Fractal Analysis of Data from Seismometer Array Monitoring Virgo Interferometer ALESSANDRO LONGO, 1,2 STEFANO BIANCHI, 1 WOLFANGO PLASTINO, 1,2 BARTOSZ IDZ ´ KOWSKI, 3 MACIEJ SUCHIN ´ SKI, 3 and TOMASZ BULIK 3 Abstract—The local Hurst exponent H(t) has been computed for an array of 38 seismometers, deployed at the Virgo West End Building for Newtonian Noise characterisation purposes. The analysed period is from January 31st, 2018 to February 5th, 2018. The Hurst exponent H is a fractal index quantifying the persistent behaviour of a time series, higher H corresponding to higher per- sistency. The adopted methodology makes use of the local Hurst exponent computed using small sliding windows, in order to characterise the properties of the seismometers. Hourly averages and averages of H(t) have been computed over the whole analysed period. Results show that seismometers placed on a concrete slab closer to the centre of the room systematically exhibit higher per- sistency than the ones that are not placed on it. Seismometers placed next to the outer walls also exhibit higher persistency. The seismometer placed on a thin metal plate exhibits instead very low values of persistency during the analysed period, compared to the rest of the array. Keywords: Newtonian Noise, virgo, detector characterisation, fractal time series analysis, DFA, local hurst exponent. 1. Introduction Mass density fluctuations, generated either by seismicity and microseismicity or by density fluctu- ations of atmospheric air masses, can induce a gravitational field which couples directly to the test masses of the interferometer, and induces a noise referred to as Newtonian noise (Harms 2015; Drig- gers et al. 2012). This gravitational field couples to each stage of the attenuation chain and also directly to the mirror. In the Virgo interferometer the test masses are isolated from the direct influence of seismic vibrations using a chain of oscillators. Such chain mitigates the amplitude of vibrations of fre- quency f at the suspension point by a factor ðf =f 0 Þ 2 at each stage, where f 0 is the frequency of a single oscillator (Beccaria et al. 1998). For Newtonian noise cancellation studies, array of seismometers are typi- cally deployed around test masses. In this article data from an array of 38 seismometers deployed in the Virgo West End Building (WEB) have been analysed and characterised based on their persistency in order to investigate the seismic response of the room using fractal algorithms. The local Hurst exponent has been computed for the 38 seismometers of the array, monitoring WEB for six consecutive days. Some applications of the local Hurst exponent for the description of persistency in radionuclide time series can be found in Longo et al. (2018), Bianchi et al. (2018a, b, 2019), Bianchi and Plastino (2018), Longo et al. (2019), while characterisation of outliers occurrence in radionuclide time series in Plastino et al. (2010). This document is organised as follows. In Sect. 2, an overview of fractal analysis, which aims at quantitatively describing self-similar pro- cesses, is given, along with the description on how to compute the local Hurst exponent. Specifically, in Sect. 2.1 Detrended Fluctuation Analysis (DFA), which is a method to quantify persistency of a time series in terms of its Hurst exponent H, is described. In Sect. 2.2, Multifractal Detrended Fluctuation Analysis (MFDFA), a generalisation of the DFA to quantitatively describe both multifractal and monofractal processes, is briefly described. Mul- tifractal processes exhibit different scaling behaviours at different scales, differently from 1 Department of Mathematics and Physics, Roma Tre University, Via della Vasca Navale 84, 00146 Rome, Italy. E-mail: alessandro.longo@uniroma3.it; stefano.bianchi@uniroma3.it; wolfango.plastino@uniroma3.it 2 INFN, Sezione di Roma Tre, Via della Vasca Navale 84, 00146 Rome, Italy. 3 Astronomical Observatory, University of Warsaw, Al. Ujazdowskie 4, 00-090 Warsaw, Poland. E-mail: bidzkowski@sirius.astrouw.edu.pl; maciej.suchinski@gmail.com; tb@astrouw.edu.pl Pure Appl. Geophys. Ó 2019 Springer Nature Switzerland AG https://doi.org/10.1007/s00024-019-02395-x Pure and Applied Geophysics