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Towards a new view of earthquake phenomena

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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.

    Google Scholar 

  • Aki, K.,A probabilistic synthesis of precursory phenomena. InEarthquake 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.

    Google Scholar 

  • Allegre, C. J., Le Mouel, andProvost, A. (1982),Scaling Rules in Rock Fracture and Possible Implications for Earthquake Prediction, Nature297, 47–49.

    Google Scholar 

  • Atmanspacher, H., Schneingraber, H., andWiedenmann, G. (1989),Determination of f(α) for a Limited Random Point Set, Phys. Rev.A40, 3954–3963.

    Google Scholar 

  • Bak, P., andTang, C. (1989),Earthquakes as a Self-organized Critical Phenomenon, J. Geophys. Res.94, 15,635–15,637.

    Google Scholar 

  • Bak, P., Tang, C., andWiesenfeld, K. (1987),Self-organized Criticality: An Explanation of 1/f Noise, Phys. Rev. Lett.59, 381–384.

    Google Scholar 

  • Bak, P., Tang, C., andWiesenfeld, K. (1988),Self-organized Criticality, Phys. Rev.A38, 364–371.

    Google Scholar 

  • Bak, P., Chen, K., andCreutz, M. (1989),Self-organized Criticality in the ‘Game of Life’, Nature342, 780–782.

    Google Scholar 

  • Bebbington, M., Vere-Jones, D., andZheng, X. (1990),Percolation Theory: A Model for Rock Fracture? Geophys. J. Int.100, 215–220.

    Google Scholar 

  • Burridge, R., andKnopoff, L. (1967),Model and Theoretical Seismicity, Bull. Seismol. Soc. Am.57, 341–371.

    Google Scholar 

  • Carlson, J. M., andLanger, J. S. (1989),Properties of Earthquakes Generated by Fault Dynamics, Phys. Rev. Lett.62, 2632–2635.

    Google Scholar 

  • Chen, K., Bak, P., andObukhov, S. P. (1991),Self-organized Criticality in Crack-progagation Model of Earthquakes, Phys. Rev.A43, 625–630.

    Google Scholar 

  • Dhar, D., andRamaswamy, R. (1989),Exactly Solved Model of Self-organized Critical Phenomena, Phys. Rev. Lett.63, 1659–1662.

    Google Scholar 

  • Durrett, R. (1988),Crabgrass, Measles, and Gypsy Moths: An Introduction to Interacting Particle Systems, Mathemat. Intelligence10, 37–47.

    Google Scholar 

  • Enya, O. (1901),On Aftershocks, Rep. Earthq. Inv. Comm.35, 35–56 (in Japanese).

    Google Scholar 

  • Gardner, M. (1970),Mathematical Games Sci. Am.223 (10), 120–123.

    Google Scholar 

  • Geilikman, M. B., Golubeva, T. V., andPisarenko, V. F. (1990),Multifractal Patterns of Seismicity, Earth Planet. Sci. Lett.99, 127–132.

    Google Scholar 

  • Glansdorff, P., andPrigogine, I.,Theory of Structure Stability and Fluctuations (Wiley and Sons, London 1971).

    Google Scholar 

  • Griffith, A. A. (1921),The Phenomena of Rupture and Flow in Solids, Phil. Trans. R. Soc.A221, 163–198.

    Google Scholar 

  • Griffith, A. A. (1924),The Theory of Rupture, Proc. Ist 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).

    Google Scholar 

  • Haken, H.,Advanced Synergetics (Springer, Berlin 1983).

    Google Scholar 

  • Halsey, T. C., Jensen, M. H., Kadanoff, L. P., Procaccia, I., andShraiman, B. I. (1986),Fractal Measures and their Singularities: The Characterization of Strange sets, Phys. Rev.A33, 1141–1151.

    Google Scholar 

  • Haskell, N. A. (1969),Elastic Displacements in the Near Field of a Propagating Fault, Bull. Seismol. Soc. Am.59, 865–908.

    Google Scholar 

  • Herrmann, H. J., andRoux, S., eds.,Statistical Models for the Fracture of Disordered Media (Elsevier, Amsterdam 1990).

    Google Scholar 

  • Herrmann, H. J.,Fractures. InFractals and Disordered Systems (eds. Bunde, A., and Havlin, S.) (Springer-Verlag, 1991) pp. 175–205.

  • Hirabayashi, T., andIto, K. (1990),Multifractal Analysis of Earthquakes, Pure and Appl. Geophys., this issue.

  • Hirata, T. (1987),Omori's Power Law Aftershock Sequences of Microfracturing in Rock Fracturing Experiment, J. Geophys. Res.92, 6215–6221.

    Google Scholar 

  • Hirata, T., andImoto, M. (1991),Multifractal Analysis of Spatial Distribution of Microearthquakes in the Kanto Region, Geophys. J. Int.107, 155–162.

    Google Scholar 

  • Hirata, T., Satoh, T., andIto, K. (1987),Fractal Structure of Spatial Distribution of Microfracturing in Rock, Geophys. J. R. Astr. Soc.67, 697–717.

    Google Scholar 

  • Hwa, T., andKardar, M. (1989),Fractals and Self-organized Criticality in Dissipative Dynamics, PhysicaD38, 198–202.

    Google Scholar 

  • Ishimoto, M., andIida, K. (1939),Observations sur les seisms energistré par le microseismograph construite dernierment (I), Bull. Earthq. Res. Inst.17, 443–478 (in Japanese).

    Google Scholar 

  • Ito, K., andMatsuzaki, M. (1990),Earthquakes as Self-organized Critical Phenomena, J. Geophys. Res.95, 6853–6860.

    Google Scholar 

  • Jensen, M. H., Kadanoff, K., Libchaber, A., Procaccia, I., andStavans, J. (1985),Global Universality at the Onset of Chaos: Results of a Forced Rayleigh-Benard Experiment, Phys. Rev. Lett.55, 2798–2801.

    Google Scholar 

  • Kagan, Y. Y. (1981),Spatial Distribution of Earthquakes: The Three-point Moment Function, Geophys. J. R. Astr. Soc.67, 697–717.

    Google Scholar 

  • Kagan, Y. Y., andKnopoff, L. (1980),Spatial Distribution of Earthquakes: The Two-point Correlation Function, Geophys. J. R. Astr. Soc.62, 697–717.

    Google Scholar 

  • Kanamori, H., andAnderson, D. L. (1975),Theoretical Basis of Some Empirical Relations in Seismology, Bull. Seismol. Soc. Am.65, 1073–1095.

    Google Scholar 

  • 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 of b-values, Pure and Appl. Geophys.121, 761–815.

    Google Scholar 

  • Kinzel, W.,Directed percolation. InPercolation Structures and Processes (ed. Weil, R.) (Adam Hilger, Bristol 1983) pp. 425–445.

    Google Scholar 

  • Leath, P. L. (1976),Cluster Size and Boundary Distribution near Percolation Threshold, Phys. Rev.B14, 5046–5055.

    Google Scholar 

  • Liggett, T. M.,Interacting Particle Systems (Springer-Verlag, New York 1985).

    Google Scholar 

  • Lomnitz-Adler, J., andLemus-Diaz, P. (1989),A Stochastic Model for Fracture Growth on a Heterogeneous Seismic Fault, Geophys. J. Int.99, 183–194.

    Google Scholar 

  • Lorenz, E. N. (1963),Deterministic Nonperiodic Flow, J. Atmos. Sci.20, 130–141.

    Article  Google Scholar 

  • Louis, E., andGuinea, F. (1989),Fracture as a Growth Process, PhysicaD38, 235–241.

    Google Scholar 

  • Mandelbrot, B. B. (1967),How Long is the Coast of Britain? Statistical Self-similarity and Fractional Dimension, Science155, 636–638.

    Google Scholar 

  • Mandelbrot, B. B.,Fractals: Form, Chance and Dimension (Freeman, San Francisco 1977).

    Google Scholar 

  • Mandelbrot, B. B.,The Fractal Geometry of Nature (Freeman, San Francisco 1982).

    Google Scholar 

  • Matsuzaki, M., andTakayasu, H. (1991),Fractal Features of Earthquake Phenomenon and a Simple Mechanical Model, J. Geophys. Res.96, 19,925–19,931.

    Google Scholar 

  • May, R. M. (1976),Simple Mathematical Models with Very Complicated Dynamics, Nature261, 459–467.

    Google Scholar 

  • McCauley, J. L. (1990),Introduction to Multifractals in Dynamical Systems Theory and Fully Developed Fluid Turbulence, Phys. Reports189, 225–226.

    Google Scholar 

  • Meakin, P. (1991),Models for Material Failure and Deformation, Science252, 226–234.

    Google Scholar 

  • Meneveau, C., andSreenivasan, K. R.,The multifractal spectrum of the dissipation field in turbulent flows. InPhysics of Chaos and Systems Far from Equilibrium (eds. Van, Minh-Duong, and Nicolis, B.) (North-Holland, Amsterdam 1987).

    Google Scholar 

  • Mori, Y., Kaneko, K., andWadati, M. (1991),Fracture Dynamics by Quenching. I. Crack Patterns, J. Phys. Soc. Japan,60, 1591–1599.

    Google Scholar 

  • Naftaly, U., Schwartz, M., Aharony, A., andStauffer, D. (1991),The Granular Fracture Model for Rock Fragmentation, J. Phys.A24, L1175-L1184.

    Google Scholar 

  • Nakanishi, H. (1991),Statistical Properties of the Cellular-automaton Model for Earthquakes, Phys. Rev.A43, 6613–6621.

    Google Scholar 

  • Nicolis, G., andPrigogine, I.,Self-organization in Nonequilibrium Systems: From Dissipative Structures to Order through Fluctuations (Wiley, New York 1977).

    Google Scholar 

  • Ogata, Y. (1988),Statistical Models for Earthquake Occurrences and Residual Analysis for Point Processes, J. Am. Stat. Assoc83 (401), 9–27.

    Google Scholar 

  • Ogata, Y. (1989),Statistical Model for Standard Seismicity and Detection of Anomalies by Residual Analysis, Tectonophys.169, 159–174.

    Google Scholar 

  • Omori, F. (1894),On Aftershocks of Earthquakes, J. Coll. Sci. Imp. Univ. Tokyo7, 111–200.

    Google Scholar 

  • Otsuka, M. (1971),A Simulation of Earthquakes Occurrences, Part 1: A Mechanical Model, Jishin24, 13–25 (in Japanese).

    Google Scholar 

  • Otsuka, M. (1972),A Chain-reaction-type Source Model as a Tool to Interpret the Magnitude-frequency Relation of Earthquakes, J. Phys. Earth20, 35–45.

    Google Scholar 

  • Pasad, R. R., Meneveau, C., andSreenivasan, K. R. (1988),Multifractal Nature of the Dissipation Field of Passive Scalars in Fully Developed Turbulent Flows, Phys. Rev. Lett.61, 74–77.

    Google Scholar 

  • Peebles, P. J. E.,Large-scale Structure of the Universe (Princeton Univ. Press, Princeton 1980).

    Google Scholar 

  • Pfeuty, P., andTuolouse, G.,Introduction to the Renormalization Group and Critical Phenomena (John Wiley and Sons, 1977).

  • Pietronero, L., andTosatti, E. eds.,Fractals in Physics (North-Holland, Amsterdam 1986).

    Google Scholar 

  • Rikitake, T. (1958),Oscillations of a System of Disk Dynamos, Proc. Cambridge Philos. Soc.54, 89–105.

    Google Scholar 

  • Sadvskiy, M. A., Golubeva, T. V., Pisarenko, V. F., andShnirman, M. G. (1984),Characteristic Dimensions of Rock and Hierarchical Properties of Seismicity, Izv. Acad. Sci. USSR, Earth Phys. Engl. Transl.,20, 87–96.

    Google Scholar 

  • Selinger, R. L. B., Wang, Z.-G., Gelbart, W. M., andBen-Shaul, A. (1991),Statistical-thermodynamic Approach to Fracture, Phys. Rev.A43, 4396–4400.

    Google Scholar 

  • Skjertorp, A. T., andMeakin, P. (1988),Fracture in Microsphere Monolayers Studied by Experiment and Computer Simulation, Nature,335, 424–426.

    Google Scholar 

  • Smalley, R. F., Turcotte, D. L., andSolla, S. A. (1985),A Renormalization Group Approach to the Stick-slip Behavior of Faults, J. Geophys. Res.90, 1894–1900.

    Google Scholar 

  • Sornette, A., Davy, Ph., andSornette, D. (1990),Structuration of the Lithosphere in Plate Tectonics as a Self-organized Critical Phenomenon, J. Geophys. Res.95, 17,353–17,361.

    Google Scholar 

  • Sornette, A., andSornette, D. (1989),Self-organized Criticality and Earthquakes, Europhys. Lett.9, 197–202.

    Google Scholar 

  • Stanley, H. G.,Introduction to Phase Transitions and Critical Phenomena (Clarendon Press, Oxford 1971).

    Google Scholar 

  • Stanley, H. E., andMeakin, P. (1988),Multifractal Phenomena in Physics and Chemistry, Nature335, 405–409.

    Google Scholar 

  • Stauffer, D.,Introduction to Percolation Theory (Taylor and Francis, London 1985).

    Google Scholar 

  • Stuketee, J. A. (1958),Some Geophysical Applications of the Elasticity Theory of Dislocations, Can. J. Phys.36, 1168–1198.

    Google Scholar 

  • Takayasu, H.,Pattern formation of dendritic fractals in fracture and electric breakdown. InFractals in Physics (eds. Pietronero, L., and Tosatti, E.) (North-Holland, Amsterdam 1986) pp. 181–184.

    Google Scholar 

  • Takayasu, H., Nishikawa, I., andTasaki, H. (1988),Power-law Distribution of Aggregation Systems with Injection, Phys. Rev.A37, 3110–3117.

    Google Scholar 

  • Termonia, Y., andMeakin, P. (1986),Formation of Fractal Cracks in Kinetic Fracture Model, Nature320, 429–431.

    Google Scholar 

  • Terada, T.,Scientific Papers by Torahiko Terada, Vols. 1–6 (Iwanami Syoten, Tokyo 1931).

    Google Scholar 

  • Thom, R.,Structural Stability and Morphogenesis, (Benjamin, Reading, MA 1975).

    Google Scholar 

  • Thompson, D'arcy W.,On Growth and Form, (Cambridge Univ. Press, Cambridge 1917).

    Google Scholar 

  • Totsuji, H., andKihara, T. (1969),The Correlation Function for the Distribution of Galaxies, Publ. Astron. Soc. Japan21, 221–229.

    Google Scholar 

  • Turcotte, D. L. (1986),A Fractal Model for Crustal Deformation, Tectonophys.132, 361–369.

    Google Scholar 

  • Utsu, T. (1969),Aftershocks and Earthquake Statistics (I), J. Fac. Sci., Hokkaido Univ., ser. VII,3, 129–195.

    Google Scholar 

  • Utsu, T. (1970),, J. Fac. Sci., Hokkaido Univ., ser. VII,3, 197–266.

    Google Scholar 

  • Wiesenfeld, K., Tang, G., andBak, P. (1989),A Physicist's Sandbox, J. Statist. Phys.54, 1441–1458.

    Google Scholar 

  • Yamashina, K. (1978),Induced Earthquakes in the Izu-Peninsula by the Izu-Hanto-Oki Earthquake of 1974, Japan, Tectonophys.51, 139–154.

    Google Scholar 

  • Zeeman, E. C.,Catastrophe Theory (Addison-Wesley, Reading, MA 1977).

    Google Scholar 

  • Zhang, Yi-C. (1989).Scaling Theory of Self-organized Criticality, Phys. Rev. Lett.,63, 470–473.

    Google Scholar 

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  1. Department of Earth Sciences, Faculty of Science, Kobe University, Nada, 657, Kobe, Japan

    Keisuke Ito

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Ito, K. Towards a new view of earthquake phenomena. PAGEOPH 138, 531–548 (1992). https://doi.org/10.1007/BF00876337

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