Multifractal measures of earthquakes in west Taiwan

The generalized fractal dimension for epicentral distribution of earthquakes in west Taiwan is measured. The entire area is first divided into two zones, i.e., north and south zones, after which the two zones are further separated into three subzones for the former and two for the latter. The logC _q (r) versus logr function, whereC _q (r) is the generalized correlation integral andr is the distance between two epicenters, shows that a linear relation between logC _q and logr exists in the range ofr smaller thanr _c . The value ofr _c is 25 km for the north zone, 40 km for the south and 12 km for the three north subzones. The valuesr _c =25 and 40 km are almost the smallest ones of the width of epicentral distributions of the north and south zones, respectively. The value ofr _c =12 km for the three north subzones is approximately the smallest size of the cluster of epicenters. For the plots of two south subzones, the pattern of data points does not bend in the range ofr in consideration, and, thus, there is not such a critical radius. TheD _q –q relations forq=0, 1, 2,..., 15 are constructed for the two zones and five subzones. Results show significant multifractality and a spatial variation in multifractality for epicentral distributions of earthquakes in west Taiwan.