A SPATIOTEMPORAL CLUSTERING OF EPICENTERS: THE MULTIFRACTAL APPROACHE. M. Blanter and M. G. Shnirman
We suggest a multifractal approach to describe seismicity and to study self-similarity properties of clustering in space and time. We suggest a clustering procedure similar to the single-link cluster analysis. We construct models (synthetic catalogs), two fractal and two multifractal ones, and compare them with four real subcatalogs from southern California. The parameters of the models are found by fitting generalized dimensions. It is shown that the multifractal model is similar to the real catalogs. The similarity between the real catalog and the corresponding multifractal model is independent of heterogeneities in the selected earthquake catalog. We demonstrate how the difference in clustering properties of the real catalog that includes all events and the other that includes main shocks only is reflected in the multifractal characteristics of the corresponding models. The result was obtained that the multifractal approach is independent of the selection of slowness $V$ defining a relation between spatial and temporal coordinates of events in a wide range of $V$ values.