Statistical physics of fracture, friction, and earthquakes

The present status of research and understanding regarding the dynamics and the statistical properties of earthquakes is reviewed, mainly from a statistical physical view point. Emphasis is put both on the physics of friction and fracture, which provides a microscopic basis for our understanding of an earthquake instability, and on the statistical physical modelling of earthquakes, which provides macroscopic aspects of such phenomena. Recent numerical results from several representative models are reviewed, with attention to both their critical and their characteristic properties. Some of the relevant notions and related issues are highlighted, including the origin of power laws often observed in statistical properties of earthquakes, apparently contrasting features of characteristic earthquakes or asperities, the nature of precursory phenomena and nucleation processes, and the origin of slow earthquakes, etc.

[1]  K. Johnson,et al.  Fault friction parameters inferred from the early stages of afterslip following the 2003 Tokachi‐oki earthquake , 2009 .

[2]  V. Gaur,et al.  Geodetic constraints on the Bhuj 2001 earthquake and surface deformation in the Kachchh Rift Basin , 2006 .

[3]  Loreto,et al.  Self-affine asperity model for earthquakes. , 1995, Physical review letters.

[4]  Bikas K. Chakrabarti,et al.  Modelling Critical and Catastrophic Phenomena in Geoscience , 2006 .

[5]  J. Dieterich Earthquake nucleation on faults with rate-and state-dependent strength , 1992 .

[6]  Julia K. Morgan,et al.  Numerical simulations of granular shear zones using the distinct element method: 2. Effects of particle size distribution and interparticle friction on mechanical behavior , 1999 .

[7]  Bikas K. Chakrabarti,et al.  Book Review: Statistical Physics of Fracture and Breakdown in Disordered Systems , 1997 .

[8]  J. Dieterich,et al.  IMAGING SURFACE CONTACTS : POWER LAW CONTACT DISTRIBUTIONS AND CONTACT STRESSES IN QUARTZ, CALCITE, GLASS AND ACRYLIC PLASTIC , 1996 .

[9]  Masayuki Kikuchi,et al.  Co‐seismic slip, post‐seismic slip, and largest aftershock associated with the 1994 Sanriku‐haruka‐oki, Japan, earthquake , 2003 .

[10]  D. Goldsby,et al.  Low frictional strength of quartz rocks at subseismic slip rates , 2002 .

[11]  H. Daniels The statistical theory of the strength of bundles of threads. I , 1945, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[12]  S. Yoshida,et al.  Episodic aseismic slip in a two‐degree‐of‐freedom block‐spring model , 2003 .

[13]  Yosihiko Ogata,et al.  Detection of anomalous seismicity as a stress change sensor , 2003 .

[14]  A. Hansen,et al.  Crossover behavior in failure avalanches. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[15]  J. Dieterich A constitutive law for rate of earthquake production and its application to earthquake clustering , 1994 .

[16]  Alex Hansen,et al.  Statistics of fracture surfaces. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[17]  Chris Marone,et al.  Particle-size distribution and microstructures within simulated fault gouge , 1989 .

[18]  M. Ohnaka,et al.  Scaling of the shear rupture process from nucleation to dynamic propagation: Implications of geometric irregularity of the rupturing surfaces , 1999 .

[19]  M. Takeo,et al.  Determination of constitutive relations of fault slip based on seismic wave analysis , 1997 .

[20]  L. Ponson,et al.  Crack propagation in brittle heterogeneous solids: Material disorder and crack dynamics , 2010 .

[21]  H. Kawamura,et al.  Spatiotemporal correlations of earthquakes in the continuum limit of the one-dimensional Burridge-Knopoff model , 2008, 0807.4588.

[22]  Javier F. Pacheco,et al.  Nature of seismic coupling along simple plate boundaries of the subduction type , 1993 .

[23]  D. Lockner,et al.  Strengths of serpentinite gouges at elevated temperatures , 1997 .

[24]  Of overlapping Cantor sets and earthquakes: analysis of the discrete Chakrabarti–Stinchcombe model , 2003, cond-mat/0312718.

[25]  N. Kato A possible model for large preseismic slip on a deeper extension of a seismic rupture plane , 2003 .

[26]  Takahiro Mori,et al.  Simulation study of spatiotemporal correlations of earthquakes as a stick-slip frictional instability. , 2005, Physical review letters.

[27]  M. Ohtake,et al.  Foreshocks and Aftershocks Accompanying a Perceptible Earthquake in Central Japan: On the Peculiar Nature of Foreshocks@@@前震の特異性 , 1964 .

[28]  Takahiro Mori,et al.  Simulation study of the two-dimensional Burridge-Knopoff model of earthquakes , 2005, physics/0504218.

[29]  K. Mogi Two kinds of seismic gaps , 1979 .

[30]  Jean-Noël Roux,et al.  Rheophysics of dense granular materials: discrete simulation of plane shear flows. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[31]  Michel Peyrard,et al.  Critical behaviour at the transition by breaking of analyticity in the discrete Frenkel-Kontorova model , 1983 .

[32]  Jin-Han Ree,et al.  Ultralow Friction of Carbonate Faults Caused by Thermal Decomposition , 2007, Science.

[33]  F. Chester,et al.  Ultracataclasite structure and friction processes of the Punchbowl Fault , 1998 .

[34]  M. Ohtake,et al.  Possible Mechanism of Precursory Seismic Quiescence: Regional Stress Relaxation due to Preseismic Sliding , 1997 .

[35]  Complexity in a spatially uniform continuum fault model , 1994 .

[36]  D. J. Andrews,et al.  Rupture velocity of plane strain shear cracks , 1976 .

[37]  A. Freed,et al.  Afterslip (and only afterslip) following the 2004 Parkfield, California, earthquake , 2007 .

[38]  János Kertész,et al.  Self-organized criticality with and without conservation , 1993 .

[39]  Barbara Drossel,et al.  Transient and stationary behavior of the Olami-Feder-Christensen model. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[40]  Yehuda Ben-Zion,et al.  Statistical properties of seismicity of fault zones at different evolutionary stages , 2007 .

[41]  Some recent (and surprising) results on interface and contact line depinning in random media , 2002, cond-mat/0204203.

[42]  Akira Hasegawa,et al.  Characteristic small‐earthquake sequence off Sanriku, northeastern Honshu, Japan , 2002 .

[43]  Terry E. Tullis,et al.  A composite rate‐ and state‐dependent law for rock friction , 2001 .

[44]  C. Scholz,et al.  Correction to “On the mechanics of earthquake afterslip” by Chris J. Marone, C.H. Scholz, and Roger Bilham , 1991 .

[45]  Presence of chaos in a self-organized critical system. , 1996 .

[46]  Tang,et al.  Self-Organized Criticality in Nonconserved Systems. , 1995, Physical review letters.

[47]  Tang,et al.  Self-Organized Criticality: An Explanation of 1/f Noise , 2011 .

[48]  Nonuniform and Unsteady Sliding of a Plate Boundary in a Great Earthquake Cycle: A Numerical Simulation Using a Laboratory-derived Friction Law , 1999 .

[49]  James L. Davis,et al.  GPS APPLICATIONS FOR GEODYNAMICS AND EARTHQUAKE STUDIES , 1997 .

[50]  H. Dragert,et al.  Episodic Tremor and Slip on the Cascadia Subduction Zone: The Chatter of Silent Slip , 2003, Science.

[51]  H. Kanamori,et al.  VARIABLE RUPTURE MODE OF THE SUBDUCTION ZONE ALONG THE ECUADOR-COLOMBIA COAST , 1982 .

[52]  Alessandro Vespignani,et al.  Experimental evidence for critical dynamics in microfracturing processes. , 1994, Physical review letters.

[53]  William D. Stuart,et al.  Forecast model for great earthquakes at the Nankai Trough subduction zone , 1988 .

[54]  Barbara Drossel,et al.  Olami-Feder-Christensen model with quenched disorder. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[55]  T. Okada,et al.  Comparison of source areas of M4.8±0.1 repeating earthquakes off Kamaishi, NE Japan: are asperities persistent features? , 2003 .

[56]  E. Jagla Realistic spatial and temporal earthquake distributions in a modified Olami-Feder-Christensen model. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[57]  A. Barabasi,et al.  Fractal Concepts in Surface Growth: Frontmatter , 1995 .

[58]  J. Ampuero,et al.  Earthquake nucleation on rate and state faults - Aging and slip laws , 2008 .

[59]  Akira Hasegawa,et al.  Repeating earthquakes and interplate aseismic slip in the northeastern Japan subduction zone , 2003 .

[60]  Criticality in models for fracture in disordered media , 1999 .

[61]  Alan T. Linde,et al.  A slow earthquake sequence on the San Andreas fault , 1996, Nature.

[62]  Stefan Hergarten Self-Organized Criticality , 2002 .

[63]  Carlson,et al.  Properties of earthquakes generated by fault dynamics. , 1989, Physical review letters.

[64]  M. D. S. Vieira Self-organized criticality in a deterministic mechanical model. , 1992 .

[65]  D. Sornette Critical Phenomena in Natural Sciences: Chaos, Fractals, Selforganization and Disorder: Concepts and Tools , 2000 .

[66]  Scaling of the critical slip distance in granular layers , 2009, 0906.3764.

[67]  Harvey Gould,et al.  Simulation of the Burridge-Knopoff model of earthquakes with variable range stress transfer. , 2005, Physical review letters.

[68]  P. C. Hemmer,et al.  Prediction of the collapse point of overloaded materials by monitoring energy emissions. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[69]  T. Shimamoto,et al.  Growth of molten zone as a mechanism of slip weakening of simulated faults in gabbro during frictional melting , 2005 .

[70]  Strong ordering by non-uniformity of thresholds in a coupled map lattice , 1995, adap-org/9503003.

[71]  G Miller,et al.  Nonuniversality and scaling breakdown in a nonconservative earthquake model. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[72]  P. Bhattacharyya,et al.  Phase transition in fiber bundle models with recursive dynamics. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[73]  Yehuda Ben-Zion,et al.  Collective behavior of earthquakes and faults: Continuum‐discrete transitions, progressive evolutionary changes, and different dynamic regimes , 2008 .

[74]  Zhang,et al.  Dynamic scaling of growing interfaces. , 1986, Physical review letters.

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

[76]  Harvey Gould,et al.  Near-mean-field behavior in the generalized Burridge-Knopoff earthquake model with variable-range stress transfer. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[77]  N. Lapusta,et al.  Three‐dimensional boundary integral modeling of spontaneous earthquake sequences and aseismic slip , 2009 .

[78]  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 .

[79]  H. Yoshino,et al.  Simulation study of the inhomogeneous Olami-Feder-Christensen model of earthquakes , 2010, 1002.3865.

[80]  Andy Ruina,et al.  Slip patterns in a spatially homogeneous fault model , 1989 .

[81]  J. Rice Spatio‐temporal complexity of slip on a fault , 1993 .

[82]  Hajime Yoshino,et al.  Periodicity and criticality in the Olami-Feder-Christensen model of earthquakes. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[83]  A Solvable Model of Interface Depinning in Random Media , 2001, cond-mat/0110470.

[84]  Malay K. Dey,et al.  Magnitude Distribution of Earthquakes: Two Fractal Contact Area Distribution , 2003, cond-mat/0306277.

[85]  D. Wolf,et al.  Numerical solution of the Kardar-Parisi-Zhang equation in one, two and three dimensions , 1991 .

[86]  J. Molinari,et al.  Finite-element analysis of contact between elastic self-affine surfaces. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[87]  P. Bak,et al.  Earthquakes as a self‐organized critical phenomenon , 1989 .

[88]  S. Edwards,et al.  The surface statistics of a granular aggregate , 1982, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[89]  J. Rice,et al.  Spontaneous and triggered aseismic deformation transients in a subduction fault model , 2007 .

[90]  H. Spohn,et al.  One-dimensional Kardar-Parisi-Zhang equation: an exact solution and its universality. , 2010, Physical review letters.

[91]  J. Carlson,et al.  Active zone size versus activity: A study of different seismicity patterns in the context of the prediction algorithm M8 , 1995 .

[92]  H. Hirose,et al.  Episodic slow slip events accompanied by non‐volcanic tremors in southwest Japan subduction zone , 2004 .

[93]  C. Scholz Earthquakes and friction laws , 1998, Nature.

[94]  G Miller,et al.  Measurements of criticality in the Olami-Feder-Christensen model. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[95]  William L. Ellsworth,et al.  A Brownian Model for Recurrent Earthquakes , 2002 .

[96]  D. Andrews Rupture dynamics with energy loss outside the slip zone , 2003 .

[97]  J. Rice Heating and weakening of faults during earthquake slip , 2006 .

[98]  Vasconcelos,et al.  First-order phase transition in a model for earthquakes. , 1996, Physical review letters.

[99]  G. A. Tomlinson B.Sc.,et al.  CVI. A molecular theory of friction , 1929 .

[100]  D. Corcoran,et al.  State-variable friction for the Burridge-Knopoff model. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[101]  M. Cocco,et al.  Slip‐weakening behavior during the propagation of dynamic ruptures obeying rate‐ and state‐dependent friction laws , 2003 .

[102]  Nadia Lapusta,et al.  Towards inferring earthquake patterns from geodetic observations of interseismic coupling , 2010 .

[103]  D. Yuen,et al.  Unsolved problems in the lowermost mantle , 2006 .

[104]  T. Shimamoto,et al.  Modelling of short-interval silent slip events in deeper subduction interfaces considering the frictional properties at the unstable-stable transition regime , 2007 .

[105]  S. P. Nishenko,et al.  A generic recurrence interval distribution for earthquake forecasting , 1987 .

[106]  M. Wyss,et al.  Precursors to the Kalapana M = 7. 2 earthquake , 1981 .

[107]  D. Shelly Possible deep fault slip preceding the 2004 Parkfield earthquake, inferred from detailed observations of tectonic tremor , 2009 .

[108]  Max Wyss,et al.  Second round of evaluations of proposed earthquake precursors , 1997 .

[109]  F. Heslot,et al.  Creep, stick-slip, and dry-friction dynamics: Experiments and a heuristic model. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[110]  Langer,et al.  Rupture propagation, dynamical front selection, and the role of small length scales in a model of an earthquake fault. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[111]  T. Shimamoto,et al.  Granular nanoparticles lubricate faults during seismic slip , 2011 .

[112]  E Altshuler,et al.  Quasiperiodic events in an earthquake model. , 2006, Physical review letters.

[113]  B. E. Shaw,et al.  Frictional weakening and slip complexity in earthquake faults , 1995 .

[114]  Hitoshi Hirose,et al.  Modeling short- and long-term slow slip events in the seismic cycles of large subduction earthquakes , 2010 .

[115]  G. D. Toro,et al.  Friction falls towards zero in quartz rock as slip velocity approaches seismic rates , 2004, Nature.

[116]  Creep of a fracture line in paper peeling. , 2007, Physical review letters.

[117]  Hugo Perfettini,et al.  Postseismic relaxation driven by brittle creep: A possible mechanism to reconcile geodetic measurements and the decay rate of aftershocks, application to the Chi-Chi earthquake, Taiwan , 2004 .

[118]  Mousseau Synchronization by Disorder in Coupled Systems. , 1996, Physical review letters.

[119]  William Menke,et al.  Repeat Times of Large Earthquakes: Implications for Earthquake Mechanics and Long-Term Prediction , 2006 .

[120]  M. Nakatani Conceptual and physical clarification of rate and state friction: Frictional sliding as a thermally activated rheology , 2001 .

[121]  N. Kato,et al.  A model for possible crustal deformation prior to a coming large interplate earthquake in the Tokai district, central Japan , 1999, Bulletin of the Seismological Society of America.

[122]  T. Shimamoto,et al.  Frictional melt and seismic slip , 2008 .

[123]  Yuji Yagi,et al.  A unified source model for the 2011 Tohoku earthquake , 2011 .

[124]  S. Schwartz,et al.  Slow slip events and seismic tremor at circum‐Pacific subduction zones , 2007 .

[125]  Dynamics of surface roughening in disordered media , 1993 .

[126]  Effect of fractal disorder on static friction in the Tomlinson model. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[127]  S. Miyazaki,et al.  A slow thrust slip event following the two 1996 Hyuganada Earthquakes beneath the Bungo Channel, southwest Japan , 1999 .

[128]  P. Grassberger,et al.  Efficient large-scale simulations of a uniformly driven system. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

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

[130]  S. Phoenix The asymptotic distribution for the time to failure of a fiber bundle , 1979, Advances in Applied Probability.

[131]  L. Ponson,et al.  Depinning transition in the failure of inhomogeneous brittle materials. , 2008, Physical review letters.

[132]  Kristine M. Larson,et al.  Frictional Properties on the San Andreas Fault near Parkfield, California, Inferred from Models of Afterslip following the 2004 Earthquake , 2006 .

[133]  J. Rice,et al.  Slip patterns and earthquake populations along different classes of faults in elastic solids , 1995 .

[134]  Julyan H. E. Cartwright,et al.  BURRIDGE-KNOPOFF MODELS AS ELASTIC EXCITABLE MEDIA , 1997 .

[135]  Takahiro Mori,et al.  Simulation study of earthquakes based on the two-dimensional Burridge-Knopoff model with long-range interactions. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[136]  Richard H. Sibson,et al.  Interactions between Temperature and Pore-Fluid Pressure during Earthquake Faulting and a Mechanism for Partial or Total Stress Relief , 1973 .

[137]  D. Corcoran,et al.  Burridge-Knopoff model: Exploration of dynamic phases. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[138]  A. Hasegawa,et al.  Recurrence intervals of characteristic M4.8±0.1 earthquakes off-Kamaishi, NE Japan—Comparison with creep rate estimated from small repeating earthquake data , 2005 .

[139]  S. Phoenix The Asymptotic Time to Failure of a Mechanical System of Parallel Members , 1978 .

[140]  J. Kurths,et al.  Similar power laws for foreshock and aftershock sequences in a spring‐block model for earthquakes , 1999 .

[141]  Anthony Sladen,et al.  Seismic and aseismic slip on the Central Peru megathrust , 2010, Nature.

[142]  Robbins,et al.  Phase transitions and universal dynamics in confined films. , 1992, Physical review letters.

[143]  Didier Sornette,et al.  Properties of foreshocks and aftershocks of the nonconservative self-organized critical Olami-Feder-Christensen model. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[144]  A. Naumovets,et al.  Nanotribology : Microscopic mechanisms of friction , 2006 .

[145]  U. Landman,et al.  Nanotribology: friction, wear and lubrication at the atomic scale , 1995, Nature.

[146]  Klein,et al.  Boltzmann Fluctuations in Numerical Simulations of Nonequilibrium Lattice Threshold Systems. , 1995, Physical review letters.

[147]  P. Spudich,et al.  What Can Strong-Motion Data Tell Us about Slip-Weakening Fault-Friction Laws? , 2000 .

[148]  J. Rice,et al.  Rate and state dependent friction and the stability of sliding between elastically deformable solids , 2001 .

[149]  T. Hatano,et al.  Flash weakening is limited by granular dynamics , 2011 .

[150]  Terry E. Tullis,et al.  Fault model for preseismic deformation at Parkfield, California , 1995 .

[151]  J. M. Carlson,et al.  Prediction of large events on a dynamical model of a fault , 1994 .

[152]  A. Ruina,et al.  Slip motion and stability of a single degree of freedom elastic system with rate and state dependent friction , 1984 .

[153]  Alvaro Corral Long-term clustering, scaling, and universality in the temporal occurrence of earthquakes. , 2004, Physical review letters.

[154]  W. Thatcher Order and diversity in the modes of Circum-Pacific Earthquake recurrence , 1990 .

[155]  P. Segall,et al.  Spatial and temporal evolution of stress and slip rate during the 2000 Tokai slow earthquake , 2006 .

[156]  Pathikrit Bhattacharya,et al.  A fractal model of earthquake occurrence: Theory, simulations and comparisons with the aftershock data , 2011 .

[157]  Sei‐ichiro Watanabe,et al.  A self‐organized model of earthquakes with constant stress drops and the b‐value of 1 , 1999 .

[158]  G. Ananthakrishna,et al.  Power laws, precursors and predictability during failure , 2003, cond-mat/0312138.

[159]  N. Kato Expansion of aftershock areas caused by propagating post‐seismic sliding , 2007 .

[160]  A. Tsutsumi,et al.  Deformation textures and mechanical behavior of a hydrated amorphous silica formed along an experimentally produced fault in chert , 2010 .

[161]  J. Ampuero,et al.  Earthquake nucleation on (aging) rate and state faults , 2005 .

[162]  Show Matsumura Focal zone of a future Tokai earthquake inferred from the seismicity pattern around the plate interface , 1997 .

[163]  C. King,et al.  A Discussion on the measurement and interpretation of changes of strain in the Earth - Kinematics of fault creep , 1973, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.

[164]  James D. Byerlee,et al.  Frictional slip of granite at hydrothermal conditions , 1995 .

[165]  Tiago P Peixoto,et al.  Network of epicenters of the Olami-Feder-Christensen model of earthquakes. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[166]  Antonio Politi,et al.  Failure time in the fiber-bundle model with thermal noise and disorder. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[167]  S. Roux,et al.  A dissipation-based analysis of an earthquake fault model , 1996 .

[168]  Yoshiaki Ida,et al.  Cohesive force across the tip of a longitudinal‐shear crack and Griffith's specific surface energy , 1972 .

[169]  Raul Madariaga,et al.  Complexity of seismicity due to highly rate‐dependent friction , 1996 .

[170]  Makoto Murakami,et al.  Detection and Monitoring of Ongoing Aseismic Slip in the Tokai Region, Central Japan , 2002, Science.

[171]  Yehuda Ben-Zion,et al.  Dynamic simulations of slip on a smooth fault in an elastic solid , 1997 .

[172]  A. Nur,et al.  Aftershocks and Pore Fluid Diffusion Following the 1992 Landers Earthquake , 2002 .

[173]  S. Pradhan,et al.  Breaking-rate minimum predicts the collapse point of overloaded materials. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[174]  B. Lawn Fracture of Brittle Solids by Brian Lawn , 1993 .

[175]  E. Rabinowicz,et al.  Friction and Wear of Materials , 1966 .

[176]  John B. Rundle,et al.  Statistical physics approach to understanding the multiscale dynamics of earthquake fault systems , 2003 .

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

[178]  Eiichi Fukuyama,et al.  Moisture‐related weakening and strengthening of a fault activated at seismic slip rates , 2006 .

[179]  Vasconcelos,et al.  Dynamics of spring-block models: Tuning to criticality. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[180]  H. Kanamori,et al.  Global survey of aftershock area expansion patterns , 1985 .

[181]  John R. Rice,et al.  Crustal Earthquake Instability in Relation to the Depth Variation of Frictional Slip Properties , 1986 .

[182]  S Lise,et al.  Self-organized criticality and universality in a nonconservative earthquake model. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[183]  Srutarshi Pradhan,et al.  Precursors of catastrophe in the Bak-Tang-Wiesenfeld, Manna, and random-fiber-bundle models of failure. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[184]  Christensen,et al.  Scaling, phase transitions, and nonuniversality in a self-organized critical cellular-automaton model. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[185]  H. Leschhorn Interface motion in a random medium: mean field theory , 1992 .

[186]  A. Barabasi,et al.  Fractal concepts in surface growth , 1995 .

[187]  S. Hergarten Self-Organized Criticality in Earth Systems , 2002 .

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

[189]  H. Kawamura,et al.  Rate-and state-dependent friction law and statistical properties of earthquakes , 2006, cond-mat/0605014.

[190]  de Carvalho JX,et al.  Self-organized criticality in the olami-feder-christensen model , 1999, Physical review letters.

[191]  A. Hansen,et al.  Crossover behavior in burst avalanches: signature of imminent failure. , 2005, Physical review letters.

[192]  Christensen,et al.  Self-organized criticality in a continuous, nonconservative cellular automaton modeling earthquakes. , 1992, Physical review letters.

[193]  R. Krenn,et al.  Synchronization and desynchronization in the Olami-Feder-Christensen earthquake model and potential implications for real seismicity , 2011 .

[194]  Bertrand Delamotte,et al.  Self-organized-criticality and synchronization in pulse coupled relaxation oscillator systems the Olami, Feder and Christensen and the Feder and Feder model , 1997 .

[195]  Bruce E. Shaw,et al.  Patterns of seismic activity preceding large earthquakes , 1992 .

[196]  John B. Rundle,et al.  Geocomplexity and the Physics of Earthquakes , 2000 .

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

[198]  Tiago P Peixoto,et al.  Distribution of epicenters in the Olami-Feder-Christensen model. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[199]  D. Corcoran,et al.  Criticality in the Burridge-Knopoff model. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[200]  H. Herrmann,et al.  Statistical models for the fracture of disordered media. North‐Holland, 1990, 353 p., ISBN 0444 88551x (hardbound) US $ 92.25, 0444 885501 (paperback) US $ 41.00 , 1990 .

[201]  V. Popov,et al.  Rate and state dependent friction laws and the prediction of earthquakes: What can we learn from laboratory models? , 2012 .

[202]  H. Yoshino,et al.  Asperity characteristics of the Olami-Feder-Christensen model of earthquakes. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[203]  A microscopic approach to the statistical fracture analysis of disordered brittle solids , 1985 .

[204]  G. Hillers,et al.  Dilatancy controlled spatiotemporal slip evolution of a sealed fault with spatial variations of the pore pressure , 2007 .

[205]  J. Carlson,et al.  Friction, Fracture, and Earthquakes , 2010 .

[206]  J. Carlson,et al.  Time intervals between characteristic earthquakes and correlations with smaller events: An analysis based on a mechanical model of a fault , 1991 .

[207]  Propagative slipping modes in a spring-block model. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[208]  J. Pelletier Spring‐Block Models of Seismicity: Review and Analysis of a Structurally Heterogeneous Model Coupled to a Viscous Asthenosphere , 2013 .

[209]  Shaw,et al.  Intrinsic properties of a Burridge-Knopoff model of an earthquake fault. , 1991, Physical review. A, Atomic, molecular, and optical physics.

[210]  J. Dieterich Modeling of rock friction: 1. Experimental results and constitutive equations , 1979 .

[211]  A. Lachenbruch,et al.  Frictional heating, fluid pressure, and the resistance to fault motion , 1980 .

[212]  Chihiro Hashimoto,et al.  Interplate seismogenic zones along the Kuril–Japan trench inferred from GPS data inversion , 2009 .

[213]  Carlson Jm Two-dimensional model of a fault , 1991 .

[214]  Y. Estrin,et al.  The effect of strain rate sensitivity on dynamic friction of metals , 1994 .

[215]  Bikas K. Chakrabarti,et al.  Stick-slip statistics for two fractal surfaces: a model for earthquakes , 1999 .

[216]  Bikas K. Chakrabarti,et al.  Failure processes in elastic fiber bundles , 2008, 0808.1375.

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

[218]  N. Kato Interaction of slip on asperities: Numerical simulation of seismic cycles on a two-dimensional planar fault with nonuniform frictional property , 2004 .

[219]  Zhigang Peng,et al.  Migration of early aftershocks following the 2004 Parkfield earthquake , 2009 .

[220]  C. Marone LABORATORY-DERIVED FRICTION LAWS AND THEIR APPLICATION TO SEISMIC FAULTING , 1998 .

[221]  A three-dimensional simulation of crustal deformation accompanied by subduction in the Tokai region, central Japan , 2002 .

[222]  A. Ruina Slip instability and state variable friction laws , 1983 .

[223]  Jürgen Kurths,et al.  Seismic quiescence as an indicator for large earthquakes in a system of self‐organized criticality , 2000 .

[224]  Matsukawa,et al.  Theoretical study of friction: One-dimensional clean surfaces. , 1994, Physical review. B, Condensed matter.

[225]  Keiiti Aki,et al.  Seismicity simulation with a rate- and state-dependent friction law , 1986 .

[226]  H. Hölscher,et al.  Principles of atomic friction: from sticking atoms to superlubric sliding , 2008, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[227]  A. Linde,et al.  Slow earthquakes and great earthquakes along the Nankai trough , 2002 .

[228]  Stefan Hergarten,et al.  Foreshocks and aftershocks in the Olami-Feder-Christensen model. , 2002, Physical review letters.

[229]  Yuri S. Kivshar,et al.  The Frenkel-Kontorova Model , 2004 .

[230]  Keisuke Ito,et al.  Earthquakes as self-organized critical phenomena , 1990 .

[231]  Ceva Influence of defects in a coupled map lattice modeling earthquakes. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[232]  Paul Segall,et al.  Space time distribution of afterslip following the 2003 Tokachi‐oki earthquake: Implications for variations in fault zone frictional properties , 2004 .

[233]  S. Ciliberto,et al.  Moisture-induced ageing in granular media and the kinetics of capillary condensation , 1998, Nature.

[234]  G. Midi,et al.  On dense granular flows , 2003, The European physical journal. E, Soft matter.

[235]  Jim Mori,et al.  Triggering of earthquakes during the 2000 Papua New Guinea earthquake sequence , 2007 .

[236]  Jean-Philippe Avouac,et al.  Heterogeneous coupling on the Sumatra megathrust constrained from geodetic and paleogeodetic measurements , 2008 .

[237]  K. Shimazaki,et al.  Seismicity in source regions of large interplate earthquakes around Japan and the characteristic earthquake model , 2009 .

[238]  J. Dieterich,et al.  Direct observation of frictional contacts: New insights for state-dependent properties , 1994 .

[239]  H. Stanley,et al.  FIRST-ORDER TRANSITION IN THE BREAKDOWN OF DISORDERED MEDIA , 1996, cond-mat/9612095.

[240]  Bikas K. Chakrabarti,et al.  FAILURE PROPERTIES OF FIBER BUNDLE MODELS , 2003 .

[241]  Hiroo Kanamori,et al.  Focal process of the great Chilean earthquake May 22, 1960☆ , 1974 .

[242]  M. Cocco,et al.  A thermal pressurization model for the spontaneous dynamic rupture propagation on a three‐dimensional fault: 1. Methodological approach , 2006 .

[243]  Karen Mair,et al.  Effects of gouge fragment shape on fault friction: New 3D modelling results , 2009 .

[244]  Amar,et al.  Numerical solution of a continuum equation for interface growth in 2+1 dimensions. , 1990, Physical review. A, Atomic, molecular, and optical physics.

[245]  H. Kanamori,et al.  A slow earthquake , 1979 .

[246]  Kunihiko Shimazaki,et al.  FAULT TRACE COMPLEXITY, CUMULATIVE SLIP, AND THE SHAPE OF THE MAGNITUDE-FREQUENCY DISTRIBUTION FOR STRIKE-SLIP FAULTS : A GLOBAL SURVEY , 1996 .

[247]  A. Rubin Episodic slow slip events and rate-and-state friction , 2008 .

[248]  Self-organized criticality in two-variable models , 2000 .

[249]  M. Kikuchi,et al.  Asperity map along the subduction zone in northeastern Japan inferred from regional seismic data , 2004 .

[250]  B K Chakrabarti,et al.  Dynamic critical behavior of failure and plastic deformation in the random fiber bundle model. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[251]  Elisabeth Bouchaud,et al.  Failure of heterogeneous materials: A dynamic phase transition? , 2011 .

[252]  Y. Fialko,et al.  Fusion by earthquake fault friction: Stick or slip? , 2005 .

[253]  N. Yoshioka A review of the micromechanical approach to the physics of contacting surfaces , 1997 .

[254]  J. Dieterich,et al.  Stress transferred by the 1995 Mw = 6.9 Kobe, Japan, shock: Effect on aftershocks and future earthquake probabilities , 1998 .

[255]  T. Shimamoto Transition Between Frictional Slip and Ductile Flow for Halite Shear Zones at Room Temperature , 1986, Science.

[256]  Shaw,et al.  Slip Complexity in a Crustal-Plane Model of an Earthquake Fault. , 1996, Physical review letters.

[257]  P Chauve,et al.  Renormalization of pinned elastic systems: how does it work beyond one loop? , 2001, Physical review letters.

[258]  A. Hansen,et al.  The Distribution of Simultaneous Fiber Failures in Fiber Bundles , 1992 .

[259]  Naoyuki Kato,et al.  Numerical simulation of recurrence of asperity rupture in the Sanriku region, northeastern Japan , 2008 .

[260]  Robert M. Nadeau,et al.  Seismological studies at Parkfield VI: Moment release rates and estimates of source parameters for small repeating earthquakes , 1998, Bulletin of the Seismological Society of America.

[261]  Depinning exponents of the driven long-range elastic string , 2006, cond-mat/0612323.

[262]  Takane Hori,et al.  A numerical simulation of earthquake cycles along the Nankai Trough in southwest Japan: lateral variation in frictional property due to the slab geometry controls the nucleation position , 2004 .

[263]  L. Smith,et al.  Effects of frictional heating on the thermal, hydrologic, and mechanical response of a fault , 1987 .

[264]  Toshihiko Shimamoto,et al.  High‐velocity frictional properties of gabbro , 1997 .

[265]  B. Shibazaki,et al.  On the physical mechanism of silent slip events along the deeper part of the seismogenic zone , 2003 .

[266]  Pierre Le Doussal,et al.  Renormalization of Pinned Elastic Systems , 2001 .

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

[268]  Failure due to fatigue in fiber bundles and solids. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[269]  Power-law friction in closely packed granular materials. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[270]  L. Knopoff,et al.  Models of aftershock occurrence , 1987 .