Skip to main content
Log in

Symmetropy of earthquake patterns: asymmetry and rotation in a disordered seismic source

  • Published:
Acta Geophysica Aims and scope Submit manuscript

Abstract

We demonstrate that the idea of symmetropy can be used for quantification of earthquake patterns. The symmetropy can be considered as a measure of asymmetry. A pattern is richer in asymmetry when the symmetropy is smaller. The specific results of its applications are obtained as follows. In a discrete model of a seismic source with self-organized criticality, the spatial patterns of earthquakes during critical states and sub-critical states are distinguished by the behaviour of the symmetropy: sub-critical patterns show that the symmetropy is approximately a constant but this has various values during critical states. The critical patterns show asymmetric property without any asymmetric force from the outside and without asymmetric intracellular rule. We show that the emergence of asymmetric patterns is a generic feature of dynamic ruptures in our model. Such a generic asymmetry results from the model which is an inherently discrete system consisting of finite-sized cells. These cells may represent geometrical disordered fault zones. We further discuss rotational motions that generate seismic rotational waves. In micromorphic continuum theory, such rotations are attributed to dynamic ruptures in disordered systems. We note that the concept of disorder in this theory is expressed by a set of finite-sized microstructures and is consistent with the concept of disorder modelled in the present study. Thus, we suggest that the spatially asymmetric patterns of earthquakes might be related to the rotational motions, because both come from dynamic ruptures in a discrete fault zone without a well-defined continuum limit.

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.

Institutional subscriptions

Similar content being viewed by others

References

  • Bak, P., and C. Tang, 1989: “Earthquakes as a self-organized critical phenomenon”, J. Geophys. Res. 94B, 15635–15637.

    Article  Google Scholar 

  • Burridge, R., and L. Knopoff, 1967: “Model and theoretical seismicity”, Bull. Seismol. Soc. Am. 57, 341–371.

    Google Scholar 

  • Gutenberg, B., and C.F. Richter, 1944: “Frequency of earthquakes in California”, Bull. Seismol. Soc. Am. 34, 185–188.

    Google Scholar 

  • Iesan, D., 1981: “Some applications of micropolar mechanics to earthquake problems”, Int. J. Eng. Sci. 19, 855–864.

    Article  Google Scholar 

  • Ito, K., and M. Matsuzaki, 1990: “Earthquakes as self-organized critical phenomena”, J. Geophys. Res. 95B, 6853–6860.

    Google Scholar 

  • Kagan, Y.Y., 1994: “Observational evidence for earthquakes as a nonlinear dynamic process”, Physica D 77, 160–192.

    Google Scholar 

  • Kondo, K., 1949a: “A proposal of a new theory concerning the yielding of materials based on Riemannian geometry, I”, J. Japan. Soc. Appl. Mech. 2, 123–128.

    Google Scholar 

  • Kondo, K., 1949b: “A proposal of a new theory concerning the yielding of materials based on Riemannian geometry, II”, J. Japan. Soc. Appl. Mech. 2, 146–151.

    Google Scholar 

  • Moriya, T., and R. Teisseyre, 1999: “Discussion on the recording of seismic rotation waves”, Acta Geophys. Pol. 47, 351–362.

    Google Scholar 

  • Nagahama, H., and R. Teisseyre, 2000: “Micromorphic continuum and fractal fracturing in the lithosphere”, Pure Appl. Geophys. 155, 559–574.

    Article  Google Scholar 

  • Nagahama, H., and R. Teisseyre, 2006: “From non-local to asymmetric deformation field”. In: R. Teisseyre, M. Takeo and E. Majewski (eds.), Earthquake Source Asymmetry, Structural Media and Rotation Effects, Springer-Verlag (in press).

  • Nanjo, K., H. Nagahama and E. Yodogawa, 2000: “Symmetry properties of spatial distribution of microfracturing in rock”, Forma 15, 95–101.

    Google Scholar 

  • Nanjo, K., H. Nagahama and E. Yodogawa, 2001: “Symmetropy and self-organized criticality”, Forma 16, 213–224.

    Google Scholar 

  • Nanjo, K., H. Nagahama and E. Yodogawa, 2004: “Symmetry in the self-organized criticality”. In: D. Nagy and G. Lugosi (eds.), Symmetry: Art and Science 2004. ISIS-Symmetry, Budapest, 302–305.

    Google Scholar 

  • Nanjo, K.Z., H. Nagahama and E. Yodogawa, 2005: “Symmetropy of fault patterns: quantitative measurement of anisotropy and entropic heterogeneity”, Math. Geol. 37, 277–293.

    Article  Google Scholar 

  • Rice, J.R., 1993: “Spatio-temporal complexity of slip on a fault”, J. Geophys. Res. 98B, 9885–9907.

    Article  Google Scholar 

  • Suhubi, E.S., and A.C. Eringen, 1964: “Nonlinear theory of micro-elastic solids II”, Int. J. Eng. Sci. 2, 389–404.

    Article  Google Scholar 

  • Takeo, M., and H.M. Ito, 1997: “What can be learned from rotational motions excited by earthquakes?”, Geophys. J. Int. 129, 319–329.

    Google Scholar 

  • Teisseyre, R., 1973: “Earthquake processes in a micromorphic continuum”, Pure Appl. Geophys. 102, 15–28.

    Article  Google Scholar 

  • Teisseyre, R., 1974: “Symmetric micromorphic continuum: wave propagation, point source solution and some applications to earthquake processes”. In: P. Thoft-Christensen (ed.), Continuum Mechanics Aspects of Geodynamics and Rock Fracture Mechanics, D. Reidel Pub., Boston, 201–244.

    Google Scholar 

  • Twiss, R.J., G.M. Protzman and S.D. Hurst, 1991: “Theory of slikenline patterns based on the velocity gradient tensor and microrotation”, Tectonophysics 186, 215–239.

    Article  Google Scholar 

  • Utsu, T., 1970: “Aftershocks and earthquake statistics (2): further investigation of aftershocks and other earthquake sequences based on a new classification of earthquake sequences”, J. Fac. Sci. Hokkaido Univ. Series 7 (Geophys.) 3, 197–266.

    Google Scholar 

  • Vesanen, E., and R. Teisseyre, 1978: “Symmetry and asymmetry in geodynamics”, Geophysica 15, 147–170.

    Google Scholar 

  • Walsh, J.L., 1999: “A closed set of normal orthogonal functions”. In: T.J. Rivlin and E.B. Saff (eds.), Joseph L Walsh Selected Papers, Springer-Verlag, New York, 109–128.

    Google Scholar 

  • Yodogawa, E., 1982: “Symmetropy, an entropy-like measure of visual symmetry”, Percept. Psychophys. 32, 230–240.

    Google Scholar 

  • Xie, X., 2004: “Discussion on rotational tectonic stress field and the genesis of circum-Ordos landmass fault system”, Acta Seismol. Sinica 17, 464–472.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Nanjo, K.Z., Nagahama, H. & Yodogawa, E. Symmetropy of earthquake patterns: asymmetry and rotation in a disordered seismic source. Acta Geophys. 54, 3–14 (2006). https://doi.org/10.2478/s11600-006-0002-2

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.2478/s11600-006-0002-2

Key words

Navigation