Multifractal analysis of spatial distribution of microearthquakes in the Kanto region

Abstract

b The spatial distribution of earthquakes is a fractal, which is characterized by a fractal dimension. However, if a spatial distribution has a heterogeneous fractal structure, a single value of fractal dimension [e.g. Do (capacity dimension) or D2 (correlation dimension)] is not enough to characterize it. From a multifractal viewpoint, we analysed the spatial distribution of microearthquakes in the Kanto region by using a local density function. Generalized dimensions, Dq, of the spatial distribution were calculated from the slopes of generalized correlation integrals, Cq(r) versus distance r, on a log‐log plot, examining the self‐similarity of the spatial distribution of microearthquakes. Self‐similar structures are held well at scales from 1.26 to 12.6 km. Our results suggest that the spatial distribution of microearthquakes in the Kanto region is not a homogeneous fractal structure but a heterogeneous one with generalized dimensions D2= 2.2 ≤D3≤…≤D∞= 1.7. The value of D∞, the lower limit of fractal dimension, is the fractal dimension of the most intensive clustering in the heterogeneous fractal set. The fractal dimension of the most intensive clustering of microearthquakes in the Kanto region is 1.7. Copyright © 1991, Wiley Blackwell. All rights reserved