Earthquake precursors: activation or quiescence?

SUMMARY We discuss the long-standing question of whether the probability for large earthquake occurrence (magnitudes m > 6.0) is highest during time periods of smaller event activation, or highest during time periods of smaller event quiescence. The physics of the activation model are based on an idea from the theory of nucleation, that a small magnitude earthquake has a finite probability of growing into a large earthquake. The physics of the quiescence model is based on the idea that the occurrence of smaller earthquakes (here considered as magnitudes m > 3.5) may be due to a mechanism such as critical slowing down, in which fluctuations in systems with long-range interactions tend to be suppressed prior to large nucleation events. To illuminate this question, we construct two end-member forecast models illustrating, respectively, activation and quiescence. The activation model assumes only that activation can occur, either via aftershock nucleation or triggering, but expresses no choice as to which mechanism is preferred. Both of these models are in fact a means of filtering the seismicity time-series to compute probabilities. Using 25 yr of data from the California–Nevada catalogue of earthquakes, we show that of the two models, activation and quiescence, the latter appears to be the better model, as judged by backtesting (by a slight but not significant margin). We then examine simulation data from a topologically realistic earthquake model for California seismicity, Virtual California. This model includes not only earthquakes produced from increases in stress on the fault system, but also background and off-fault seismicity produced by a BASS–ETAS driving mechanism. Applying the activation and quiescence forecast models to the simulated data, we come to the opposite conclusion. Here, the activation forecast model is preferred to the quiescence model, presumably due to the fact that the BASS component of the model is essentially a model for activated seismicity. These results lead to the (weak) conclusion that California seismicity may be characterized more by quiescence than by activation, and that BASS–ETAS models may not be robustly applicable to the real data.

[1]  P. Shearer,et al.  Evidence for Mogi doughnut behavior in seismicity preceding small earthquakes in southern California , 2009 .

[2]  Kristy F. Tiampo,et al.  Mean-field threshold systems and phase dynamics: An application to earthquake fault systems , 2002 .

[3]  Yosihiko Ogata,et al.  Seismicity and geodetic anomalies in a wide area preceding the Niigata-Ken-Chuetsu earthquake of 23 October 2004, central Japan , 2007 .

[4]  John B. Rundle,et al.  A physical model for earthquakes: 3. Thermodynamical approach and its relation to nonclassical theories of nucleation , 1989 .

[5]  H. Kanamori,et al.  Application of an inhomogeneous stress (patch) model to complex subduction zone earthquakes: A discrete interaction matrix approach , 1987 .

[6]  Qinghua Huang,et al.  Search for reliable precursors: A case study of the seismic quiescence of the 2000 western Tottori prefecture earthquake , 2006 .

[7]  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 .

[8]  Shang‐keng Ma.  Modern Theory of Critical Phenomena , 1976 .

[9]  Francis W. Zwiers,et al.  On the ROC score of probability forecasts , 2003 .

[10]  S. Jaumé.  Changes in Earthquake Size‐Frequency Distributions Underlying Accelerating Seismic Moment/Energy Release , 2000 .

[11]  Taku Urabe,et al.  Quantitative mapping of a precursory seismic quiescence to the Izu–Oshima 1990 (M6.5) earthquake, Japan , 1996 .

[12]  Qinghua Huang,et al.  Seismicity changes prior to the Ms8.0 Wenchuan earthquake in Sichuan, China , 2008 .

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

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

[15]  A. Bell,et al.  Comment on “Relationship between accelerating seismicity and quiescence, two precursors to large earthquakes” by Arnaud Mignan and Rita Di Giovambattista , 2009 .

[16]  G. C. Fox,et al.  A simulation-based approach to forecasting the next great San Francisco earthquake , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[17]  Rita Di Giovambattista,et al.  Relationship between accelerating seismicity and quiescence, two precursors to large earthquakes , 2008 .

[18]  I. Jolliffe,et al.  Forecast verification : a practitioner's guide in atmospheric science , 2011 .

[19]  Earthquake forecasting and its verification , 2005, cond-mat/0508476.

[20]  Andrew J. Michael,et al.  Improved tests reveal that the accelerating moment release hypothesis is statistically insignificant , 2008 .

[21]  Matthew C. Gerstenberger,et al.  Real-time forecasts of tomorrow's earthquakes in California , 2005, Nature.

[22]  R. Tibshirani,et al.  An introduction to the bootstrap , 1993 .

[23]  John B. Rundle,et al.  BASS, an alternative to ETAS , 2007 .

[24]  James D. Gunton,et al.  Introduction to the Theory of Metastable and Unstable States , 1983 .

[25]  Simon J. Mason,et al.  On Using ``Climatology'' as a Reference Strategy in the Brier and Ranked Probability Skill Scores , 2004 .

[26]  James S. Langer,et al.  Theory of the condensation point , 1967 .

[27]  W. Klein,et al.  Pattern Dynamics and Forecast Methods in Seismically Active Regions , 2002 .

[28]  L. Knopoff,et al.  Is the sequence of earthquakes in Southern California, with aftershocks removed, Poissonian? , 1974, Bulletin of the Seismological Society of America.

[29]  A. H. Murphy,et al.  Skill Scores Based on the Mean Square Error and Their Relationships to the Correlation Coefficient , 1988 .

[30]  J. Rundle.  Magnitude-frequency relations for earthquakes using a statistical mechanical approach , 1993 .

[31]  Kristy F. Tiampo,et al.  The 1999 Chi‐Chi, Taiwan, earthquake as a typical example of seismic activation and quiescence , 2005 .

[32]  Y. Ogata.  Synchronous seismicity changes in and around the northern Japan preceding the 2003 Tokachi-oki earthquake of M8.0 , 2005 .

[33]  Chien-Chih Chen,et al.  An improved region—time—length algorithm applied to the 1999 Chi-Chi, Taiwan earthquake , 2006 .

[34]  D. Turcotte,et al.  Model for the distribution of aftershock interoccurrence times. , 2005, Physical Review Letters.

[35]  Charles E Ebeling,et al.  An Introduction to Reliability and Maintainability Engineering , 1996 .

[36]  V. Kossobokov.  Testing earthquake prediction methods: «The West Pacific short-term forecast of earthquakes with magnitude MwHRV ≥ 5.8» , 2006 .

[37]  A. H. Murphy.  A New Vector Partition of the Probability Score , 1973 .

[38]  A. H. Murphy,et al.  “Good” Probability Assessors , 1968 .

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

[40]  Yosihiko Ogata,et al.  Monitoring of anomaly in the aftershock sequence of the 2005 earthquake of M7.0 off coast of the western Fukuoka, Japan, by the ETAS model , 2006 .

[41]  W. Klein,et al.  Pseudospinodals, spinodals, and nucleation , 1983 .

[42]  Charles G. Sammis,et al.  Intermittent Criticality and the Gutenberg-Richter Distribution , 2004 .

[43]  A. H. Murphy,et al.  The attributes diagram A geometrical framework for assessing the quality of probability forecasts , 1986 .

[44]  Chung-Pai Chang,et al.  Deformation and „deformation quiescence” prior to the Chi-Chi earthquake evidenced by DInSAR and groundwater records during 1995–2002 in Central Taiwan , 2006 .

[45]  A. H. Murphy,et al.  A General Framework for Forecast Verification , 1987 .

[46]  D. M. Green,et al.  Signal detection theory and psychophysics , 1966 .

[47]  P. R. Bevington,et al.  Data Reduction and Error Analysis for the Physical Sciences , 1969 .

[48]  F. Atger.  Relative impact of model quality and ensemble deficiencies on the performance of ensemble based probabilistic forecasts evaluated through the Brier score , 2004 .

[49]  Barbara G. Brown,et al.  Forecast verification: current status and future directions , 2008 .

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

[51]  M. Yikilmaz.  Studies of Fault Interactions and Regional Seismicity Using Numerical Simulations , 2010 .