Analysis of the spatial distribution between successive earthquakes.

Spatial distances between subsequent earthquakes in southern California exhibit scale-free statistics, with a critical exponent $\ensuremath{\delta}\ensuremath{\approx}0.6$, as well as finite size scaling. The statistics are independent of the threshold magnitude as long as the catalog is complete, but depend strongly on the temporal ordering of events, rather than the geometry of the spatial epicenter distribution. Nevertheless, the spatial distance and waiting time between subsequent earthquakes are uncorrelated with each other. These observations contradict the theory of aftershock zone scaling with main shock magnitude.

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