A Point Process Distance Metric with Applications to Earthquake Aftershock Activity

• Activity Number: 312
• Type: Contributed
• Date/Time: Wednesday, August 11, 2004 : 8:30 AM to 10:20 AM
• Sponsor: General Methodology
• Author(s): Katherine E. Tranbarger*+ and Frederic P. Schoenberg
• Companies: University of California, Los Angeles and University of California, Los Angeles
• Keywords: point process ; earthquakes ; distance metrics ; cluster analysis

Abstract

This work considers the problem of how to measure the distance between two point process sequences. Several properties of distance metrics proposed by Victor and Purpura are examined, and algorithms for their calculation are outlined. Using such a distance metric, a prototype sequence can be determined such that the distance between the prototype and all sequences in the dataset is minimized. This measurement approach, and a two-dimensional extension of it, are applied to global earthquake data and used to characterize the typical aftershock activity following a main shock of magnitude 7.5. Clustering techniques are also employed to identify groups of earthquakes with similar aftershock behavior, and to identify those outliers whose aftershock activity differs most from the prototype of the data. Comparisons are also made with the prototype sequence corresponding to the ETAS model, which is commonly used to describe aftershock activity.