@misc{oai:ir.soken.ac.jp:00000758,
 author = {庄, 建倉 and ジュアン, ジャンカン and ZHUANG, Jiancang},
 month = {2016-02-17},
 note = {The idea of probability prediction was quite difficult to be accepted at the beginning by geophysicists and physicists. People become more and more interested in probability prediction, because they found after so many year's research that the causes of earthquakes are very complicated and the occurrences of precursors and earthquakes are not a simple one-to-one relationship.  Some earthquakes occurred after we observed a certain kind of anomaly phenomena, but some earthquakes occurred without these precursors observed, or no earthquakes occurred after we observed the same anomalies.<br />　　In this paper, the central topic is on the development of point process models to describe and to predict the earthquake risk based on the previous observation, including earthquake occurrences and precursors.<br />　　The conditional intensity is used for the model specification, which has a natural form for prediction.  Several models are given in the paper including the Poisson model, the stress release model, the self- and mutual-excitation process and the epidemic type aftershock sequence (ETAS) model.<br />　　The ETAS model is discussed in more detail.  First, its properties, its criticality and moments are analyzed.<br />　　The technique, called stochastic declustering, is concerned with an objective estimation of the spatial intensity function of the background earthquake occurrences from an earthquake catalogue which includes numerous clustered events in space and time, and with an algorithm of producing declustered catalogues from it, and also the reconstruction of the catalogue into the explicit clusters.  It is shown that the background intensity function can be evaluated if the total spatial seismicity intensity and the branching structure are estimated.  Or, the whole space-time process can be practically split into two sub-processes, the background and the clustered ones. Specifically, in the paper, a space-time epidemic type aftershock sequence (ETAS) model is adopted to describe the branching structure of earthquake occurrences.  This algorithm combines a parametric maximum likelihood estimation for the clustering structures in the space-time ETAS model and a non-parametric approach to the density estimation of the background seismicity, which is called a weighted variable kernel method.  As a demonstration of the presented methods, we estimate the background seismic activities in the central New Zealand region and in the central western Japan region to produce the catalogues of background events.<br />　　For the prediction purposes, we give the simulation procedures for Poisson models and ETAS models.  Besides Ogata's thinning method, we propose another faster method, called the composition method, for the simulation of the ETAS model.<br />　　An example is also given for modeling the relationship between precursors and an earthquake.  The precursor data are the signals from four stations monitoring the ultra-low frequency components electric field in the vicinity of Beijing, and are used as explanatory variables in forecasting the occurrence of events with magnitude M〓4 within 300 km circle centered on Beijing.  The model used is a version of Ogata's LIN-LIN algorithm for examining the influence of an explanatory signal on the occurrence of events in a stochastic point process.  The explanatory effect is shown to be highly significant, and greatly superior to the explanatory effect of the same signals applied to a randomized version of the earthquake data.  All four stations show significant explanatory power, although in combination the two most effective tend to dominate the forecasts.  The results are stable against perturbations in the time period or region of observation.  The predictions appear to be most effective for events with M 〓 5, and for events closer to the observing stations, although some of the smaller events appear to produce detectable signals at distances of over 100 km from the source.  Probability gains over the simple Poisson process are in the region up to 3 - 4 for the events of magnitude 5 or larger.  A special study is made of predicted and unpredicted events in the region around the M 7.8 Tangshan earthquake of 1976, to reveal the common spatial pattern of the classified events corresponding to all individual stations., 総研大甲第648号},
 title = {Some Applications of Point Processes in Seismicity Modeling and Prediction},
 year = {}
}