Description of earthquake aftershock sequences using prototype point patterns

We introduce the use of prototype point patterns to characterize the behavior of a typical aftershock sequence from the global Harvard earthquake catalog. These prototypes are used not only for data description and summary but also to identify outliers and to classify sequences into groups exhibiting similar aftershock behavior. We find that a typical shallow earthquake of magnitude between 7.5 and 8.0 has approximately five aftershocks of magnitude at least 5.5, and that within an observation window of 0.113 days to 2.0 years after the mainshock, these aftershocks are roughly evenly distributed in log‐time. The relative magnitudes and distances from the mainshock for the typical aftershock sequence are characterized as well. Copyright © 2007 John Wiley & Sons, Ltd.

[1]  Robert Firth,et al.  Earthquakes , 1923, The Classical Review.

[2]  F. L. Hitchcock The Distribution of a Product from Several Sources to Numerous Localities , 1941 .

[3]  R. Cowan An introduction to the theory of point processes , 1978 .

[4]  Robert F. Ling,et al.  Cluster analysis algorithms for data reduction and classification of objects , 1981 .

[5]  A. Dziewoński,et al.  Centroid-moment tensor solutions for July-September, 1983 , 1984 .

[6]  A. Dziewoński,et al.  Centroid-moment tensor solutions for July–September 1985 , 1986 .

[7]  Yosihiko Ogata,et al.  Statistical Models for Earthquake Occurrences and Residual Analysis for Point Processes , 1988 .

[8]  Yan Y. Kagan,et al.  Observational evidence for earthquakes as a nonlinear dynamic process , 1994 .

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

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

[11]  Ian G. Main,et al.  Statistical physics, seismogenesis, and seismic hazard , 1996 .

[12]  Jonathan D. Victor,et al.  Metric-space analysis of spike trains: theory, algorithms and application , 1998, q-bio/0309031.

[13]  S. Sipkin,et al.  Moment-tensor solutions estimated using optimal filter theory: global seismicity, 1995 , 1997 .

[14]  Giuliano F. Panza,et al.  Multi-scale seismicity model for seismic risk , 1997, Bulletin of the Seismological Society of America.

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

[16]  T. Utsu Representation and Analysis of the Earthquake Size Distribution: A Historical Review and Some New Approaches , 1999 .

[17]  C. Frohlich,et al.  How well constrained are well‐constrained T, B, and P axes in moment tensor catalogs? , 1999 .

[18]  Yan Y. Kagan,et al.  Testable Earthquake Forecasts for 1999 , 1999 .

[19]  S. Sipkin,et al.  Moment-tensor solutions estimated using optimal filter theory: global seismicity, 1998 , 2000 .

[20]  A. Dziewoński,et al.  Centroid-moment tensor solutions for July–September 1999 , 2000 .

[21]  Y. Y. Kagan,et al.  Estimation of the upper cutoff parameter for the tapered Pareto distribution , 2001, Journal of Applied Probability.

[22]  David Vere-Jones,et al.  Remarks on the accelerated moment release model: problems of model formulation, simulation and estimation , 2001 .

[23]  Yan Y. Kagan,et al.  Accuracy of modern global earthquake catalogs , 2003 .

[24]  Frederic Paik Schoenberg,et al.  Multidimensional Residual Analysis of Point Process Models for Earthquake Occurrences , 2003 .

[25]  Katherine E. Tranbarger Freier,et al.  On the Computation and Application of Prototype Point Patterns , 2010 .

[26]  Y. Kagan Short-Term Properties of Earthquake Catalogs and Models of Earthquake Source , 2004 .

[27]  Leonidas J. Guibas,et al.  The Earth Mover's Distance as a Metric for Image Retrieval , 2000, International Journal of Computer Vision.

[28]  Arthur Cayley,et al.  The Collected Mathematical Papers: On Monge's “Mémoire sur la théorie des déblais et des remblais” , 2009 .