Increasing power-law range in avalanche amplitude and energy distributions

TL;DR

This paper introduces a methodology to extend the observable power-law range in avalanche distributions by combining data from different observation windows, revealing broader exponents in acoustic emission experiments.

Contribution

A novel approach to overcome empirical constraints, enabling the estimation of global power-law exponents across multiple decades for avalanche properties.

Findings

Broader power-law ranges for amplitude and energy distributions.

Global exponents of 4.5 decades for amplitudes and 9.5 decades for energies.

Experimental limitations may influence the observed power-law behavior.

Abstract

Power-law type probability density functions spanning several orders of magnitude are found for different avalanche properties. We propose a methodology to overcome empirical constrains that limit the power-law range for the distributions of different avalanche observables like amplitude, energy, duration or size. By considering catalogs of events that cover different observation windows, maximum likelihood estimation of a global power-law exponent is computed. This methodology is applied to amplitude and energy distributions of acoustic emission avalanches in failure-under- compression experiments of a nanoporous silica glass, finding in some cases global exponents in an unprecedented broad range: 4.5 decades for amplitudes and 9.5 decades for energies. In the later case, however, strict statistical analysis suggests experimental limitations might alter the power-law behavior.