Condensation of earthquake location distributions: Optimal spatial information encoding and application to multifractal analysis of south Californian seismicity.

We present the "condensation" method that exploits the heterogeneity of the probability distribution functions (PDFs) of event locations to improve the spatial information content of seismic catalogs. As its name indicates, the condensation method reduces the size of seismic catalogs while improving the access to the spatial information content of seismic catalogs. The PDFs of events are first ranked by decreasing location errors and then successively condensed onto better located and lower variance event PDFs. The obtained condensed catalog differs from the initial catalog by attributing different weights to each event, the set of weights providing an optimal spatial representation with respect to the spatially varying location capability of the seismic network. Synthetic tests on fractal distributions perturbed with realistic location errors show that condensation improves spatial information content of the original catalog, which is quantified by the likelihood gain per event. Applied to Southern California seismicity, the new condensed catalog highlights major mapped fault traces and reveals possible additional structures while reducing the catalog length by ∼25%. The condensation method allows us to account for location error information within a point based spatial analysis. We demonstrate this by comparing the multifractal properties of the condensed catalog locations with those of the original catalog. We evidence different spatial scaling regimes characterized by distinct multifractal spectra and separated by transition scales. We interpret the upper scale as to agree with the thickness of the brittle crust, while the lower scale (2.5 km) might depend on the relocation procedure. Accounting for these new results, the epidemic type aftershock model formulation suggests that, contrary to previous studies, large earthquakes dominate the earthquake triggering process. This implies that the limited capability of detecting small magnitude events cannot be used to argue that earthquakes are unpredictable in general.