  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.
