Correlations and invariance of seismicity under renormalization-group transformations

TL;DR

This paper investigates how seismicity patterns, specifically recurrence times and magnitude correlations, remain invariant under renormalization-group transformations, linking seismic behavior to critical phenomena.

Contribution

It introduces a framework connecting seismic recurrence time distributions with self-similarity and critical phenomena, deriving a scaling relation involving key seismic exponents.

Findings

Recurrence time distribution is invariant under renormalization transformations.

Correlations between earthquake magnitudes and recurrence times are fundamental.

A general form of the distribution is derived based on self-similarity.

Abstract

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.