# Seismic and Newtonian Noise in the GW Detectors

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## Abstract

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## 1. Introduction

## 2. An Introduction to Seismic Noise in GW Detectors

**seismic waves**travelling through the Earth’s layers at different speeds and produced by phenomena such as wind, ocean waves, earthquakes, anthropogenic sources, etc. Seismic wave speeds can change depending on the density and the elasticity of the crossed medium, as well as on their depth. Moving from the Earth’s crust to the deep mantle, the speed increases from a few m/s up to 13 km/s [6,7].

**Body waves**include all those waves travelling through the Earth. The density and stiffness of the crossed material depend on temperature, chemical composition, and material phase. For this reason, body waves show different velocities with increasing depth of propagation. They are classified into primary waves (P-waves) and secondary waves (S-waves). P-waves cause a compression/decompression displacement along their propagation direction, whereas S-waves produce a shear displacement perpendicular to their propagation direction. In an earthquake event, S-waves are slower than P-waves (with a typical speed value of about 60% of that of P-waves). S-waves can only travel through solid materials. Indeed, fluids (liquids and gases) do not support shear stresses (see Figure 1). P-waves generate density variations in the medium, so they produce gravity fluctuations. S-waves, being shear waves, can instead produce density variations only in presence of some discontinuity (see Section 4.2).**Figure 1.**Body and surface waves [8].**Surface waves**travel on the Earth’s surface and their amplitude decreases exponentially as a function of their depth from the surface. Their speed is slower compared to the speed of body waves (P and S) and their amplitudes can reach several cm in an earthquake event. Mathematically, they arise from the interaction of body waves with a medium discontinuity. They can be distinguished into**Rayleigh waves**(or ground rolls) and**Love waves**. Rayleigh waves produce both longitudinal and transverse motion of surface particles, generating a retrograde vertical ellipse motion in the plane normal to the surface and containing the wave’s propagation direction. In a homogeneous and isotropic half-space, Rayleigh waves have a slightly lower velocity than S-waves (${v}_{R}\simeq 0.9\phantom{\rule{0.277778em}{0ex}}{v}_{S}$) and are non-dispersive (the velocity does not depend on the frequency). Instead, if the half-space is composed of homogeneous and isotropic layers, the waves become dispersive. The dispersion model has an important impact on the gravity fluctuations generated by Rayleigh waves (see Section 4.2).Love wave polarization is perpendicular to the propagation direction and parallel to the surface. Moreover, these waves have larger amplitudes and speed compared to Rayleigh waves (see Figure 1). Contrary to Rayleigh waves, they cannot propagate in homogeneous and isotropic half-space, but they arise in layered mediums, showing a dispersive model. Being surface shear waves, they do not produce density variations; thus, they are not a source of gravity fluctuations.

#### 2.1. Seismic Noise: NLNM and NHNM Models

**microseismic noise**, generated every time atmospheric phenomena such as typhoons, storms, and climatic variations occur [10,11]. The most energetic seismic waves that comprise microseisms are Rayleigh waves, but Love and body waves can also contribute.

**tidal effects**(generated by the Sun–Moon gravitational attraction), start to manifest themselves in the seismic spectrum, whereas all the vibrations included in the range 1–10 Hz are classified as

**anthropogenic noise**, i.e., all the noise produced by human activities such as industrial processes, vehicles, agricultural machinery, wind turbines, etc.

#### 2.2. Seismic Noise in Underground Sites

## 3. Mechanical Attenuators

- At frequency $\omega \ll {\omega}_{0}$, the transfer function is equal to 1 and the force is totally transmitted from the input to the output;
- When $\omega ={\omega}_{0}$, the applied force to the input determines a continuous transfer of energy from the input to the output and an amplification of the system motion with a quality factor Q;
- At frequency $\omega \gg {\omega}_{0}$, the system behaves as a second-order low-pass mechanical filter.

#### 3.1. Seismic Isolation Systems

#### 3.1.1. LIGO Seismic Isolation System

**BSC (Basic Symmetric Chamber)**, which houses the test mass and the transfer function of the quadruple pendulum, are shown in Figure 7. The BSC chamber, a 4.5 m tall suspension, consists of three cascade systems. The first system, the active Hydraulic External Pre-Isolator (The HEPI), provides the first isolation stage. The second system, the Internal Seismic Isolation platform (BSC-ISI), provides two stages of isolation. The test mass is suspended by 480 micron-fused silica fibres to a quadruple pendulum. This system shows resonance frequencies ranging from 0.45 to 4 Hz; thus, the isolation from ground vibrations is provided above these frequencies. Finally, vertical attenuation is provided by maraging steel blades installed in the first three stages of the quadruple pendulum.

#### 3.1.2. KAGRA Seismic Isolation System

**Type A system**. With reference to Figure 8, it consists of a multi-stage pendulum that is 13.5 m tall. It is based on the second floor of an underground mine, supported by three inverted pendulum legs (1 m). The payload, comprising four stages, is installed inside a cryostat and cooled down to 20 K. The vertical attenuation is provided by triangular maraging blades installed in all the filters present in the chain, which are called Geometrical Anti Spring (GAS) filters.

#### 3.1.3. Virgo Seismic Isolation System

**Super-Attenuator (SA)**, which is composed of a multi-stage seismic isolation system [24,25]. Referring to Figure 9, it consists of a pre-isolator, which is a soft inverted pendulum (30 mHz), from which is suspended a 9.2 m long multistage chain connected by means of a single wire at the center of mass of each stage. This chain comprises a first filter at the top of the inverted pendulum (filter 0), four standard filters (the pendulums), and a last filter (Filter 7). Below this is the marionette, from which the test mass is suspended by 480 micron-fused silica fibres. To achieve vertical attenuation, the filter chain is equipped with triangular maraging blades and magnetic anti-springs.

## 4. Newtonian Noise

#### 4.1. Atmospheric Newtonian Noise

#### 4.2. Seismic Newtonian Noise

## 5. Other Sources of Newtonian Noise

## 6. Newtonian Noise Cancellation

^{th}and j

^{th}witness sensors and it is denoted as ${\overline{\mathbf{P}}}_{YY}$. ${P}_{{XY}_{i}}\left(\omega \right)=E\left[{Y}_{\mathrm{i}}^{*}\left(\omega \right)X\left(\omega \right)\right]$ is the i

^{th}element of the the N-vector of the Cross-PSD between the target signal (the NN in the detector) and the i

^{th}witness sensor signal; it is denoted as ${\mathbf{P}}_{XY}$. With this result we can define the residual as $R=E\left[{e}^{*}e\right]/{P}_{XX}$ and obtain

#### Newtonian Noise Cancellation in Surface and Underground Detectors

## 7. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

AdV | Advanced Virgo |

ANN | Atmospheric Newtonian Noise |

BSC | Basic Symmetric Chamber |

CE | Cosmic Explorer |

ET | Einstein Telescope |

NHNM | New High Noise Model |

NLNM | New Low Noise Model |

NN | Newtonian Noise |

PSD | Power Spectral Density |

SA | Super Attenuator |

SNN | Seismic Newtonian Noise |

WF | Wiener Filter |

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**Figure 2.**Square root of the power spectral density of the seismic displacement of Peterson’s New Low and High Noise Models (NLNM and NHNM), the average of their logarithmic values and 5 times the NLNM.

**Figure 3.**This figure shows the typical spectral density of the seismic noise displacement measured in an underground location at Kamioka (red curve) and compared to those measured at the surface (Tokyo areas). This plot was made using the data shown in Figure 4 in [13].

**Figure 4.**This plot shows the spectral density of the seismic noise displacement measured at the Sos-Enattos mine, compared to those measured near the Central building of Virgo (Pisa, Italy) and at the former mine of Homestake (Lead, SD -USA). The Homestake seismic profile was reconstructed using the data shown in the bottom right of Figure 6.10 in [14].

**Figure 5.**Ground displacement measured at the Cascina site (blue curve) and at the Sos-Enattos mine (red curve) compared to the design sensitivity of the Advanced Virgo detector (AdV). At 10 Hz, the ground displacement is about eight orders of magnitude higher than the sensitivity of the GW detector.

**Figure 6.**Mechanical transfer functions of a single (blue curve) and a double pendulum (red curve) having the same length.

**Figure 7.**Schematic model (

**a**) and technical drawing (

**b**) of the BSC chamber supporting the LIGO test masses [17]. For completeness, panel (

**c**) shows the quadruple pendulum mechanical transfer function from the ground to the test mass along the longitudinal degree of freedom. This transfer function was reconstructed following Figure 5 in [18].

**Figure 8.**Panel (

**a**) shows a technical drawing of a Type A system. From top to bottom, the isolation stages are: the pre-isolator (inverted pendulum and top filter—F0), four GAS filters, and the cryogenic payload (platform, intermediate-mass, marionette, and mirror) [23]. Panel (

**b**) shows the Type A mechanical transfer function from the ground to the test mass along the longitudinal degree of freedom.

**Figure 9.**Panel (

**a**) shows a technical drawing of the Virgo SA. From top to bottom, the isolation stages are: pre-isolator (inverted pendulum and top filter—F0), five filters and the payload (marionette and mirror). Panel (

**b**) shows the SA mechanical transfer function from the ground to the test mass along the longitudinal degree of freedom.

**Figure 10.**Ground displacement not filtered (blue) and filtered through the SA (red) compared to the design sensitivity of the AdV detector.

**Figure 11.**ANN generated by external infrasound and advected temperature fields at the Earth’s surface compared with the sensitivity of Virgo foreseen for O4 and with the ET-D sensitivity curve. The ET curve was plotted only to show that building ET on the surface would lead to the requirement of reducing ANN generated by infrasound and advected temperature fields of some orders of magnitude. The ANN produced by infrasound and advected temperature fields were calculated with the models of [35]. The curves for the NN from advected temperature fields were estimated for wind velocities of 10 m/s and 30 m/s. The necessary data to plot the NN produced by infrasound fields were taken from the 75th percentile of Figure 3 in [43].

**Figure 12.**ET-D sensitivity curve compared with the seismic noise and NN of seismic origin. The seismic noise curve was obtained using a seismic spectrum lying exactly at the midpoint between Peterson’s NLNM and NHNM (see Figure 2). The same spectrum was used to evaluate the NN generated by Rayleigh waves. For the NN from body waves, we used 5 times the Low Noise Model spectrum, as was done in [37].

**Figure 13.**Comparison between the optimal array obtained for the West End Building (WEB) in Virgo (

**left**) and the optimal array obtained for an isotropic and homogeneous Rayleigh wave field (

**right**). The blue dots in the

**left**figure represent sensors placed on the tower platform (which is anchored to the bedrock with pillars), whereas the red dots represent sensors placed on the floor of the building. The optimal array in the

**right**figure is represented with different values of SNR. The

**right**figure was taken from [62].

**Figure 14.**

**Left**: seismic correlations between the origin and all the other points in the presence of a homogeneous and isotropic seismic field composed only of P-waves.

**Right**: seismic correlations between the origin and all the other points in the presence of a homogeneous and isotropic seismic field composed of 1/3 of P-waves and 2/3 of S-waves (assuming an equal distribution of energy between the three polarizations: one for P-waves and two for S-waves). Figure taken from [62].

**Table 1.**Comparison between the square root of the power spectral densities of the ANN generated by different mechanisms: h is the depth of the underground interferometer, R is the radius of the cavern/room, and d is the shortest distance between the test mass and the moving air flow.

NN Type | Coupling Factor | Condition |
---|---|---|

External Infrasound | $\propto 1/{h}^{2}$ | $h\gg \frac{{c}_{s}}{4\pi f}$ |

Internal Infrasound | $\propto {R}^{2}$ | $R\ll \frac{{c}_{s}}{2\pi f}$ |

Advected Temperature | $\propto {e}^{-2\pi fd/v}$ | $d\gg \frac{v}{2\pi f}$ |

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Trozzo, L.; Badaracco, F.
Seismic and Newtonian Noise in the GW Detectors. *Galaxies* **2022**, *10*, 20.
https://doi.org/10.3390/galaxies10010020

**AMA Style**

Trozzo L, Badaracco F.
Seismic and Newtonian Noise in the GW Detectors. *Galaxies*. 2022; 10(1):20.
https://doi.org/10.3390/galaxies10010020

**Chicago/Turabian Style**

Trozzo, Lucia, and Francesca Badaracco.
2022. "Seismic and Newtonian Noise in the GW Detectors" *Galaxies* 10, no. 1: 20.
https://doi.org/10.3390/galaxies10010020