Correlations and invariance of seismicity under renormalization-group transformations

The effect of transformations analogous to those of the real-space renormalization group are analyzed for the temporal occurrence of earthquakes. The distribution of recurrence times turns out to be invariant under such transformations, for which the role of the correlations between the magnitudes and the recurrence times are fundamental. A general form for the distribution is derived imposing only the self-similarity of the process, which also yields a scaling relation between the Gutenberg-Richter b-value, the exponent characterizing the correlations, and the recurrence-time exponent. This approach puts the study of the structure of seismicity in the context of critical phenomena.