Fractal dimension confidence interval estimation of epicentral distributions
Estimates of the fractal dimension of hypocentral distributions require evaluating the range of independent variables in which fractal parameters exhibit a power law. Systematic and accidental errors are produced mainly by the subjective selection of this range, the insufficiency of data sets as well as by hypocenter mislocations. Therefore it is very important to determine the confidence intervals which are associated with fractal dimension estimates. The effects of various sources of errors are studied using different geometric clusters of epicenters, which have been synthetically generated using a multicluster algorithm with different hierarchical levels, so as to reproduce some characte…
Monte Carlo Studies of Relations between Fractal Dimensions in Monofractal Data Sets
Within the fractal approach to studying the distribution of seismic event locations, different fractal dimension definitions and estimation algorithms are in use. Although one expects that for the same data set, values of different dimensions will be different, it is usually anticipated that the direction of fractal dimension changes among different data sets will be the same for every fractal dimension. Mutual relations between the three most popular fractal dimensions, namely: the capacity, cluster and correlation dimensions, have been investigated in the present work. The studies were performed on the Monte Carlo generated data sets. The analysis has shown that dependence of the fractal …