A Boolean Delay Equation Model of Colliding Cascades. Part II: Prediction of Critical Transitions

We consider here prediction of abrupt overall changes (“critical transitions”) in the behavior of hierarchical complex systems, using the model developed in the first part of this study. The model merges the physical concept of colliding cascades with the mathematical framework of Boolean delay equations. It describes critical transitions that are due to the interaction between direct cascades of loading and inverse cascades of failures in a hierarchical system. This interaction is controlled by distinct delays between switching of elements from one state to another: loaded vs. unloaded and intact vs. failed. We focus on the earthquake prediction problem; accordingly, the model's heuristic constraints are taken from the dynamics of seismicity. The model exhibits four major types of premonitory seismicity patterns (PSPs), which have been previously identified in seismic observations: (i) rise of earthquake clustering; (ii) rise of the earthquakes' intensity; (iii) rise of the earthquake correlation range; and (iv) certain changes in the size distribution of earthquakes (Gutenberg–Richter relation). The model exhibits new features of individual PSPs and their collective behavior, to be tested in turn on observations. There are indications that the premonitory phenomena considered are not seismicity-specific, but may be common to hierarchical systems of a more general nature.

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

[2]  C. D. Ferguson,et al.  Long-range earthquake fault models , 1998 .

[3]  V. Keilis-Borok.  A worldwide test of three long-term premonitory seismicity patterns—a review , 1982 .

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

[5]  G. Molchan,et al.  Earthquake prediction as a decision-making problem , 1997 .

[6]  Frank Press,et al.  Chandler Wobble, earthquakes, rotation, and geomagnetic changes , 1975, Nature.

[7]  Michael Ghil,et al.  Boolean difference equations. I - Formulation and dynamic behavior , 1984 .

[8]  William I. Newman,et al.  A Statistical Physics Approach to Earthquakes , 2013 .

[9]  Allan J. Lichtman.  The Keys to the White House , 1996 .

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

[11]  L. Knopoff,et al.  Bursts of aftershocks, long-term precursors of strong earthquakes , 1980, Nature.

[12]  D. Sornette,et al.  Data-Adaptive Wavelets and Multi-Scale SSA , 2000 .

[13]  I. Vorobieva.  Prediction of a subsequent large earthquake , 1999 .

[14]  Vladimir Kossobokov,et al.  Localization of intermediate‐term earthquake prediction , 1990 .

[15]  D. Sornette,et al.  Data-adaptive wavelets and multi-scale singular-spectrum analysis , 1998, chao-dyn/9810034.

[16]  Newman,et al.  log-periodic behavior of a hierarchical failure model with applications to precursory seismic activation. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

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

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

[19]  Newman,et al.  Critical transitions in colliding cascades , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[20]  Ilya Zaliapin,et al.  Colliding cascades model for earthquake prediction , 2000 .

[21]  A. Prozorov,et al.  Real time test of the long-range aftershock algorithm as a tool for mid-term earthquake prediction in Southern California , 1990 .

[22]  Anatoly Soloviev,et al.  On dynamics of seismicity simulated by the models of blocks-and-faults systems , 1997 .

[23]  Michael Ghil,et al.  Boolean delay equations. II. Periodic and aperiodic solutions , 1985 .

[24]  James H. Stock,et al.  Pre‐recession pattern of six economic indicators in the USA , 2000 .

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

[26]  M. Braga,et al.  Exploratory Data Analysis , 2018, Encyclopedia of Social Network Analysis and Mining. 2nd Ed..

[27]  Vladimir I. Keilis-borok,et al.  Earthquake Prediction: State-of-the-Art and Emerging Possibilities , 2002 .

[28]  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 .

[29]  J. Gu,et al.  Earthquake aftereffects and triggered seismic phenomena , 1983 .

[30]  Earthquake prediction : state of the art , 1997 .

[31]  B. Romanowicz.  Spatiotemporal Patterns in the Energy Release of Great Earthquakes , 1993, Science.

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

[33]  V. I. Keilis-Borok,et al.  Symptoms of instability in a system of earthquake-prone faults , 1994 .

[34]  John B. Rundle,et al.  Models of earthquake faults with long-range stress transfer , 2000, Comput. Sci. Eng..

[35]  Frank Press,et al.  Pattern recognition applied to earthquake epicenters in California , 1976 .

[36]  A. Prozorov,et al.  Study of the properties of seismicity in the Mexico region , 1984 .

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

[38]  V. Gaur,et al.  On self-similarity of premonitory patterns in the regions of natural and induced seismicity , 1989, Proceedings of the Indian Academy of Sciences, Earth and Planetary Sciences.

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

[40]  M. G. Shnirman,et al.  Hierarchical model of defect development and seismicity , 1990 .

[41]  W. Ellsworth,et al.  Seismicity Remotely Triggered by the Magnitude 7.3 Landers, California, Earthquake , 1993, Science.

[42]  V. I. Keylis-Borok,et al.  One regularity in the occurrence of strong earthquakes , 1964 .

[43]  I. Zaliapin,et al.  Premonitory spreading of seismicity over the faults' network in southern California: Precursor Accord , 2002 .

[44]  Mixed hierarchical model of seismicity: scaling and prediction , 1999 .

[45]  I. Zaliapin,et al.  Premonitory raise of the earthquakes’ correlation range: Lesser Antilles , 2000 .

[46]  D. Sornette,et al.  Precursors, aftershocks, criticality and self-organized criticality , 1998 .

[47]  Warwick D. Smith.  The b-value as an earthquake precursor , 1981, Nature.

[48]  Vladimir I. Keilis-borok,et al.  What comes next in the dynamics of lithosphere and earthquake prediction , 1999 .

[49]  J. Kurths,et al.  Observation of growing correlation length as an indicator for critical point behavior prior to large earthquakes , 2001 .

[50]  William I. Newman,et al.  Nonlinear Dynamics and Predictability of Geophysical Phenomena: Newman/Nonlinear Dynamics and Predictability of Geophysical Phenomena , 1994 .

[51]  N. Beeler,et al.  Transient triggering of near and distant earthquakes , 1997, Bulletin of the Seismological Society of America.

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

[53]  C. R. Allen,et al.  Patterns of seismic release in the southern California region , 1995 .

[54]  L. Knopoff,et al.  Model for intermediate‐term precursory clustering of earthquakes , 1992 .

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

[56]  G. Toulouse,et al.  Ultrametricity for physicists , 1986 .

[57]  A. Provost,et al.  Scaling rules in rock fracture and possible implications for earthquake prediction , 1982, Nature.