This includes checking the seismic noise at EGO in various frequency bands
corresponding to different sources (microseim related to sea activity on the
Tuscany shoreline or local anthropogenic activities: see [30] for details),
the sea activity and the weather.

####  6.1.3 Performance of the Virgo O3 dqr framework

This section briefly summarizes the performance of the Virgo dqr, via a
statistical analysis using data from O3b that correspond to the final, most
complete, version of that framework during the O3 run. As time distributions
can include outliers due to occasional technical problems impacting the dqr
dataflow somewhere along its way, from gracedb to the EGO HTCondor farm and
back, the results presented in the following two tables include the $50^{\rm
th}$ and $95^{\rm th}$ percentiles in addition to the mean values.

Table 4 provides the measured latencies for the processing steps that occur
upstream of the dqr. The meaning of each row is reported below.

  * •

The first figure is the difference between the time when the trigger is
recorded in gracedb and the time when the corresponding data were acquired.

  * •

The second measures the time needed for gracedb to send the lvalert and to
have this message trigger the Virgo dqr framework upon reception.

  * •

The third number reports the time needed to create and configure a new dqr
instance, until it is ready for processing. One should note that this duration
includes a 300 s wait time, imposed in order to allow gracedb to receive,
process and gather all triggers found by the different online searches that
analyse strain data in parallel and independently. The assumption is that,
after these five minutes, the low-latency information available in gracedb
should be optimal and stable in the vast majority of cases. Therefore, the
actual dqr configuration phase only takes a few tens of seconds: the needed
data are located in the low-latency streams just made available by the daq and
the 30+ check scripts are generated one after the other.

  * •

Finally, the last reported duration accounts for the time needed to start
processing the dqr on the EGO HTCondor farm. This depends on the occupancy of
the farm and of the EGO internal network performance.

Table 4: Summary of the performance of the low-latency + Virgo dqr dataflow during O3b, from the GPS time of a trigger to the start of the Virgo dqr on the EGO HTCondor farm: see text for details. Operation | Time taken [s]
---|---
Median | Mean |  $95^{\rm th}$ percentile
Data acquired $\to$ Candidate on gracedb | 52 | 166 | 331
Candidate on gracedb $\to$ lvalert trigger | 4 | 4 | 11
lvalert trigger $\to$ Virgo dqr configured | 331 | 339 | 383
Virgo dqr configured $\to$ Virgo dqr started | 8 | 10 | 21

We can see that the mean time elapsed between the recording of the data by the
different detectors and the creation of a new record in gracedb is under three
minutes; the median time is even under one minute while the tail of the time
distribution extends beyond five minutes. This includes the reconstruction of
the gw strain channels; the transfer of these data alongside the associated
online data quality information to computing centers; the processing of these
data by real-time gw searches; the automated analysis of the results and the
final transfer of trigger information to gracedb. Then, the new alert is
received at EGO a few seconds later, triggering the creation and the
configuration of a new dqr instance. Removing the compulsory wait time of 300
s, the dqr configuration takes a few tens of seconds only. Finally, about 10
additional seconds are needed on average to have the first dqr jobs processed
on the EGO HTCondor farm.

Table 5 summarizes the performance of the Virgo O3 dqr framework in terms of
running time. Each row corresponds to a category of checks. The quoted
durations increase from one row to the next as each new set of checks includes
the previous ones.

  * •

The quick checks whose outputs are mandatory to vet a trigger take about 6
minutes to be all available, with a few minutes spread.

  * •

Adding information about the Omicron triggers around the candidate takes about
10 more minutes. During O3, this latency was dominated by the fact that
Omicron triggers were computed in real time and stored internally by the
online server: they were only written to disk every 600 s, in order to allow
the framework to cope with the incoming data flow. Work will be done prior to
O4 to optimize this latency and to make the dqr aware of when the needed data
have been written to disk, so that their processing can start immediately
after.

  * •

Omicron-scanning all the available channels (more than 2,000 in total, with
the vast majority of them sampled at 10 kHz) around the trigger time requires
15-20 additional minutes.

  * •

Finally, the full dqr took from 1.5 to 2 h to complete. The longest checks
were bruco and upv, plus the scan of all online logfiles described above.

Table 5: Summary performance of the Virgo dqr processing during the last $\sim$100 days of the O3b run. The quoted durations include the time to upload dqr check results back to gracedb that usually takes from $\sim$5 to $\sim$20 s. Operation | Time from start [s]
---|---
Median | Mean |  $95^{th}$ percentile
Quick key checks | 374 | 383 | 619
Adding Omicron trigger distributions | 868 | 816 | 935
Adding full Omicron scans | 1740 | 2159 | 4690
End | 5185 | 4954 | 6330

Another key figure of merit of the dqr framework is the number of (software)
check failures per dqr instance. Table 6 shows the results of a statistical
analysis based on the subset of the dqr that were automatically processed in
real time during O3b because the candidate false-alarm rate was below the
1/day threshold. Only 13% (2%) of the dqr had 1 (2) failed checks. No
exhaustive analysis of these failures has been performed, as most of these dqr
were never checked by hand because the associated trigger was not significant
enough. The two main causes of problems were, however, incomplete handling of
edge-cases with the input data and actual bugs in processing algorithms. These
issues did not affect the rapid vetting of any public alert during O3, and
this framework worked smoothly as well for the validation of the offline
events found later by the archival gw searches. Both issues are being
addressed as part of the upgrade of the dqr framework for the O4 run.

Table 6: Percentages of the O3b Virgo dqr with 0, 1 and 2 unsuccessful checks respectively. Number of unsuccessful checks | 0 | 1 | 2
---|---|---|---
Percentage of O3b automatically processed dqr | 85% | 13% | 2%

###  6.2 O3 public alerts

####  6.2.1 Public alerts retracted because of an issue with Virgo data

Figure 23: Number of Virgo dqr automatically processed per day during the O3b
run. The peak of 31 entries corresponds to November 24, 2019 when there was a
transient problem with the Virgo $h(t)$ reconstruction: that generated several
online triggers, finally including S191124be that passed the public alert
threshold and was promptly retracted.

During O3, 24 public alerts out of 80 have been retracted: 8 during O3a and 16
during O3b. Out of these retractions, only two were due to Virgo data:

  * •

S191124be [99] was due to a problem in the noise removal procedure included in
the reconstruction of the $h(t)$ GW stream [39]. Two such cleaning algorithms
running in sequence started interfering, leading to a noise increase over
time. An online pipeline started triggering on that excess noise, creating
several non-astrophysical gw candidates in rapid succession (Figure 23) until
one of them had a false alarm rate lower than the public alert threshold. That
led to the generation of an automated alert that was then quickly retracted.
A similar problem should not happen again in future runs for three reasons: i)
improved noise cleaning procedures are being developed within the Virgo $h(t)$
reconstruction; ii) an online monitoring dedicated to such noise removal
interferences will be in place during O4; iii) a monitoring of the pipeline
trigger rates in gracedb will be running as well during future data taking
periods, in order to spot quickly any misbehavior, like an excess trigger rate
(thee case of S191124be) or the opposite: a too long data-taking time period
without any trigger, even of low significance.

  * •

S200303ba [100] was a single-pipeline trigger with most of its snr
concentrated in Virgo. At that time, Virgo data were quite noisy due to bad
weather. An Omicron-scan around the trigger time (Figure 24) showed evidence
of scattering light noise at low frequency. The unusually-long delay to send
out the retraction circular (about 80 min) was partly due to an issue with the
Gamma-ray Coordinates Network broker connection.

Figure 24: Omicron spectrogram around the time of the S200303ba trigger. The
search template time-frequency track (solid line) overlaps with low-frequency
scattering-light glitches (yellow color) caused by bad weather.

####  6.2.2 Virgo contribution to O3 public alerts

Out of the 56 non-retracted O3 public alerts, 42 involved the Virgo detector.
For 10 out of the 14 LIGO-only alerts, Virgo was not controlled in its nominal
configuration at the GPS time of the trigger. This fraction is consistent with
the average duty cycle of Virgo during O3 (see Section 3.5). For the four
remaining alerts, described in detail next, Virgo was fully controlled at the
time of the trigger and had a bns range consistent with its typical
performance at that moment.

S190720a occurred during a $\sim 1$ min segment between lock acquisition and
beginning of nominal observing mode, so Virgo data were not used for low-
latency analyses. Offline analyses later confirmed S190720a as a significant
detection and were able to use the low-noise Virgo data, finding a non-
negligible amount of signal power in them. S190720a was published as
GW190720_000836 in GWTC-2 [8].

S190910d occurred during nominal observing mode in Virgo. It was a marginal
candidate, only reported by a subset of the low-latency searches. These
searches did not find a significant amount of signal power in Virgo data, and
did not report Virgo as being used for the candidate. S190910d was not
confirmed by offline analyses.

S190923y occurred while Virgo was undergoing commissioning activity. It was
not confirmed by offline analyses.

S200225q occurred while Virgo was undergoing a calibration run. Offline
analyses confirmed S200225q as a significant detection and were able to
include the low-noise Virgo data, although no significant signal power was
found there. S200225q was published as GW200225_060421 in GWTC-3 [10].

##  7 Global data quality studies

This final section presents examples of global data quality studies made
during or after the O3 run: noise transients, spectral analyses,
classification of auxiliary channels based on their potential sensitivity to
gw signals and offline data quality studies leading to the final Virgo O3
dataset.

###  7.1 Glitches and pipeline triggers

####  7.1.1 Glitch rates during the O3 run

Figure 25: Virgo glitch rate, using Omicron triggers, for the final O3 dataset
(Science segments that have not been CAT1-vetoed). The blue dots are averages
over one hour while the red curve shows the corresponding weekly moving
average. The gap in between O3a and O3b corresponds to the 1-month
commissioning break.

During data taking, Omicron runs online on a few hundred channels, including
the gw strain $h(t)$, and monitors glitches in real time: these triggers are
stored on disk with a few minutes latency. Figure 25 displays the evolution of
the glitch rate during the O3 run. Figure 26 provides more details by breaking
the global Omicron glitch rate into snr (top plot) and peak frequencies
(bottom plot). In these plots, the glitch rates have been smoothed by
computing their weekly moving average to ease the reading.

Figure 26: Glitch rates (weekly moving average) using Omicron triggers during
the O3 run for Virgo— the gap in between O3a and O3b corresponds to the
1-month commissioning break. The top plot breaks the glitch rate into snr
ranges, while the bottom one categorizes it in terms of frequency ranges for
the glitch peak frequency. The choice of the frequency bands has been mainly
driven by the need to isolate some frequencies: 50 Hz (mains fundamental power
in Europe), 150 Hz (second harmonics of the mains) and the range around 450 Hz
(another harmonics of the mains, plus the range in which the frequencies of
the suspension wire violin modes are located).

The large majority of glitches identified by Omicron have a moderate snr:
between 5 (the minimum value from which the Omicron trigger is kept) and 8.
The highest trigger rate at the very beginning of O3a corresponding to
glitches with a peak frequency between 440 and 460 Hz is an artefact due to a
mis-configuration of the Omicron online server that was quickly fixed. The
significant increase of the trigger rate in O3b with respect to O3a is mainly
due to the bad weather conditions during the fall and winter seasons (see [30]
for more details). The weather was actually very quiet in January 2020 and the
associated drop in glitch rate is quite strong.

####  7.1.2 Offline searches

Non-stationary instrumental noise can potentially impact searches for
transient gw, which must include methods to robustly separate astrophysical
candidates from noise fluctuations. Despite the power of such methods,
inspecting the candidates produced by a search remains a sensitive way to
identify problematic operating conditions of gw detectors.

In this section, we focus on candidates produced from Virgo O3 archival data
by one of the pipelines used by the LIGO and Virgo collaborations to detect
compact binary mergers, namely PyCBC [95]. This analysis performs a broad-
space search for compact binary mergers involving neutron stars, black holes,
or a mix of both. It uses a bank of model waveforms and matched filtering to
generate candidates from LIGO and Virgo data. Each single-detector candidate
is ranked by a combination of its matched-filter snr and various statistics
designed to reject candidates produced by non-stationary noise.

Figure 27 shows the rate of candidate events recorded by PyCBC from Virgo
data. The horizontal axis shows either the matched-filter snr of the candidate
(left plot) or a ranking statistic which combines the snr of the candidate and
two $\chi^{2}$ signal-based discriminators [101, 102] (right plot). The
vertical axis shows the rate of candidates that are ranked higher than the
value in the horizontal axis 555At this early stage of the PyCBC analysis,
candidates with merger times within fractions of a second from each other can
be highly correlated, because a given transient in the data typically “rings
off” several templates with high overlaps between each other. The estimated
rate of candidates is biased if this correlation is not accounted for. We do
so by means of a clustering procedure: a given candidate is ignored if a
higher-ranked one exists within a time window of $\pm 5$ s..

Figure 27: Rate of compact binary merger candidates produced from Virgo O3
data using a broad-space search based on PyCBC. Left: rate as a function of
the matched-filter snr. Right: rate as a function of the reweighted snr, which
combines the snr and two $\chi^{2}$ discriminators. Red, blue and green curves
correspond respectively to templates lasting less than $0.6$ s, $0.6$–$4$ s,
and more than $4$ s. Curves of the same color represent different chunks of
Virgo data, each lasting $\sim 5$ days. The black curves show the rate over
the entire run and search space. They extend to lower rates than the
individual chunks due to the much longer duration of the entire run.

If the Virgo noise had been Gaussian and stationary throughout O3, we would
expect the rate to decrease exponentially for larger and larger values of the
ranking, and be independent on the template parameters and particular chunks
of data. Instead, the rate-vs-snr curves show a more complicated behavior,
with a large variation across the search space and particular data chunks. We
observe a non-negligible rate at snr as high as 100, while astrophysical
signals are typically expected to have snr between ${\sim}$5 and ${\sim}$10\.
After the application of the $\chi^{2}$ discriminators, the behavior changes
drastically, and the exponential behavior of the rate is recovered, at least
as long as we restrict to a subset of the search space. We still observe a
large variation of the exponential slope and amplitude across the search space
and data chunks, except for the longest templates (green curves of Figure 27),
which are more robust to instrumental artifacts due to their particular time-
frequency signature. However, the same variation is also seen with candidates
from the LIGO detectors, and it is taken into account by the analysis when
ranking the multidetector candidates [103].

A detailed inspection of the candidates in the tails of these plots shows that
the highest snr can be attributed to a single segment of ${\sim}$15 min of
data on November 11, 2019. These data contain narrowband, loud and rapidly-
varying excesses of power (coming from transient problems with the noise
subtraction algorithms used to reconstruct the gw strain channel $h(t)$) which
temporarily affected the data conditioning algorithm used by PyCBC. Most of
these high-snr triggers were removed by the $\chi^{2}$ discriminators,
effectively vetoing the entire problematic segment. On the other hand, most
top candidates by $\chi^{2}$-weighted snr are clearly associated with
scattered-light glitches. We conclude that the $\chi^{2}$ discriminators used
by PyCBC, which were designed for and tuned on LIGO data, are also reasonably
effective in Virgo, and should be further developed to more effectively reduce
the impact of scattered light.

###  7.2 Channel safety: channel (in)sensitivity to gravitational waves

Many Virgo data quality analyses aim at ensuring that gw candidates are of
astrophysical origin and not caused by terrestrial noise. Typically, searches
for correlations between auxiliary channels (monitoring the environment, the
detector status, the accuracy of its control, etc.) and the $h(t)$ strain
channel are run to produce vetoes, that reject times when such correlations
are identified. This strategy can lead to a loss of interesting signals if any
of the auxiliary channels is sensitive to gw, which means that it picks up
disturbances induced in the detector by these. Hence, a good knowledge of the
couplings of auxiliary channels to $h(t)$ is essential. To gather such
information, a statistical analysis of all auxiliary channels is performed,
using the approach proposed in [104].

This method relies on hardware injections that mimick the effects of gw on the
detector, by moving in a deterministic way one of its test masses. They are
used to workaround the fact that the transfer functions between $h(t)$ and
most auxiliary channels are not well-known, nor understood. The injected
signals are 0.6 s long sinusoidal Gaussian functions of various frequencies
(between 19 Hz and 811 Hz) and amplitudes (SNR between ${\sim}$20 and
${\sim}$500). The frequencies injected are chosen to scan the entire detection
band while avoiding any known resonant frequency (like violin modes). Each
waveform is injected three times, spaced by 15 s.

This safety analysis assumes that glitches in a given auxiliary channel are
distributed according to a stationary Poisson process, whose rate and
$p$-value time series are measured using stretches of data during which no
hardware injection is performed. These $p$-value time series are used to
define a classification threshold. Then, a null test is applied to see whether
the $p$-value distribution changes significantly in the presence of hardware
injections. Auxiliary channels that exhibit anomalously small $p$-values (i.e.
lower than the defined threshold) are classified as unsafe, meaning that they
are likely to mirror excess power coming from the strain channel. The other
channels, called safe are the only ones used to produce vetoes.

Virgo DetChar hardware injections were organized at short notice, in the few
days between the anticipated end of the O3b run (because of the pandemic) and
the moment when the detector was switched off. Among the ${\sim}$2500
auxiliary channels analysed, 69 are found to be unsafe. The safety analysis of
these data allowed to validate the existing sets of safe and unsafe channels
determined by a previous study. These results matched as well the a priori
safe status one could infer based on the definition of the auxiliary channels,
i.e. which measurements they perform and how they do them.

###  7.3 Spectral noise

The term spectral noise, introduced in Section 2.3, identifies the class of
detector disturbances appearing as an persistent excess in the noise power
spectrum estimation of the data.

Spectral noise has a negative impact especially on searches for persistent gw,
which aim at detecting astrophysical or cosmological signals mainly through
the identification of their spectral features. Two typical signal categories
of persistent waves are cw [105] and a sgwb [106]. The signals are very weak
with respect to the already detected coalescing binary emission. Due to their
persistent nature, they can be looked for in the frequency domain where the
accumulated power over long observation times can show up at a detectable
level, after applying effective signal processing techniques. Moreover, some
spectral features of the signals can help in discriminating them from detector
noise. On the other hand, spectral noise can mask signals, or produce false
candidates, in both cases reducing the search sensitivity.

Searches for persistent signals are typically run off-line, once long
stretches of data have been collected. An early identification of spectral
disturbances and of their instrumental source would allow to remove, or at
least reduce, the source of noise, thus improving the quality of the data.

Different actions can be accomplished at the detector characterization level
in support of data analysis. A first action is to identify, and possibly
remove, the instrumental source of spectral noises as soon as possible during
a data taking period. This is a non trivial task that typically requires a
significant amount of work to nail down which detector component is
responsible for a given disturbance and to eliminate the noise source, which
may imply to replace the noisy component (for instance a cooling fan, an
electric motor, etc.) [31], to shut it down (if not needed) or to modify it
properly. This could consist, for instance, in shifting the frequency of a
calibration line which non-linearly couples to another noise source, in order
to move the noise line frequency into a less relevant band for the GW search
[12, 107].

A second action is the use of additional techniques to differentiate between
possible signals and other spectral features. These methods strongly depend on
the analysis and on the type of gw signals searched An example of such
techniques relies on the Doppler effect. An astrophysical cw signal is
expected to be modulated in frequency by the Doppler effect, due to the Earth
rotation, which induces a shift $\Delta f(t)\simeq
f_{0}\frac{\vec{v}(t)\cdot\hat{n}}{c}$, where $f_{0}$ is the source frequency,
$\vec{v}$ the detector velocity, $\hat{n}$ the unit vector identifying the sky
direction and $c$ the speed of light. cw searches correct this Doppler effect,
thus any monochromatic line present in the h(t) signal is spread by a maximum
amount of $\Delta f_{max}\simeq 10^{-4}f_{0}\cdot cos{\beta}$— where $\beta$
is the ecliptic declination. This shift corresponds to up of hundreds or even
thousands of frequency bins for typical cw searches.

Potential candidates found in the analysis lead to follow-up investigations to
identify a possible instrumental source. This follow-up is also based on a
combination of DetChar activity, to spot the source of the disturbances, and
application of CW or SGWB algorithms to build confidence in the astrophysical
nature of the candidate, see e.g. [108].

Although spectral noises cannot always be removed, it is still useful to
characterize them by constructing a list of noisy lines. This list can be used
to exclude those disturbing frequency bands from the analysis, or to veto
candidates with frequency too close to those of these noisy lines

The identification of lines is typically done by automated pipelines (see
Sections. 4.4.1, 4.4.2 and 4.4.3), based on

  1. 1.

user-defined thresholds set on data power spectrum or on line persistency,
defined as the fraction of fft, compared to the total number covering the full
observation time, in which the “normalized” power content of a given frequency
bin was above such a threshold (typically set to six times the average value);

  2. 2.

by highlighting coincidences or significant coherence among different
channels;

  3. 3.

by highlighting a pattern in time-frequency maps of the data.

Candidates found in gw searches are subject to verification steps, in which
the identification of possible noise counterparts is done by processing the
data in the relevant frequency band and period of time and/or running manually
one or more of the previously mentioned line identification pipelines,
described in Sections. 4.4.1, 4.4.2, 4.4.3. In the following we report and
discuss a few examples of lines identified in Virgo O3 data. Readers can refer
to the LIGO-Virgo gwosc [79] for the full official list of lines.

####  7.3.1 Combs

Combs are families of lines separated by a constant frequency interval.
Typically, noise combs are electromagnetic disturbances generated by digital
devices (e.g. microprocessors, programmable communication devices like logical
controllers, ethernet cables, wireless repeaters) that leak into the strain
signal. Comb lines can have an impact on searches for persistent gw due to
their large number and usually high strength. This makes the identification of
combs an important task. There are several combs present in Virgo O3 data,
which we describe in the following.

A 1 Hz spaced comb with 0 Hz offset was already present during previous runs.
A new 1 Hz comb discovered during O3 has a 0.333 Hz offset with respect to
integer frequencies. This comb was discovered following investigations of a
line at 22.333 Hz that falls within a region of interest for the Vela pulsar
cw search. The instrumental origin of the comb has been confirmed by finding
lines at the same frequency in the magnetometers deployed at EGO.

Figure 28 shows the line persistency computed over the frequency range
21.8-23.5 Hz on O3 Virgo data. Both 1 Hz combs are clearly visible.
Furthermore, there is a comb with 0.2 Hz spacing, whose origin is unknown. The
grey area indicates the frequency region explored by a narrow-band cw search
targeting the Vela pulsar. The strong line at 22.333 Hz produced an outlier in
the search, which was discarded after its instrumental origin was identified.

Finally, two more combs which have been identified by DetChar studies, have
both $\sim$9.99 Hz spacing, one with 0 Hz offset and the other with 0.5 Hz
offset.

Figure 28: Plot of line persistency over the frequency band 20-30 Hz. The grey
box identifies the frequency range covered by a narrow-band search of cw
signals from the Vela pulsar in O3a data. The line at 23.333 Hz, which
contributed to produce a candidate in the search is clearly visible. In fact,
several other lines belonging to the 1 Hz comb, both at integer frequencies
and shifted by 0.333 Hz, and to a weaker 0.2 Hz comb, are present.

####  7.3.2 Wandering line around 83 Hz – 84 Hz

A wandering line is a peculiar kind of spectral noise where the frequency of a
spectral line changes with time, with no apparent reason. This is also called
a _drifting line_ once the mechanism driving the frequency change is at least
partially identified, making its variations not entirely random anymore.

An example that triggered lots of DetChar investigations during O3 is the
line, normally located between 83 and 84 Hz, as shown in Figure 17, that
reached about 110 Hz at the maximum of its excursion and had variations of a
few Hertz over about one hour [109, 110]. Its origin dates back to the Virgo
commissioning run 10 (C10) of August 2018 [59], and possibly even earlier, in
the preparatory phase preceding O2 [111]. Neither of the mechanism that make
the line to depart from its typical frequency of about 83 Hz or what produces
its variations with time have ever been understood, although several data
analysis techniques have been applied and newer ones developed for _line
tracking_ [59]. An analysis with Bruco (see 4.4.3) revealed no witness channel
coherent with $h(t)$ around that line. Moreover, we tracked the frequency
evolution of this line, and we correlated the corresponding time series with
the auxiliary channels monitoring Virgo [109]. This technique has proven
successful in the past, in the case of drifting lines driven by the
temperature of some optical components [112], but has produced no convincing
correlation in the case of this line, whose origin has remained unknown.

####  7.3.3 Spectral noise bump around 55 Hz

Figure 29a) shows the power spectrum of the Virgo gw strain channel $h(t)$
computed at two different dates, February 26 and March 2, 2019 (before the
start of the O3 run), showing that a wide bump around 55 Hz had been cured in
the meantime. Indeed, a detailed study had shown that this disturbance was
present most of the time and was observed also in the prcl channel. This
allowed to remove most of this noise excess when producing the reconstructed
strain $h(t)$, by accurately subtracting the remaining prcl contribution [39].
Note that this 55 Hz bump affected the frequencies around 55.6 Hz, where the
cw signal possibly emitted by pulsar PSR J1913+1011 is expected. Furthermore,
this bump was located within the most sensitive region of the Virgo spectrum
for an (isotropic) stochastic background search.

####  7.3.4 Spectral noise around the 50 Hz power line frequency

The GW strain signal in the frequency region between 45 Hz and 55 Hz was
significantly affected by ambient electromagnetic fields originating from the
interferometer infrastructure. This noise was studied and mitigated in
subsequent steps during the run [31].

The intense 50 Hz line, corresponding to the frequency of the electricity
mains, was mitigated and substantially eliminated from $h(t)$ (see Figure
29b), by implementing a feed-forward noise cancellation scheme using as sensor
a voltage monitor of the detector uninterruptible power supply system [31].
This operation did not reduce the 50 Hz harmonics also present in the $h(t)$
spectrum (see Figure 6) because they are not due to a non-linear response of
the interferometer. They are present in the global environmental disturbances
and enter the GW strain channel through different coupling paths.

Sidebands of the mains frequency, at approximately 49.5 Hz and 50.5 Hz, were
generated by the pulse width modulation of the electric heater controller of
the imc building. The noise was mitigated by decoupling the electric ground of
the building from the central experimental area with an isolation transformer.

Figure 29c) illustrates a wide-band noise affecting the same region. The
origin of this noise was eventually found to be a noisy static voltage
accidentally applied to the signal wires of the motors used for positioning
and balancing the WE mirror suspension, then coupling capacitively to the
mirror coil actuator wires. The noise was mitigated by un-plugging the drivers
of the motors, which are not used in science mode.

Finally, Figure 29d) illustrates a family of lines between 47 Hz and 49 Hz
which have been identified as vertical mechanical modes of the last stage of
the test mass suspension system. These modes are excited by ambient magnetic
fields coupling to the magnetic actuators along the suspension chain. This
noise was suppressed by an active mechanical damping of the modes.

Figure 29: Four steps of the reduction process of the strain spectral noise
between 40 Hz and 60 Hz during O3. In all sub-figures the blue curve is before
the mitigation, and the red curve is after the mitigation. a) Cancellation of
the spectral noise structure around 55 Hz which was common to the prcl signal.
b) Subtraction of the 50 Hz line associated to the power grid. c) Mitigation
of a wide-band noise associated to the motor driver crate of the WE
suspension. d) Suppression of a few noise lines associated to mechanical modes
of the test masses payload.

###  7.4 Offline data quality

####  7.4.1 Offline studies and checks

While Section 5.1.2 describes the online CAT1 vetoes, we focus here on the
final set of offline CAT1 vetoes. They supersede online vetoes and have been
used by all analyses processing the final O3 Virgo dataset. These include
analyses using the O3 LIGO-Virgo public dataset: that is why the gwosc website
[113] includes detailed public information about these vetoes [114].

Like the online CAT1 vetoes, all these veto flag segments of bad data that are
unusable. They are defined with a 1 s granularity and the figure-of-merit used
to quantify their impact is their dead time, that is the fraction of Science
time that is removed by applying them individually. Yet, the vetoes are not
independent and they may overlap. Therefore, they are meant to be applied
globally on the dataset, by taking the logical OR of all of them.

The offline vetoes defined during the O3 run can be classified into three main
categories.

  * •

The duplication—after crosscheck and potential additions or fixes—of online
CAT1 vetoes: this includes the saturations of dark fringe photodiodes or
mirror suspensions, and the monitoring of the reconstructed gw strain $h(t)$.

  * •

The upgrade of existing online vetoes: the excess rate of glitches is
monitored offline using $h(t)$ whereas only the darm channel could be used
online due to latency constraints.

  * •

The addition of new vetoes, based on information that was not available in low
latency, or that was not known at the time online flags were generated. These
categories are described below.

    * –

Checks of the consistency and of the completeness of the files storing the
$h(t)$ GW stream: these vetoes flag segments in which $h(t)$ is missing or
contains missing samples.

    * –

The $h(t)$ stream is reconstructed by blocks of eight consecutive seconds of
data. Therefore, a control loss can possibly impact up to the eight seconds of
data that predate it. As the exact time of a control loss is not easy to
define, the last ten seconds preceding each recorded control loss have been
removed.

    * –

The Science dataset has been scanned accurately to identify segments during
which the detector was not taking good quality data, contrary to what its
status was indicating. These segments were removed from the final dataset.

    * –

Finally, a workaround was applied to the detector control system during some
weeks in O3b in order to mitigate transient data losses due the failure of an
hardware component. That patch allowed to maintain the working point of the
instrument, thus sparing a ${\sim}$20 min control acquisition procedure each
time it prevented a global control loss. Yet, the application of that
workaround could degrade the quality of the data. Thus, the impacted segments
were removed from the final dataset, with some safety margin on both ends (the
last 10 seconds before having the control patch be applied automatically, and
the first 110 seconds following the end of the transition back to the nominal
control system).

Table 7 summarizes the impact of CAT1 vetoes on the final O3 Science dataset:
overall, only 0.2% of the Science data have had to be removed due to various
problems.

Table 7: Virgo O3 offline Science dataset and CAT1 vetoes. | O3a | O3b | O3a + O3b
---|---|---|---
Science dataset | 12,057,731 s | 9,611,843 s | 21,669,574 s
Logical OR | 18,802 s | 20,636 s | 39,438 s
of all offline CAT1 vetoes | (0.16%) | (0.22%) | (0.18%)

Conversely, a few minutes of good quality data that had not been included in
the online Science dataset for various and clearly understood reasons
(software issue, human error, etc.) were added to the offline, final, dataset.

####  7.4.2 Event validation

To assess whether the detection alerts produced by transient searches [57, 94,
115, 116] should be considered as “candidate events”, a procedure of
_validation_ is implemented after each generated trigger [10, 45]. This task
has the role to verify if data quality issues, such as instrumental artifacts,
environmental disturbances, etc., can impact the analysis results and decrease
the confidence of a detection, or even foster a rejection [117].

The validation of the online triggers found by gw transient searches includes
two separate stages. A prompt evaluation is typically completed within few
tens of minutes after an event trigger has been generated, as represented by
the data flow in Figure 4. Its goal is to determine a preliminary detection
confidence and sky localization, in order to deliver public alerts to the
astronomy community and support for multi-messenger follow up observations
[117], as described in Section 6, or to vet that trigger if evidence of severe
contamination from non-astrophysical artifacts is present. A team of DetChar
shifters is in charge of this task as part of the rapid-response team (Section
3.4). The decision about the event is primarily based on the quick results
provided by the dqr within a few minutes from the trigger. This decision takes
into account the evaluation of the operational status of the detector and its
subsystems, the environmental conditions, as well as preliminary checks on the
strain data. In particular, the shifters are asked to verify the presence of
excess noise, namely glitches, around the time of the trigger and the validity
of the hypotheses of stationarity and Gaussianity of the data, as discussed in
Sections 4.2.3 and 4.3. Moreover, it is examined the possible presence of
correlations between the strain data and the auxiliary sensors, which may
advise a non-astrophysical origin of the trigger.

With higher latency, a second stage of validation is performed by a
_validation team_ to finally check candidate events before publications,
including those found by offline analyses [56, 95]. Besides of
(double-)checking the astrophysical origin of the event trigger, the main
purpose of this process is to carefully assess whether the parameter
estimation of the source properties can be affected by noise artifacts. This
procedure takes advantage of dedicated reruns of the dqr, as well as from
additional tools and metrics, including, for example, signal consistency
checks [45, 118].

For those events where non-stationary noise, such as glitches, are found in
the vicinity of the putative gw signal, or even overlapping with it, a
procedure of noise _mitigation_ is implemented [119, 120]. During O3b, such
process has involved 12 events, including one with Virgo data, GW191105e [10,
121], where the process of mitigation and validation of the data quality has
improved the parameter estimation results and credibility. Various O3a events
have undertaken a preliminary version of this procedure [8].

##  8 Preparation of the O4 run

The LIGO-Virgo O3 run has lead to the discovery of dozens of new gw signals
from compact binary mergers, which have boosted our knowledge of these
populations in our local Universe and allowed further, more stringent, tests
of general relativity. The O3 run has also been the first long data-taking
period for the adv detector. Thus, it represents a full-scale, extended and
non-stop stress test of the organization and work methods of the Virgo DetChar
group. The experience accumulated during these 11 months will form the base of
the DetChar activities, both to prepare and operate for O4 and the following
runs.

Although the Virgo DetChar group has fulfilled all its main requirements
during the O3 run, work has been going on since then to improve its
performance and extend its activities. In particular, the anticipated
differences between the O3 and O4 runs lead to new challenges that the group
should tackle. The adv detector will have evolved significantly, with the
completion of the Phase I of the adv+ project. The main changes on the
instrument side are the addition of the signal-recycling mirror in between the
beam splitter and the output port of the Virgo interferometer, a higher input
laser power and the implementation of frequency-dependent squeezing. This new
configuration will require dedicated instrument characterization activities,
while many new data quality features will have to be discovered, understood
and later mitigated or solved. On the data analysis side, progress in terms of
sensitivity while keeping the network duty cycle high will lead to more gw
detections. On the one hand, more work will be required to validate this
excess of signal candidates compared to O3; on the other hand, the triggers
passing a given false alarm rate threshold will remain dominated by noises,
meaning that the bulk of computing resources used by the Virgo DetChar group
will not change significantly.

Gathering experience from the past and predictions for the future, a few top
priorities have emerged for the DetChar group. A first and obvious one is to
broaden the scope of the DetChar monitoring, to make sure that no relevant
area remains uncovered, from raw data to the final analyses. Then, the latency
of the various DetChar products should be decreased when it is relevant and
possible: either by making the corresponding software framework more
efficient, or by processing new data more regularly. Finally, some emphasis
should be put on increasing the automation of the DetChar analyses and the
reporting of their results. In that respect, the dqr is a good example of the
realization of these plans. Parallel to common LIGO-Virgo-KAGRA developments
on the framework architecture to make dqr more uniform among the three
collaborations and to improve its performance, additional data quality checks
will be implemented. They will provide combined results that should give a
partial digest of the global vetting of a given gw signal candidate.

The increase of the information available and the help to identify quickly its
most relevant points should allow maintaining, if not improving, the high and
steady level of Virgo performances observed during O3.

## Acknowledgements

September 2021 version – https://tds.virgo-gw.eu/ql/?c=17224

The authors gratefully acknowledge the Italian Istituto Nazionale di Fisica
Nucleare (INFN), the French Centre National de la Recherche Scientifique
(CNRS) and the Netherlands Organization for Scientific Research (NWO), for the
construction and operation of the Virgo detector and the creation and support
of the EGO consortium. The authors also gratefully acknowledge research
support from these agencies as well as by the Spanish Agencia Estatal de
Investigación, the Consellera d’Innovació, Universitats, Ciència i Societat
Digital de la Generalitat Valenciana and the CERCA Programme Generalitat de
Catalunya, Spain, the National Science Centre of Poland and the European
Union— European Regional Development Fund; Foundation for Polish Science
(FNP), the Hungarian Scientific Research Fund (OTKA), the French Lyon
Institute of Origins (LIO), the Belgian Fonds de la Recherche Scientifique
(FRS-FNRS), Actions de Recherche Concertées (ARC) and Fonds Wetenschappelijk
Onderzoek— Vlaanderen (FWO), Belgium, the European Commission. The authors
gratefully acknowledge the support of the NSF, STFC, INFN, CNRS and Nikhef for
provision of computational resources.

We would like to thank all of the essential workers who put their health at
risk during the COVID-19 pandemic, without whom we would not have been able to
complete this work.

The authors would also like to thank Samuel Salvador for his extensive and
careful proofreading of the manuscript.

[name=List of Abbreviations]

##  Appendix A Additional tool information

In this Appendix, we describe in more detail some of the data analysis
techniques presented in Section 4, and their implementations into tools. A.1
and A.2 provide additional information on the statistics adopted to test the
hypotheses of stationarity and Gaussianity with the bristol and
rayleighSpectro tools, and their interplay. A.3 and A.4 are devoted to the
tools for spectral noise investigations BruCo and MONET. The former uses the
coherence as a figure of merit to study the linear transfer of power between a
set of auxiliary channels and a main channel, usually the GW strain $h(t)$.
The latter investigates non-linear couplings between channels, by studying the
coherence of the main channel (usually $h(t)$) with a synthetic one, created
by modulating a carrier signal (either an existing DAQ channel or a sinusoid
with a fixed frequency) with the low-frequency part of an auxiliary channel.

###  A.1 BRiSTOL - a Band-limited RMS Stationarity Test Tool

This statistical test aims at verifying the hypothesis of _wide_ (or _weak_)
_sense_ stationarity of the data, i.e. that the covariance function is left
unchanged by shifts in time. We test this by verifying that subsequent psd
estimates, in predefined frequency bands, are compatible with the same
probability distribution. The corresponding test statistics are based on a set
of brms time series, estimated on an equal number of bands:

$\mathit{BRMS}_{t}(b)=\sqrt{\int_{f\in
b}\hat{S}_{t}(f)\,df},\qquad\mathrm{for}\quad
b\in\left\\{[f_{1}^{\max},f_{1}^{\min}],\ldots,[f_{K}^{\max},f_{K}^{\min}]\right\\}$
(4)

for data $x_{t_{n}}$ recorded at Nyquist rate $f_{S}$, $t_{n}=t+n/f_{S}$,
where $\hat{S}_{t}(f)$ is a psd estimate referred to time $t$, and obtained
with the _periodogram_ method [122]:

$\hat{S}_{t}(f_{k})=\frac{1}{N}\bigg{|}\sum_{n=0}^{N-1}x_{t_{n}}e^{-2\pi
i\,nf_{k}/f_{S}}\bigg{|}^{2},\qquad
f_{k}=\frac{k\,f_{S}}{N},\quad\text{for}\quad k=0,\ldots,N-1$ (5)

Two modifications have been implemented to make (4) more suitable for the
study of transient noise, in particular to highlight slow non-stationarity.
Firstly, spectral lines (refer to Section 4.4.2 for more details) have been
removed from the integral. These are narrow features in the psd of the data,
originating from resonances in various parts of the interferometer and their
harmonics. Their intensities can be orders of magnitude larger than the
neighboring noise floor. Hence, if a line is present in a band where we are
about to compute the brms, it is likely to dominate the final estimate, and
also the corresponding fluctuations, preventing us from probing the features
of the underlying noise floor. To remove these lines, we identify them with an
algorithm similar to the one developed for the noemi pipeline [77], and based
on the _prominence_ of their psd [123].

Second, glitches are also typically removed from the brms time series. These
fast transients can manifest at a rate of about 10 per minute, as shown in
Figure 25, which means that every data segment longer than a few seconds is
likely to contain one of them. To focus on slower noise transients, which
typically are not targeted by tools specifically devoted to excess power
identification, such as those presented in Section 5, we must exclude the data
segments affected by glitches from the stationarity test. This is done by
means of an algorithm based on a rolling _median absolute deviation_ , defined
as the median absolute difference from the median, to identify outliers in the
brms data.

Then, the time series corresponding to the resulting modified brms are divided
into “chunks” where estimate their empirical distribution function. The
stationarity hypothesis is tested by means of a two-sample Kolmogorov–Smirnov
test [60] for each pair of consecutive chunks, whose $p$-values are compared
to a test significance $\alpha$ (to be decided in advance), and the (_null_)
hypothesis of stationarity rejected when the latter is exceeded.

There are two advantages in using the brms. First, averaging over the
frequencies of each band has a similar variance reduction effect than the
means in Welch’s psd estimation method [124]. This in turn allows a finer time
resolution while maintaining a moderate variance for our test statistics, that
is, the empirical distribution of the brms. Second, the various non-
stationarities typically manifest in specific frequency bands, closely related
to the noise source that generated them. For example, the main harmonic of
scattered light is usually visible below 30 Hz; non-linear and non-stationary
couplings of the angular controls with the 150 Hz harmonic line are
characteristic of a tight region around it, etc. So, without losing much of
resolution, we can perform the noise characterization directly on these bands
instead of on each frequency bin comprising the spectrum of the signal.

###  A.2 rayleighSpectro - Gaussianity test

Similarly to what was discussed for the stationarity hypothesis, Gaussianity
is likewise important to be tested separately in the different regions of the
spectrum where noise sources can show up. rayleighSpectro does this by means
of a consistency check on the psd estimated from the data with what is
expected for stationary Gaussian noise. Indeed, if the data is compatible with
the hypothesis od Gaussianity, the periodogram estimator in Equation (5) is
asymptotically (with $N$) described by an _exponential distribution_ of
parameter $S(f_{k})^{-1}$ [125], where $S(f_{k})$ is the process psd. The
corresponding asd estimator, obtained as the square root of Equation (5), is
described by a Rayleigh distribution with parameter $\sqrt{S(f_{k})/2}$. The
scaling property of this distribution can be used to construct consistency
tests. For example, the standard deviation of the asd estimates obtained on
non-overlapping segments provides an estimator of the standard deviation of
this variable, which equals $\sqrt{(4-\pi)\,S(f_{k})}/2$. Similarly, the mean
of these estimates provides an estimator of the mean: $\sqrt{\pi S(f_{k})}/2$.
The ratio of these two quantities gives a statistic that, at each frequency
$f_{k}$, is _asymptotically_ equal to a constant whose numerical value is
given in Equation (1), in the null hypothesis that the data is described by a
stationary and Gaussian distribution. The actual value of the previous
quantity for a finite number of averages and the corresponding critical values
for performing statistical tests have been computed in [126, 61].

By dividing the data into chunks of duration $\Delta t$, one can obtain a
time–frequency map, similar to a spectrogram, showing with time resolution
$\Delta t$ the frequencies and times where the data significantly depart from
the expected value of Equation (1). Smaller values of this statistic are
associated with data having smaller fluctuations than those expected for a
Gaussian process; spectral lines usually behave in this way. Larger values are
instead typical of non-stationary noises, such as glitches, that produce a
larger variance of the asd estimates.

The interplay between this tool and bristol for the assessment of the
stationarity and Gaussianity of the data is the following. The latter assesses
where the data is compatible with the hypothesis of wide sense stationarity,
that is, the second order moments (i.e. the covariance or the RMS) are left
unchanged by shifts in time. This corresponds also to _strong sense
stationarity_ if the data is also Gaussian, that is, completely characterized
by its mean and covariance functions, as tested by rayleighSpectro.
Conversely, deviations from these assumptions can be tested independently.

###  A.3 BruCo

The bruco python code (version 2017-01-23) [80], is publicly available from
the git repository [81], which also provides a description of the argument
list. An instance of the repository is kept with Virgo-specific data access
features.

bruco computes the magnitude-squared coherence between a main channel
(typically, but not necessarily, the detector strain channel $h(t)$) and all
auxiliary channels that, at the time of interest, are recorded by the daq
system. Optionally, a set of redundant channels which are known a priori to be
correlated with the main one, can be excluded. In Virgo, during the O3 run,
there were approximately 3,000 non-redundant channels with a sampling
frequency $\geq$1 kHz. To deal with the high computational load required by
this analysis, bruco implements the option of multi-core parallel processing
in up to $10$ threads.

In the bruco implementation adopted for Virgo during O3, a continuous Science
data segment of length $T=800$ s is selected for the main channel $h(t)$ and,
in turn, for each auxiliary channel $n(t)$. Each data segment is resampled to
a targeted output frequency of 2 kHz with the Fourier resampler
scipy.signal.resample, divided into $N_{ave}=100$ sub-segments (8 s long) and
the averaged magnitude-squared coherence is computed, as:

$C_{h,n}(f_{i})=\frac{\mid<FFT_{n}(f_{i})^{*}FFT_{h}(f_{i})>\mid^{2}}{<\mid
FFT_{h}(f_{i})\mid^{2}><\mid FFT_{n}(f_{i})\mid^{2}>}$ (6)

where $FFT$ denotes the windowed fast Fourier transform, "$<>$" denotes the
averaging operation, $f_{i}$ is the $i^{\textrm{th}}$ frequency bin, and "∗"
the complex conjugate operation. With these parameters, the frequency
resolution is $df=N_{ave}/T=0.125$ Hz. Coherence is examined up to 1 kHz, and
its value is deemed significant if it exceeds a threshold set to 0.03, a value
corresponding to the 95% confidence level of the distribution of averaged
coherence between random data [127], given the selected parameters.

Daily bruco results are html-formatted and made accessible in a dedicated vim
web page (see Section 4.1.3). The bruco vim summary page allows to quickly
spot noise paths contributing to the gw strain $h(t)$ in specific frequency
bands. A summary table is generated: each row corresponds to a given frequency
bin and contains the list of the most coherent channels in descending order.
The cell background is color coded in shades of red from full red (maximum
coherence: 1) to white (no coherence) as shown in Figure 30. For each
auxiliary channel, a plot (see Figure 19) of the projected coherence quantity,
$h_{n}(f)=<FFT_{h}(f)>\sqrt{C_{h,n}(f)}$, is produced and linked to the table.
In the hypothesis of linear coupling, this quantity estimates the contribution
to the strain channel of the noise witnessed by the $n^{\textrm{th}}$
auxiliary channel [127]. Additionally, the vim daily summary page contains the
list of the top ranked channels in the frequency bins with coherence greater
than 0.3 (Table 8), and a plot of the combined projected coherence greater
than 0.5 (Figure 31).

Figure 30: An example of bruco result webpage displaying, for each frequency bin (leftmost column), the most coherent channels sorted by decreasing coherence value, also represented by the red shade intensity. These data are from November 11, 2019. The large coherence detected at frequencies $155-170$ Hz triggered some further investigations of the noise [128]. Table 8: An excerpt (15 top lines) from top ranked channels’ summary with coherence greater than 0.3 for GPS time 1264319383 (2020/01/29 at 07:49:25 UTC).  Frequency [Hz] | Coherence | Type of channel
---|---|---
9.375 | 0.348 | West arm transmitted power measurement
9.500 | 0.371 | Angular correction of the last stage
of wi payload suspension
13.375 | 0.308 | Sensing signal measured at the dark fringe port,
used to control optical cavity alignment
13.625 | 0.349 | Same sensing signal
13.750 | 0.347 | Same sensing signal
14.125 | 0.311 | Same sensing signal
14.250 | 0.310 | Same sensing signal
14.375 | 0.335 | Same sensing signal
14.625 | 0.309 | Same sensing signal
15.375 | 0.323 | Same sensing signal
16.250 | 0.589 | Longitudinal correction of the last stage
of bs payload suspension
16.375 | 0.532 | Same longitudinal correction
16.750 | 0.303 | Same sensing signal
60.375 | 0.403 | Calibration signal applied
to the we test mass actuators
Figure 31: A bruco vim daily combined projection of the GW strain channel
$h(t)$, showing coherences greater than 0.3 for the same GPS time 1264319383
(2020/01/29 at 07:49:25 UTC) as the previous plot.

###  A.4 MONET

monet computes the magnitude-squared coherence between a main channel
(typically the DARM channel) and a list of other signals, that are constructed
multiplying in the time domain a carrier signal and a set of modulating
auxiliary channels to which a low-pass filter (with a typical cutoff frequency
of a few Hz) is applied; the carrier signal can be a real channel or a
simulated signal (e.g. a sinusoidal signal). Similarly to what is done with
bruco, also with monet continuous science data segments of a specific time
length $T$ are selected for all the channels to be investigated; then each
data segment is resampled to a targeted output frequency ($f^{\rm out}$) and,
finally, the magnitude-squared coherence is computed with Equation 6. For the
analysis of O3 Virgo data we typically used a cutoff frequency of 5 Hz,
$T=1200$ s and $f^{\rm out}$=1 kHz.

monet can be executed on demand, investigating dozens of auxiliary channels
and spectral lines every single run. The outputs are organized in a directory
structure:

  * $\bullet$

A main directory, whose name indicates the main channel, the initial gps time
and the time length of the segment of data to be analysed.

  * $\bullet$

A secondary directory, named after the carrier signal used.

  * $\bullet$

Several sub-directories, one for each modulator channel.

The secondary directory contains an ascii table and a summary figure. The
ascii table contains three columns: the frequency bins, the computed above-
theshold coherence values for each bin (ordered from the lowest to the
highest) and the corresponding modulator channels name. Figure 32 shows the
MONET summary plot for the DARM channel during O3. Superimposed to the main
channel’s asd there are red points marking the frequencies at which coherence
above threshold is found with at least one auxiliary channel.

Figure 32: asd of the darm channel (in black), together with red points that
mark the frequencies at which the coherence is above the threshold, fixed in
this case at 0.3; the initial GPS time of the analysed data and the chosen
carrier signal are indicated on the top of the figure.

In each sub-directory, a table and a plot are generated, in which the
coherence values associated with the specific modulator channel for each
frequency bin are reported; several other plots are also produced, in which
the asd of the main channel is reported, together with the noise projection
based on the coherence values, around the specific spectral lines to be
investigated (see Figure 33).

Figure 33: asd of the main channel (DARM) around the 350 Hz spectral line (in
black), together with the noise projection, based on the coherence values
obtained with the modulator channels ASC$\\_$Diffp$\\_$TY and
ASC$\\_$Diffp$\\_$TX, in blue and orange respectively (these two channels are
used to control the angular movement of the mirrors in the detector arms, to
guarantee the proper ricombination of the laser beams at the beam splitter);
the initial gps time of the analysed data and the chosen carrier signal are
indicated on the top of the figure.

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