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\DOI{10.5802/crgeos.241}
\datereceived{2023-01-27}
\daterevised{2023-07-31}
\datererevised{2024-02-14}
\dateaccepted{2023-10-12}
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\dateposted{2024-05-22}
\begin{document}

\begin{noXML}

%\makeatletter
%\def\TITREspecial{\relax}
%\def\cdr@specialtitle@english{New Developments in Passive Seismic Imaging and Monitoring}
%%\def\cdr@specialtitle@french{Nouveaux d\'eveloppements en mati\`ere d'imagerie sismique passive et de surveillance}
%\makeatother

\title{Dynamic of seismic noise sources in the Mediterranean Sea:
implication for monitoring using noise correlations}

\alttitle{Dynamique des sources de bruit sismique en mer
M{\'e}diterran\'{e}e : implication pour le suivi de l'{\'e}volution
temporelle de la croute terrestre \`{a} partir de corr\'{e}lations de
bruit}

\author{\firstname{Laurent} \lastname{Stehly}\CDRorcid{0000-0002-1854-7157}\IsCorresp}
\address{Univ. Grenoble Alpes, Univ. Savoie Mont Blanc, CNRS, IRD, UGE, ISTerre, 38000 Grenoble, France}
\email[L. Stehly]{laurent.stehly@univ-grenoble-alpes.fr}

\author{\firstname{Estelle} \lastname{Delouche}\CDRorcid{0000-0002-4725-0256}}
\addressSameAs{1}{Univ. Grenoble Alpes, Univ. Savoie Mont Blanc, CNRS, IRD, UGE, ISTerre, 38000 Grenoble, France}
\email[E. Delouche]{estelle.delouche@univ-grenoble-alpes.fr}

\author{\firstname{Lisa} \lastname{Tomasetto}\CDRorcid{0009-0009-0705-1541}}
\addressSameAs{1}{Univ. Grenoble Alpes, Univ. Savoie Mont Blanc, CNRS, IRD, UGE, ISTerre, 38000 Grenoble, France}
\email[L. Tomasetto]{lisa.tomasetto@univ-grenoble-alpes.fr}

\author{\firstname{Pratul} \lastname{Ranjan}\CDRorcid{0000-0002-2482-3808}}
\addressSameAs{1}{Univ. Grenoble Alpes, Univ. Savoie Mont Blanc, CNRS, IRD, UGE, ISTerre, 38000 Grenoble, France}
\email[P. Ranjan]{patrul.ranjan@univ-grenoble-alpes.fr}

\shortrunauthors

\keywords{\kwd{Seismic noise}
\kwd{Microseisms}
\kwd{Autocorrelation}
\kwd{Monitoring}}

\altkeywords{\kwd{Bruit sismique}
\kwd{Micros{\'e}ismes}
\kwd{Autocorr{\'e}lation}
\kwd{Surveillance}}

\begin{abstract}
We study the dynamics of short-period (1--3~s) seismic noise across
Europe and its implication on the convergence speed of noise
auto-correlation coda waves. Our aim is not to describe the source of
the seismic noise with high spatial resolution, since this has already
been done by a number of previous studies. Instead, the goal of this
work is to study how the dynamics of the seismic noise affect the
possibility of monitoring the evolution of the crust, in particular the
temporal resolution and accuracy of the velocity change that can be
detected.

To that end, we perform a single station analysis at all available
European broadband stations in 2021 using a proxy that quantifies the
extent to which the frequency content of the noise wavefield is
stationary over time, independently of its amplitude variations. We
show that at short periods (${<}$3~s), the noise field in Europe is
dominated by surface waves coming from the north Atlantic ocean, with
also a significant contribution from the Adriatic and Aegean Seas in
southern Europe. The relative contribution of these two source regions
depends on the season, with the influence of the Adriatic and Aegean
Sea increasing in summer.

The interplay of these two sources regions creates lateral variations
in the properties of the seismic noise. Thus, the noise field is more
stable in northern Europe where the influence of the Atlantic Ocean
predominates, while along the Adriatic coast and around the Aegean Sea,
micro-seismic events lasting several hours are regularly detected,
especially in summer. This leads to strong lateral variation in the
convergence velocity of the coda waves, and thus in the accuracy and
temporal resolution of the velocity changes that can be detected in
Europe.
\end{abstract}


\begin{altabstract} 
Nous {\'e}tudions la dynamique du bruit sismique \`{a} courte p{\'e}riode
(1--3~s) \`{a} travers l'Europe et son implication sur la vitesse de
convergence des ondes de coda d'autocorr\'{e}lation du bruit. Notre
objectif n'est pas de d\'{e}crire la source du bruit sismique avec une
haute r\'{e}solution spatiale, puisque cela a d\'{e}j\`{a} \'{e}t\'{e} fait par un
certain nombre d'\'{e}tudes ant\'{e}rieures. Le but de ce travail est plut\^{o}t
d'\'{e}tudier comment la dynamique du bruit sismique affecte la
possibilit\'{e} de surveiller l'\'{e}volution de la cro\^{u}te, en particulier
la r\'{e}solution temporelle et la pr\'{e}cision du changement de vitesse qui
peut \^{e}tre d\'{e}tect\'{e}. \`{A} cette fin, nous effectuons une analyse d'une
seule station dans toutes les stations europ\'{e}ennes \`{a} large bande
disponibles en 2021 en utilisant un proxy qui quantifie la mesure dans
laquelle le contenu fr\'{e}quentiel du champ d'ondes de bruit est
stationnaire dans le temps, ind\'{e}pendamment de ses variations
d'amplitude. Nous montrons que sur de courtes p\'{e}riodes (${<}$3~s), le champ
de bruit en Europe est domin\'{e} par des ondes de surface provenant de
l'oc\'{e}an Atlantique nord, avec \'{e}galement une contribution
significative des mers Adriatique et \'{E}g\'{e}e dans le sud de l'Europe. La
contribution relative de ces deux r\'{e}gions sources d\'{e}pend de la
saison, l'influence de la mer Adriatique et de la mer {\'E}g\'{e}e
augmentant en {\'e}t{\'e}. L'interaction de ces deux r\'{e}gions sources
cr\'{e}e des variations lat\'{e}rales dans les propri\'{e}t\'{e}s du bruit
sismique. Ainsi, le champ de bruit est plus stable dans le nord de
l'Europe o\`{u} l'influence de l'oc{\'e}an Atlantique pr\'{e}domine, tandis
que le long de la c\^{o}te adriatique et autour de la mer \'{E}g\'{e}e, des
\'{e}v\'{e}nements microsismiques de plusieurs heures sont r\'{e}guli\`{e}rement
d\'{e}tect\'{e}s, en particulier en \'{e}t\'{e}. Cela entra\^{i}ne une forte variation
lat\'{e}rale de la vitesse de convergence des ondes coda, et donc de la
pr\'{e}cision et de la r\'{e}solution temporelle des changements de vitesse
qui peuvent \^{e}tre d\'{e}tect\'{e}s en Europe.
\end{altabstract}

\thanks{Real-time Earthquake Risk Reduction for a Resilient Europe
(RISE) (Grant agreement number 821115)}

\maketitle

\clearpage

\twocolumngrid

\end{noXML}

\section{Introduction}

In the last two decades, the advent of dense networks of seismic
stations and the use of seismic noise to reconstruct Green's functions
between station pairs have opened up new possibilities for studying the
internal structure of the Earth and its temporal evolution. Indeed,
several theoretical studies have established that the correlations of
random wavefields between two receivers yields the Green's function of
the medium between these two receivers, assuming that the wavefield is
equipartitioned (see for instance 
\citet{Weaver_2001,Wapenaar_2004,Roux_2005,Cdv_2006,Cdv_2006b,SanchezSesma_2006,Campillo_2006,Margerin_2011}).


This has led to a new interest in the study of seismic ambient noise.
Indeed, the possibility to recover the Green's function between
(ideally) any pair of stations has been widely and successfully used to
image the Earth's structure \citep{Shapiro_2004, Shapiro_2005,
Sabra_2005}, and to monitor changes in seismic wave velocity resulting
from the response of the Earth's crust to seismicity and tectonic
processes \citep{Brenguier_2008a, Chen_2010,
Rivet_2011,Zaccarelli_2011, Froment_2013, Soldati_2015, Wang_2019}, as
well as to environmental changes such as thermoelastic stress and
precipitation \citep{SensSchoenfelder_2006, Meier_2010,
Lecocq_2017,Clements_2018,Taira_2018, Poli_2020, Barajas_2021,
Vidal_2021,Berbellini_2021,Hillers_2015,Wang_2017,Mao_2022}.


The ideal case for retrieving Green's functions would be to have a
spatially homogeneous distribution of stationary noise sources and to
average the noise correlations over a sufficiently long time interval.
However, in practice, the long-period seismic noise comes from discrete
locations and the noise field is neither isotropic nor fully
equipartitioned. In other words, the ambient seismic noise does not
fully satisfy the assumptions of the theory. Indeed, at periods greater
than 1~s, the seismic noise is mainly generated by the interaction
between the atmosphere, the ocean and the solid Earth by different
mechanisms depending on the period considered, and it consists mainly
of surface waves with a smaller amount of body waves
\citep{Toksoz_1968,Ekstroem_2001, Landes_2010, Boue_2013,
Gualtieri_2014}.

In the 1--20~s period band, the seismic noise is dominated by two
distinct energy peaks, the primary and secondary microseisms, which are
observed globally. The primary microseism has periods similar to the
main swell (10--20~s) with a maximum energy at about 14~s. It results
from a direct interaction between the swell and the sea floor in
shallow water \citep{Hasselmann_1963}. The secondary microseism peak is
more energetic and has -on average- a dominant period around 7~s. It is
generated by the non-linear interaction of swell reflections near the
coast or by swells propagating in opposite directions in the deep ocean
that cause half-period (5--10~s) pressure variations
\citep{LonguetHiggins_1950,Hasselmann_1963,Ardhuin_2013}. In this
particular case, the pressure fluctuation in the water column does not
present an exponential decay with depth, making it possible to generate
seismic noise in deep water. For primary and secondary microseisms, the
complexity of the noise field is increased by lateral variations in
seafloor bathymetry and in the scattering properties of the crust that
affect the ocean-solid earth coupling and tend to randomise the
wavefield \citep{Saito_2010,Ardhuin_2018,Lu_2022}.


In Europe, the use of seismic noise correlations for tomographic and
monitoring studies has been supported by the development of permanent
networks of stations across the continent complemented by the
deployment of large and dense temporary networks such as IberArray and
Pyrope in the Pyrenees, Cifalps I\&II and AlpArray in the greater
Alpine region \citep{Diaz_2010,Chevrot_2014a,Zhao_2015,Hetenyi_2018,Paul_2022}.


Many authors have studied the origin of seismic noise in Europe in the
3--20~s period band.\unskip\break Several~approaches have been used to investigate the
sources of seismic noise on a continental scale using either distant
arrays distributed across Europe\unskip\break \citep{Essen_2003,
Chevrot_2007,Juretzek_2016} or even seismic arrays on different
continents \citep{Friedrich_1998,Stehly_2006, Retailleau_2017}. Other
studies have instead focused on the origin of the noise at specific
networks and locations \citep{Pedersen_2007, Beucler_2015,
Tanimoto_2015, Craig_2016, Lepore_2020, Guerin_2022}. On the other
hand, \citet{Lu_2020} used a decade (2011--2019) of data collected at all
European broadband stations to map lateral variations of the noise
field properties. All these studies indicate that the north Atlantic
ocean, in particular south of Greenland and off the coast of the
British Isles and Norway, are the main sources of surface waves in the
3--20~s period band, with additional contributions from the Mediterranean
coast (see for example \citet{Evangelidis_2012, Lu_2022}).

Further development of imaging and monitoring methods based on noise
correlations can be supported by a better understanding of the noise
field and its variations in time and space. In particular, most studies
to date have focused on the origin of microseisms at 3--20~s, and
little is known about the generation of seismic noise at shorter
periods (1--3~s). \citet{Gimbert_2015} and \citet{Gal_2015} have shown
that seismic noise in the 0.5--2~s period band is mostly caused by local
wind-waves occuring less than 2000 km of the seismic station rather
than by the ocean swell like at periods greater that 3~s. Using three
components array analysis at a dense array located in Pilbara, Autralia
\citet{Gal_2017} found that Rayleigh waves are more energetic than Love
waves between 1.5--3~s, Rayleigh waves coming from convex coastlines, and
Love waves from seafloor sedimentary basins. In addition to allowing
the study of velocity changes associated with earthquakes
\citep{Maeda_2010, Zaccarelli_2011, Soldati_2015}, the 1--3~s period
band is of particular interest for tracking changes in groundwater
levels, providing a unique opportunity to monitor the response of the
crust to the hydrological cycle \citep{Poli_2020,Barajas_2021}.

Unlike previous studies of the seismic noise in Europe, we do not aim
at investigating the origin of the seismic noise per se. Instead, our
aim is to study how lateral variations of the noise field affect the
speed of convergence of the noise auto-correlations coda waves and thus
the possibility of monitoring velocity changes in the Earth's crust.
Indeed, we may wonder how the temporal resolution of monitoring studies
is affected by the dynamics of seismic noise sources? In particular, at
the European scale, do autocorrelation coda waves converge everywhere
at a similar rate, or are there lateral variations that are due either
to different scattering properties of the crust or to the dynamics of
the seismic noise sources?


To answer these questions, we first study the origin of the seismic
noise and its seasonal variations around 2 and 7~s of periods. We then
introduce a proxy to quantify whether the seismic noise is stationary
(Section~\ref{sec:dyn}). This allows us to characterise the dynamics of
the short-period seismic noise at the European scale. This makes it
then possible to study the relationship between the dynamics of the
seismic noise and the convergence speed of the auto-correlations coda
waves (Section~\ref{sec:ac}). We highlight the influence of seasonal
variations of the contribution of the Atlantic Ocean and of the
particular dynamics of the Adriatic and Aegean seas that influence the
reconstruction of coda waves. Finally, this allows us to show that the
temporal resolution and the accuracy with which it is possible to
measure velocity changes at short periods exhibit lateral variations
across Europe. Our results shows that there is a strong contrast
between southern and northern Europe, depending on whether the
influence of the Adriatic/Aegean Sea or the Atlantic Ocean dominates.


\section{Average noise wavefield in Europe}\label{sec:av} 
\subsection{Data used}
 
We use all broadband stations with publicly available data in Europe in
2021 located between ${-}$5 and 31 degrees of longitude and between 34
and 53 degrees of latitude. To complete the stations coverage in the
Pyrenees, we included the temporary networks Pyrope (X7, 2011--2013)
and IberArray (IB, 2009--2011). We thus use data from 47 European
networks and 1960 stations for which we have at least 300 days of data.
The stations map is presented in Figure~\ref{fig:sta_map}. We represent with
red triangles the stations with data in 2021, with blue triangles the
IberArray network and with yellow triangles the Pyrope network.


\begin{figure*}
{\vspace*{2pt}}
\includegraphics{fig01}
{\vspace*{2pt}}
\caption{Map of the broadband seismic networks used in this study
including permanent networks for which we use continuous noise records
from 2021 (red triangles), the IberArray network (2009--2011, blue
triangles) and the Pyrope network (2011--2013, yellow
triangles).\label{fig:sta_map}}
{\vspace*{2pt}}
\end{figure*}


\subsection{Median level in Europe}
To study the average noise level across Europe and its seasonal
variations, we use an approach inspired by \citet{McNamara_2004} by
analysing continuous waveform data without removing any signal such as
earthquakes or instrumental glitches. We processed the vertical records
of each station day by day. Each daily record was band pass filtered
between 0.5~s and 300~s, corrected from the instrumental response,
decimated to a sampling frequency of 5~Hz. For each station and for each
day of data we compute Power Spectral Densities (PSD) with a sliding
window of one hour with no overlap. A 10\% cosine taper is applied to
both ends of each 1~h segment to suppress the effect of side lobes
in the Fast Fourier Transform. The PSD of each 1~h segment is
obtained from the FFT of the seismic data. Finally the PSDs are
converted into decibels with respect to  velocities.

To obtain the median noise level at each station as a function of the
season, we compute for each station the median noise level for
January--February (winter) and July--August (summer). We remind the
reader that we used data from 2009--2013 from the IBerArray and the
Pyrope temporary network in the Pyrenees, and from 2021 elsewhere (see
Figure~\ref{fig:sta_map}). We use specifically the median rather than
mean to reduce the contribution of large amplitude events such as
earthquakes and glitches. The median noise level obtained during the
winter and the summer at 2~s and 7~s of periods are presented in Figure
\ref{fig:psd}. The noise level depends mainly on the distribution and
energy of noise sources and on the attenuation of seismic wave during
their propagation. It is also influenced by the scattering of waves by
crustal heterogeneities and topography \citep{Wu_1985, Snieder_1986,
Levander_1990}. In addition, sedimentary basins affect the wave field
in complex ways, amplifying certain frequency ranges
\citep{SanchezSesma_1988,Boue_2016, Gisselbrecht_2023}.

\begin{figure*}
\includegraphics{fig02}
\caption{Spatial distribution of the median noise level at 2~s and 7~s
of period in January (left) and July (right).\label{fig:psd}}
\end{figure*}

As shown on the lower panels in Figure~\ref{fig:psd}, at 7~s in January
we observe a large-scale variation of the median seismic noise level
across Europe. The noise level is maximum on the west coast of France
(${-}$115~dB) and it decreases progressively towards the southeast, the
minimum being reached in Greece (${-}$140~dB). This noise level gradient is
consistent with a dominant noise source located in the north Atlantic
ocean as it was previously observed by various studies 
\citep{Friedrich_1998,Stehly_2006,Chevrot_2007,Kedaretal2008,Retailleau_2017}.
 
On the other hand, during the month of July we observe an almost
homogeneous noise level in\unskip\break Europe, with a median level of ${-}$140~dB. This
illustrates that at 7~s of period the noise level in Europe varies
strongly depending on the season, the noise level being higher during
the winter in the northern hemisphere when the wave height is larger in
the north Atlantic ocean.


We observe that the seismic noise level differs strongly at 2~s period,
indicating that the distribution of seismic noise source is not the
same at 2~s and 7~s of period (Figure~\ref{fig:psd}). In January at 2~s of
period, the noise level is maximum on the coast reaching ${-}$125~dB on
the west coast of France, southeast France, and in southern Greece.
Conversely, the noise level decreases towards the East (and not towards
the southeast as it was the case at 7~s of period) when moving away from
the Mediterranean and Atlantic coasts. Thus, the minimum median noise
level is reached in Romania (${-}$145~dB). This indicates that the
seismic noise is mainly generated locally near the Atlantic and
Mediterranean coasts.

Just as at 7~s of period, the median noise level at 2~s exhibits clear
seasonal variations, the noise level decreasing in the summer. However
the lateral variation of the seismic noise level remains similar during
the summer and the winter. Thus in July the median noise level range
reaches ${-}$135~dB in the west part of France and Spain and decreases
towards the East becoming less than ${-}$145~dB past Switzerland.

In addition to this West--East gradient, we note that in Italy the noise
level is larger towards the Mediterranean and the Adriatic coast (about
${-}$140~dB) than in the Apennines (${-}$147~dB). 
This observation is compatible
with a generation of seismic noise along the coasts. Similarly, high
noise levels are also observed in Greece (for example, the Cyclades).


To summarise, the noise level maps show that the origin and the
seasonal variations of the micro-seismic noise differ at 2~s and 7~s of
period. At 7~s, the median noise level is consistent with a dominant
noise source located in the north Atlantic ocean, while in the summer
the homogeneity of the noise level indicates a distant origin, probably
with a significant contribution of the southern hemisphere. On the
other hand, there is no clear local maximum near the coasts that would
indicate a local coupling. This seasonal variation implies that the
quality of the Green function retrieved from cross-correlation may
differ during the summer and the winter. Hence for tomographic studies,
simultaneously using data recorded during winter and summer is a common
way to improve the quality of the traveltime measurements performed on
noise correlations. For monitoring applications, it implies that the
precision of the  $\updelta v/v$  measurements may depend on\break the season.

Conversely, at 2~s of period, the lateral variations of the seismic
noise are similar in January and July suggesting that the sources are
always located in the same areas. In January as well as in July the
maximum noise levels are reached in specific regions along the coasts,
hence indicating local coastal noise sources. This is consistent with
theoretical expectations: at 2~s of period the primary and secondary
mechanism can generate seismic noise in shallower water than at 7~s
\citep{LonguetHiggins_1950}.


\subsection{Dominant periods in the 2--10~s period band}

Figure~\ref{fig:per} shows a spatial map of the dominant period of the
seismic noise measured in the 2--10~s period band corresponding to the
secondary microseism. It represents the period at which the median PSD
of the seismic noise record is maximum. The median PSD is defined as
the median of the PSDs computed with a one-hour sliding window. If the
noise originated from a single region, and assuming a constant quality
factor across Europe, the dominant period of the noise should increase
smoothly with distance from the source \citep{Lu_2022}. However, this
is not what we observe in either January or July (Figure
\ref{fig:per}) between 2--10~s, the seismic noise is influenced by two
distinct source regions located in the north Atlantic and in the
south-east Mediterranean. Thus the spatial distribution of the dominant
period results from the interaction between these two source areas.
This interaction is itself dependent on the season.

\begin{figure*}
\includegraphics{fig03}
\caption{Spatial distribution of the dominant period of seismic noise:
period at which the median PSD of the seismic noise is maximum in (a)
January  and (b) July. The median PSD is defined as the median of PSDs
computed with a sliding window of one hour that is shifted by
5~min.\label{fig:per}}
\end{figure*}


In January (Figure~\ref{fig:per}a), the dominant period is 6~s in
northern Europe (France, Germany, Switzerland). It decreases
progressively towards the south-east to about 5~s in northern Italy.
This would be consistent with a dominant source located in southeastern
Europe. However, we note an abrupt change between northern Italy and
southern Italy where the dominant period is less than 3.5~s. In Greece
values lower than 3~s are observed around the Aegean Sea. These
observations are consistent with a dominant noise source in the
south-east Mediterranean explaining the north-west/south-east gradient
of the dominant period, with moreover a short-period noise source close
to the southern Italy coastline explaining the abrupt change observed
in Italy.

In July, the spatial distribution of the dominant period is completely
different (Figure~\ref{fig:per}b). We observe a shift toward shorter
periods, with a dominant period of 5~s throughout Europe with 3
exceptions: in southern Greece, near Galicia (Spain) and at several
stations on the Italian, French and Spanish coasts, the dominant period
is less than 3.5~s. This suggests that short period microseismic noise
is generated locally close to in these areas.

These observations have two implications for monitoring studies: the
seasonal behaviour of the seismic noise does not guarantee that noise
correlations coda waves converge to a similar waveform in summer and
winter and as we will see in the next sections the coda of correlations
in coastal regions dominated by a 2~s period in summer converges more
slowly.

\section{Dynamic of the noise wavefield in Europe in the 0.5--0.7~Hz
frequency band} \label{sec:dyn}

In the previous section we presented the noise level in Europe at 2~s
and 7~s and the dominant period of seismic noise records. In the present
section we study the dynamics of the seismic noise and its temporal
evolution specifically in the 0.5--0.7~Hz frequency band. We choose
specifically to focus on this frequency band since it is often used to
monitor the temporal evolution of the crust using seismic noise
correlations in particular for tracking groundwater level change
\citep{Poli_2020, Barajas_2021}. Moreover, little is known about the
generation of seismic noise in the period band, since previous studies
on the secondary micro-seismic noise tend to focus on the 3--20~s
period band. We use only European networks for which we have continuous
record in 2021, and we thus discard the data of the IberArray and
Pyrope experiments.

\subsection{Quantifying the stationarity of the wavefield} 

Our goal is to quantify the impact of the dynamic of the seismic
ambient noise on the convergence of coda waves obtained from noise
correlations. To that end, in this section we define a proxy to
quantify whether the seismic noise is stationary or not. We look for a
proxy that does not depend on the amplitude of the seismic noise, since
a change of noise level per se does not modify the waveform of the
correlations. Instead, we design a proxy which depends only on the
temporal evolution of the frequency content of the seismic noise.

To define this proxy, we first compute at each station PSDs with a 
30~min sliding window which is shifted by 5~min. These
30-min PSDs are then used to quantify the temporal evolution of the
frequency content of the seismic noise over several time scales ranging
from 1 day to 30 days, independently of the amplitude of the seismic
noise. We thus define a stationarity coefficient (SC) obtained in the
following way:
\begin{itemize} 
\item Each 30~min PSD is smoothed over frequency using a moving
average gaussian filter having a width of 0.05~Hz. We thus study
specifically the first order variations of the frequency content of the
noise.
\item Each 30~min PSD is then normalised by its energy in the
target frequency band, i.e.~0.5--0.7~Hz.
\item At each date, we define the current PSD as the PSD computed with
a 30~min window that ends at the current date, and the $N$-days PSD as
the PSDs averaged over the previous $N$-days, with $N$ ranging from 1 day
to 30~days. We then compute the normalised correlation coefficients of
the current PSD and each $N$-days PSD. We note that this correlation
coefficient is independent of the noise level and depends only on
temporal evolution of the frequency content of the noise. 
\item Finally, we define the stationarity coefficient for each 
30~min window as the lowest coefficient of correlation between the
current and the $N$-days PSDs. A stationarity coefficient close to 1,
indicates that the current 30~min PSD is similar to the PSDs
averaged over the previous $N$ days, i.e.\ that the noise is stationary
over all time scales. A value close to 0 indicates that the current PSD
differs strongly from at least one of the PSD averaged over the $N$
previous days, i.e.\ that the frequency content of the noise is not
stationary on at least one time scale. 
\end{itemize}


\subsection{Stationarity coefficient at a single station in Italy}

Figure~\ref{fig:sc} shows as an example the stationarity coefficient
measured in the 0.5--0.7~Hz frequency band at the station NRCA located
close to Norcia in Italy from June 6th to June 30th. As shown on the
upper panel, the stationarity coefficient typically varies between 0.96
and 1 which reflects the usual variability of the frequency content of
the seismic noise. In addition to these variations, we observe several
events on June 14, 15, 18 and 30 during which the stationarity
coefficient drops to values below 0.94 for a few hours.

\begin{figure*} 
{\vspace*{4pt}}
\includegraphics{fig04}
{\vspace*{4pt}}
\caption{(Left) Map showing the location of the NRCA station located in
Norcia, Italy.  (Right, upper panel) Stationarity coefficient measured at the station
NRCA in the 0.5--0.7~Hz from june 6th to June 30th. (Right, lower panel) Spectrogram in dB
measured at the station NRCA in the 0.05--1~Hz frequency band on the same
date. The 0.5--0.7~Hz frequency band where the stationarity coefficient
is measured is shaded in gray. The dates of type I and type II events
are indicated by red and white marks.\label{fig:sc}}
{\vspace*{4pt}}
\end{figure*}


Looking at the spectrogram presented on the lower panel in Figure
\ref{fig:sc}, we can correlate changes in the stationarity coefficient
with changes of the frequency contents of the noise. We first observe
that in central Italy, the seismic noise has a maximum of energy
between 0.2 and 0.4~Hz which corresponds to the secondary
microseismic peak. This peak of energy is continuous in time. Above
0.4~Hz,---apart from particular events---the energy of the noise
decreases continuously with frequency. In addition to this average
behavior, we observe two kinds of microseismic events:
\begin{itemize}
\item The first type of events are characterised by a clear increase
($\sim$5--10~dB) of the noise level above 0.4~Hz. This occurs on June
14, 15, 22, and 30. These events modify the decay of the noise level
with frequency measured between 0.5 and 0.7~Hz, and are thus
associated with a drop of the stationarity coefficient which become
less than 0.94 (Figure~\ref{fig:sc} upper panel). 
\item On June 18th we observe a second kind of event: a local maximum
of energy appears between 0.5 and 0.8~Hz, the noise level remaining in
the usual range. This type of event, characterized by a first order
change in the shape of the spectrum but without a significant change in
noise level, is associated with a sharp drop in stationarity
coefficient which become less than 0.9. 
\end{itemize}

This example illustrates that the stationarity coefficient computed in
the 0.5--0.7~Hz allows us to distinguish the usual fluctuations of the
frequency content of the seismic noise ($SC >0.96$) from discrete
events lasting a few hours ($SC < 0.94$) corresponding to either (1)
microseismic events characterized by a sharp increase in the noise
level between 0.4--0.6~Hz, or (2) to a first order change in the shape
of the\break spectrum.



\subsection{Stationarity coefficient maps for two particular events} 

In this section we quantify the spatial extent of the noise wavefield
perturbations that were introduced in the previous section. We would
like to know if they are detected at the scale of Europe, or if on the
contrary they are located in a particular region. To that end, we look
at the spatial distribution of the stationarity coefficient for the
events of June 30th and June 18th that were discussed in the previous
section.

\subsubsection{Stationarity coefficient map for the June 30 event}

The first event that occurred on June 30th was detected along the
Adriatic coastline as shown in Figure~\ref{fig:nsc_map1}. The lower
panel in Figure~\ref{fig:nsc_map1} shows the seismic noise recorded at
the station IV.NRCA located in central Italy (see Figure~\ref{fig:sc})
filtered in the 0.5--0.7~Hz frequency band. The time series runs from
June 29 to July 2. The amplitude of the seismic noise increases by a
factor of 3 from June 30 to July 1 compared to the noise level of June
29th. This change in amplitude observed in the time domain is also
visible in the spectrogram computed at the same station (Figure
\ref{fig:nsc_map1}, third panel): in addition to the secondary\unskip\break 
microseismic peak visible at 0.2--0.4~Hz, an increase in energy is
observed between 0.4 and 0.7~Hz from June 30 to July 2.

\begin{figure*}
{\vspace*{6pt}}
\includegraphics{fig05}
\caption{Detail of the June 30 microseismic event. (a) The spatial
distribution of the stationarity coefficient measured between 0.5 and
0.7~Hz on June 30, averaged from 6:00 a.m.\ to 9:00 a.m. (b) Map of the
relative change in the percentage of the average noise level on June 30
between 3:00 a.m.\ and 9:00 a.m.\ compared to the average noise level of
the last 10~days. (c) Spectrogram in dB computed at the station NRCA
located in central Italy from June 29 to July 2 with a sliding window
of 30~min shifted by 5~min. (d)~Vertical noise record at the
station NRCA filtered between 0.5 and 0.7~Hz from June 29 to July
2.\label{fig:nsc_map1}}
{\vspace*{5pt}}
\end{figure*}

In order to see which European stations are affected by this event, we
present in Figure~\ref{fig:nsc_map1}a, the value of the stationarity coefficient of June
30, 2021 averaged between 3 to 9 a.m. We note that over the whole of
Europe the stationarity coefficient is greater than 0.97 except around
the Adriatic Sea, in particular in Italy and Slovenia where we obtain
values lower than 0.95. This indicates that this event originates from
the Adriatic Sea.

This event is also associated with an increase in noise level between
0.4 and 0.7~Hz. Figure~\ref{fig:nsc_map1}b shows the difference between the measured
noise level measured on June 30, 2021 between 3:00--9:00~a.m.\ and the
noise level averaged over the past 10~days. This difference is
expressed as a percentage. Across Europe the noise level is similar on
June 30 and the previous 10 days, with the exception of the stations
located around the Adriatic Sea in Italy and Slovenia where the noise
level increases by more\break than~3\%.

To summarize, this microseismic event lasted almost 2 days and induced
a change in noise level and in the frequency content of the noise
detectable locally around the Adriatic Sea in Italy and Slovenia, but
not elsewhere in Europe.


\subsubsection{Stationarity coefficient map for the June 18 event}

The second event occurred on June 18th around 4 p.m. In contrast to the
previous example, it is not associated with a significant change in the
amplitude of the noise level at station IV.NRCA (Figure
\ref{fig:nsc_map2}, bottom panel). As shown in the spectrogram in
Figure~\ref{fig:nsc_map2}, usually between 0.6 and 0.8~Hz, the noise
energy decreases with frequency, except on June 18 when a local maximum
of energy is observed. However, the absolute noise level varies little,
the noise level being about ${-}$135~dB on June 18 compared to ${-}$140~dB
on the other days.


\begin{figure*}
{\vspace*{6pt}}
\includegraphics{fig06}
\caption{Detail of the June 18 microseismic event. (a) The spatial
distribution of the stationarity coefficient measured between 0.5 and
0.7~Hz on June 18, averaged from 13:30 to 16:30 a.m. (b) Map of the
relative change in the percentage of the average noise level on June 30
between 10:30 and 16:30~a.m.\ compared to the average noise level of the
last 10 days. (c) Spectrogram in dB computed at the station NRCA located
in central Italy from June 17 to June 20 with a sliding window of 
30~min shifted by 5~min. (d) Vertical noise record at the
station NRCA filtered between 0.5 and 0.7~Hz from June 17 to\break June
20.\label{fig:nsc_map2}}
{\vspace*{5pt}}
\end{figure*}


This change in the shape of the noise spectrum, induces a decrease in
the stationarity coefficient measured on the Adriatic coast of Italy as
shown in Figure~\ref{fig:nsc_map2}a. Elsewhere in Europe, the noise is
stationary, the stationarity coefficient remaining above 0.96 except
around the Aegean Sea. However, this event is not associated with a
significant change in noise levels, so that at the European stations
the noise level is similar on June 18 and during the previous 10 days
(Figure \ref{fig:nsc_map2}b). This illustrates the \mbox{stationary}
coefficient allows detecting events that are not clearly visible on the
absolute noise level but that are nevertheless likely to affect the
noise correlations\break waveform.




\subsection{Stationarity of the noise field at the scale of Europe}

In this section, we seek to quantify whether the noise wavefield is
stationary at the scale of Europe. In particular, we wish to identify
lateral variations in the dynamics of the seismic noise wavefield that
could affect seismic waves velocity variations measurements ($\updelta
v/v$) obtained from seismic noise correlations.

On Figure~\ref{fig:ns}, we present the percentage of time when the
stationarity coefficient is less than 0.98 in the 0.5--0.7~Hz frequency
band during the months of January (left panel) and July (right panel).
First of all, we observe larger values in July than in January
indicating the seismic noise is more unstable in summer than in winter.
In January the wavefield is extremely stable in the north of the Alps,
especially in France, Germany, Holland and Romania. On the contrary,
the stationarity coefficient is lower than 0.98 more than 20\% of the
time around the Aegean Sea and in Italy along the Mediterranean and
Adriatic coasts. This means that there is a particular dynamic in the
Aegean and Adriatic seas generating \mbox{microseismic} events that are
detected between 0.5 and 0.7~Hz. The fact that these two seas are
almost closed areas may explain this particular dynamic by favouring
coastal reflections.


\begin{figure*}
{\vspace*{4pt}}
\includegraphics{fig07}
{\vspace*{3pt}}
\caption{Percentage of time where the stationarity coefficient is less
than 0.98 in January 2021 (left) and August 2021 (right) in the 0.5--0.7~Hz
frequency band.\label{fig:ns}}
{\vspace*{3pt}}
\end{figure*}



This contrast between Italy, Greece and the rest of Europe is more
significant in July (Figure~\ref{fig:ns}, right panel). The stationarity
coefficient is below 0.98, more than 30\% of the time around the Aegean
Sea, the Adriatic Sea and in the south of France along the
Mediterranean coast. Conversely, few events are detected elsewhere in
Europe.

This indicates that there is a particular dynamic off the southern
coast of Europe that generate high frequency (${>}$0.4~Hz) microseismic
noise, especially in the Adriatic and Agean seas that are enclosed
spaces. These high-frequency events are visible mainly along the
southern coastline of Europe, and attenuate rapidly so that they are
not detected further away on the continent. The number of detected
events is larger during the summer than during the winter
(Figure~\ref{fig:ns}). It is difficult to say whether this is because
microseismic noise coming from the north Atlantic has less energy in
summer than in winter (Figure~\ref{fig:psd}) which reveals the dynamics of
the Mediterranean, or whether the Mediterranean is indeed more active
in summer than in winter.



\section{Dynamic of seismic noise and convergence of auto-correlations coda waves}
\label{sec:ac}

Central Italy and Greece are amongst the most seismically active areas
in Europe so that there is a particular interest to follow the
spatial-temporal evolution of the mechanical properties of the earth's
crust related to the seismic cycle in these regions. Seismic noise
(auto)-correlations coda waves offers a unique opportunity to measure
the evolution of seismic wave velocity ($\updelta v/v$) over time
\citep{Brenguier_2008a}. Measuring the $\updelta v/v$ on several
frequency bands allows in theory to measure the changes at different
crustal depths. However, in southern Europe, above 4~s of period,
seasonal variations in the distribution of noise sources create
apparent velocity variations that are strong enough to mask the
dynamics of the crust. Thus several studies such as
\citet{Poli_2020,Barajas_2021} focus specifically on the 1--2~s period
band. Measuring the $\updelta v/v$  at different lapse-time makes it then
possible to assess at least qualitatively the depth of the detected
changes in the crust \citep{Obermann_2013a,Obermann_2014,Poli_2020}.
\looseness=1

To monitor the temporal evolution of the medium using seismic noise
correlation coda waves, ideally we would like the noise sources to be
stable over time so that changes in the coda would reflect only changes
in the medium and would not be biased by changes in the distribution of
the noise sources. However, we have seen that between 1--3~s the seismic
noise field exhibits seasonal variations and that moreover microseismic
events lasting several hours up to a few days are regularly detected
around the Adriatic and the Aegean Sea. They can represent up to 30\%
of the records around the Adriatic coast.

We now quantify the impact of these microseismic events on the
convergence speed of noise correlations coda waves. In other words, we
investigate whether the dynamics of the noise affect the temporal
resolution at which changes can be detected in the crust. To monitor
the temporal evolution of the crust, the most common approach is to
evaluate the relative change in velocity over time by comparing coda
waves of a reference correlation with a set of correlations computed
with a sliding window of\break $N$-days.


Noise correlations coda waves emerge from a constructive averaging
process, so that the signal-to-noise ratio of the coda waves depends on
the amount of data used to compute the correlations \citep{Sabra_2005,
Weaver_2005b}. \citet{Weaver_2011}, have shown that when the stretching
method is used to infer velocity changes, the root mean square of the
errors of the estimate of the relative velocity change between a
reference correlation and an \mbox{$N$-days} (auto)correlations is given by:
{\begin{eqnarray}\label{eq1}
\mathrm{rms}(\updelta v/v) = \frac{\sqrt{1-C^{2}}}{2C}  \sqrt{\frac{6
\sqrt{\frac{\uppi}{2}}T}{\omega_{c}^{2}(t^{3}_{2}-t^{3}_{1})}},
\end{eqnarray}}\unskip
where $C$ is the correlation coefficient between the reference and the
$N$-days correlation, $T$ is the inverse of the frequency bandwidth,
$\omega_{c}$ the central pulsation, $t_1$ and $t_{2}$ are begin and end
time of the coda window analysed. Hence, the accuracy of the $\updelta
v/v$ measurements increases with the correlation coefficient between
the reference and the $N$-days correlations. This correlation coefficient
$C$ depends on several factors, amongst which the amount of data used
to compute the correlations, the dynamic of the seismic noise
wavefield, the attenuation and scattering properties of the medium.


To quantify the precision of the $\updelta v/v$   measurements, we study
how $C$ varies spatially when considering 1-day, 3-days and 20-days
auto-correlations. We study specifically the 2--3~s period band which is
particularly interesting for monitoring studies of southern Europe,
longer periods measurements being contaminated by seasonal changes of
the source. We consider specifically auto-correlations to avoid any
influence of varying inter-station distance. We study separately the
convergence of autocorrelations computed at each European station in
summer (July--August) and winter (January--February), and we consider two
different time windows in the coda: 5--25~s which correspond to the
beginning of the coda and to a single scattering regime and 20--40~s
where coda waves are closer to a multiple scattering regime.


Specifically, for each station, we compute daily auto-correlations in
summer and winter. We did not apply any temporal or spectral
normalization to the noise records as our aim is not to discuss the
effect of processing on the convergence of the auto-correlations. The
daily auto-correlations are normalized to one and then stacked to
obtain $N$-day correlations. This normalization reduces the contribution
of the most energetic days. For each season, we define a reference
auto-correlation that is the correlations averaged over the considered
season (2 months). To evaluate the average correlation coefficient
between $N$-days auto-correlations and the reference, we select randomly
$N$ daily auto-correlations that are then normalized to one and stacked
to obtain an $N$-days auto-correlation. We then compute the correlation
coefficient between this $N$-days auto-correlation and the reference
auto-correlation for two different time windows: 5--25~s and 20--40~s that
may typically be used for monitoring studies. This procedure is
repeated 10 times and we average the result to obtain the average
correlation coefficient between $N$-days auto-correlations and the
reference. Here we show the result obtained for daily auto-correlations
($N=1$), 3-days ($N=3$) and 20-days auto-correlations ($N=20$).


\subsection{Results for the 5--25~s time window}

We present the results obtained for the 5--25~s (beginning of the coda)
and the 20--40~s time windows in Figures~\ref{fig:cmap_5_25s}
and~\ref{fig:cmap_20_40s}, respectively. The bottom panel of Figure
\ref{fig:cmap_5_25s} shows an example of auto-correlation computed at
station IV.NRCA and filtered between 2~s and 3~s period, with the 2--25~s
coda window shaded in yellow. We note immediately a strong correlation
between the results presented in Figures~\ref{fig:ns} 
and~\ref{fig:cmap_5_25s}a,b: the average correlation coefficients
calculated between daily auto-correlations and the reference are
strongly correlated to the percentage of time where the stationarity
coefficient is less than 0.98 (Figure~\ref{fig:ns}). This is true for
the winter (Figure~\ref{fig:cmap_5_25s}a) and in summer
(Figure~\ref{fig:cmap_5_25s}b). In winter, the average correlation
coefficient is close to 1 in France, Germany, the Netherlands and
Romania, where the stationarity coefficient is greater than 0.98 more
than 95\% of the time. Conversely, around the Adriatic Sea, the coda of
daily auto-correlations differs from the reference and the correlation
coefficients are around 0.7 in Italy and 0.5 in Slovenia.

\begin{figure*}
\includegraphics{fig08}
\caption{Average correlation coefficient between one day
auto-correlations and a reference averaged over two months obtained in
the 2--3~s period band and for the time window 5--25~s (a) in
January--February and (b) in July--August. (c), (d), (e), (f) are
similar to (a) and (b) but for 3 and 20-days auto-correlations. (g)
Example of an auto-correlation at the Italian station NRCA filtered in
the 2--3~s period band and averaged over one year (2021). The 5--25~s
time window that is studied here is shaded in
yellow.\label{fig:cmap_5_25s}}
\end{figure*}

\begin{figure*}
\includegraphics{fig09} 
\caption{Average correlation coefficient between one day
auto-correlations and a reference averaged over two months obtained in
the 2--3~s period band and for the time window 20--40~s (a) in
January--February and (b) in July--August. (c), (d), (e), (f) are similar
to (a) and (b) but for 3 and 20-days auto-correlations. (g) Example of
an auto-correlation at the Italian station NRCA filtered in the 2--3~s
period band and averaged over one year (2021). The 20--40~s time window
that is studied here is shaded in yellow.\label{fig:cmap_20_40s}}
\end{figure*}



In summer, we observe a contrast between the Mediterranean coast and
the rest of Europe: the average correlation coefficients are close to 1
everywhere in Europe except along the Mediterranean and Adriatic coast
where we observe correlation coefficients between 0.2 and 0.7. This
result is directly correlated with the stationarity coefficient
analyses presented in Figure~\ref{fig:ns}: the areas where high
frequency microseismic events are detected are those where the daily
auto-correlations coda waves differ the most from the reference.


Considering 3-day autocorrelations, the correlation coefficient becomes
more spatially homogeneous in winter and summer
(Figure~\ref{fig:cmap_5_25s}c,d). However, we still observe the imprint
of the dynamics of noise sources on the convergence speed of the
auto-correlations coda waves: the mean correlation coefficient between
the 3-days correlations and the reference are close to 0.8 in Italy and
around the Aegean Sea and greater than 0.9 further north. In summer
correlation coefficients are lower, especially near the Mediterranean
and Adriatic coasts. In other words, the noise wavefield is less
stationary during the summer than the winter (Figure~\ref{fig:ns})
which slows down the convergence of the auto-correlations coda waves.
On the other hand with 20-days autocorrelations, the correlation
coefficient are close to one everywhere in Europe whatever the season
(Figure~\ref{fig:cmap_5_25s}e,f).



\subsection{Results for the 20--40~s time window}



As we go into larger lapse-time, coda waves are more scattered by the
medium heterogeneities, so that we expect to lose gradually the imprint
of the source. This could reveal the influence of the later variations
of the crust on the convergence speed of the coda waves. \citet{Lu_2020}
have shown that the wavefield is more random in the Alps which
constitute a highly heterogeneous medium. However, as shown in
Figure~\ref{fig:cmap_20_40s}, we do not observe a clear correlation\unskip\break 
between the convergence of the coda waves and the geology: despite the
Earth's crust in the Alps and the Apennines is thought to be highly
heterogeneous, it does not improve significantly the convergence of the
coda waves at least in the 20--40~s lapse time window.

On the other hand, the influence of the dynamic of the seismic noise
wavefield is still clearly visible and is two-fold.  Firstly, the
convergence of the auto-correlation coda waves depends strongly on the
season. Considering 3 days or 20-days auto-correlations
(Figure~\ref{fig:cmap_20_40s}c--f), the correlation coefficients are
larger during winter when the frequency content of the noise is more
stable than in summer. This is especially true in the westernmost part
of Europe.  Secondly, during winter and summer we observe lateral
variations. With 3-days auto-correlation 
(Figure~\ref{fig:cmap_20_40s}c,d) there is a clear contrast between
Western and Eastern Europe. In winter the average correlations
coefficient with the reference is greater than 0.7 in France and
Switzerland, and less than 0.5 in Romania, Greece, Slovenia and Italy
along the Adriatic coastline. This lateral variation remains clearly
visible in winter and summer when considering 20-days auto-correlation
(Figure~\ref{fig:cmap_20_40s}e,f).



\subsection{Temporal resolution for monitoring studies in the 2--3~s
period band}

We now look at the extent to which the dynamics of the seismic noise,
and in particular the microseismic activity around the Adriatic and
Aegean seas limits the temporal resolution with which it is possible to
measure velocity changes between 2 and 3~s. To that end, we map the
spatial variation of the smallest number of days $N$ for which the
average correlation coefficient $C$ between an $N$-day auto-correlation
and a 2-month reference auto-correlation is greater than or equal to a
given threshold (Figure~\ref{fig:nday}). The reference auto-correlation
being averaged over 60 days, we explore a numbers of days $N$ ranging
from 1~to~59.



\begin{figure*}
{\vspace*{-3pt}}
\includegraphics{fig10}
{\vspace*{-2pt}}
\caption{Number of days required to get a correlation coefficient
greater than 0.95 between a reference auto-correlation averaged over
the season (2 months) and a $N$-day auto-correlation, in the time window
5--25~s corresponding to the beginning of the coda, in (a) winter
(January--February) and (b) summer (July--August). (c) and (d) are
similar to (a) and (b) but for a correlation coefficient of 0.8. (e)
and (f) are similar to (a) and (b) but for the 20--40~s time window and a
correlation coefficient of 0.7.\label{fig:nday}}
\end{figure*}



In Figure~\ref{fig:nday}a,b we represent the number of days $N$
required to get a correlation coefficient $C$ of 0.95 considering the
coda time window 5--25~s. According to Equation~(\ref{eq1}), when measuring
relative velocity changes $\updelta v/v$  with the stretching method, a
correlation coefficient of 0.95 over the time window 5--25~s between 2
and 3~s of period implies that the errors on the estimate of the
relative velocity changes have a root mean square of 0.07\%
\citep{Weaver_2011}. This may seem large, as the velocity changes
associated with large magnitude earthquakes and the hydrological cycle
are of the order of 0.1\%
\citep{SensSchoenfelder_2006,Brenguier_2008a,Chen_2010,Zaccarelli_2011,
Barajas_2021,Mao_2022}. This is due to the fact that we consider
measurements made at a single station over a relatively small time
window (5--25~s). In winter, the convergence speed of the
auto-correlation in the 5--25~s time window is faster in France ($N<10$
days) than further east in Germany, Switzerland, and Italy ($N>15$
days). In summer the speed of convergence decreases as the noise field
is less stationary. More than 20 days are required to get a correlation
coefficient greater than 0.95 along the Mediterranean Adriatic coast
and around the Aegean sea.

Figure~\ref{fig:nday}c,d represent the number of days $N$ needed
to obtain on the 5--25~s time window a correlation coefficient $C$ of
0.8. This corresponds to an RMS of the $\updelta v/v$  measurement errors
of 1.6\%. We see a sharp contrast between two regions: in winter it
takes less than 3 days in the northwest  (France, Germany, Switzerland)
to obtain a correlation coefficient of 0.8. On the contrary, it takes
more than 3 days in Italy, Austria and Slovenia. In summer, the spatial
variation of $N$ relates directly to the percentage of time for which
the stationarity coefficient is lower than 0.98 (Figure~\ref{fig:ns}):
the coda of correlation converges more slowly in Greece, Italy, on the
south coast of France ($N >10$ days) where short period microseismic
events are detected, and the convergence is faster on the rest of the
continent ($N<3$ days) where the noise is more stationnary.

Figure~\ref{fig:nday}e,f presents the speed of convergence of the
auto-correlations coda waves over the 20--40~s time window for $C= 0.7$.
This corresponds to a RMS of the $\updelta v/v$ measurement errors of
1.1\%. For this time window the results are different: the effect of
the dynamic of the noise sources is less visible. In particular in
summer, the number of days required to achieve $C=0.7$ varies randomly
from site to site with no clear regional variations.



These results indicate that the evolution of noise sources over time,
the interaction between the north Atlantic and the southeastern
Mediterranean source region and its seasonal variations, the dynamics
of sources on smaller time scales in the Adriatic and Aegean Seas,
limits the convergence speed of the noise auto-correlations coda waves
and thus the temporal resolution of monitoring studies. The impact of
local noise sources along the coast limits the temporal resolution
particularly on the 5--25~s coda window. Seasonal variations in seismic
noise affect the two time windows 5--25~s and 20--40~s, the convergence
being slower in summer than in winter. Thus, even when going further
into the coda, the imprint of the source dynamics is still visible. In
winter as in summer, there is a clear difference between Western and
Eastern Europe, the temporal resolution of the $\updelta v/v$ 
measurements decreasing towards the East.


\section{Conclusion} 

The aim of this work was to study the relationship between the dynamics
of the noise field across Europe and the convergence speed of noise
auto-correlation coda waves. It shows that the accuracy and temporal
resolution with which it is possible to detect changes in the medium at
2~s period presents strong seasonal and lateral variations that depends
on the time window which is analysed.

The noise level maps computed using all available broadband seismic
stations in Europe in 2021, complemented by temporary stations from the
\mbox{Pyrope} and IberArray networks, show strong seasonal variations at 2~s
periods and a clear increase in noise level near the Atlantic and
Mediterranean coast. This suggests that the seismic noise originates
simultaneously from the Mediterranean Sea and the Atlantic Ocean and
attenuates as it propagates across the continent
(Figure~\ref{fig:psd}).

To study the dynamics of the noise field, we introduce a proxy that
quantifies the non-stationarity of the frequency content of the noise
independently of its amplitude. It shows that in the regions mainly
influenced by the north Atlantic ocean, the frequency content is stable
over time which is favourable for monitoring the Earth's crust
(Figure~\ref{fig:ns}). Conversely, this proxy allows us to detect short
periods microseismic events originating from the southeast of the
Mediteranean sea. This highlights that unlike the north Atlantic ocean,
the Mediterranean sources are intermittent and generate an unstable
wavefield over time (Figures~\ref{fig:nsc_map1},~\ref{fig:nsc_map2}).

Noise level maps and noise stationarity maps
(Figures~\ref{fig:psd},~\ref{fig:ns}) show that the dynamics of the
seismic noise operates on two distinct time scales that modulate the
speed of convergence of correlations coda waves. First, the noise field
evolves seasonally: this results in seasonal changes in the noise
level, but also in the relative influence zones of the Atlantic Ocean
and the Mediterranean Sea. In addition, there are dynamics on a smaller
time scale of the order of hours to days related to the intermittent
generation of short period noise by the Adriatic and Aegean Seas, which
are closed areas.

The contribution of these two main areas and the existence of these two
time scales imply that the convergence speed of the correlation coda
waves varies spatially, and that this spatial variation itself depends
on the season and the lag-time considered. The beginning of the coda is
the most sensitive to the dynamics of the noise sources over short
times, and its convergence speed directly reflects the lateral
variations of the noise non-stationarity (Figures~\ref{fig:ns},
\ref{fig:cmap_5_25s}). At longer times, over the 20--40~s coda window,
convergence is slower, the influence of Mediterranean dynamics is
weaker, but there remains a strong contrast between Western Europe
where convergence is faster while as one moves away from the Atlantic
Ocean, convergence of correlations slows down
(Figure~\ref{fig:cmap_20_40s}).

To summarise, this study shows that the spatial and temporal
variability of the noise sources \mbox{determines} to first order the accuracy
and temporal resolution with which it is possible to detect changes in
the crust at 2~s of period, while lateral variations of scattering
properties have less influence. In particular, the influence of strong
heterogeneities of the alpine crust on the convergence speed of the
coda is not clearly seen.

\section{Origin of data}

Waveform data used in this paper belong to the networks with codes:

CL \citep{CL}, CQ \citep{CQ}, CR \citep{CR}, CZ \citep{CZ}, EI \citep{EI}, ES \citep{ES}, FR \citep{FR},
GE \citep{GE}, GR \citep{GR}, GU \citep{GU}, HA \citep{HA}, HC \citep{HC}, HL \citep{HL}, HP \citep{HP},
HS \citep{HS}, HT \citep{HT}, HU \citep{HU}, IV \citep{IV}, KO \citep{KO}, LX \citep{LX}, MD \citep{MD},
MN \citep{MN}, NI \citep{NI}, NL \citep{NL}, NS \citep{NS}, OE \citep{OE}, OT \citep{OT}, OX \citep{OX},
PM \citep{PM}, RD \citep{RD}, RO \citep{RO}, SJ \citep{SJ}, SK \citep{SK}, SL \citep{SL}, SX \citep{SX},
UD \citep{UD}, UP \citep{UP}.

We also used data of temporary experiments, PYROPE (network code X7
(2010--2014), \citet{Chevrot_2017} and IberArray \citep{IB}.

\section*{Declaration of interests}  
The authors do not work for, advise, own shares in, or receive funds
from any organization that could benefit from this article, and have
declared no affiliations other than their research organizations.

\section*{Dedication}
The manuscript was written through the contributions of all authors. All
authors have given approval to the final version of the manuscript.

\section*{Funding}
Real-time Earthquake Risk Reduction for a Resilient Europe (RISE)
project Grant agreement number 821115 (LS, ED, PR).

\CDRGrant[RISE]{821115}

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