The effect of thresholding on temporal avalanche statistics

TL;DR

This paper investigates how thresholding affects the statistical properties of avalanche-like events in time series, combining simple toy models with complex self-organized criticality simulations to understand correlations and noise effects.

Contribution

It introduces a detailed analysis of thresholding effects on avalanche statistics using toy models and the Manna sandpile model, highlighting the impact of noise and detection thresholds.

Findings

Thresholding can induce correlations in avalanche statistics.

Random walk models explain most scaling behaviors observed.

Added noise significantly alters waiting time distributions.

Abstract

We discuss intermittent time series consisting of discrete bursts or avalanches separated by waiting or silent times. The short time correlations can be understood to follow from the properties of individual avalanches, while longer time correlations often present in such signals reflect correlations between triggerings of different avalanches. As one possible source of the latter kind of correlations in experimental time series, we consider the effect of a finite detection threshold, due to e.g. experimental noise that needs to be removed. To this end, we study a simple toy model of an avalanche, a random walk returning to the origin or a Brownian bridge, in the presence and absence of superimposed delta-correlated noise. We discuss the properties after thresholding of artificial timeseries obtained by mixing toy avalanches and waiting times from a Poisson process. Most of the resulting scalings for individual avalanches and the composite timeseries can be understood via random walk theory, except for the waiting time distributions when strong additional noise is added. Then, to compare with a more complicated case we study the Manna sandpile model of self-organized criticality, where some further complications appear.