Scaling of clustered space-time-magnitude structure of seismicity

The spatiotemporal properties of seismicity as a function of magnitude are investigated for worldwide earthquake catalogs and for local catalogs in the stationary case (constant rate of occurrence), showing a nearly universal scaling behavior. Distributions of distances between consecutive earthquakes (which we call jumps) are magnitude independent and show two power-law regimes, separated by jump values about 200 km in the worldwide case and a smaller value in the local case. The power law corresponding to long jumps reflects the spatial fractal geometry of epicenters, whereas the short-jump power law is of dynamical origin, characteristic of the triggering process. Measuring distributions of times between consecutive events conditioned to the value of jumps shows two regimes as well: a Poisson time occurrence for distant events and a sharp decreasing power-law distribution for close events, the difference between distant and close events given by the crossover value of the jump distribution (200 km in the worldwide case). Moreover, both variables (times and jumps) are uncorrelated in each regime. Finally, diffusion profiles, showing the jump distribution not for consecutive events but for a fixed time separation, are found to be similar to the jump distributions, and independent on the magnitude, contrary to what the waiting-time distributions suggest. These results indicate a complex random-walk-like picture with the existence of Levy flights and other scale-invariant properties. References A. Corral, Universal Earthquake-Occurrence Jumps, Correlations with Time, and Anomalous Diffusion. Phys. Rev. Lett. 97, 178501 (2006). A. Corral, Structure of earthquake occurrence in space, time, and magnitude. Terra Nova (in press).