Statistical analysis of the spatial distribution of earthquakes—variation of the spatial distribution of earthquakes before and after large earthquakes

Abstract We have investigated the spatial distribution of earthquakes using the Polya-Eggenberger model and the Morishita index which is used for the analysis of the spatial dispersion of bio-species. First, we found that the spatial distribution of earthquakes is characterised by clustering. When we divide the certain area into equal area meshes, the frequency distribution of meshes with same number of events fits well to the Polya-Eggenberger model. On the basis of this result, we examined the degree of spatial clustering of earthquakes, by using the Morishita index defined by I δ =Q ∑ i=1 Q n i (n i −1) N(N−1) . Where Q, N and ni are the numbers of meshes, total events and events of the i-th mesh, respectively. The index Iδ corresponds to the contagious coefficient plus 1 in the Polya-Eggenberger statistics. The dependence of Iδ on the mesh size provides information about clustering. We analysed the actual distribution patterns of earthquakes before and after the Miyagi-oki (1978, M = 7.4), the Tokachi-oki (1968, M = 7.9) and the Nihonkai-chubu (1983, M = 7.7) earthquakes. Large scale clusters of about 50–100 km are dominant in the aftershock sequences. After the aftershock activity, earthquakes tend to distribute randomly. Prior to large earthquakes, small patches of 10–20 km are created. This statistical feature of the earthquake distribution seems to be related to the phenomena of the precursory clusterings of earthquakes, doughnut patterns, preseismic quiescence and foreshocks prior to large earthquakes.