Clausthal, Trans Tech Publications, pp. 265–274.
Trifu, C-I., Urbancic, T.I. and Young, R.P. (1993) Non-similar frequency-magnitude distribution for m<1 seismicity, Geophysical Research Letters, Vol. 20, pp. 427–430.
Węglarczyk, S. and Lasocki, S. (2008) Studies of long and short memory in mining-induced seismic processes. Acta Geophysica (submitted).