Search for chaotic dynamics manifestation in multiscale seismicity

• Autorzy: Kortas Ł.
• Języki publikacji: EN

Abstrakty

EN

This paper contains a description of the methods of studying non-linear dynamics revealed in the collected data sets, and the estimations of selected parameters of non-linear dynamics. Sets of data referring to seismic phenomena of different origin and, most importantly, different scale of observed rock fracturing and destruction processes were analysed. Collected sets were related to fracturing: starting from a microscale, i.e., seismoacoustic emission registered in rock samples subjected to compression, through mining induced seismicity, to a macroscale that is represented by earthquakes. The data was examined in terms of the presence of non-linear dynamics and deterministic chaos. An attempt to quantify the parameters of chaos was made in order to define to what extent the process of cracking and destruction of rocks has features common in different scales. Several parameters of chaotic dynamics were applied. The fractal dimensions, Lyapunov's exponents, the dimension of reconstructed phase space, and the dimension of the attractor were calculated from descriptors characteristic to seismological processes, i.e., time-space distribution and energy distribution of quakes. The usefulness was assessed of the applied methods of data analysis for the description of seismological processes and seismological hazard evaluation.

Słowa kluczowe

EN

chaos; natural seismicity; mining seismicity; acoustic emission

• Wydawca: Instytut Geofizyki PAN
• Czasopismo: Acta Geophysica Polonica
• Rocznik: 2005
• Tom: Vol. 53, nr 1
• Strony: 47--74
• Opis fizyczny: Bibliogr. 26 poz.

Twórcy

autor

Kortas Ł.

• Central Mining Institute, Plac Gwarków 1, 40-166 Katowice, Poland,

Bibliografia

• Baker, G.L., and J.P. Gollub, 1995, Chaotic Dynamics - an Introduction, Cambridge Univer¬sity Press, Cambridge, 192 pp.
• De Luca, L., S. Lasocki, D. Luizio and V. Massimo, 1999, Fractal dimension confidence inter¬val estimation of epicentral distributions, Ann. Geof. 42, 5, 911-25.
• Eneva, M., 1996, Effect of limited data sets in evaluating the scaling properties of spatially dis¬tributed data: an example from mining-induced seismic activity, Geophys. J. Int. 124, 773-786.
• Grassberger, P., and I. Procaccia, 1983, Measuring the Strangeness of Strange Attractors, Physica 9 D; Nonlin. Phenomena, North-Holland Publ. Сотр., Amsterdam, 189-208.
• Idziak, A., and W.M. Zuberek, 1995, Fractal analysis of mining induced seismicity in the Up¬per Silesian Coal Basin. In: H.-P. Rossmanith (ed.). Proc. Int. Conf. "Mechanic of Jointed and Faulted Rock", Vienna 1995, Balkema, Rotterdam, 679-682.
• Laskownicka, A., 1999, The potential forecasting abilities of selected parameters of the seis¬mic tremors series: examples from coal, copper and gold mines. Pubis. Inst. Geophys. Pol. Acad. Sc. M-22 (310), 257-265 (in Polish with English abstract, table and figure captions).
• Lasocki, S., and B. Kustowski, 2002, Analysis of deflection for identification of epicenter mi¬gration directions of swarm activity from Hida Mountains in Japan, Acta Geophys. Pol. 50, 1-12.
• Lasocki, S., and Z. Mortimer, 1998, Variations of MS source distribution geometry before a strong tremor occurrence in mines. In: H.R. Hardy (Jr.), Proc. of the 6th Conference on "Acoustic Emission/Microseismic Activity in Geologic Structures and Materials", Trans. Tech. Pubis., Clausthal, 325-337.
• Majewska, Z., and Z. Mortimer, 1998, Fractal description of acoustic emission produced in systems: coal-gas and coal-water. In: K. Ono (ed.), "Progress in Acoustic Emission IX Transition in AE for the 21th Century, Proc. of Intern. AE Conference", 109-118.
• Majewska, Z., and Z. Mortimer, 2000, Studies of the non-linear dynamics of acoustic emission generated in rocks. Proc. of 24"' European Conference on Acoustic Emission Testing EWGAE, Senlis, France, 1-7.
• Majewska, Z., Z. Mortimer and A. Cichy, 2000, Non-linear dynamics application for the de¬scription of accoustic emission phenomena in rocks. Dokumentacja AGH (unpub¬lished, in Polish).
• Mane, R., 1981, On the dimension of the compact invariant sets of certain non-linear maps in dynamical systems and turbulence. In: D.A. Rand and L.S. Young (eds.), "Dynamical Systems and Turbulance Lecture Notes in Mathematics", Springer-Verlag, Beriin, 898, 230-242.
• Marcak, H., 1995, Fractal properties of the seismic records sets from mines. In: "Poradnik Geofizyka Górniczego", Biblioteka Szkoły Eksploatacji Podziemnej, Kraków, 2, 208-213 (in Polish).
• Mendecki, A.J., 1997, Principles of monitoring seismic rockmass response to mining. In: S.J. Gibowicz and S. Lasocki (eds.), "Rockburst and Seismicity in Mines", Balkema, Rot¬terdam, 69-80.
• Mortimer, Z., 1997, Fractal statistics for the local induced seismicity in some Polish coal mines. In: S.J. Gibowicz and S. Lasocki (eds.), "Rockburst and Seismicity in Mines", Balkema, Rotterdam, 49-53.
• Mortimer, Z., 2001a, Studies on the chaotic dynamics of mining induced seismicity. In: H.
• Ogasawara, T. Yanagidani and M. Ando (eds.), "Seismogenic Process Monitoring", Balkema, Rotterdam, 341-354.
• Mortimer, Z., 2001b, An analysis of non-linear dynamics of the induced seismicity - fractals and chaos. In: J. Dubiński, Z. Pilecki and W. Zuberek (eds.), "Badania Geofizyczne w Kopalniach", Wyd. IGSMiE PAN, Kraków, 147-151.
• Mortimer, Z., and A. Cichy, 2001, Nonlinear dynamics parameters estimated from the induced seismicity in Polish coal mines. Acta Geophys. Pol. 49, 3, 303-316.
• Mortimer, Z., and S. Lasocki, 1996, Studies offractality of epicentre distribution geometry in mining induced seismicity. Acta Mont. A, 10 (102), 31-37.
• Mortimer, Z., Z. Majewska and S. Lasocki, 1999a, Generalised fractal dimension of induced seismicity and acoustic emission. Pubis. Inst. Geophys. Pol. Acad. Sc. M-22 (310), 89-94 (in Polish with English abstract, table and figure captions).
• Mortimer, Z., A. Marchewka and A. Cichy, 1999b, The pursuit of deterministic chaos or the study of non-linear dynamics of induced seismicity. In: Materiały V Konferencji Nauk.-Techn. "Geofizyka w Geologii, Górnictwie i Ochronie Środowiska", Kraków, 23 czerwca 1999, 282-289.
• Nerenberg, M.A.H., and C. Essex, 1990, Correlation dimension and systematic geometric ef¬fects, Phys. Rev. A 42, 7065-7074.
• Packard, N.H., J.P. Crutchfield, J.D. Farmer and R.S. Shaw, 1980, Geometry from a time se¬ries, Phys. Rev. Lett. 45, 712-716.
• Radu, S., M. Sciocatti and A.J. Mendecki, 1997, Nonlinear dynamics of seismic flow of rock. In: A.J. Mendecki (ed.), "Seismic Monitoring in Mines", Chapman & Hall, London, 159-177.
• Takens, F., 1980, Detecting strange attractors in turbulence. In: D.A. Rand and L.S. Young (eds.), "Dynamical Systems and Turbulence", Lecture Notes in Mathematics, Springer-Verlag, Berlin, 898, 366-381.
• Wolf, A., J.B. Swift, H.L. Swinney and J.A. Vastano, 1985, Determining Lyapunov exponents from a time series, Physica 16D, 285-317.