[6,9]S. Quitadamo

1] Climate Simulations and Predictions Division, Euro-Mediterranean Centre on
Climate Change (CMCC) Foundation, Bologna, 40127, Italy

2] Dipartimento di Fisica e Astronomia, Alma Mater Studiorum – Università di
Bologna, Bologna, 40126, Italy

3] Istituto Nazionale di Fisica Nucleare – Sezione di Bologna, Bologna, 40127,
Italy

4] Istituto Nazionale di Fisica Nucleare – Sezione di Milano Bicocca, Milano,
20126, Italy

5] Dipartimento di Fisica, Università di Milano - Bicocca, Milano, 20126,
Italy

6] Istituto Nazionale di Fisica Nucleare – Laboratori Nazionali del Gran
Sasso, L’Aquila, 67100, Italy

7] Istituto Nazionale di Geofisica e Vulcanologia - Osservatorio Nazionale
Terremoti - Sede di L’Aquila, L’Aquila, 67100, Italy

8] Wright Laboratory, Department of Physics, Yale University, New Haven,
06520, CT, USA

9] Gran Sasso Science Institute, L’Aquila, 67100, Italy

10] Department of Physics, University of California, Berkeley, 94720, CA, USA

11] Nuclear Science Division, Lawrence Berkeley National Laboratory, Berkeley,
94720, CA, USA

12] Alma Mater Studiorum – Università di Bologna, Bologna, 40126, Italy

# The environmental low-frequency background for macro-calorimeters at the
millikelvin scale

L. Aragão  A. Armigliato  R. Brancaccio  C. Brofferio  S. Castellaro  A.
D’Addabbo  G. De Luca  F. Del Corso  S. Di Sabatino  R. Liu  L. Marini  I.
Nutini<EMAIL_ADDRESS>P. Ruggieri  K. J. Vetter  M. Zavatarelli  S.
Zucchelli  [  [  [  [  [  [  [  [  [  [  [  [

###### Abstract

Many of the most sensitive physics experiments searching for rare events, like
neutrinoless double beta ($0\nu\beta\beta$) decay and dark matter
interactions, rely on cryogenic macro-calorimeters operating at the mK-scale.
Located underground at the Gran Sasso National Laboratory (LNGS), in central
Italy, CUORE (Cryogenic Underground Observatory for Rare Events) is one of the
leading experiments for the search of $0\nu\beta\beta$ decay, implementing the
low-temperature calorimetric technology. We present a novel multi-detector
analysis to correlate environmental phenomena with the low-frequency noise of
low-temperature calorimeters. Indeed, the correlation of marine and seismic
data with data from a pair of CUORE detectors indicates that cryogenic
detectors are sensitive not only to intense vibrations generated by
earthquakes, but also to the much fainter vibrations induced by marine
microseisms in the Mediterranean Sea due to the motion of sea waves. Proving
that cryogenic macro-calorimeters are sensitive to such environmental sources
of noise opens the possibility of studying their impact on the detectors
physics-case sensitivity. Moreover, this study could pave the road for
technology developments dedicated to the mitigation of the noise induced by
marine microseisms, from which the entire community of cryogenic calorimeters
can benefit.

###### keywords:

Low-temperature calorimeters, Marine microseisms, Seismometers, Environmental
noise, Neutrinoless double beta decay, Rare events

##  1 Introduction

Low-temperature calorimeters are known to be extremely sensitive to
vibrations. Indeed, an external force acting on the cryogenic system can
induce a power dissipation on the hosted detectors. Depending on the nature of
the source of vibration and on which elements are involved in the transmission
of the associated power, different characteristic frequencies of the cryogenic
setup can be excited and transmitted to the detectors. As a result, the
operating temperature or the noise of the detectors can momentarily change.
From the case study of the noise of CUORE low-temperature calorimeters, a
correlation arises between the detectors low-frequency noise components and
the marine microseismic activity.

Here we report a multi-detector analysis technique for the study of the
correlation of the low-frequency noise of cryogenic calorimeters with
environmental sources of vibrations, namely the marine microseismic activity
of the Mediterranean Sea. Section 2 is dedicated to a general description of
low-temperature calorimeters (or bolometers), with a particular focus on the
sources of noise which can affect their performance. Section 3 is dedicated to
the description of the seismometers used for this study, their location at
LNGS and their mutual compatibility. Section 4 focuses on the marine data
provided by Copernicus Marine Environment Monitoring Service and their
compatibility with seismometers at LNGS. Finally, in section 5 we describe in
detail the analysis procedure we applied to correlate marine, seismic and
bolometric data in order to study the impact of marine microseisms in the
Mediterranean Sea on the low-frequency noise of a couple of CUORE detectors.

##  2 Low-temperature calorimeters

Cryogenic detectors operated at the mK-scale represent cutting-edge technology
in the field of low-temperature physics and precision measurements. They
operate by detecting the phonons generated by an energy deposition in the
detector, which results in a measurable temporary increase of its temperature.
A thermal sensor is coupled to the energy absorber in order to measure such
temperature variation and convert it into an electric signal. The size of the
absorber depends on the physics applications: micro-calorimeters
($\sim$$\mu$g-scale) are usually implemented for X-ray spectroscopy and
$\beta$-decay studies, while macro-calorimeters ($\sim$g to kg-scale) are used
for $\gamma$-ray spectroscopy, for coherent neutrino scattering experiments,
and for 0$\nu\beta\beta$ decay and dark matter searches. Macro-calorimeters
are often read out by means of semiconductor thermistors, with $\sim$ms
response time. Therefore they are sensitive to thermalized phonons, thermal
quanta which reached a new equilibrium after degrading their energy via
several interactions in the absorber. In this case the temperature variation
induced by an energy deposition is proportional to the deposited energy
itself. Neutron Transmutation Doped germanium (Ge-NTD) thermistors are among
the most widely used devices, since they can be operated in a wide range of
temperatures by means of a simple read-out circuit at room temperature and no
need of cold electronics [1, 2].

Operating detectors at the mK-scale ensures that the thermal noise is
minimized, allowing for exceptional energy resolution and sensitivity. This
makes such detectors particularly suited for a wide range of scientific
endeavors, from the detection of rare events to astrophysical dark matter
searches [3, 4].

###  2.1 Noise and signal bandwidth of cryogenic detectors

Noise in cryogenic detectors is a critical factor that can significantly
affect their performance. At ultra-low temperatures thermal noise is
suppressed due to the reduced thermal excitation of electrons and phonons.
However, other sources of noise become prominent. One major contributor is
electronic noise, arising from the intrinsic fluctuations in the electronic
circuitry for the detector read-out. Dedicated low-noise electronics must
therefore be designed [5]. Other sources of noise are due to the motion of
charge carriers in the load resistor of the thermistor read-out circuit
(Johnson-Nyquist noise [6, 7]) and to the presence of stray electromagnetic
fields.

Vibrational noise constitutes a noteworthy challenge in achieving high
precision measurements. Mechanical vibrations from various sources, such as
acoustic disturbances or microphonic effects, can perturb the detectors and
degrade their performance. Therefore cryogenic detectors are often coupled to
sophisticated suspension and isolation systems and to mechanical filters in
order to absorb and attenuate vibrations.

Depending on the detector size and the type of read-out sensors, the signal
bandwidth can span from less that 1 Hz up to hundreds of kHz. Various sources
of noise, such as electronic and vibrational disturbances, can induce
fluctuations in the measured signal at frequencies within the detector signal
bandwidth, limiting its capability to accurately resolve the signal and
evaluate the associated energy deposition.

###  2.2 The case study: CUORE detectors

CUORE is an experiment designed for the search of $0\nu\beta\beta$ decay of
130Te [8]. Hosted at LNGS, in central Italy (42.45∘ N, 13.58∘ E), it is the
first ton-scale experiment based on cryogenic calorimeters. Taking data since
2017, CUORE consists of 988 TeO2 crystals, organized in 19 towers,
instrumented with Ge-NTDs (Figure 1) and operated as low-temperature
calorimeters at $\sim$10 mK by means of a custom designed cryostat with a
3He/4He dilution refrigerator [9].

Figure 1: (a) A CUORE low-temperature calorimeter: a Ge-NTD thermistor for
signal read-out and a Si-heater for thermal stabilization are glued on a TeO2
crystal. (b) Average Noise Power Spectrum (ANPS) of a CUORE low-temperature
calorimeter. The insert shows a linear scale zoom of the ANPS in the [0,4.5]
Hz region, which is the frequency range corresponding to the CUORE signal
band. Noise peaks related to pulse tube cryocoolers harmonics are labeled in
blue, while the ones related to the suspension system are labeled in red.

To maximise the performance in terms of sensitivity and energy resolution, it
is mandatory for CUORE to minimize every source of noise induced on the
detectors from the cryogenic infrastructure and the external environment. The
CUORE cryostat is equipped with pulse tube (PT) cryocoolers, acting as a stage
of the refrigeration system. Their operation generates vibrational noise at
1.4 Hz and harmonics. An active noise cancellation technique has been
developed and implemented in order to stabilize and attenuate the PT-induced
noise on the cryogenic detectors [10]. Suspension and decoupling systems are
deployed in order to isolate as much as possible the detectors from the
surrounding environment [9]. The detector payload at 10 mK is decoupled from
the cryogenic system by a suspension system held by a support structure
(Y-beam) mounted on top of three mechanical insulators based on the negative-
stiffness decouplers technology [11] manifactured by Minus K Technology. The
entire structure of CUORE may feature a resonant behaviour at $\simeq$ 0.5-0.7
Hz, which could enhance vibrations in the sub-Hz domain picked-up from the
external environment.

The spectral shape of the noise of CUORE detectors is very complex, being the
sum of several contributions (Figure 1). One can easily identify the high-
frequency cut-off at 120 Hz due to the anti-aliasing Bessel filters [5], and
several peaks in the noise spectrum. As already mentioned, the 1.4 Hz peak and
its harmonics are generated by the PT operation. Other peaks are attributed to
residual mechanical vibrations and oscillations of the suspension system and
support structure (e.g. 0.6 Hz and 0.85 Hz) [12].

The support structure can also pick up vibrations generated by environmental
phenomena. Indeed, many years of data taking established that CUORE detectors,
and in general macro-calorimeters operated at the mK-scale, are sensitive to
earthquakes-induced vibrations. The motion of sea waves and the developments
of marine storms are additional known sources of environmental vibrations [13,
14, 15]. Such events are the sources of marine microseismic activity,
characterized by much fainter vibrations with respect to earthquakes and by
characteristic frequencies in the sub-Hz domain. While the effects of seismic
activity on cryogenic detectors is well established, the impact of
microseismic activity is still not extensively studied.

##  3 Seismometric devices

Low-frequency environmental noise consists of ground vibrations caused by a
variety of sources, such as seismic events (e.g. earthquakes) and microseismic
events (marine activity), atmospheric perturbations and human activities.
Seimometetric devices can be deployed as complementary tools for highly-
sensitive physics experiments, in order to study and mitigate environmental
perturbations which can affect their experimental performance.

###  3.1 Seismometers at LNGS

The CUORE experiment installed two seismometers (called SEISMO 1, SEISMO 2) in
its experimental area, mainly to identify and eliminate instabilities in the
detectors data due to seismic and anthropic noises. Their sensitive element
consists of a SARA SS45 velocimeter [16], which is a triaxial velocimeter with
a sampling rate of 400 Hz, characterized by a sensitivity bandwidth in the
0.2-400 Hz and by an almost flat response in the 1.0-50.0 Hz range.

Moreover the LNGS underground facility hosts a seismic station (called GIGS)
from the Italian National Institute of Geophysics and Vulcanology (INGV) [17].
Previously hosted by the homonym GIGS (Geophysical Interferometer at Gran
Sasso) experiment, the GIGS seismometer is part of a network of stations
spread all through the Italian Peninsula to monitor and study geological
phenomena in the Mediterranean region. GIGS [18, 19] is a Nanometric
Trillium-240S seismometer with a sampling rate of 100 Hz, characterized by
enhanced sensitivity at low frequencies and by a flat broadband response from
4 mHz to 35 Hz. The GIGS sensing elements are arranged in a symmetric triaxial
configuration, ensuring the same response on vertical and horizontal
directions.

###  3.2 Correlation of GIGS and SEISMO data

GIGS is located $\simeq$130 m away from the CUORE experimental area, where
SEISMO are installed. Therefore these seismometers allow to investigate the
vibrational noise in different locations at LNGS and possibly identify if its
sources are internal or external to the underground facility. While the
horizontal axes of GIGS are oriented in the North-South and East-West
directions, the orientation of SEISMO was performed in relation to their
hosting experimental hall. Due to the difficulties in achieving a precise
comparison between the orientation of the horizontal axes of GIGS and SEISMO,
the vertical Z axes is the only one directly comparable among the three
seismometers. For this reason, here we will focus only on their vertical axes.
The root mean square (RMS) of the vertical measurements is a good estimator of
the variation of the vibrational activity at LNGS.

Figure 2 shows the comparison between the time profiles of RMS Z of GIGS and
SEISMO during September 2020. Due to their relative distance, local
disturbances, such as anthropogenic noise, generated around the area in which
one seismometer is located are not detected by the other device. Differently,
non-local events involving the entire LNGS are detected by all the seismic
stations. Non-local perturbations can be attributed to different sources, like
seismic or marine activities. By correlating seismometric data with marine
data, we could identify the source of the prominent perturbation in the end of
the month as a storm developing in the Mediterranean Sea (more details will be
discussed in section 4). During the storm development the responses of GIGS
and SEISMO are strongly correlated (Figure 2) (in the period of maximum
perturbation the Pearson correlation coefficient is
$\rho_{GIGS,SEISMO}$$>$0.90), highlighting the non-local nature of the
environmental event responsible for such perturbation.

Figure 2: Time evolutions of GIGS and SEISMO RMS Z (a) and of their
correlation coefficient (b) in September 2020. The spikes of high correlation
can be attributed to earthquakes, since they affect all the seismometers.

##  4 Copernicus Marine Environment Monitoring Service

The Copernicus Program [20] is the Earth monitoring component of the European
Union space programme, which provides environmental data based on satellites
and in-situ measurements, and on numerical models. The Copernicus Marine
Environment Monitoring Service (CMEMS) [21] is the Copernicus sector dedicated
to marine observation, providing free-of-charge, state-of-the-art ocean data
at global and regional scales.

Here we refer to two CMEMS products, namely Mediterranean Sea Waves Reanalysis
and Forecast [22] and Mediterranean Sea Waves Analysis and Forecast [23]),
whose data originate from the implementation of the wave numerical model WAM
[24] to the Mediterranean Sea (Med-WAM). The model domain covers the whole
Mediterranean Sea with a regular grid with $\frac{1}{24}^{\circ}$ horizontal
resolution ($\simeq$4.6 km). It is designed to enclose the Atlantic Ocean
swells, obtained from CMEMS, propagating to the Mediterranean Sea through the
Gibraltar strait. The atmospheric forcing is rendered by surface winds,
obtained from the fifth generation ReAnalysis (ERA5) produced by the European
Center for Medium-range Weather Forecast (ECMWF) [25].

###  4.1 Data selection

In this work we refer to two oceanographic fields among those provided, with a
time granularity of 1 h, by CMEMS:

  1. 1.

VHM0: the spectral significant wave height, approximately equal to the average
height of the highest one-third of the recorded waves heights:

$\text{VHM0}=\frac{1}{N/3}\sum_{n=1}^{N/3}H_{n}$ (1)

where $H_{n}$ is the wave height, sorted from the highest wave ($H_{1}$) to
the lowest ($H_{N}$), and $N$ is the size of the set from which the highest
one-third waves sub-set is extracted;

  2. 2.

VTPK: the sea surface wave period at maximum variance spectral density; the
inverse of VTPK defines the sea waves frequency $\nu_{sea}$.

Here we select and average CMEMS data in two rectangular regions in the
Adriatic and Tyrrhenian Seas (labeled as Domain 1 and Domain 2 in Figure 3):

  1. 1.

Adriatic Sea: [42.5, 43.0]∘ N $\times$ [14.0, 16.0]∘ E ($\simeq$53$\times$222
km2);

  2. 2.

Tyrrhenian Sea: [40.0, 41.0]∘ N $\times$ [12.0, 14.0]∘ E
($\simeq$108$\times$222 km2).

They have been chosen to cover two areas of the sea surrounding central Italy,
close to the coastlines (as in previous studies [26, 27]) and located along an
ideal line passing through LNGS and perpendicular to the Apennine Mountains.
In this work we will always refer to the sea waves amplitude as the average of
VHM0 data in the two marine domains. It has to be noticed that the behaviour
of the Adriatic and Tyrrhenian Seas are highly correlated with each other
during a storm development (more details will be discussed in section 5),
since the size of Mediterranean storms is such to engulf large portions of the
sea surrounding the Italian Peninsula. Therefore, we do not expect the outcome
of this work to noticeably depend on this particular choice of the sea areas
under investigation.

Figure 3: Map of the Adriatic and Tyrrhenian Seas (a) and of their respective
domains extracted from CMEMS for the analysis in this work (b). The LNGS
position and its distance from the two domains is also highlighted.

###  4.2 Correlation of CMEMS and seismometers data

Several measurements and models over decades assessed the power spectral
density of the environmental noise and the sources of its different frequency
components [28, 13, 14]. Many natural phenomena are sources of vibrations in
the sub-Hz range. An example is represented by the marine microseismic
activity, namely faint seisms caused by the motion of sea waves and by marine
storms. They induce sub-Hz vibrations ($0.02\lesssim\nu\lesssim 1$ Hz), which
can propagate from the sea to the ground, and can therefore be detected also
in the hinterland through seismometers. LNGS is located at $\simeq$50-100 km
from the Italian coastlines, and it is therefore reached by microseismic waves
coming from both the Adriatic and Tyrrhenian Seas.

In section 3.2 we discussed the capability of identifying non-local seismic
perturbations by correlating the responses of two distant seismometers (GIGS
and SEISMO) at LNGS. This allows us to compare the time profile of the sea
activity provided by CMEMS with the response of any of the two seismometers.
Figure 4 shows such comparison during September 2020. CMEMS detected the
outbreak of a marine storm in the last ten days of the month. In the same
days, GIGS and SEISMO detected an increase in the seismic activity at LNGS,
with a time evolution identical to the storm development. Since any
seismographic station at LNGS is affected by the combined microseismic waves
from any direction from the Mediterranean Sea, we evaluate the Pearson
correlation coefficients between GIGS data and the combined VHM0 data from
both Adriatic and Tyrrhenian Seas. The correlation coefficient is
$\rho_{GIGS,Seas}$=0.65 in the first twenty days of September 2020, increasing
up to $\rho_{GIGS,Seas}$=0.86 in the last ten days of the month, during the
storm development. Such high correlation between CMEMS and seismographic data
highlights that the microseismic waves generated by the Mediterranean Sea
activity can propagate up to LNGS and induce time-dependent perturbations,
common to the entire LNGS and clearly detectable by seismometers.

Figure 4: Comparison between the time profiles of VHM0 for Adriatic Seas,
Tyrrhenian Sea and for their combined contribution, and the time profile of
RMS Z of GIGS seismometer (rescaled by a constant factor for a better
comparison with VHM0 data), during September 2020.

We extended the study of the correlation between CMEMS and GIGS data to a
period of more than three years, from January 1st, 2019 to July 31st, 2022
(Figure 5). The time evolution of the correlation coefficients, evaluated
month by month, shows a clear seasonal modulation, with maximum correlation
during the boreal hemisphere winter and minimum during summer. Such
modulation, with a period compatible with 1 yr, is closely related to the
modulation of the Mediterranean Sea activity. Indeed the sea activity is
maximum during winter, being characterized by more intense and frequent storms
and microseismic activity. Such microseismic noise is detected by seismometers
at LNGS, resulting in a higher correlation between the seismic noise at LNGS
and the status of the sea. Differently, the sea activity during summer is at
its minimum and the induced microseismic noise contributed less to the total
seismic noise at LNGS, which instead can be dominated by other sources of
noise.

Figure 5: Time evolution of the correlation coefficient between the Adriatic
and Tyrrhenian Seas activity (VHM0) with the GIGS response, from January 2019
to July 2022. The green line represents the outcome of a sinusoidal fit, whose
period is compatible with 1 yr. Dashed orange and pink lines represent
respectively summer and winter solstices.

We established a chain of correlations between CMEMS data, providing insight
on the Mediterranean Sea status, and seismometric data, measuring the induced
microseismic activity at LNGS. Moreover, SEISMO seismometers share the same
location of the CUORE experiment. Thanks to the established correlation
between the various devices, we can directly correlate CMEMS and CUORE data,
in order to determine if marine microseisms can affect the performance of
CUORE low-temperature calorimeters.

##  5 Correlation between marine microseisms and CUORE low-frequency noise

In this section we will assess and evaluate the impact of microseismic
activity on the low-frequency noise of a couple of CUORE low-temperature
calorimeters. Based on both CMEMS and seismometric data, we will focus on the
time period from September 21st, 2020 to October 1st, 2020, during which a
storm developed in the Mediterranean Sea. Figure 6 shows the corresponding
time profiles of the sea waves amplitude. The time evolution of the Adriatic
and Tyrrhenian Seas are strongly correlated (correlation coefficient
$\rho_{Adriatic,Tyrrhenian}$=0.81), proving that the two seas are influenced
by the same environmental phenomenon. Since the size of such storm is large
enough to affect the two sides of the Italian Peninsula, the outcome of the
analysis presented in this work is mildly affected by the choice of the
positions of the two marine domains under study, as anticipated in section
4.1.

Figure 6: (a) Time profile of the sea waves height for Adriatic Sea,
Tyrrhenian Sea and for their combined contribution, from September 21st, 2020
to October1st, 2020. (b) Sea waves frequency for Adriatic and Tyrrhenian Seas
in September 2020.

###  5.1 Time evolution of CUORE low-frequency noise

The output voltage of CUORE detectors, referred to as baselines, shows the
fluctuations and variations of their temperature, and is acquired and saved as
a continuous stream, with a sampling frequency of 1 kHz. Subsequently, a
software trigger is applied to such data streams to extract a random selection
of noise fluctuations of the baselines, while a triggering algorithm is
applied to identify thermal pulses. Time windows of a chosen length are then
built around the noise/pulse triggers, defining noise events and pulse events.

In order to select a clean sample of noise-only events, we apply the following
analysis cuts:

  1. (a)

reject time windows in which thermal pulses are triggered;

  2. (b)

reject time windows in which the maximum value of the baseline exceeds by five
times its own RMS, to reject both events developing on decay tails of previous
signal pulses and untriggered events featuring signals with significant
amplitude;

  3. (c)

reject time periods affected by instabilities of the detectors and by
earthquakes.

The most intense earthquakes, inducing instabilities in the bolometers
baseline, are removed during periodic quality checks of CUORE data. Less
intense seismic events are identified from the report provided by INGV. We
reject all seismic events with epicenter within $\simeq$50 km from LNGS with
local magnitude LM$\geq$1.0, all seismic events with epicenter in Italy and
with local magnitude LM$\geq$1.5, and all seismic events with epicenter abroad
of Italy (teleseisms) and detected by the INGV monitoring system. For each of
them, we reject a time period of ten minutes centered at the detection time
provided by INGV. The rejected time window is longer in the case of teleseisms
or earthquake swarms.

The frequency content of the CUORE detectors noise can be studied by applying
a fast Fourier transform (FFT) routine to noise-only events. Marine
microseisms are characterized by frequencies in the sub-Hz domain (Figure 6).
The FFT sensitivity to low-frequency components of the noise can be enhanced
by defining wide time windows for the detector events; for this analysis, we
set the windows length to 60 s. By applying a FFT routine on noise data over a
given time period we can build, for each detector, an average noise power
spectrum (ANPS), representing the distribution of noise in the frequency
domain. Since the contribution to the bolometer noise from marine microseisms
is expected in the sub-Hz domain, we focus on noise components with
frequencies below 1.4 Hz. This upper limit is set by a peak in the ANPS
generated by the PT operation. The PT-induced noise is expected to be
unaffected by the changes of the sea conditions, and therefore it is included
in the analysis as a reference. Figure 7 shows the comparison of ANPS acquired
by a CUORE detector during three different days: during quiet sea conditions,
during a storm in the Mediterranean Sea, and during a high-intensity
earthquake swarm with epicenter in central Italy. Several peaks appear at
frequencies below 1 Hz. While their position is not affected by the storm
development, their amplitude changes over time, increasing during the stormy
day. Conversely, the amplitude of the PT-induced peak is almost unaffected.
Figure 7 also shows that if time periods affected by high-intensity seismic
events are not properly rejected, they can dominate the low-frequency noise,
making it impossible to distinguish the effect of marine storms.

Figure 7: Comparison of ANPS acquired by one CUORE bolometer in three
different days: with and without storms in the Mediterranean Sea, and during a
high-intensity earthquake swarm.

In order to scan the evolution of the bolometers noise during the storm
development, we generate an ANPS each $\simeq$12 h. The integration of the
ANPS in a given frequency range $\nu$ provides the power of the noise
$P_{\nu}$ in that frequency interval. Since the position of the noise peaks is
stable over time, we can define time-independent integration intervals (listed
in Figure 8).

The relative variation of $P_{\nu}$ over time, with respect to a reference
period, provides a preliminary information of the sensitivity of the various
frequency components of the noise to changes of the marine activity. Therefore
we define the noise power ratio $R_{\nu}$:

$R_{\nu}=\dfrac{P_{i,\nu}}{P_{ref,\nu}}$ (2)

where $P_{ref,\nu}$ is the noise power of a frequency component $\nu$ during a
reference period of quiet sea activity and $P_{i,\nu}$ is the noise power of
the same frequency component in other time intervals $i$.

Figure 8 shows the comparison between the time evolution of the sea waves
height (combining the contributions from Adriatic and Tyrrhenian Seas) and the
time evolution of $R_{\nu}$ for various frequency components of the noise, for
two detectors placed at the bottom (Figure 8) and at the top (Figure 8) of a
tower of CUORE bolometers. The comparison shows that the low-frequency noise
of CUORE bolometers is excited when a storm develops in the Mediterranean Sea.
However not all the frequency components are affected in the same way: noise
at $\simeq$0.6 Hz is the most excited, while noise above $\simeq$0.9 Hz is
almost unaffected.

Figure 8: Comparison between the time evolutions of the sea waves height and
of the noise power ratio $R_{\nu}$ for various frequency components of the
noise, for two detectors placed at the bottom (a) and at the top (b) floors of
a CUORE tower.

###  5.2 Correlation between low-frequency noise and sea activity

To correlate the detectors low-frequency noise with marine microseisms we need
to evaluate a proxy of the sea activity $I_{S}$, which we define as the
integral over time of the sum of the wave amplitude of both Adriatic Sea
(VHM0A) and Tyrrhenian Sea (VHM0T):

$I_{S}=\int_{t_{i}}^{t_{f}}\left[\text{VHM0}_{A}(t)+\text{VHM0}_{T}(t)\right]dt$
(3)

where $t_{i}$ and $t_{f}$ are the start and stop time of each time period over
which the ANPS are generated. We associate to $I_{S}$ a systematic uncertainty
due to the fact that the timing of CMEMS data may not coincide with the
beginning/end of the 12 h long periods over which the detectors ANPS are
built. We define such systematic uncertainty as the sea activity at the
beginning and at the end of each time period over which the bolometers noise
is evaluated.

Figure 9 shows that the power $P_{\nu}$ of various frequency components of the
low-frequency noise of the two CUORE bolometers under study is linearly
correlated with the sea activity $I_{S}$. By performing a linear fit for each
frequency component of the noise, the angular coefficient $m_{\nu}^{rel}$,
normalized by the minimum value of the corresponding noise power $P_{\nu}$,
represents the relative variation of each noise component due to changes of
the sea activity with respect to a period of quiet marine condition.
Therefore, $m_{\nu}^{rel}$ quantifies the sensitivity of each noise component
to changes of the sea activity.

Figure 9: Noise power of five frequency components of the low-frequency noise
as a function of the sea activity, for two detectors placed at the bottom (a)
and at the top (b) floors of a CUORE tower.

Figure 10 shows the sensitivity profile of the low-frequency noise with
respect to changes of the sea activity. Noise components at $\simeq$0.6 Hz are
the most sensitive to variations of the sea activity, while above $\simeq$0.9
Hz the noise is almost unaffected to such environmental effects. The fact that
CUORE detectors respond maximally at 0.6 Hz is possibly a consequence of the
peculiar structure of the CUORE suspension system, which may feature a
resonant behaviour at $\simeq$0.5-0.7 Hz. Microseismic waves, with
characteristic frequencies mainly in the 0.1$\lesssim$$\nu_{sea}$$\lesssim$0.4
Hz range (Figure 6), could excite such resonant mode, and therefore induce
vibrations with corresponding frequencies to the detectors.

Figure 10: Sensitivity of the the low-frequency noise components to changes of
the sea activity for two detectors, at the bottom and at the top of a CUORE
tower.

##  6 Conclusions

Here we demonstrate for the first time that low-temperature macro-calorimeters
operated at $\simeq$10 mK can be sensitive to environmental vibrations induced
by marine microseisms, despite the sea being distant $\simeq$50-100 km from
the detectors position. We presented a novel multi-detector approach to
correlate environmental data about the Mediterranean Sea (provided by CMEMS),
the seismic activity at LNGS (provided by GIGS seismometer from INGV and
SEISMO from CUORE), and the response of a couple of CUORE low-temperature
calorimeters. We assessed that marine microseisms induce an increase of the
noise of CUORE detectors in the sub-Hz frequency range. Such noise is linearly
correlated with the sea waves activity reconstructed by CMEMS in two regions
of the Adriatic and Tyrrhenian Seas close to the Italian coastline. The
$\simeq$0.6 Hz component of the CUORE noise is the most sensitive to
variations of the marine activity, and it is possibly the outcome of the
excitation of a resonant mode of the CUORE suspension system by the marine
microseism-induced vibrations.

The highlighted dependence between sub-Hz noise and sea activity can play a
relevant role in limiting the energy resolution of macro-calorimeters, due to
the impracticability of effectively filtering away such low-frequency noise,
which belongs to the same frequency band of physics signals generated by
energy depositions in the detectors.

The marine microseismic activity detected by the CUORE detectors is common to
the entire LNGS underground facility, as supported by the combined detection
by both GIGS and SEISMO seismometers. As a consequence such source of
environmental noise can have relevant impact also on other cryogenic
experiments hosted at LNGS which are searching for rare events, like
$0\nu\beta\beta$ decay or dark matter interactions.

Acknowledgments This study has been conducted using E.U. Copernicus Marine
Service information, and data from the GIGS seismic station from INGV. We
thank the CUORE Collaboration for providing the data sample for the case study
and for helping to make this work possible. This study was supported by
Istituto Nazionale di Fisica Nucleare (INFN). The analysis reported in this
work makes use of DIANA data analysis and APOLLO data acquisition software
packages, which were developed by CUORICINO, CUORE, LUCIFER, and CUPID-0
Collaborations.

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