HR: 14:25h
AN: S13E-04 INVITED    [Abstracts]
TI: Stochastic declustering: visualizing of the family trees in earthquake catalogs with uncertainty
AU: * Zhuang, J
EM: zhuangjc@ism.ac.jp
AF: Institute of Statistical Mathematics, 4-6-7 Minami Azabu, Minato-Ku, Tokyo, 1068569, Japan
AU: Ogata, Y
EM: ogata@ism.ac.jp
AF: Institute of Statistical Mathematics, 4-6-7 Minami Azabu, Minato-Ku, Tokyo, 1068569, Japan
AU: Vere-Jones, D
EM: dvj@mcs.vuw.ac.nz
AF: MCS, Victoria University, P.O. Box 600, Wellington, 0000, New Zealand
AB: This presentation is concerned with objectively producing declustered catalogs from the original catalog that includes numerous clustered events in space and time. The method is based a space-time branching process model (the ETAS model), which is used for describing how each event generates offspring events. It is shown that the whole space-time process can split into two subprocesses, the background events and the clustered events stochastically. The proposed algorithm combines a parametric maximum likelihood estimate for the clustering structures using the space-time ETAS model and a nonparametric estimate of the background seismicity that we call a variable weighted kernel estimate. To demonstrate the present methods, we estimate the background seismic activities in the central region of New Zealand and in the central and western regions of Japan, then use these estimates to produce catalogs of background events. The key points of this method are the probabilities of one event being triggered by another previous event and being a background event. Making use of these probabilities, we can reconstruct the functions associated with the characteristics of earthquake clusters to test a number of important hypotheses about the earthquake clustering phenomena, such as: (1) The functions for each component in the formulation of the space-time ETAS model are good enough as a first-order approximation for describing earthquake clusters; (2) a background event triggers less offspring in expectation than a triggered event of the same magnitude; (3) the magnitude distribution of the triggered event depends on the magnitude of its direct ancestor; (4) the diffusion of the aftershock sequence is mainly caused by cascades of individual triggering processes, while no evidence shows that each individual triggering process is diffusive; and (5) the scale of the triggering region is still an exponential law, as formulated in the model but not the same one for the expected number of offspring. Another important application of the stochastic declustering methods is in evaluating the probability that an earthquake is a foreshock. The proportion of events that have 1 or more larger descendants in total events is found to be as high as about 15% from the ETAS model theory and the real catalog, which the proportion of foreshocks in background events is only 8%. Such a difference can be explained by the differences between background events and triggered event in the behavior of triggering children, which can be tested by using the stochastic declustering methods.
DE: 7209 Earthquake dynamics (1242)
DE: 7223 Earthquake interaction, forecasting, and prediction (1217, 1242)
DE: 7260 Theory
SC: Seismology [S]
MN: 2007 Fall Meeting