Skip to main content
Log in

Fractal variations of the Transcarpathians, West Ukraine, seismicity and their potential relation to changing phases of local seismic cycles

  • Published:
Acta Geophysica Aims and scope Submit manuscript

Abstract

The evolution of spatial arrangement of the Transcarpathian earthquakes is studied by means of fractal analysis. Spatial correlation dimension is evaluated for a subset of fixed number of catalogue events consecutively shifted in time by one event forward. Distinctive patterns that may be related to different phases of local seismic cycle/cycles have been identified, corresponding to extreme values of the dimension. Their potential relation to evolution of the seismogenic stress field is discussed. The time it takes for the capacity dimension to reach the so-called percolation threshold is estimated for a subset consecutively extended by adding next catalogue events. Temporal and spatial frames of percolation analysis are discussed in relation to parameters of the future earthquake.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Bowman, D.D., and G.C.P. King, 2001a, Accelerating seismicity and stress accumulation before large earthquakes, Geophys. Res. Lett. 28, 4039–4042.

    Article  Google Scholar 

  • Bowman, D.D., and G.C.P. King, 2001b, Stress transfer and seismicity changes before large earthquakes, C.R. Acad. Sci. Paris, Sciences de la Terre et des planets 333, 591–599.

    Google Scholar 

  • Bune, V.I., and G.P. Gorshkov (eds.), 1980, Seismic zoning of the territory of the USSR. Methodic principles and regional description of the 1978 map, Izd. Nauka, Moscow, 97–107 (in Russian).

    Google Scholar 

  • De Rubeis, V., P. Dimitriu, E. Papadimitriou and P. Tosi, 1993, Recurrent patterns in the spatial behavior of Italian seismicity revealed by the fractal approach, Geophys. Res. Lett. 20, 1911–1914.

    Article  Google Scholar 

  • Dimitriu, P.P., E.M. Scordilis and V.G. Karacostas, 2000, Multifractal analysis of the Arnea, Greece, seismicity with potential implications for earthquake prediction, Natural Hazards 21, 277–295.

    Article  Google Scholar 

  • Eckmann, J.P., and D. Ruelle, 1992, Fundamental limitations for estimating dimensions and Lyapunov exponents in dynamical systems, Physica D 56, 185–187.

    Google Scholar 

  • Gnyp, A., 2006, Fractal features of the Transcarpathians, West Ukraine, seismicity. In: Proc. Shevchenko Scientific Society, Geophysics 17, 82–106 (in Ukrainian).

  • Gnyp, A.R., and T.Z. Verbitskiy, 2005, Some peculiarities of spatial and temporal distribution of seismicity in the Transcarpathians. In: V.I. Starostenko (ed.), “Studies of recent geodynamics of the Ukrainian Carpathians”, Kyiv, 87–102 (in Ukrainian).

  • Gnyp, A.R., T.Z. Verbitskiy, R.S. Pronishyn, O.M. Novotna, I.M. Nishchimenko and I.I. Yarema, 2005, Studies of the spatial and temporal structure of seismic activity of the Zakarpattya (=Transcarpathians) using Morishita indices, Geophys. J. 27, 655–666 (in Ukrainian).

    Google Scholar 

  • Grassberger, P., 1983, Generalized dimensions of strange attractors, Phys. Lett. A 97, 227–230.

    Google Scholar 

  • Grassberger, P., and I. Procaccia, 1983, Measuring the strangeness of attractors, Physica D 9, 189–208.

    Google Scholar 

  • Havstad, J.W., and C.L. Ehlers, 1989, Attractor dimension of nonstationary dynamical systems from small data sets, Phys. Rev. A 39, 845–853.

    Google Scholar 

  • Kagan, Y.Y., and L. Knopoff, 1980, Spatial distribution of earthquakes: the two-point correlation function, Geophys. J. Roy. Astron. Soc. 62, 303–320.

    Google Scholar 

  • King, G.C.P., 1983, The accommodation of large strains in the upper lithosphere of the Earth and other solids by self-similar fault systems: the geometrical origin of b-value, Pure Appl. Geophys. 121, 761–815.

    Article  Google Scholar 

  • King, G.C.P., and D.D. Bowman, 2003, The evolution of regional seismicity between large earthquakes, J. Geophys. Res. B2 108, 2096, doi: 10.1029/2001JB000783.

    Article  Google Scholar 

  • Kostiuk, O., E. Sahalova and I. Rudenska, 1997, Catalogue of earthquakes of the Carpathian region for the period of 1091-1990. In: Proc. Shevchenko Scientific Society, Geology and Geophysics 1, 121–137 (in Ukrainian).

  • Kutas, V.V., I.M. Rudenskaya and I.A. Kalitova, 1999, Carpathian hodograph of P and Swaves and lithospheric inhomogeneities, Geophys. J. 21, 45–55 (in Russian).

    Google Scholar 

  • Main, I.G., 1988, Prediction of failure times in the Earth for a time-varying stress, Geophys. J. 92, 455–464.

    Google Scholar 

  • Mandelbrot, B.B., 1977, The fractal geometry of nature, Freeman, New York.

    Google Scholar 

  • Martinez, V.J., 1999, Is the universe fractal?, Science 284, 445–446.

    Article  Google Scholar 

  • Murray, N., and M. Holman, 1999, The origin of chaos in the outer solar system, Science 283, 1877–81.

    Article  Google Scholar 

  • Pronishyn, R.S., and B.G. Pustovitenko, 1981, Peculiarities of processes in the epicentral zone of the Transcarpathian earthquakes in 1979, Geophys. J. 3, 71–85 (in Russian).

    Google Scholar 

  • Pronishyn, R.S., and B.G. Pustovitenko, 1982, Some aspects of seismic “climate and weather” in the Transcarpathians, Izv. Acad. Sci. USSR, Phys. Solid Earth 18, 74–81 (in Russian).

    Google Scholar 

  • Sadovskiy, M.A., T.V. Golubeva, V.F. Pisarenko and M.G. Shnirman, 1984, Characteristic dimensions of rock and hierarchy properties of seismicity, Izv. Acad. Sci. USSR, Phys. Solid Earth 20, 87–96 (English translation).

    Google Scholar 

  • Sahimi, M., M.C. Robertson and C.G. Sammis, 1992, Relation between the earthquake statistics and fault patterns, and fractals and percolation, Physica A 151, 57–68.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gnyp, A. Fractal variations of the Transcarpathians, West Ukraine, seismicity and their potential relation to changing phases of local seismic cycles. Acta Geophys. 55, 288–301 (2007). https://doi.org/10.2478/s11600-007-0015-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.2478/s11600-007-0015-5

Key words

Navigation