Earthquakes as a Complex System

Earthquakes are a direct consequence of the deformation of the Earth's crust. They are primarily associated with stick-slip behavior on preexisting faults. This chapter focuses on an approach to earthquake mechanics in which the crust is considered as a complex self-organizing system that can be treated by techniques developed in statistical physics. The basic hypothesis states that deformation processes interact on a range of scales from thousands of kilometers to millimeters or less. The chapter explores the validity of Gutenberg–Richter frequency–magnitude relation for both regional and global earthquakes. It examines the idea that complex phenomena often exhibit fractal scaling in magnitude, space, and time. Complex phenomena also exhibit chaotic behavior. Concepts of complexity also have direct applicability to probabilistic earthquake hazard studies and to intermediate-term earthquake prediction. The universal applicability of the Gutenberg–Richter relation provides one of the principal means of estimating the earthquake hazards. The rate of occurrence of small earthquakes provides a quantitative measure of the rate of occurrence of larger earthquakes. The concepts of complexity thus provide a rational basis for extrapolation and for intermediate-range earthquake prediction.

[1]  Y. Kagan,et al.  Earthquakes Cannot Be Predicted , 1997, Science.

[2]  C. Cornell Engineering seismic risk analysis , 1968 .

[3]  Benoit B. Mandelbrot,et al.  Fractal Geometry of Nature , 1984 .

[4]  Jean-Luc Chatelain,et al.  A fractal approach to the clustering of earthquakes: Applications to the seismicity of the New Hebrides , 1987 .

[5]  D. Sornette,et al.  Discrete Scaling in Earthquake Precursory Phenomena: Evidence in the Kobe Earthquake, Japan , 1996 .

[6]  Didier Sornette,et al.  Complex Critical Exponents from Renormalization Group Theory of Earthquakes: Implications for Earthquake Predictions , 1995 .

[7]  John B. Rundle,et al.  The statistical mechanics of earthquakes , 1997 .

[8]  V. I. Keilis-Borok,et al.  The lithosphere of the Earth as a nonlinear system with implications for earthquake prediction , 1990 .

[9]  B. P. Watson,et al.  Renormalization group approach for percolation conductivity , 1976 .

[10]  David J. Varnes,et al.  Predictive modeling of the seismic cycle of the Greater San Francisco Bay Region , 1993 .

[11]  Lynn R. Sykes,et al.  Seismic activity on neighbouring faults as a long-term precursor to large earthquakes in the San Francisco Bay area , 1990, Nature.

[12]  D. L. Turcotte,et al.  A fractal approach to probabilistic seismic hazard assessment , 1989 .

[13]  T. Camelbeeck,et al.  Large earthquake in northern Europe more likely than once thought , 1996 .

[14]  D. Sornette,et al.  An observational test of the critical earthquake concept , 1998 .

[15]  Sammis,et al.  Fractal distribution of earthquake hypocenters and its relation to fault patterns and percolation. , 1993, Physical review letters.

[16]  C. Frohlich,et al.  Teleseismic b values; Or, much ado about 1.0 , 1993 .

[17]  Relation between the earthquake statistics and fault patterns, and fractals and percolation , 1992 .

[18]  Arch C. Johnston,et al.  Recurrence rates and probability estimates for the New Madrid Seismic Zone , 1985 .

[19]  A. Frankel Mapping Seismic Hazard in the Central and Eastern United States , 1995 .

[20]  Keiiti Aki,et al.  Magnitude‐frequency relation for small earthquakes: A clue to the origin of ƒmax of large earthquakes , 1987 .

[21]  Vladimir I. Keilis-borok,et al.  Diagnosis of time of increased probability of strong earthquakes in different regions of the world , 1990 .

[22]  Bruce E. Shaw,et al.  Dynamics of earthquake faults , 1993, adap-org/9307001.

[23]  G. M. Molchan,et al.  Statistical analysis of the results of earthquake prediction, based on bursts of aftershocks , 1990 .

[24]  Kerry E Sieh,et al.  Slip along the San Andreas fault associated with the great 1857 earthquake , 1984 .

[25]  David R. Brillinger,et al.  A more precise chronology of earthquakes produced by the San Andreas fault in southern California , 1989 .

[26]  E. Engdahl,et al.  Global teleseismic earthquake relocation with improved travel times and procedures for depth determination , 1998, Bulletin of the Seismological Society of America.

[27]  S. Redner,et al.  Introduction To Percolation Theory , 2018 .

[28]  D. Sornette Discrete scale invariance and complex dimensions , 1997, cond-mat/9707012.

[29]  R. Harris Forecasts of the 1989 Loma Prieta, California, earthquake , 1998, Bulletin of the Seismological Society of America.

[30]  Lawrence W. Braile,et al.  Intermediate-term earthquake prediction using precursory events in the New Madrid Seismic Zone , 1998, Bulletin of the Seismological Society of America.

[31]  Christopher H. Scholz,et al.  FREQUENCY-MOMENT DISTRIBUTION OF EARTHQUAKES IN THE ALEUTIAN ARC: A TEST OF THE CHARACTERISTIC EARTHQUAKE MODEL , 1985 .

[32]  L. Knopoff,et al.  Model and theoretical seismicity , 1967 .

[33]  D. Turcotte Seismicity and self-organized criticality , 1999 .

[34]  Agust Gudmundsson Geometry, formation and development of tectonic fractures on the Reykjanes Peninsula, southwest Iceland , 1987 .

[35]  D. Turcotte,et al.  Precursory Seismic Activation and Critical-point Phenomena , 2000 .

[36]  T. Utsu A statistical study on the occurrence of aftershocks. , 1961 .

[37]  T. Hirata Fractal dimension of fault systems in Japan: Fractal structure in rock fracture geometry at various scales , 1989 .

[38]  P. Bak,et al.  Self-organized criticality. , 1988, Physical review. A, General physics.

[39]  Nakanishi Statistical properties of the cellular-automaton model for earthquakes. , 1991, Physical review. A, Atomic, molecular, and optical physics.

[40]  D. L. Anderson,et al.  Theoretical Basis of Some Empirical Relations in Seismology by Hiroo Kanamori And , 1975 .

[41]  Wu,et al.  Scaling and universality in avalanches. , 1989, Physical review. A, General physics.

[42]  B. D. Malamud,et al.  Implications of a Statistical Physics Approach for Earthquake Hazard Assessment and Forecasting , 2000 .

[43]  Didier Sornette,et al.  Discrete scale invariance, complex fractal dimensions, and log‐periodic fluctuations in seismicity , 1996 .

[44]  I. Main,et al.  Scattering attenuation and the fractal geometry of fracture systems , 1990 .

[45]  D. Turcotte,et al.  A cellular-automata, slider-block model for earthquakes II. Demonstration of self-organized criticality for a 2-D system , 1992 .

[46]  D. Turcotte,et al.  Self-organized criticality , 1999 .

[47]  J. Angelier,et al.  Fractal Distribution of Fault Length and Offsets: Implications of Brittle Deformation Evaluation—The Lorraine Coal Basin , 1995 .

[48]  L. R. Sykes,et al.  Evolving Towards a Critical Point: A Review of Accelerating Seismic Moment/Energy Release Prior to Large and Great Earthquakes , 1999 .

[49]  John B. Rundle,et al.  Physical Basis for Statistical Patterns in Complex Earthquake Populations: Models, Predictions and Tests , 1999 .

[50]  M. Sahimi,et al.  Fractal analysis of three‐dimensional spatial distributions of earthquakes with a percolation interpretation , 1995 .

[51]  A cellular-automata, slider-block model for earthquakes I. Demonstration of chaotic behaviour for a low-order system , 1992 .

[52]  M. Gardner,et al.  Rat C-type virus induced in rat sarcoma cells by 5-bromodeoxyuridine. , 1972, Nature: New biology.

[53]  B. Gutenberg,et al.  Seismicity of the Earth and associated phenomena , 1950, MAUSAM.

[54]  O. Novikova,et al.  Performance of the earthquake prediction algorithm CN in 22 regions of the world , 1999 .

[55]  Nakanishi,et al.  Cellular-automaton model of earthquakes with deterministic dynamics. , 1990, Physical review. A, Atomic, molecular, and optical physics.

[56]  John B. Rundle,et al.  A simplified spring-block model of earthquakes , 1991 .

[57]  J. McCloskey,et al.  Time and magnitude predictions in shocks due to chaotic fault interactions , 1992 .

[58]  D. L. Turcotte,et al.  Evidence for chaotic fault interactions in the seismicity of the San Andreas fault and Nankai trough , 1990, Nature.

[59]  Bruce D. Malamud,et al.  An inverse-cascade model for self-organized critical behavior , 1999 .

[60]  Javier F. Pacheco,et al.  Changes in frequency–size relationship from small to large earthquakes , 1992, Nature.

[61]  C. Scholz Size distributions for large and small earthquakes , 1997, Bulletin of the Seismological Society of America.

[62]  V I Keilis-Borok,et al.  Intermediate-term earthquake prediction. , 1996, Proceedings of the National Academy of Sciences of the United States of America.

[63]  Vladimir Kossobokov,et al.  Premonitory activation of earthquake flow: algorithm M8 , 1990 .

[64]  S. Schreider Formal definition of premonitory seismic quiescence , 1990 .

[65]  T. Levshina,et al.  Increased long‐range intermediate‐magnitude earthquake activity prior to strong earthquakes in California , 1996 .

[66]  Chaotic and self-organized critical behavior of a generalized slider-block model , 1992 .

[67]  I. P. Dobrovolsky,et al.  Estimation of the size of earthquake preparation zones , 1979 .

[68]  Michio Otsuka A simulation of earthquake occurrence , 1972 .

[69]  B. Bodri A FRACTAL MODEL FOR SEISMICITY AT IZU-TOKAI REGION, CENTRAL JAPAN , 1993 .

[70]  Carlson,et al.  Mechanical model of an earthquake fault. , 1989, Physical review. A, General physics.

[71]  Eugene S. Schweig,et al.  THE -ENIGMA OF THE NEW MADRID EARTHQUAKES OF 1811-1812 , 1996 .

[72]  T. Lay,et al.  Modern Global Seismology , 1995 .

[73]  Christopher C. Barton,et al.  Fractals in the Earth Sciences , 1995 .

[74]  Lawrence W. Braile,et al.  Intermediate-term earthquake prediction using the modified time-to-failure method in southern California , 1999, Bulletin of the Seismological Society of America.

[75]  Y. Ogata,et al.  The Centenary of the Omori Formula for a Decay Law of Aftershock Activity , 1995 .

[76]  E. Lorenz Deterministic nonperiodic flow , 1963 .

[77]  Vladimir Kossobokov,et al.  Testing an earthquake prediction algorithm , 1997 .

[78]  Donald L. Turcotte,et al.  Are earthquakes an example of deterministic chaos , 1990 .

[79]  Vladimir Kossobokov,et al.  TESTING EARTHQUAKE PREDICTION ALGORITHMS : STATISTICALLY SIGNIFICANT ADVANCE PREDICTION OF THE LARGEST EARTHQUAKES IN THE CIRCUM-PACIFIC, 1992-1997 , 1999 .