Abstract
Recent advances in the theory of fracture and fragmentation are reviewed. Empirical laws in seismology are interpreted from a fractal perspective, and earthquakes are viewed as a self-organized critical phenomenon (SOC). Earthquakes occur as an energy dissipation process in the earth’s crust to which the tectonic energy is continuously input. The crust self-organizes into the critical state and the temporal and spatial fractal structure emerges naturally. Power-law relations known in seismology are the expression of the critical state of the crust. An SOC model for earthquakes, which explains the Gutenberg-Richter relation, the Omori’s formula of aftershocks and the fractal distribution of hypocenters, is presented. A new view of earthquake phenomena shares a common standpoint with other disciplines to study natural complex phenomena with a unified theory.
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References
Aki, K. (1979), Characterization of Barriers on an Earthquake Fault, J. Geophys. Res. 84, 6140–6148.
Aki, K., A probabilistic synthesis of precursory phenomena. In Earthquake Prediction: An International Review, M. Ewing Ser., vol. 4 (eds. Simpson, D. W., and Richards, P. G.) (AGU, Washington, D. C. 1981) pp. 566–574.
Allegre, C. J., Le Mouel, and Provost, A. (1982), Scaling Rules in Rock Fracture and Possible Implications for Earthquake Prediction, Nature 297, A7–A9.
Atmanspacher, H., Schneingraber, H., and Wiedenmann, G. (1989), Determination of f(α) for a Limited Random Point Set, Phys. Rev. A40, 3954–3963.
Bak, P., and Tang, C. (1989), Earthquakes as a Self-organized Critical Phenomenon, J. Geophys. Res. 94, 15, 635–15,637.
Bak, P., Tang, C., and Wiesenfeld, K. (1987), Self-organized Criticality: An Explanation of 1/f Noise, Phys. Rev. Lett. 59, 381–384.
Bak, P., Tang, C., and Wiesenfeld, K. (1988), Self-organized Criticality, Phys. Rev. A38, 364–371.
Bak, P., Chen, K., and Creutz, M. (1989), Self-organized Criticality in the ‘Game of Life’ Nature 342, 780–782.
Bebbington, M., Vere-Jones, D., and Zheng, X. (1990), Percolation Theory: A Model for Rock Fracture? Geophys. J. Int. 100, 215–220.
Burridge, R., and Knopoff, L. (1967), Model and Theoretical Seismicity, Bull. Seismol. Soc. Am. 57, 341–371.
Carlson, J. M., and Langer, J. S. (1989), Properties of Earthquakes Generated by Fault Dynamics, Phys. Rev. Lett. 62, 2632–2635.
Chen, K., Bak, P., and Obukhov, S. P. (1991), Self-organized Criticality in Crack-progagation Model of Earthquakes, Phys. Rev. A43, 625–630.
Dhar, D., and Ramaswamy, R. (1989), Exactly Solved Model of Self-organized Critical Phenomena, Phys. Rev. Lett. 63, 1659–1662.
Durrett, R. (1988), Crabgrass, Measles, and Gypsy Moths: An Introduction to Interacting Particle Systems, Mathemat. Intelligence 10, 31–41.
Enya, O. (1901), On Aftershocks, Rep. Earthq. Inv. Comm. 35, 35–56 (in Japanese).
Gardner, M. (1970), Mathematical Games, Sci. Am. 223(10), 120–123.
Geilikman, M. B., Golubeva, T. V., and Pisarenko, V. F. (1990), Multifractal Patterns of Seismicity, Earth Planet. Sci. Lett. 99, 127–132.
Glansdorff, P., and Prigogine, I., Theory of Structure Stability and Fluctuations (Wiley and Sons, London 1971).
Griffith, A. A. (1921), The Phenomena of Rupture and Flow in Solids, Phil. Trans. R. Soc. A221, 163–198.
Griffith, A. A. (1924), The Theory of Rupture, Proc. 1st Intern. Cong. Appl. Mech., Delft, pp. 55-63.
Haken, H., Synergetics: Nonequilibrium Phase Transitions and Self-organization in Physics, Chemistry and Biology (Springer, Berlin 1977).
Haken, H., Advanced Synergetics (Springer, Berlin 1983).
Halsey, T. C., Jensen, M. H., Kadanoff, L. P., Procaccia, I., and Shraiman, B. I. (1986), Fractal Measures and their Singularities: The Characterization of Strange Sets, Phys. Rev. A33, 1141–1151.
Haskell, N. A. (1969), Elastic Displacements in the Near Field of a Propagating Fault, Bull. Seismol. Soc. Am. 59, 865–908.
Herrmann, H. J., and Roux, S., eds., Statistical Models for the Fracture of Disordered Media (Elsevier, Amsterdam 1990).
Herrmann, H. J., Fractures. In Fractals and Disordered Systems (eds. Bunde, A., and Havlin, S.) (Springer-Verlag, 1991) pp. 175-205.
Hirabayashi, T., and Ito, K. (1990), Multifractal Analysis of Earthquakes, Pure and Appl. Geophys., this issue.
Hirata, T. (1987), Omor’s Power Law Aftershock Sequences of Microfracturing in Rock Fracturing Experiment, J. Geophys. Res. 92, 6215–6221.
Hirata, T., and Imoto, M. (1991), Multifractal Analysis of Spatial Distribution of Microearthquakes in the Konto Region, Geophys. J. Int. 107, 155–162.
Hirata, T., Satoh, T., and Ito, K. (1987), Fractal Structure of Spatial Distribution of Microfracturing in Rock, Geophys. J. R. Astr. Soc. 67, 697–717.
Hwa, T., and Kardar, M. (1989), Fractals and Self-organized Criticality in Dissipative Dynamics, Physica D38, 198–202.
Ishimoto, M., and Iida, K. (1939), Observations sur les seisms energistré par le microseismograph construite dernierment (I), Bull. Earthq. Res. Inst. 17, 443–478 (in Japanese).
Ito, K., and Matsuzaki, M. (1990), Earthquakes as Self-organized Critical Phenomena, J. Geophys. Res. 95, 6853–6860.
Jensen, M. H., Kadanoff, K., Libchaber, A., Procaccia, I., and Stavans, J. (1985); Global Universality at the Onset of Chaos: Results of a Forced Rayleigh-Benard Experiment, Phys. Rev. Lett. 55, 2798–2801.
Kagan, Y. Y. (1981), Spatial Distribution of Earthquakes: The Three-point Moment Function, Geophys. J. R. Astr. Soc. 67, 697–717.
Kagan, Y. Y., and Knopoff, L. (1980), Spatial Distribution of Earthquakes: The Two-point Correlation Function, Geophys. J. R. Astr. Soc. 62, 697–717.
Kanamori, H., and Anderson, D. L. (1975), Theoretical Basis of Some Empirical Relations in Seismology, Bull. Seismol. Soc. Am. 65, 1073–1095.
King, G. (1983), The Accommodation of Large Strains in the Upper Lithosphere of the Earth and Other Solids by Self-similar Fault Systems: The Geometrical Origin ofb-values, Pure and Appl. Geophys. 121, 761–815.
Kinzel, W., Directed percolation. In Percolation Structures and Processes (ed. Weil, R.) (Adam Hilger, Bristol 1983) pp. 425–445.
Leath, P. L. (1976), Cluster Size and Boundary Distribution near Percolation Threshold, Phys. Rev. B14, 5046–5055.
Liggett, T. M., Interacting Particle Systems (Springer-Verlag, New York 1985).
Lomnitz-Adler, J., and Lemus-Diaz, P. (1989), A Stochastic Model for Fracture Growth on a Heterogeneous Seismic Fault, Geophys. J. Int. 99, 183–194.
Lorenz, E. N. (1963), Deterministic Nonperiodic Flow, J. Atmos. Sci. 20, 130–141.
Louis, E., and Guinea, F. (1989), Fracture as a Growth Process, Physica D38, 235–241.
Mandelbrot, B. B. (1967), How Long is the Coast of Britain? Statistical Self-similarity and Fractional Dimension, Science 155, 636–638.
Mandelbrot, B. B., Fractals: Form, Chance and Dimension (Freeman, San Francisco 1977).
Mandelbrot, B. B., The Fractal Geometry of Nature (Freeman, San Francisco 1982).
Matsuzaki, M., and Takayasu, H. (1991), Fractal Features of Earthquake Phenomenon and a Simple Mechanical Model, J. Geophys. Res. 96, 19,925–19,931.
May, R. M. (1976), Simple Mathematical Models with Very Complicated Dynamics, Nature 261, 459–467.
McCauley, J. L. (1990), Introduction to Multifractals in Dynamical Systems Theory and Fully Developed Fluid Turbulence, Phys. Reports 189, 225–226.
Meakin, P. (1991), Models for Material Failure and Deformation, Science 252, 226–234.
Meneveau, C., and Sreenivasan, K. R., The multifractal spectrum of the dissipation field in turbulent flows. In Physics of Chaos and Systems Far from Equilibrium (eds. Van, Minh-Duong, and Nicolis, B.) (North-Holland, Amsterdam 1987).
Mori, Y., Kaneko, K., and Wadati, M. (1991), Fracture Dynamics by Quenching. I. Crack Patterns, J. Phys. Soc. Japan 60, 1591–1599.
Naftaly, U., Schwartz, M., Aharony, A., and Stauffer, D. (1991), The Granular Fracture Model for Rock Fragmentation, J. Phys. A24, L1175–L1184.
Nakanishi, H. (1991), Statistical Properties of the Cellular-automaton Model for Earthquakes, Phys. Rev. A43, 6613–6621.
Nicolis, G., and Prigogine, I., Self-organization in Nonequilibrium Systems: From Dissipative Structures to Order through Fluctuations (Wiley, New York 1977).
Ogata, Y. (1988), Statistical Models for Earthquake Occurrences and Residual Analysis for Point Processes, J. Am. Stat. Assoc. 83(401), 9–27.
Ogata, Y. (1989), Statistical Model for Standard Seismicity and Detection of Anomalies by Residual Analysis, Tectonophys. 169, 159–174.
Omori, F. (1894), On Aftershocks of Earthquakes, J. Coll. Sci. Imp. Univ. Tokyo 7, 111–200.
Otsuka, M. (1971), A Simulation of Earthquakes Occurrences, Part 1: A Mechanical Model, Jishin 24, 13–25 (in Japanese).
Otsuka, M. (1972), A Chain-reaction-type Source Model as a Tool to Interpret the Magnitude-frequency Relation of Earthquakes, J. Phys. Earth 20, 35–45.
Pasad, R. R., Meneveau, C., and Sreenivasan, K. R. (1988), Multifractal Nature of the Dissipation Field of Passive Scalars in Fully Developed Turbulent Flows, Phys. Rev. Lett. 61, 14–77.
Peebles, P. J. E., Large-scale Structure of the Universe (Princeton Univ. Press, Princeton 1980).
Pfeuty, P., and Toulouse, G., Introduction to the Renormalization Group and Critical Phenomena (John Wiley and Sons, 1977).
Pietronero, L., and Tosatti, E., eds., Fractals in Physics (North-Holland, Amsterdam 1986).
Rikitake, T. (1958), Oscillations of a System of Disk Dynamos, Proc. Cambridge Philos. Soc. 54, 89–105.
Sadvskiy, M. A., Golubeva, T. V., Pisarenko, V. F., and Shnirman, M. G. (1984), Characteristic Dimensions of Rock and Hierarchical Properties of Seismicity, Izv. Acad. Sci. USSR, Earth Phys., Engl. Transi., 20, 87–96.
Selinger, R. L. B., Wang, Z.-G., Gelbart, W. M., and Ben-Shaul, A. (1991), Statistical-thermodynamic Approach to Fracture, Phys. Rev. A43, 4396–4400.
Skjertorp, A. T., and Meakin, P. (1988), Fracture in Microsphere Monolayers Studied by Experiment and Computer Simulation, Nature 335, 424–426.
Smalley, R. F., Turcotte, D. L., and Solla, S. A. (1985), A Renormalization Group Approach to the Stick-slip Behavior of Faults, J. Geophys. Res. 90, 1894–1900.
Sornette, A., Davy, Ph., and Sornette, D. (1990), Structuration of the Lithosphere in Plate Tectonics as a Self-organized Critical Phenomenon, J. Geophys. Res. 95, 17,353–17,361.
Sornette, A., and Sornette, D. (1989), Self-organized Criticality and Earthquakes, Europhys. Lett. 9, 197–202.
Stanley, H. G., Introduction to Phase Transitions and Critical Phenomena (Clarendon Press, Oxford 1971).
Stanley, H. E., and Meakin, P. (1988), Multifractal Phenomena in Physics and Chemistry, Nature 335, 405–409.
Stauffer, D., Introduction to Percolation Theory (Taylor and Francis, London 1985).
Stuketee, J. A. (1958), Some Geophysical Applications of the Elasticity Theory of Dislocations, Can. J. Phys. 36, 1168–1198.
Takayasu, H., Pattern formation of dendritic fractals in fracture and electric breakdown. In Fractals in Physics (eds. Pietronero, L., and Tosatti, E.) (North-Holland, Amsterdam 1986) pp. 181–184.
Takayasu, H., Nishikawa, I., and Tasaki, H. (1988), Power-law Distribution of Aggregation Systems with Injection, Phys. Rev. A37, 3110–3117.
Termonia, Y., and Meakin, P. (1986), Formation of Fractal Cracks in Kinetic Fracture Model, Nature 320, 429–431.
Terada, T., Scientific Papers by Torahiko Terada, Vols. 1-6 (Iwanami Syoten, Tokyo 1931).
Thom, R., Structural Stability and Morphogenesis (Benjamin, Reading, MA 1975).
Thompson, D’arcy W., On Growth and Form (Cambridge Univ. Press, Cambridge 1917).
Totsuji, H., and Kihara, T. (1969), The Correlation Function for the Distribution of Galaxies, Publ. Astron. Soc. Japan 21, 221–229.
Turcotte, D. L. (1986), A Fractal Model for Crustal Deformation, Tectonophys. 132, 361–369.
Utsu, T. (1969), Aftershocks and Earthquake Statistics (I), J. Fac. Sci., Hokkaido Univ., ser. VII, 3, 129–195.
Utsu, T. (1970), ibid (II), J. Fac. Sci., Hokkaido Univ., ser. VII, 3, 197–266.
Wiesenfeld, K., Tang, G., and Bak, P. (1989), A Physicist’s Sandbox, J. Statist. Phys. 54, 1441–1458.
Yamashina, K. (1978), Induced Earthquakes in the Izu-Peninsula by the Izu-Hanto-Oki Earthquake of 1974, Japan, Tectonophys. 51, 139–154.
Zeeman, E. C., Catastrophe Theory (Addison-Wesley, Reading, MA 1977).
Zhang, Yi-C. (1989). Scaling Theory of Self-organized Criticality, Phys. Rev. Lett., 63, 470–473.
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Ito, K. (1992). Towards a New View of Earthquake Phenomena. In: Sammis, C.G., Saito, M., King, G.C.P. (eds) Fractals and Chaos in the Earth Sciences. Pageoph Topical Volumes. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-6191-5_2
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DOI: https://doi.org/10.1007/978-3-0348-6191-5_2
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