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The Einstein Telescope (ET) will be a third-generation Gravitational Wave (GW) detector that will tackle cutting-edge technological challenges. The ET will be constructed at a depth of 200–300 m to isolate it from vibrations caused by seismic waves and human activities, which are sources of noise for GW detection. To meet the ET’s objectives, it will be necessary to improve low-frequency sensitivity by about two orders of magnitude compared to current interferometers (LIGO, Virgo). Magnetic noise is a limiting noise in the frequency range from a few Hz up to around 100 Hz in future GW detectors. This article will discuss the magnetic noise mitigation strategies under development, based on experiences from Virgo.

The first twenty years of operation of gravitational-wave interferometers have shown that these detectors are affected by physical disturbances from the surrounding environment. These are seismic, acoustic, or electromagnetic disturbances that are mainly produced by the experiment infrastructure itself. Ambient noise can limit the interferometer sensitivity or potentially generate transients of non-astrophysical origin. Between 1 April 2019 and 27 March 2020, the network of second generation interferometers—LIGO, Virgo and GEO—performed the third joined observing run, named O3, searching for gravitational signals from the deep universe. A thorough investigation has been done on each detector before and during data taking in order to optimize its sensitivity and duty cycle. In this paper, we first revisit typical sources of environmental noise and their coupling paths, and we then describe investigation methods and tools. Finally, we illustrate applications of these methods in the hunt for environmental noise at the Virgo interferometer during the O3 run and its preparation phase. In particular, we highlight investigation techniques that might be useful for the next observing runs and the future generation of terrestrial interferometers.

A methodology using adaptive time series analysis is tested on data from a seismometer monitoring the north end building (NEB) of the Virgo interferometer during four acoustic noise injections. Empirical mode decomposition (EMD) is used for adaptive detrending, while the recently developed time-varying filter EMD algorithm is used for narrowband mode extraction. Mode persistency is evaluated with detrended fluctuation analysis, and denoising is achieved by setting a threshold Hthr on the Hurst exponent of the obtained modes. The adopted methodology is proven useful in adaptively separating the seismic noise induced by the acoustic noise injections from the underlying nonlinear non-stationary recordings of the seismometer monitoring NEB. The Hilbert–Huang transform provides a high-resolution time–frequency representation of the data. Furthermore, the local Hurst exponent exhibits a drop due to the injections that is of the same order of Hthr. This suggests that the local Hurst exponent could be calculated as an initial step in order to select the threshold Hthr. The algorithms could be used for detector characterisation purposes such as the investigation of non-Gaussian noise.

Terrestrial gravity perturbations caused by seismic fields produce the so-called Newtonian noise in gravitational-wave detectors, which is predicted to limit their sensitivity in the upcoming observing runs. In the past, this noise was seen as an infrastructural limitation, i.e., something that cannot be overcome without major investments to improve a detector’s infrastructure. However, it is possible to have at least an indirect estimate of this noise by using the data from a large number of seismometers deployed around a detector’s suspended test masses. The noise estimate can be subtracted from the gravitational-wave data, a process called Newtonian noise cancellation (NNC). In this article, we present the design and implementation of the first NNC system at the Virgo detector as part of its AdV+ upgrade. It uses data from 110 vertical geophones deployed inside the Virgo buildings in optimized array configurations. We use a separate tiltmeter channel to test the pipeline in a proof-of-principle. The system has been running with good performance over months.

The area surrounding the dismissed mine of Sos Enattos (Sardinia, Italy) is the Italian candidate site for hosting Einstein Telescope (ET), the third-generation gravitational wave (GW) observatory. One of the goals of ET is to extend the sensitivity down to frequencies well below those currently achieved by GW detectors, i.e. down to 2 Hz. In the bandwidth [1,10] Hz, the seismic noise of anthropogenic origin is expected to represent the major perturbation to the operation of the infrastructure, and the site that will host the future detector must fulfill stringent requirements on seismic disturbances. In this paper we describe the operation of a temporary, 15-element, seismic array deployed in close proximity to the mine. Signals of anthropogenic origin have a transient nature, and their spectra are characterized by a wide spectral lobe spanning the [3,20] Hz frequency interval. Superimposed to this wide lobe are narrow spectral peaks within the [3,8] Hz frequency range. Results from slowness analyses suggest that the origin of these peaks is related to vehicle traffic along the main road running east of the mine. Exploiting the correlation properties of seismic noise, we derive a dispersion curve for Rayleigh waves, which is then inverted for a shallow velocity structure down to depths of ≈ 150 m. This data, which is consistent with that derived from analysis of a quarry blast, provide a first assessment of the elastic properties of the rock materials at the site candidate to hosting ET.

Density changes in the atmosphere produce a fluctuating gravity field that affect gravity strainmeters or gravity gradiometers used for the detection of gravitational-waves and for geophysical applications. This work addresses the impact of the atmospheric local gravity noise on such detectors, extending previous analyses. In particular we present the effect introduced by the building housing the detectors, and we analyze local gravity-noise suppression by constructing the detector underground. We present also new sound spectra and correlations measurements. The results obtained are important for the design of future gravitational-wave detectors and gravity gradiometers used to detect prompt gravity perturbations from earthquakes.

The KAGRA gravitational-wave detector in Japan is the only operating detector hosted in an underground infrastructure. Underground sites promise a greatly reduced contribution of the environment to detector noise thereby opening the possibility to extend the observation band to frequencies well below 10 Hz. For this reason, the proposed next-generation infrastructure Einstein Telescope in Europe would be realized underground aiming for an observation band that extends from 3 Hz to several kHz. However, it is known that ambient noise in the low-frequency band 10 Hz - 20 Hz at current surface sites of the Virgo and LIGO detectors is predominantly produced by the detector infrastructure. It is of utmost importance to avoid spoiling the quality of an underground site with noisy infrastructure, at least at frequencies where this noise can turn into a detector-sensitivity limitation. In this paper, we characterize the KAGRA underground site to determine the impact of its infrastructure on environmental fields. We find that while excess seismic noise is observed, its contribution in the important band below 20 Hz is minor preserving the full potential of this site to realize a low-frequency gravitational-wave detector. Moreover, we estimate the Newtonian-noise spectra of surface and underground seismic waves and of the acoustic field inside the caverns. We find that these will likely remain a minor contribution to KAGRA's instrument noise in the foreseeable future.

Fluctuations of gravitational forces cause so-called Newtonian noise (NN) in gravitational-wave (GW) detectors which is expected to limit their low-frequency sensitivity in upcoming observing runs. Seismic NN is produced by seismic waves passing near a detector's suspended test masses. It is predicted to be the strongest contribution to NN. Modeling this contribution accurately is a major challenge. Arrays of seismometers were deployed at the Virgo site to characterize the seismic field near the four test masses. In this paper, we present results of a spectral analysis of the array data from one of Virgo's end buildings to identify dominant modes of the seismic field. Some of the modes can be associated with known seismic sources. Analyzing the modes over a range of frequencies, we provide a dispersion curve of Rayleigh waves. We find that the Rayleigh speed in the NN frequency band 10 Hz - 20 Hz is very low (\\(\\lesssim\\)100\\,m/s), which has important consequences for Virgo's seismic NN. Using the new speed estimate, we find that the recess formed under the suspended test masses by a basement level at the end buildings leads to a 10 fold reduction of seismic NN.

A methodology of adaptive time series analysis, based on Empirical Mode Decomposition (EMD), and on its time varying version tvf-EMD has been applied to strain data from the gravitational wave interferometer (IFO) Virgo in order to characterise scattered light noise affecting the sensitivity of the IFO in the detection frequency band. Data taken both during hardware injections, when a part of the IFO is put in oscillation for detector characterisation purposes, and during periods of science mode, when the IFO is fully locked and data are used for the detection of gravitational waves, were analysed. The adaptive nature of the EMD and tvf-EMD algorithms allows them to deal with nonlinear non-stationary data and hence they are particularly suited to characterise scattered light noise which is an intrinsically nonlinear and non-stationary noise. Obtained results show that tvf-EMD algorithm allows to obtain more precise results compared to the EMD algorithm, yielding higher cross-correlation values with the auxiliary channels that are the culprits of scattered light noise.

A system was recently implemented in the Virgo detector to cancel noise in its data produced by seismic waves directly coupling with the suspended test masses through gravitational interaction. The data from seismometers are being filtered to produce a coherent estimate of the associated gravitational noise also known as Newtonian noise. The first implementation of the system uses a time-invariant (static) Wiener filter, which is the optimal filter for Newtonian-noise cancellation assuming that the noise is stationary. However, time variations in the form of transients and slow changes in correlations between sensors are possible and while time-variant filters are expected to cope with these variations better than a static Wiener filter, the question is what the limitations are of time-variant noise cancellation. In this study, we present a framework to study the performance limitations of time-variant noise cancellation filters and carry out a proof-of-concept with adaptive filters on seismic data at the Virgo site. We demonstrate that the adaptive filters, at least those with superior architecture, indeed significantly outperform the static Wiener filter with the residual noise remaining above the statistical error bound.