Characterization of gravitational-wave detector noise with fractals*

Current ground-based gravitational-wave detectors such as the Laser Interferometer Gravitational-wave Observatory (LIGO), Virgo, and KAGRA, are exquisite scientific instruments of extreme sensitivity. Characterization of detector noise and data quality investigations are essential to improve the instruments, provide feedback to commissioners, as well as validate detection candidates in low-latency and increase the significance of gravitational-wave signals in searches. We present a new method, based on fractal analysis, to characterize the data of gravitational-wave interferometric detectors. We show that a measure of the fractal dimension of the main detector output (strain channel) can be used to determine the instrument state, test data stationarity, and identify non-astrophysical excess noise in low latency. When applied to instrument control and environmental data (auxiliary channels) the fractal dimension can be used to identify the origins of noise transients, non-linear couplings in the various detector subsystems, and provide a means to flag stretches of low-quality data.