Long-term earthquake forecasts based on the epidemic-type aftershock sequence (ETAS) model for short-term clustering

Based on the ETAS (epidemic-type aftershock sequence) model, which is used for describing the features of short-term clustering of earthquake occurrence, this paper presents some theories and techniques related to evaluating the probability distribution of the maximum magnitude in a given space-time window, where the Gutenberg-Richter law for earthquake magnitude distribution cannot be directly applied. It is seen that the distribution of the maximum magnitude in a given space-time volume is determined in the longterm by the background seismicity rate and the magnitude distribution of the largest events in each earthquake cluster. The techniques introduced were applied to the seismicity in the Japan region in the period from 1926 to 2009. It was found that the regions most likely to have big earthquakes are along the Tohoku (northeastern Japan) Arc and the Kuril Arc, both with much higher probabilities than the offshore Nankai and Tokai regions.

[1]  Y. Kagan,et al.  High-Resolution Long-Term and Short-Term Earthquake Forecasts for California , 2011 .

[2]  T. Utsu.  Aftershocks and Earthquake Statistics(1) : Some Parameters Which Characterize an Aftershock Sequence and Their Interrelations , 1970 .

[3]  Cliff Frohlich,et al.  Single-link cluster analysis, synthetic earthquake catalogues, and aftershock identification , 1991 .

[4]  Jiancang Zhuang,et al.  Distribution of the largest event in the critical epidemic-type aftershock-sequence model. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[5]  D. Vere-Jones,et al.  Stochastic Declustering of Space-Time Earthquake Occurrences , 2002 .

[6]  F. Omori,et al.  On the after-shocks of earthquakes , 1894 .

[7]  Y. Kagan,et al.  Comparison of Short-Term and Time-Independent Earthquake Forecast Models for Southern California , 2006 .

[8]  Y. Ogata.  Space-Time Point-Process Models for Earthquake Occurrences , 1998 .

[9]  Yan Y. Kagan,et al.  Statistical search for non-random features of the seismicity of strong earthquakes , 1976 .

[10]  T. Utsu.  A method for determining the value of b in a formula log n=a-bM showing the magnitude frequency relation for earthquakes , 1965 .

[11]  Jiancang Zhuang,et al.  Space–time ETAS models and an improved extension , 2006 .

[12]  Jiancang Zhuang,et al.  Second‐order residual analysis of spatiotemporal point processes and applications in model evaluation , 2006 .

[13]  Yosihiko Ogata,et al.  On Lewis' simulation method for point processes , 1981, IEEE Trans. Inf. Theory.

[14]  D. Sornette,et al.  Are aftershocks of large Californian earthquakes diffusing , 2003, physics/0303075.

[15]  D. Vere-Jones,et al.  Analyzing earthquake clustering features by using stochastic reconstruction , 2004 .

[16]  Distribution of the largest aftershocks in branching models of triggered seismicity: theory of the universal Båth law. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[17]  Annemarie Christophersen,et al.  Differences between spontaneous and triggered earthquakes: Their influences on foreshock probabilities , 2008 .

[18]  Warner Marzocchi,et al.  On the Increase of Background Seismicity Rate during the 1997-1998 Umbria-Marche, Central Italy, Sequence: Apparent Variation or Fluid-Driven Triggering? , 2010 .

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

[20]  Yosihiko Ogata,et al.  Detecting fluid signals in seismicity data through statistical earthquake modeling , 2005 .

[21]  Yosihiko Ogata,et al.  Space‐time model for regional seismicity and detection of crustal stress changes , 2004 .

[22]  Jiancang Zhuang,et al.  Next-day earthquake forecasts for the Japan region generated by the ETAS model , 2011 .

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

[24]  P. Reasenberg.  Second‐order moment of central California seismicity, 1969–1982 , 1985 .

[25]  Rodolfo Console,et al.  A simple and testable model for earthquake clustering , 2001 .

[26]  C. Frohlich,et al.  Single‐Link Cluster Analysis As A Method to Evaluate Spatial and Temporal Properties of Earthquake Catalogues , 1990 .

[27]  R. Dennis Cook,et al.  Cross-Validation of Regression Models , 1984 .

[28]  Rodolfo Console,et al.  Refining earthquake clustering models , 2003 .

[29]  Jiancang Zhuang,et al.  Properties of the probability distribution associated with the largest event in an earthquake cluster and their implications to foreshocks. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[30]  D. Vere-Jones,et al.  A Variable-Grid Algorithm for Smoothing Clustered Data , 1986 .

[31]  D. Vere-Jones,et al.  Elementary theory and methods , 2003 .

[32]  Chung-Pai Chang,et al.  A study on the background and clustering seismicity in the Taiwan region by using point process models : Stress transfer, earthquake triggering, and time-dependent seismic hazard , 2005 .

[33]  Roger Fletcher,et al.  A Rapidly Convergent Descent Method for Minimization , 1963, Comput. J..

[34]  Daryl J. Daley,et al.  An Introduction to the Theory of Point Processes , 2013 .