Earthquake statistics and fractal faults

TL;DR

This paper introduces a fractal fault model for earthquakes that reproduces key seismic laws and clustering behavior by simulating fault roughness with fractional Brownian profiles, emphasizing the role of fault geometry.

Contribution

The novel Self-affine Asperity Model explicitly incorporates fault fractal geometry, linking it to seismicity patterns and scaling laws, differing from traditional self-organized criticality models.

Findings

Reproduces Gutenberg-Richter law with a β exponent related to fault roughness.

Displays clustering of epicenters similar to real seismic data.

Exhibits Omori law for aftershock distribution in an extended version.

Abstract

We introduce a Self-affine Asperity Model (SAM) for the seismicity that mimics the fault friction by means of two fractional Brownian profiles (fBm) that slide one over the other. An earthquake occurs when there is an overlap of the two profiles representing the two fault faces and its energy is assumed proportional to the overlap surface. The SAM exhibits the Gutenberg-Richter law with an exponent $\beta$ related to the roughness index of the profiles. Apart from being analytically treatable, the model exhibits a non-trivial clustering in the spatio-temporal distribution of epicenters that strongly resembles the experimentally observed one. A generalized and more realistic version of the model exhibits the Omori scaling for the distribution of the aftershocks. The SAM lies in a different perspective with respect to usual models for seismicity. In this case, in fact, the critical behaviour is not Self-Organized but stems from the fractal geometry of the faults, which, on its turn, is supposed to arise as a consequence of geological processes on very long time scales with respect to the seismic dynamics. The explicit introduction of the fault geometry, as an active element of this complex phenomenology, represents the real novelty of our approach.