Seismic and Newtonian noise modeling for Advanced Virgo and Einstein Telescope Bader, M.K.M.
2021
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Bader, M. K. M. (2021). Seismic and Newtonian noise modeling for Advanced Virgo and Einstein Telescope.
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Chapter
5
Newtonian noise at Advanced Virgo
Newtonian noise is one of the fundamental noise sources that limit the design sensitivity of ground based gravitational wave detectors below 20 Hz. State of the art seismic and Newtonian noise models rely on simplified geological and seismic conditions. As detectors such as Ad-vanced Virgo and AdAd-vanced LIGO are constantly improving their performance and are moving towards their final sensitivity goals, the need for an improved understanding of Newtonian noise contributions at low frequencies arises. This ultimately means that more realistic seismic and Newtonian noise models are required.
This section focuses on the derivation of a seismic and Newtonian noise model that takes into account a wave field from a complete solution of the elastodynamic wave equation together with the characteristic geology and source distribution at EGO, the Advanced Virgo detector site. The first part of the section will describe the seismic study from which all relevant soil parameters, such as subsurface layer composition, layer densities, wave speeds and local distribution of seismic noise sources have been obtained. In the second part of this section, these parameters are used to obtain a solution of the wave equation in such a Virgo-like, horizontally layered geology. By combining the fields of several seismic sources, a model of an ambient seismic field is derived. In the third section, Newtonian noise at the Advanced Virgo detector is calculated from this realistic seismic field model.
5.1 Seismic characterization of the Advanced Virgo site
A passive seismic array study has been performed at the EGO site of the Advanced Virgo gravitational wave detector in Italy between 13 and 29 August 2016 [144, 145]. An array of 64 geophone based TN-1 sensors (see Section 4.3) was deployed in concentric circles, dis-tributed within the 3 km long arms of the Advanced Virgo interferometer with the aim to con-tinuously record ambient seismic noise (Fig. 5.1, left panel). This specific design choice for the network geometry allowed to maximize the array sensitivity at low frequencies and to avoid spatial aliasing at the same time. With a minimum inter-sensor spacing of 6 m in the center of the array and a maximum aperture of 3000 m, the array resolved low frequencies down to 0.2 Hz and high frequencies up to 8 Hz.
The PSD measurement of the array corresponds to the average over the PSDs from all sensors and for the full measurement period. It is referred to as site-characteristic PSD and it represents the average seismic noise level that can ultimately be achieved at the site. Due to high anthro-pogenic activity, seismic noise at the Virgo site is high in the frequency band of interest for
N E CEB NEB WEB -2000 -1000 0 1000 Longitude [m] -1500 -1000 -500 0 500 1000 1500 L at it ud e [m ] -18.6 -18.4 -18.2 -18 -17.8 -17.6 -17.4 -17.2 -17 -16.8 -16.6 lo g10 (P SD ) [m 2/Hz ] Longitude [m] -2000 -1000 0 1000 Lattitiude [m] 1500 1000 500 0 -500 -1000 -1500 log 10 (PSD) [m 2 /Hz] -16.6 -16.8 -17 -17.2 -17.4 -17.6 -17.8 -18 -18.2 -18.4 -18.6 CEB NEB WEB NHNM
Figure 5.1: Left: Seismic sensor array layout (triangular markers) within the 3 km long Ad-vanced Virgo interferometer arms (blue). The color of the markers displays the average from
2 to 20 Hz over the mean PSD from the full measurement period of the corresponding sensor.
Sensors that record a high PSD are in the vicinity of streets (light grey), bridges and buildings. Right: Vertical mean power spectral density of the site-characteristic PSD. The transparent band indicates the 10thand 90thpercentiles. High anthropogenic activity leads to a high seismic noise
level above 1 Hz.
Newtonian noise below 20 Hz; it even surpasses Peterson’s new high noise model below 4 Hz. Beam forming analysis of the ambient seismic noise at the Virgo site showed that the main noise sources can be grouped into three categories (see Fig. 5.2). At frequencies between 0.2 and 1.5 Hz the seismic noise originates from oceanic microseismic activity of the
Mediter-N
E
5 km
Figure 5.2: Left: Surface wave direction of incidence for four representative frequencies, where the inverse surface wave velocity is denoted with p, the incident angle with Θ, measured from the positive y-axis (north). The color scale indicates the normalized beam power and the peak corresponds to the dominant noise sources at the given frequency. Below 1.5 Hz the noise orig-inates from the Mediterranean sea in the western direction (not shown), from 1.5 - 4 Hz noise from road bridges and a wind park is dominant and above 4 Hz noise originates from local sources such as a road through the sensor array. Right: Geographical locations of the noise sources in the area of the Advanced Virgo detector.
5.1. SEISMIC CHARACTERIZATION OF THE ADVANCED VIRGO SITE ranean Sea, which is located in the western direction from the sensor array. For this analysis the seismic data of the sensor array were correlated to oceanic swell, that has been measured with a buoy that is anchored about 200 km off the coast of Pisa in the north-western direction in the Ligurian sea. As this frequency range is not relevant for Newtonian noise, the corresponding analysis results are not shown here and the reader is referred to [75, 145].
In the frequency band from 1.5 to 4 Hz seismic noise originates from traffic on road bridges and streets of the nearby highway surrounding the sensor array at distances between 1 and 3 km. Correlation between seismic noise at the Advanced Virgo site and traffic on nearby roads has been measured during a dedicated study, where seismic sensors have been placed at the Ad-vanced Virgo Central Building and at five bridge locations in the area [75, 145]. Furthermore, a nearby wind park in the eastern direction has previously been identified as additional noise source in this frequency range [161].
Due to the fast attenuation of surface waves at high frequencies, typically after a few hundred meters, seismic noise above 4 Hz corresponds to human activity and local disturbances such as shaking of buildings during times of high wind activity or traffic on roads through or nearby the sensor array. 2 4 6 8 Frequency [Hz] 100 150 200 250 300 350 400 Phase velocity [m/s] Theoretical expectation Measurement 2 2.5 ρ [g/cm 3 ] 1 2 3 V [km/s] S-wave P-wave 100 101 102 103 Depth [m] 5 15 25 D [10 -3 ]
Figure 5.3: Left: Measured dispersion curve (red) of the surface waves is obtained from the beam forming analysis [75]. The theoretically expected fundamental and higher order mode dispersion curves, based on the soil parameters in the right panel, are depicted in black. Right: From top to bottom, a visualization of density ρ, P- and S-wave speeds V and material damp-ing D for P- and S-waves for the nine layers derived with the inversion method.
In addition to the identification of local noise sources, the surface wave velocities in terms of the fundamental mode dispersion curve were derived from the beam forming analysis (Fig. 5.3, left panel). This dispersion curve was used to conduct the inversion analysis to a depth greater than 1 km, whereas the subsurface parameter space was confined with results from previous borehole, gravimetric and inversion studies at the Virgo site to shallow depths of 70 m [162]. The inversion was carried out for a nine layer model and the densities of these layers were fixed. In total 60 000 theoretical subsurface models and their corresponding dispersion curves were explored. The damping parameters of each layer were obtained by a similar analysis, where a frequency dependent attenuation coefficient of surface waves has been derived. This attenua-tion coefficient has been inverted to derive P- and S-wave material damping factors for each layer [75]. The subsurface model that minimizes the misfit between measured and theoretical dispersion is displayed in Fig. 5.3, right panel, and the corresponding parameters are listed in Table 5.1.
Thickness [m] ρ [kg/m3] V p[m/s] Vs[m/s] Dp [10−3] Ds[10−3] 1.8 1700 183 90 8.7 17.4 5.1 1700 226 127 6.2 12.3 5.5 1800 301 155 6.2 12.4 5.5 1900 390 188 5.8 11.7 7.5 1900 552 240 13.7 27.5 36.6 2092 767 272 10.2 20.3 109.2 2459 1435 451 4.6 9.2 613.8 2556 2368 1261 4.4 8.8 ∞ 2631 3900 2287 3.7 7.4
Table 5.1: Material parameters for the nine-layer subsurface model of the geology at the Advanced Virgo site derived with the inversion of the dispersion curve. The parameters are the layer thickness, density ρ, P- and S-wave speed and material damping.
5.2 Ambient seismic field model
To recreate a representation of the local seismic field that reproduces data as measured with the sensor array at Advanced Virgo in the Newtonian noise integration range, we calculate the re-sponse of the Virgo geology given in Table 5.1 to vertical source excitations. The full solution of the wave equation (see Section 3.3) is derived with the direct stiffness method. The correspond-ing algorithm that solves the elastodynamic wave equation is part of the Matlab Elastodynamics toolbox [117].
2 R R
Figure 5.4: Displacement PSD re-sponse to seismic disturbances at the Virgo site down to 200 m depth. The local geology has been excited by
180 vertical 3 Hz sources, which are
distributed in a λR wide ring about
6λR from the center. Note that the
Rayleigh wavelength is 70 m at 3 Hz. The relative strength of the sources is scaled according to the measured beam power at 3 Hz (see Fig. 5.5) and the absolute strength is such that at the center of the coordinate grid the PSD at the Virgo Central Build-ing is reproduced. Each sheet cor-responds to the top surface of a new layer and the color scale indicates the PSD. The Newtonian noise integration range around the test mass is indi-cated in white. It is about λRfor low
5.2. AMBIENT SEISMIC FIELD MODEL The ambient seismic field within the Newtonian noise integration range (see Fig. 5.4) is then modeled by incoherently summing over the seismic displacement fields from sources at 180 excitation points (see Eq. (3.3.1)). These excitation points are distributed in a ring of
thick-ness λR, which has a radius of several λR from the test mass. The distance of the excitation
points depends on the frequency and is aimed to reproduce measured horizontal and vertical surface spectra, while remaining consistent with source locations as obtained by beam forming, where sources are at distances greater than 1 km for low and within a few hundred meter of the test mass at high frequencies. Furthermore, the distance of the sources from the receiver grid is sufficiently large for the plane wave assumption to be valid. Each excitation point is randomly placed within a 2° wide segment of the ring.
E S W N E Geographic direction 0 0.2 0.4 0.6 0.8 1 Relative beampower
1 Hz 3 Hz 8 Hz Figure 5.5: Measured beam power
distribution of representative frequen-cies as used to derive the relative scal-ing factor. At low frequencies the noise originates from a broad western direction, whereas it moves towards a peak in the eastern direction for high frequencies.
The frequency band of interest for Newtonian noise is from 1 to 20 Hz. The relative strength of the sources is frequency dependent and has been scaled with the measured beam power in each frequency bin (see Fig. 5.5). Below 1 Hz the noise originates from activity of the Tyrrhenian Sea in the west. In the intermediate frequency band the noise peaks in north-eastern, south-eastern and north-western direction, pointing towards road-bridges at the close-by highway crossings and the wind farm. For frequencies above 4 Hz the noise is very local and originates from the road passing through the sensor array, which is located east of the center of the array. For simulation frequencies above 8 Hz, the maximum frequency the array can resolve, a uniform relative scaling in all azimuth directions has been assumed.
The surface PSD that has been simulated is based on the characteristic PSD of the site, which corresponds to the average of the vertical spectra measured with all sensors from the array study in 2016 during the full measurement period (Fig. 5.1, right panel).
5.2.1 Coherence and correlation
To simulate an ambient seismic field the soil response to 180 source excitations has been calcu-lated. It is assumed that these excitations are incoherent, meaning that the total field is calculated by summing incoherently over the PSD and Newtonian noise contributions of the individual sources (see Section 3.3). For a qualitative test of the response of the geology, the modeled coherence and correlation between two points is compared to measurement results.
The sources are placed at large distances from the test mass, and for simplicity it is assumed that their strength is uniform. The coherence is then obtained from the absolute value and the correlation from the real part of the normalized cross-correlation spectral density as derived in
Section 3.2. A pair of test receivers, with a separation of 35 m and of 800 m, are placed at the center of the geometry. Figure 5.6 shows that the expected correlation and coherence are high at low frequencies and decreases strongly above 1 Hz for a 35 m separation and already above 0.1 Hz for a 800 m separation of the sensors. This behavior is consistent with what has been pre-viously observed at the Virgo site [45]. Due to the nearly uniform distribution and strength of the sources, the correlation of the synthetic data between two receivers is in reasonable agreement with the expected behavior of the Bessel function given in Eq. (3.2.8).
In reality, the assumption of a uniform source distribution is invalid, as the strength of the sources depends on their geographic location and the measured cross-correlation, thus on the orientation of the receiver pair with respect to the source. To reduce this directionality in the measurement, the correlation and coherence have been averaged over all receiver pairs within a 10 % range of the predefined distance of 35 m and 800 m.
0 0.5 1 Correlation 10-1 100 101 Frequency [Hz] -0.5 0 0.5 1 Correlation Measurement Bessel function Expectation 800 m 35 m 0 0.5 1 Coherence 10-1 100 101 Frequency [Hz] 0 0.5 1 Coherence Expectation Measurement 35 m 800 m
Figure 5.6: Simulated and measured correlation (left) and coherence (right) between two re-ceivers at short (35 m) and long (800 m) distance. Qualitatively, measurement and simulation are in good agreement. Deviations below 0.3 Hz originate from uncorrelated instrument noise that is not taken into account in the simulation. For short receiver distances the measured result surpasses the simulated coherence due to the presence of local noise sources within the sensor array, which have not been considered in the simulation.
Qualitatively, measured and expected correlation are in reasonable agreement with each other for short and long receiver distances above 0.3 Hz (Fig. 5.6, left panels). Disagreement below 0.3 Hz is due to uncorrelated instrument noise between the sensors (see Section 4.3). At short distances, the characteristic Bessel function behavior of the correlation is visible and in good agreement with expectations. Deviations may originate from the fact that in reality, noise sources are not uniformly distributed, not of equal strength or may even be located within the sensor array - all factors that lead to a degradation of the Bessel function behavior. For short distances, the coherence from 0.3 to 2 Hz is in good agreement with the measurement re-sults (Fig. 5.6, right panels). Above 2 Hz local seismic noise from a road through the sensor array (see Fig. 5.1, left panel) leads to an enhanced coherence with respect to the expectation from the simulation, where the noise sources are located at great distances outside the sensor array. Previous measurements along the interferometer arms show a short-distance coherence that is comparable to the expectations of this simulation [45] . For large sensor distances, the measured and expected coherence are in reasonable agreement above 0.3 Hz, where seismic noise dominates over uncorrelated sensor noise.
5.2. AMBIENT SEISMIC FIELD MODEL As simulated and measured coherence and correlation are in reasonable agreement, it can be concluded that the modeled geology is a reasonable approximation of the conditions at the Virgo site.
5.2.2 Beam power and dispersion
For an additional validation of the simulated geology and source distribution, the beam form-ing analysis has been performed on data from the model. For this analysis the soil has been excited with 180 incoherent sources, where the relative strength of each source was selected according to the measured beam power. The left panel in Fig. 5.7 shows the beam forming of the simulated vertical surface displacement across the whole frequency band. The direction of incidence and the beam power of the modeled source distribution are in reasonable agreement with the measurement, shown in the left panel of Fig. 5.2. As measured, the noise at low fre-quencies originates from a more uniform direction from west over south to east, while at higher frequencies the main noise contribution originates from the eastern direction.
2 4 6 8 Frequency [Hz] 100 150 200 250 300 350 400 Phase velocity [m/s] Theoretical expectation Measurement Synthetic data
Figure 5.7: Left: Results from beam forming of simulated surface waves for four representative frequencies, where the inverse velocity is denoted with p, the direction of incidence with θ, mea-sured from the positive y-axis which represents north. The colorbar shows the normalized beam power. Direction of incidence and beam power from beam forming of synthetic data are in fair agreement with the measurement (Fig. 5.2, left panel), except for 5 Hz where the sensor array also records local noise sources within the array, which have been neglected in the simulation. Right: Comparison of dispersion curves derived from measured and synthetic data for selected frequencies. Both are in good agreement with the theoretical expectations for the subsurface geology.
Both data sets, measured and synthetic, recover well the slowness peaks of the fundamental Rayleigh wave mode. Due to the possibility to design the synthetic grid denser and larger than the sensor array, the beam forming of the synthetic data also allowed to recover the first higher order Rayleigh wave mode, which is characterized by a higher velocity than the fundamental mode. Higher order modes can be understood as the constructive interference of transmitted and reflected waves in the layered medium [109]. The specific geometry of the sensor array of the study described in Section 5.1 did not record the higher order mode for two reasons. At frequencies below 4 Hz, the large wavelength of the higher order mode could not be recorded
as the array was limited by its specific aperture and inter-sensor spacing. A different sensor array geometry might have allowed the measurement of the higher order mode, which would have given additional constraints on the soil model during the inversion analysis. At frequencies above 4 Hz the dominant noise sources were in the close vicinity of the array. The short travel distance of the waves to the receivers prohibited a noticeable separation between fundamental and higher order mode in the array data. Finally, overtones will be high in amplitude on the surface in case the subsurface geology exhibits a high velocity contrast at shallow depths - a condition that is not valid in the geology at the Virgo site. This means that even with a suitable array geometry, the amplitude of the overtone may be simply too small to be measured with the seismic sensors at hand.
The dispersion curve has been retrieved from beam forming of the synthetic data. The ve-locities of the fundamental mode derived from synthetic data are in good agreement with the measured fundamental mode dispersion curve (Fig. 5.7, right panel). Since the first order sur-face wave velocities agree as well with the expected theoretical dispersion curve for this type of medium it can be concluded that the horizontally layered geology model with the correspond-ing source distribution is a valid representation of the seismic conditions at the Advanced Virgo detector site.
5.2.3 Power spectral density
To reproduce the seismic spectra at the Virgo site, the source strengths are scaled individually with the relative scaling factor according to Eq. (3.3.1) to reproduce the measured beam power of the array and with the absolute scaling factor according to Eq. (3.3.2) such that the measured horizontal and vertical surface PSDs are reproduced by the simulation. Due to the TN-1 sensor characteristics, only data of vertical ground motion have been acquired during the seismic
cam-10-24 10-22 10-20 10-18 10-16 PSD [m 2 /Hz] Horizontal Vertical 0 2 4 6 8 10
Distance from source [λ
R] 100 101 102 H/V (PSD) 10-20 10-18 10-16 10-14 PSD [m 2 /Hz] Measured PSD v Simulated PSD v Simulated PSD h 100 101 Frequency [Hz] 1 3 H/V (PSD) NHNM
Figure 5.8: Left: Horizontal and vertical unscaled, simulated displacement PSD of a single
3 Hz source together with the expected H/V ratio (black) as a function of distance. The value of
the measured H/V ratio at 3 Hz is indicated by the horizontal dashed black line and the optimized distance is marked in red. Right: Simulated horizontal and vertical site-characteristic PSD at Advanced Virgo from 180 sources that are scaled according to the measured beam power and are located such that the measured H/V ratio [163], see bottom panel, is reproduced at the test mass location. The absolute scaling factor is chosen such that the simulated vertical PSD reproduces the measured vertical PSD. The horizontal PSD follows then from the simulation.
5.3. NEWTONIAN NOISE paign. However, horizontal Newtonian noise, which is the most relevant for Advanced Virgo, is generated by horizontal seismic displacements and therefore knowledge of horizontal seismic spectra at the site is needed to design a model that is a valid representation of the local conditions. This information can be inferred from the ratio of horizontal to vertical PSD. This so called H/V
ratio is characteristic for a given site, as it depends on the local geology, source mechanisms
and distance between source and receiver [113]. Coincident horizontal and vertical spectra of the Virgo site are available from a one year long measurement campaign in 2014 with a single Episensor FBA-EST seismometer [163] and the H/V ratio obtained from these data can be used to reproduce representative horizontal spectra in the simulation.
The expected H/V ratio for a single source can be computed from the simulation and it depends strongly on the distance to the source (Fig. 5.8, left panels). These fluctuations are characteristic for a single source and average out, if many sources are placed in a ring, that varies in thickness, around the test mass. The radius of the ring is then chosen such that at each frequency the measured H/V ratio is reproduced by the model at the location of the test mass. For a given frequency several source distances may reproduce the measured H/V ratio. In this case a distance that is compatible with the noise source locations as indicated by the beam forming analysis is chosen. At low frequencies this is at distances of 1 km or larger, while sources at high frequencies are within a few hundred meters of the test mass. Once the radius of the ring is determined for a given frequency, the distance of the individual sources is allowed to vary
within λR/2, thus producing a ring of thickness λRof sources around the test mass.
After deriving the optimized distance from the measured H/V ratio for each frequency and scaling the strength of each source according to the beam power distribution with the relative scaling factor according to Eq. (3.3.1), the absolute scaling factor is then derived from the
mea-sured vertical PSD, denoted with PSDV, following Eq. (3.3.2) as
m(f ) = PSDV/|uv(⃗x, f )|2, (5.2.1)
where |uv(⃗x, f )|2 denotes the vertical component of the quadratic sum of the individual
re-sponses. The horizontal PSD can then be reconstructed from the measured H/V ratio as
|uH(⃗x, f )|2 = (H/V ratio)(f )· |uv(⃗x, f )|2, (5.2.2)
where |uh(⃗x, f )|2 refers to the mean horizontal component of the unscaled PSD. The horizontal
and vertical PSDs in the seismic model that have been derived with the measured H/V ratio and vertical PSD are displayed in Fig 5.8, right panel.
5.3 Newtonian noise
Our site-based Newtonian noise at Advanced Virgo is calculated from the full solution of the wave equation according to Eq. (3.4.8), Eq. (3.4.11) and Eq. (3.4.12) in the horizontally layered geology with nine subsurface layers as listed in Table. 5.1. The ambient seismic field model comprises surface and body waves, reflection, transmission and mode conversion of waves at interfaces as well as damping of seismic amplitudes with distance from the source. The strength of the seismic sources is scaled according to the measured beam power distribution and their distance from the test mass is optimized such that the measured ratio of horizontal over vertical PSDs is reproduced by the simulation. The absolute strength of the sources is scaled such that the simulated PSD at the test mass follows the site-characteristic PSD at EGO (see Fig. 5.9,
left panel). The test mass height in the simulation is 1.6 m above the ground, which is the same height as the Virgo test masses [37]. The test mass height further serves as a natural, lower cutoff radius in the Newtonian noise integral. The integral is carried out through Gaussian quadrature, a numerical integration method (see Appendix B).
To increase the computational efficiency, a maximum integration radius is calculated for each frequency. The integration radius is the integration distance after which the cumulative Newtonian noise remains within 10 % from its asymptotic value. Previous studies in homo-geneous half-space geologies with Rayleigh waves and surface detectors have shown that an
integration radius of λR/2 is sufficient to reach a stable Newtonian noise level [45]. In this
model Newtonian noise is calculated as the incoherent sum of the Newtonian noise contribu-tions from the individual seismic sources (see Eq. (3.4.11)). The maximum integration radius at each frequency is then determined from the contribution of a single source by subsequently
increasing the integration radius, starting from 0.5λRand reaching up to a distance where
fluc-tuations stay within a small percentage of the asymptotic value. Figure 5.9, right panel, shows
that at low frequencies an integration radius of λRor even less is sufficient. Higher frequencies
require a larger integration radius of up to 2λR, because at these high frequencies the
wave-lengths of the Rayleigh waves are short and therefore they attenuate fast. As a result, nearby body waves contribute to Newtonian noise as well and their larger wavelengths lead to a higher maximum integration radius.
NHNM 0.5 1 1.5 2 2.5 3 Integration radius [λ R] 60 80 100 120 140 160 180 Newtonian noise [%] 2 Hz 5 Hz 10 Hz 15 Hz 20 Hz 10 % threshold
Figure 5.9: Left: Horizontal site-characteristic PSD at EGO as obtained from the simulation, based on data from the array study in 2016. This PSD is used to derive the site-based Newtonian noise. For reference the PSD of the Newtonian noise in the design sensitivity is shown by the black dotted curve. Right: Newtonian noise from a single source on a 1.6 m high test mass as a function of increasing integration radius as percentage of the Newtonian noise obtained with the largest integration radius for various frequencies. At low frequencies (< 10 Hz) an integration radius of λRis sufficient whereas at high frequencies (10 − 20 Hz) a radius of 2λRis required.
The resulting site-based Newtonian noise estimate at Advanced Virgo is displayed in Fig. 5.10. The characteristic Newtonian noise is derived from the site-characteristic PSD measured at EGO and it represents the ultimate noise limit that can be reached due to the seismic properties of the detector location. The mode, that is the most common value during the measurement period, of the site-characteristic Newtonian noise is compliant with the Advanced Virgo design sensitivity curve at low frequencies and it reaches several orders of magnitude below the analytical estimate at frequencies above 6 Hz. However, considering the Newtonian noise that corresponds to the
5.3. NEWTONIAN NOISE
90thpercentile, that is the curve below which the Newtonian noise will reside 90% of the time,
it surpasses the Advanced Virgo sensitivity below 6 Hz. Even though the detector performance during O3 has not been limited by site-based Newtonian noise, it will prohibit reaching sensi-tivity goals during future science runs. The installation of permanents seismic sensor arrays at the Virgo central and end buildings to integrate online Newtonian noise cancellation schemes in the context of the Advanced Virgo Plus upgrade is aimed to measure and overcome these limitations [55].
Figure 5.10: Mode of our site-based Newtonian noise estimate at Advanced Virgo, derived for a test mass height of 1.6 m above the ground. The full solution of the wave equation in a layered geology is taken into account. The lower and upper bounds of the transparent band correspond to the 10th and 90th percentile of the Newtonian noise, respectively. Site-based
Newtonian noise is a factor 2 below the design sensitivity above 8 Hz and the 90th percentile
surpasses the Advanced Virgo sensitivity curve only below 8 Hz. This site-based Newtonian noise represents the ultimate limit that can be reached at the EGO site due to the properties of the local geology and the ambient seismic noise level. Furthermore, site-based Newtonian noise is more than a factor 10 below the O3 sensitivity and did not limit the detector performance. The Newtonian noise estimate of the design sensitivity, that is based on Saulson’s expression, deviates from our site-based Newtonian noise as it neglects seismic displacements in the vicinity of the test mass at low frequencies and overestimates seismic wave amplitudes at high frequencies.
Our site-based Newtonian noise estimate can be compared to the Newtonian noise that is used in the derivation of the Advanced Virgo design sensitivity. This Newtonian noise is eval-uated according to Eq. (3.5.2) and based on Saulson’s analytical model of a half-space geology
with density ρ = 1800 mkg3, and a test mass on the surface that is surrounded by a cavern with
a frequency dependent radius of λ/4. Moreover, a constant displacement without wave
attenu-ation, that follows the 90th-percentile spectrum of the horizontal PSD measured at the Central
Building of the detector as shown in Fig. 5.9, left panel, is assumed [52, 53].
As elaborated in Section 3.5, the height of a test mass above the ground and the absence of a frequency dependent lower cutoff radius in the our site-based Newtonian noise integral lead to an increase with respect to the analytical Newtonian noise derived with Eq. (3.5.2). As a result
the 90th percentile of the site-based Newtonian noise surpasses the analytical estimate below
about 8 Hz. At higher frequencies, the dispersive wave speed properties and the fast attenuation of surface waves that are incorporated in the realistic seismic field model lead to a site-based Newtonian noise that is significantly below the analytical expectation at high frequencies. This underlines the necessity that in order to develop realistic, site-based Newtonian noise estimates it is important to consider a seismic model that incorporates a seismic field with surface and body waves in a geology model that encompasses a realistic subsurface composition, seismic source distribution and seismic spectrum that is representative of the detector location, without the necessity to neglect seismic displacement in the vicinity of the test mass due to computational limitations.
Furthermore, the PSDs that are used in our site-based Newtonian noise estimate are more quiet than the PSD used in the analytical estimate of the design sensitivity curve above 4 Hz (see Fig. 5.9, left panel). The seismic noise at the Central Building surpasses the site-characteristic PSD at high frequencies, due to higher anthropogenic activity and noise through local infras-tructure at the detector site like vacuum pumps, ventilation fans and the air conditioning sys-tem. To improve the Newtonian noise level at the detector site in order to reach the ultimate site-characteristic limit that has been derived with our site-based approach, the anthropogenic contributions of each building need to be reduced and smart infrastructure needs to be installed. First steps towards a noise characterization of each building and the installation of a new air conditioning system have been taken in 2019 [164].
5.4 Summary and conclusion
In August 2016 a seismic sensor array study has been performed at the site of Advanced Virgo, that allowed to identify the main seismic noise sources and to set up a horizontally layered subsurface geology model. This information has been used to derive a seismic wave model, which incorporates the full solution of the wave equation and reproduces the dispersion curve and power spectral densities measured at the detector site. This realistic, geology-based method overcomes the limitations of the analytical Newtonian noise model which is up to today used for Newtonian noise estimates at the Advanced Virgo detector. Our site-based Newtonian noise estimate, derived from the full model, shows that the analytical model based on Saulson’s ex-pression underestimates Newtonian noise at low and overestimates Newtonian noise at high frequencies. Furthermore, anthropogenic and infrastructure noise lead to a noise level at high frequencies which is higher than the sensitivity that can in principle be achieved at the EGO site. To overcome these limitations, mitigation and noise subtraction schemes based on permanent sensor arrays at the detector site will be of importance.
