Testing fractal coefficients sensitivity on real and simulated earthquake data

We examined the behavior of different fractal dimensions when applied to study features of earthquake spatial distribution on different types of data. We first examined simulated spatial fields of points of different clustering level, following the so called Soneira-Peebles model. The model was chosen because it displays some similarity to the real clustering structure of earthquakes occurring on hierarchically ordered faults. The analysis of the capacity, clustering and correlation dimensions revealed that their behavior did not completely correlate with the clustering level of the simulated data sets. We also studied temporal variations of the fractal coefficients, characterizing the spatial distribution of the 1999 İzmit-Düzce aftershock sequence. The calculated coefficient values demonstrated analogous behavior like for the simulated data. They exposed different variability in time, but for all of them a systematic fluctuation was observed before the occurrence of the Düzce earthquake. Our analysis revealed that although fractal coefficients could be applied to measure earthquake clustering, they should be used with caution, trying to figure out the best coefficient for a certain data set.