Delineation of support domain of feature in the presence of noise

Clustered events are usually deemed as feature when several spatial point processes are overlaid in a region. They can be perceived either as a precursor that may induce a major event to come or as offspring triggered by a major event. Hence, the detection of clustered events from point processes may help to predict a forthcoming major event or to study the process caused by a major event. Nevertheless, the locations of existing clustered events alone are not sufficient to identify the area susceptible to a potential major future event or to predict the potential locations of similar future events, so it is desirable to know the shape and the size of the region (the "territory" of feature events) that the feature process occupies. In this paper, the support domain of feature (SDF), the region over which any feature event has the equivalent likelihood to occur, is employed to approximate the "territory" of feature events. A method is developed to delineate the SDF from a region containing spatial point processes. The method consists of three major steps. The first is to construct a discrimination function for separating feature points from noise points. The second is to divide the entire area into a regular mesh of points and then compute a fuzzy membership value for each grid point belonging to the SDF. The final step is to trace the boundary of the SDF. The algorithm was applied to two seismic cases for evaluation, one is the Lingwu earthquake and the other is the Longling earthquakes. Results show that the main earthquakes in both areas as well as most aftershocks triggered by them fell into the estimated SDFs. The case study of Longling shows that the algorithm can deal with a region containing more than two processes. (C) 2007 Elsevier Ltd. All rights reserved.