Inter-event correlations from avalanches hiding below the detection threshold

TL;DR

This paper demonstrates that finite detection thresholds can induce apparent correlations in bursty systems, by splitting large events into sub-events, which explains observed clustering in various physical phenomena.

Contribution

It introduces a scaling framework showing how measurement thresholds create artificial inter-event correlations in crackling noise data.

Findings

Thresholding causes apparent burst correlations in experiments and simulations.

Sub-avalanches emerge due to thresholding, explaining observed clustering.

The scaling description accurately models threshold-induced correlations.

Abstract

Numerous systems ranging from deformation of materials to earthquakes exhibit bursty dynamics, which consist of a sequence of events with a broad event size distribution. Very often these events are observed to be temporally correlated or clustered, evidenced by power-law distributed waiting times separating two consecutive activity bursts. We show how such inter-event correlations arise simply because of a finite detection threshold, created by the limited sensitivity of the measurement apparatus, or used to subtract background activity or noise from the activity signal. Data from crack propagation experiments and numerical simulations of a non-equilibrium crack line model demonstrate how thresholding leads to correlated bursts of activity by separating the avalanche events into sub-avalanches. The resulting temporal sub-avalanche correlations are well-described by our general scaling description of thresholding-induced correlations in crackling noise.