<html><head><meta name="color-scheme" content="light dark"></head><body><pre style="word-wrap: break-word; white-space: pre-wrap;">\makeatletter
\@ifundefined{HCode}
{\documentclass[screen,CRGEOS,Unicode,biblatex,published]{cedram}
\addbibresource{crgeos20241071.bib}
\newenvironment{Table}{\begin{table}}{\end{table}}
\newenvironment{noXML}{}{}
\let\citep\parencite
\let\citet\textcite
\def\xcitealp#1#2{\citeauthor{#1}, \citelink{#1}{#2}}
\def\xciteyear#1#2{\citelink{#1}{#2}}
\newcommand*{\citelink}[2]{\hyperlink{cite.\therefsection @#1}{#2}}
\def\defcitealias#1#2{}
\let\citetalias\textcite
\let\citepalias\parencite
\def\thead{\noalign{\relax}\hline}
\def\endthead{\noalign{\relax}\hline}
\def\tabnote#1{\vskip4pt\parbox{.95\linewidth}{#1}}
\def\botline{\\\hline}
\def\dollar{\$}
\def\tbody{\noalign{\relax}}
\def\tsup#1{$^{{#1}}$}
\def\tsub#1{$_{{#1}}$}
\skip\footins=12pt
\let\permil\textperthousand
\RequirePackage{etoolbox}
\usepackage{upgreek}
\usepackage{wasysym}
\usepackage{pifont}
\def\jobid{crgeos20241071}
%\graphicspath{{/tmp/\jobid_figs/web/}}
\graphicspath{{./figures/}}
\newcounter{runlevel}
\usepackage{multirow} 
\def\nrow#1{\@tempcnta #1\relax%
\advance\@tempcnta by 1\relax%
\xdef\lenrow{\the\@tempcnta}}
\def\morerows#1#2{\nrow{#1}\multirow{\lenrow}{*}{#2}}
\let\MakeYrStrItalic\relax
\def\refinput#1{}
\def\back#1{}
\csdef{Seqnsplit}{\\}
\newcommand*{\hyperlinkcite}[1]{\hyper@link{cite}{cite.#1}}
\DOI{10.5802/crgeos.295}
\datereceived{2024-12-20}
\daterevised{2025-03-27}
\dateaccepted{2025-05-20}
\ItHasTeXPublished
}
{
\PassOptionsToPackage{authoryear}{natbib}
\documentclass[crgeos]{article}
\usepackage[T1]{fontenc} 
\usepackage{pifont}
\def\CDRdoi{10.5802/crgeos.295}
 \def\citelink#1#2{\citeyear{#1}}
 \def\xcitealp#1#2{\citealp{#1}}
 \def\xciteyear#1#2{\citeyear{#1}}
\makeatletter
\def\CDRsupplementaryTwotypes#1#2{}
 \def\hyperlinkcite#1#2{\citeyear{#1}}
\let\newline\break
}
\makeatother

\dateposted{2025-06-17}
\begin{document}

\begin{noXML}

\TopicFR{G\'eophysique de surface}
\TopicEN{Surface geophysics}

\CDRsetmeta{articletype}{research-article}

\shortrunauthors

\title{A decade of geophysical monitoring to help conserve the Lascaux
cave} 

\alttitle{Une d\'{e}cennie de mesures g\'{e}ophysiques au service de la
conservation de la grotte de lascaux}

\author{\firstname{Colette} \lastname{Sirieix}\CDRorcid{0000-0003-4558-6896}\IsCorresp}
\address{Univ. Bordeaux, CNRS, Bordeaux INP, I2M, UMR 5295, F-33400,
Talence, France} 
\address{Arts et Metiers Institute of Technology, CNRS, Bordeaux INP,
I2M, UMR 5295, F-33400 Talence, France} 
\curraddr[C. Sirieix]{I2M, B\^{a}timent A11 - 351 Cours de la
Lib\'{e}ration, 33405 Talence Cedex, France}
\email[C. Sirieix]{colette.sirieix@u-bordeaux.fr}

\author{\firstname{C\'{e}cile} \lastname{Verdet}\CDRorcid{0000-0002-7646-1749}}
\addressSameAs{1}{Univ. Bordeaux, CNRS, Bordeaux INP, I2M, UMR 5295,
F-33400, Talence, France} 
\addressSameAs{2}{Arts et Metiers Institute of Technology, CNRS,
Bordeaux INP, I2M, UMR 5295, F-33400 Talence, France} 
\email[C. Verdet]{cecile.verdet@u-bordeaux.fr}

\author{\firstname{Joelle} \lastname{Riss}\CDRorcid{0000-0003-3533-5831}}
\addressSameAs{1}{Univ. Bordeaux, CNRS, Bordeaux INP, I2M, UMR 5295,
F-33400, Talence, France} 
\addressSameAs{2}{Arts et Metiers Institute of Technology, CNRS,
Bordeaux INP, I2M, UMR 5295, F-33400 Talence, France} 
\email[J. Riss]{joelle.riss@u-bordeaux.fr}

\author{\firstname{Antoine} \lastname{Marache}\CDRorcid{0000-0003-3141-6212}}
\addressSameAs{1}{Univ. Bordeaux, CNRS, Bordeaux INP, I2M, UMR 5295,
F-33400, Talence, France} 
\addressSameAs{2}{Arts et Metiers Institute of Technology, CNRS,
Bordeaux INP, I2M, UMR 5295, F-33400 Talence, France} 
\email[A. Marache]{antoine.marache@u-bordeaux.fr}

\author{\firstname{Habiba}\nobreakauthor\lastname{Lharti}\CDRorcid{0000-0002-4630-7855}}
\address{Laboratoire M\'{e}canique et G\'{e}nie Civil (LMGC), IMT Mines
Ales, University of Montpellier, CNRS, F-30100 Ales, France} 
\email[H. Lharti]{habiba.lharti@mines-ales.fr}

\author{\firstname{Fabien} \lastname{Salmon}\CDRorcid{0000-0001-7735-1181}}
\address{Inria, Univ. Bordeaux, CNRS, Bordeaux INP, IMB, UMR 5251, 200
Avenue de la Vieille Tour, Talence, 33405, France} 
\email[F. Salmon]{fabien.salmon@inria.fr}

\author{\firstname{Marie} \lastname{Larcanch\'{e}}\CDRorcid{0000-0002-3385-6505}}
\addressSameAs{1}{Univ. Bordeaux, CNRS, Bordeaux INP, I2M, UMR 5295,
F-33400, Talence, France} 
\addressSameAs{2}{Arts et Metiers Institute of Technology, CNRS,
Bordeaux INP, I2M, UMR 5295, F-33400 Talence, France} 
\email[M. Larcanch\'{e}]{marie.larcanche@u-bordeaux.fr}

\author{\firstname{Philippe} \lastname{Malaurent}\CDRorcid{0009-0003-4034-5847}}
\addressSameAs{1}{Univ. Bordeaux, CNRS, Bordeaux INP, I2M, UMR 5295,
F-33400, Talence, France} 
\addressSameAs{2}{Arts et Metiers Institute of Technology, CNRS,
Bordeaux INP, I2M, UMR 5295, F-33400 Talence, France} 
\email[P. Malaurent]{malaurent.philippe@orange.fr}

\author{\firstname{Sylvain}\nobreakauthor\lastname{Mat\'{e}o}\CDRorcid{0000-0002-9755-8523}}
\addressSameAs{1}{Univ. Bordeaux, CNRS, Bordeaux INP, I2M, UMR 5295,
F-33400, Talence, France} 
\addressSameAs{2}{Arts et Metiers Institute of Technology, CNRS,
Bordeaux INP, I2M, UMR 5295, F-33400 Talence, France} 
\email[S. Mat\'{e}o]{sylvain.mateo@u-bordeaux.fr}

\author{\firstname{Delphine} \lastname{Lacanette}\CDRorcid{0000-0003-2954-5963}}
\addressSameAs{1}{Univ. Bordeaux, CNRS, Bordeaux INP, I2M, UMR 5295,
F-33400, Talence, France} 
\addressSameAs{2}{Arts et Metiers Institute of Technology, CNRS,
Bordeaux INP, I2M, UMR 5295, F-33400 Talence, France} 
\email[D. Lacanette]{delphine.lacanette@u-bordeaux.fr}

\keywords{\kwd{Electrical resistivity
tomography}\kwd{Clustering}\kwd{Critical zone}\kwd{Heat 
transfer}\kwd{Time-lapse}\kwd{Cultural heritage}\kwd{Geostatistics}}

\altkeywords{\kwd{Tomographie de r\'{e}sistivit\'{e}
\'{e}lectrique}\kwd{Classification}\kwd{Zone critique}\kwd{Transfert de
chaleur}\kwd{Suivi temporel}\kwd{Patrimoine
culturel}\kwd{Geostatistique}}

\thanks{French Ministry of Culture}

\begin{abstract} 
The Lascaux Cave has been studied and instrumented for over 60 years.
Since 1963, the cave has been increasingly monitored in an effort to
order to better examine and manage the various diseases and dissolution
linked to environmental factors that have begun to emerge, risking
damage to the rock art and the supporting rock. Over the past decade,
non-invasive geophysical methods, particularly electrical resistivity
tomography, have been employed to study the surrounding massif. This
approach combines monthly measurements along profiles and 2D surveys at
varying scales, locations and seasons, enabling the reconstruction of
3D models using geostatistics.

Analysis of both a decade profile time-lapse and of the 3D models
acquired at different periods has improved understanding of water
circulation in this unsaturated zone, highlighting temporary
reservoirs.

Long-term datasets have also been repurposed to, for example, identify
the impact of tree felling on resistivity measurements and the massif.
Electrical resistivity heterogeneities in 3D models, linked to
geological formations and alteration levels, have provided input
thermal studies, demonstrating their influence on heat propagation and
natural convection within the cave. These findings underscore the
critical role of the surrounding massif in preserving the cave.
\end{abstract}

\begin{altabstract} 
La grotte de Lascaux est \'{e}tudi\'{e}e, instrument\'{e}e depuis plus
de 60 ans. Depuis 1963, le suivi de la grotte s'est amplifi\'{e} en
raison de la n\'{e}cessit\'{e} de mieux surveiller et contr\^{o}ler les
diff\'{e}rentes maladies ou dissolution qui ont commenc\'{e} \`{a}
apparaitre et pourraient endommager les \oe{}uvres ou la roche support.
Depuis plus de 10 ans, le site environnant la grotte est \'{e}tudi\'{e}
par m\'{e}thodes g\'{e}ophysiques qui ont la caract\'{e}ristique
d'\^{e}tre non dommageable pour le milieu. La tomographie de
r\'{e}sistivit\'{e} \'{e}lectrique est mise en \oe{}uvre sous deux
formes. D'une part un suivi temporel mensuel est conduit sur plusieurs
profils, d'autre part, plusieurs campagnes de lev\'{e} en 2D ont
\'{e}t\'{e} conduites \`{a} diff\'{e}rentes \'{e}chelles, sur
diff\'{e}rentes parties du massif et \`{a} diff\'{e}rentes saisons
permettant de reconstruire des mod\`{e}les 3D au moyen de la
g\'{e}ostatistique. 

L'analyse d'un des profils sur plus de 10 ans et
des mod\`{e}les 3D acquis \`{a} diff\'{e}rentes p\'{e}riodes, permet
une meilleure compr\'{e}hension de la circulation de l'eau dans cette
partie non satur\'{e}e avec la mise en \'{e}vidence de r\'{e}servoir
temporaire et le r\^{o}le de chaque partie du massif au-dessus de la
grotte. 

L'acc\`{e}s \`{a} des donn\'{e}es acquises au fil des
ann\'{e}es, permet de les r\'{e}utiliser dans des objectifs apparus
r\'{e}cemment. Ainsi, les donn\'{e}es du suivi temporel permettent de
montrer l'influence de l'abattage des arbres sur les mesures et par
cons\'{e}quent sur le massif. Les h\'{e}t\'{e}rog\'{e}n\'{e}it\'{e}s de
r\'{e}sistivit\'{e} \'{e}lectrique identifi\'{e}es sur les mod\`{e}les
3D qui ont pu \^{e}tre reli\'{e}es \`{a} diff\'{e}rentes formations
g\'{e}ologiques ou des niveaux d'alt\'{e}ration diff\'{e}rentiels, sont
quant \`{a} elles r\'{e}utilis\'{e}es pour l'\'{e}tude thermique du
massif. On a ainsi montr\'{e} que ces
h\'{e}t\'{e}rog\'{e}n\'{e}it\'{e}s avaient une influence sur la
propagation de la chaleur \`{a} travers le massif et donc sur les
circulations a\'{e}rauliques dans la grotte elle-m\^{e}me. Il est ainsi
montr\'{e} comment le massif environnant la grotte joue un r\^{o}le
primordial dans l'\'{e}tude de la conservation de celle-ci.
\end{altabstract} 

\maketitle

\twocolumngrid

\end{noXML}

\defcitealias{LeroiGourhanAllain1979}{ibid.}
\defcitealias{Salmonetal2023}{ibid.}
\defcitealias{Lhartietal2024}{ibid.}

\section{Introduction}\label{sec1}

Painted caves have long been the focus of study for prehistorians, and
they carry symbolic value for the populations. The conservation of
these significant sites has also drawn particular attention in
scholarship; with a focus on their location in the critical zone, as
defined by geophysicists \citep{Leeetal2023}, mainly situated in the
unsaturated zone. The thermal and hydric equilibrium of these caves is
contingent on various factors, including the overlying massif, water
circulation in fractures and altered zones, and the extent of
vegetation covering the massif which plays a major role in this
equilibrum. Long-term monitoring programmes provide valuable data that
facilitate a comprehensive understanding of the critical zone. In
particular, the rising temperatures observed since the 1980s are
altering the hydric state, bringing changes to condensation and
precipitation phenomena that may endanger parietal works 
\citep[Malaurent, in][]{Coye2011}. In addition, alterations
of microbiological or physico-chemical origin linked to thermo-hydric
conditions can damage both the rock and the art on it.

A number of research programmes are currently being developed around
certain sites that contain decorated caves. The Altamira cave in Spain,
for example, has been the focus of particular attention for many years.
Recently, \citet{Bayarrietal2024} developed photogrammetry methods
inside and outside the cave, as well as RADAR measurements with 400 and
900~MHz antennas. Their work demonstrates the essential role of water
circulation in the massif that results from a dense network of vertical
fractures and a central fracture partially filled with cement. They
demonstrate the decisive role played by this rapid circulation of water
in the alteration of the rock art, as well as of the rock material
through its dissolution; and they propose limited access to the cave
during periods of high water accumulation. \citet{Valoisetal2010}
studied the surroundings of the prehistoric cave of Mayenne Sciences
(Saults, France); using Electrical Resistivity Tomography (ERT) and
seismic refraction tomography, they detected karstic dissolution zones
as well as a filled cave below the prehistoric cave. The circulation of
water surrounding caves has also been studied. \citet{Leopoldetal2021},
again using ERT, studied the infiltration of water in the massif
\mbox{surrounding} the Golgotha cave (Australia) up to the cave itself. They
identified permanent reservoirs and fast hydrological flow pathways.
Their data were correlated with those recorded on the drips. Eucalyptus
roots were observed at a depth of 40~m. The same type of monitoring was
carried out on the Villars cave by \citet{Zhangetal2024}.  They
demonstrated that there is a link between temporary reservoirs
identified by ERT time-lapse and geochemical drip monitoring,
confirming flow times ranging from rapid to several months. To
demonstrate the impact of rainfall on the conservation of rock art in
an arid and shallow environment, \citet{Liuetal2020} set up artificial
watering and took ERT measurements above the Mogao Grottoes (Gansu
Province, China). The migration of rainwater in the form of water
vapour induces salt damage in wall paintings. At the thermal level,
which also governs condensation and precipitation phenomena,
\citet{DominguezVillaretal2023} show that the temperature inside the
Los Pinos cave (Spain) has been stable for five years, demonstrating
that the transfer takes place solely by thermal conduction through the
massif. By contrast, \citet{Sedaghatkishetal2024} show that the effect
of convection dominates the aeraulic behaviour of open caves in direct
relation to the outside temperature. In their study of the caves of
Chauvet Pont d'Arc and Pech Merle, \citet{Perrieretal2023} show that
atmospheric pressure variations affect temperature, groundwater
dripping in underground cavities and aquifer piezometric levels. A
number of recent studies show the decisive role played by forests in
water circulation in the vadose zone \citep{Carriereetal2020,
Larcancheetal2024, Loiseauetal2023}. Given the findings of the research
cited above, it is now clear that the conservation of rock art in caves
requires precise knowledge of the entire critical zone.

One of the many caves studied to date is Lascaux. The Lascaux cave was
discovered in 1940, early on in the Second World War. It was opened to
the public in 1948, after major development work had been carried out,
particularly at the entrance, where dozens of cubic metres of scree had
been excavated. The beauty and density of the cave paintings have
earned Lascaux the nickname the ``Sistine Chapel of the Palaeolithic''.
It has welcomed up to 1800 visitors a day, despite its small size
(total developed length 250~m, average height 4~m) and shallow depth
(from surface to 20~m). Condensation \mbox{phenomena} linked to visits and
driving pigments were described as early as 1955 and, in 1960, green
disease was observed 
\citep[Sarradet M., in][]{LeroiGourhanAllain1979}.
Faced with the progress of the
deterioration, in 1963 Andr\'{e} Malraux, then Minister of Cultural
Affairs, decided to close the cave to the public and set up a
scientific council. The cave was subsequently purchased by the French
state in 1972. The Lascaux cave was the first prehistoric site to be
the subject of large-scale scientific studies for conservation
purposes. The initial studies concerned geology, hydrogeology and
geochemistry, led by H. Schoeller \citepalias{LeroiGourhanAllain1979}, and
after by \citet{Vouve1968}.
Studies of thermal and aeraulic behaviour
followed \citep{LacanetteMalaurent2014,Malaurentetal2007}. Research
programmes in hydrogeology have also been conducted in recent years,
culminating in PhD theses written by \citet{Lopez2009},
\citet{Minvielle2015} and  \citet{Houillon2016}. The need to avoid
destructive drilling on the cave site in the interests of preservation
led to a ban on drilling in the 1970s. Attempts at geophysical
measurements were soon made, in particular a microgravimetry survey
\citep[Vouv\'{e} J., in][]{LeroiGourhanAllain1979}.
Some ERT measurements were carried
out in the context of Lopez's PhD thesis \citep{Lopez2009}.
At the request of
both the scientific council and the DRAC Nouvelle-Aquitaine (Regional
Department of Cultural Affairs), a major geophysical measurement survey
was initiated in 2012 to describe the geometry of the limestone
promontory and its heterogeneities \citep{Xuetal2016}. A time-lapse ERT
device was set up to the north of the cave entrance in the same year
\citep{Xuetal2017}. While the initial aim of the measurements was to
describe the contacts between the limestone and detrital formations,
they soon proved to be of major interest in understanding the spatial
distribution of temporary reservoirs. More recently, it has shown the
importance of studying the influence of forest cover on the unsaturated
massif \citep{Larcancheetal2024}. Taking into account the geological
heterogeneities highlighted by geophysical measurements
\citep{Lhartietal2023} has also facilitated a detailed study of the
thermal behaviour of the massif surrounding the cave.

Lascaux is a highly protected site and has been subject to metrological
monitoring for more than 60 years. Here, geophysics has proven itself
an \mbox{indispensable} tool for describing the cave environment and
quantifying the impact of the environment on the conservation of the
cave. The long-term nature of this work has been a factor in its
successful implementation. The aim of this article is to demonstrate
the value of geophysical monitoring over a period of more than 10 years
in an unsaturated karstic environment that houses an internationally
renowned decorated cave; indeed, Lascaux has been a UNESCO World
Heritage Site since 1979. The site has been equipped with sensors for
so long now that we have been able to calibrate and correct data and
validate certain results. Complete knowledge of the phenomena observed
over a long period of time is the key to being able to both analyse and
interpret the data reliably.

The first part of this article is devoted to the various measurements
and methods used, with details of the corrections and precautions
necessary for their quality and repeatability. The second part will
then describe the main results of the time-lapse survey performed over
these 11 years, explore the role of the forest and characterise the
impact of the massif's heterogeneities on its thermal behaviour. The
article then proposes how all of these results may be analysed.

\section{Site description, materials and methods}\label{sec2}
\subsection{The Lascaux cave site}\label{ssec21}

The Lascaux cave is located in an unsaturated limestone massif that
formed in the Cretaceous period. The cave is located on the western
flank of the Lascaux Hill. Geological and geomorphological knowledge of
the site was refined in 2020 by Verdet etal The geological map
extracted from this study \citep{Verdetetal2020} shows that the
Santonian limestone is present in the upper part of the cave up to
around 180~m NGF, and that most of the cave develops in Coniacian
limestone (Figure~\ref{fig1}). Both are detrital limestones, but the
Santonian limestone is composed of small plates, whereas the Coniacian
is more compact. The interface between these limestones therefore
appears to be a permeability interface, calling into question the
existence of a marly interface \citep{Vouve1968}, which has never been
observed at the site.

\begin{figure*}
\includegraphics{fig01}
\caption{\label{fig1}Plan view of the geology of Lascaux Hill with a
projection of the cave and the position of the various ERT profiles,
trees and felled trees. Geological background after
\citet{Verdetetal2020}.}
\end{figure*}

The map in Figure~\ref{fig2} presents the names of the different
chambers in the Lascaux cave.

\begin{figure}
{\vspace*{-1pt}}
\includegraphics{fig02}
{\vspace*{-2pt}}
\caption{\label{fig2}Map of the Lascaux cave after
\citet{Aujoulat2013}.}
{\vspace*{-2pt}}
\end{figure}

The site is essentially covered by forest, with downy oak dominating
the limestone section above the cave, pine to the west over sandy-clay
detrital formations and chestnut to the east over sandy detrital
formations. All trees within the enclosure have been inventoried and
georeferenced. These trees, along with those felled in 2016 and 2021,
are shown in Figure~\ref{fig1}.

In addition, a Digital Terrain Model (DTM) survey of the Lascaux Hill
surface was acquired in 2017 with a definition of 0.2~m, along with a
3D survey of the cave linked to the DTM. All geophysical measurements
(the position of each electrode) and the sensors used are recorded in a
topographic survey using a tacheometer. All of these data ensure that
the sensors on the Lascaux site are well positioned and that the 3D
analysis has been conducted with exceptional accuracy.

\subsection{Microclimatic sensors}\label{ssec22}

Numerous sensors (174) have been installed in the cave and in the
outside environment to ensure the conservation of the rock art and the
support of the cave. Temperature sensors, with a sensitivity of
0.001~\textdegree C and relative accuracy of 0.01~\textdegree C, are
installed in the cave itself, at more than 20 positions in the rock
(0.02~m deep in the walls) and more than 120 in the air. The outdoor
sensors are installed from the surface at depths of 0.5~m and 1~m, and
more recently at 0.04, 0.07, 0.20 and 0.35~m. Three weather stations
are located on the hillside: in direct sunlight; under the pines; and
under the oaks. All of this equipment is described in detail in
Lharti's PhD thesis \citep{Lharti2023}.

The cave has no perennial water inflow, but non-perennial water inflow
is observed every year in airlock~1; in the Sanded Halls; in the
Chamber of Felines; in the Shaft of the Dead Man; and seeping into the
Great Hall of the Bulls, as described by \citet{Houillon2016}. The flow rate
of the emergence located in airlock~1 of the cave is measured
continuously.

\subsection{Electrical resistivity tomography}\label{ssec23}

Slingram, Spontaneous PolariSation and RADAR methods were deployed at
this site. Their depth of investigation remained very limited, probably
due to the low resistivity of the Santonian limestone and the noise
associated with the sensors and acquisition units installed on site. It
was therefore decided very quickly to deploy ERT on the site.

To date, 2D ERT has been used for a number of purposes. It was employed
not only was it to provide monitoring of the upstream part of the
non-perennial source at airlock~1 \citep{Xuetal2017}, but also to
reconstruct a 3D model of the site \citep{Xuetal2016, Verdetetal2020}.

Four profiles (Figure~\ref{fig1}) have been measured on a monthly basis
since 2012, with an interruption in 2014. In this article, we present
one of these profiles, called N50 (represented by the blue dotted line
in Figure~\ref{fig1}), which is 35.5~m long and comprises 72 electrodes
spaced 0.5~m apart.

Several 3D reconstructions were carried out using 2D surveys acquired
at different times and scales in order to gain a better understanding
of the geometry of the formations encountered on the site. The first
was carried out in March and April 2013. ERT {profiles} were laid out
perpendicular to the known major fracture network \citep{Lopez2009} and
in two other \mbox{directions.} Most profiles were made using 96 electrodes
spaced at 1.5~m. Profiles with only 1~m and 0.5~m spacing completed the
measurements to optimise the geostatistical modelling. The position of
these profiles is shown in Figure~\ref{fig1}. To gain a better
understanding of the site geometry to the north of the enclosure,
upstream of the emergence of airlock~1, new measurement surveys were
carried out in March and June 2016. These were conducted using 72
electrodes 1~m and 0.5~m apart, giving better resolution. The layout of
these profiles is shown in Figure~\ref{fig1}.\looseness=-1

In all cases, the electrical arrays used are gradient and forward and
reverse pole--dipole. These three electrical arrays are then
concatenated to form a single image. Concatenation is performed by
taking the gradient array first, then the pole--dipole arrays, to ensure
that the position of the remote electrode is correctly taken into
account with Res2dinv software (v.405.38). Inversion is performed using
an L1 norm and mesh refinement.

\subsection{Clustering method}\label{ssec24}

After applying a clustering method to temporal resistivity monitoring
data acquired at a hazardous waste landfill cover
\citep{Genelleetal2012}, this method was adapted and applied to the
data acquired at Lascaux. The clustering method used is Hierarchical
Ascending Classification (HAC). This method consists of establishing,
{a~posteriori} as opposed to {a~priori} (unsupervised
method), a partitioning or a sequence of nested partitions of a set of
individuals whose pairwise distances and agglomeration method are
known. This method uses Euclidean distance and Ward's 
(\xciteyear{Ward1963}{1963}\nocite{Ward1963}) 
agglomeration method, and is described in detail
by \citet{Lharti2023}. The resulting dendrogram takes the form of a
tree schematising the stages in the grouping of individuals, enabling
the choice of the desired number of clusters (partitions) and the
distances separating them. The reasons for choosing this method over a
K-means method, a hybrid method or a DBSCAN \citep{Saboretal2021} are
examined by \citet{Lhartietal2023}. The HAC is based on
{a~posteriori} selection of the number of clusters and improved
data segmentation. This method is applied not only to the ERT
time-lapse, but also to the data acquired over a large area covering
the volume surrounding the cave, in order to simplify them by
partitioning.

In the case of time-lapse, we have chosen to normalise resistivity
values by the block size. This is because the block size assigned by
the inversion varies with depth: the deeper the blocks, the larger
their size. As a result, a given volume of rock will be represented by
an unequal number of blocks, and therefore resistivity values,
depending on whether it is shallow or deep. The choice of normalisation
means taking into account surface resistivity densities. In the case
studied here (profile N50, Figure~\ref{fig1}), where resistivity
decreases with depth, this has the advantage of increasing the contrast
between the lower resistivity values present at depth and the higher
values on the surface.

This method is, however, used without normalisation when it is applied
to the classification of 3D data acquired at great depth.

\subsection{Correcting the effect of temperature on electrical
resistivity}\label{ssec25}

Electrical resistivity is affected by the temperature of the rock. The
implementation of the time-lapse and the need to compare resistivity
values acquired in both winter and summer mean that these values must
be corrected for the effect of temperature. In the case of 2D
resistivity tomography images, we apply a correction to the centre of
the blocks of each image level (i.e., to the depth of the different
levels making up the image). Among the many existing models for
correcting resistivity for the effect of temperatures, we chose the
ratio model \citep{Xuetal2015}. The difficulty then lies in collecting the
temperature at different depths.

As a first step \citep{Xuetal2017}, we employed the thermal diffusion
model outlined by \citet{LacanetteMalaurent2014}. This thermal model takes
into account external air temperatures and temperatures recorded in the
cave walls at different depths and makes the assumption that thermal
diffusivity is homogeneous and isotropic over all the massif
surrounding the cave. This enables the temperature of the massif to be
estimated as a function of depth. Close to the surface, two temperature
sensors were installed at depths of 0.5~m and 1~m, with a measurement
interval of 15~min. Having noted a discrepancy between the model data
and the sensor measurements on the day of the measurement, we performed
a calibration of the temperature data from the model, close to the
surface, the principle of which is detailed by \citet{Xu2015}.

Noting that this discrepancy between measurements and model could be
significant at shallow depths and at certain times of the year, it
appeared necessary to refine our model in order to increase the
accuracy of resistivity values close to the surface. This is absolutely
essential when we are concerned with the effect of the forest on the
massif, i.e., the very shallow part of the massif. Instead of using air
temperature data at the surface, a new model based on a heat balance at
the surface has been developed. This takes into account exchanges by
radiation, convection and conduction, as well as energy losses in the
soil due to evapotranspiration. The latter is estimated by the classic
Penman--Monteith model, widely used by agronomists
\citep{Salmonetal2023}. The input data for this model (radiation,
temperature, air speed and relative humidity) are measured on site by
weather stations installed in different positions: directly in the sun;
under the oaks; and under the pines. Additional data are also supplied
by M\'{e}t\'{e}o France. To validate the new model, a temperature
sensor was installed 0.04~m deep in the soil and left to gather data
for 4 months. This model enabled us to determine a better single
optimal thermal diffusivity for the whole massif. While the study by
\citetalias{Salmonetal2023} showed that the massif could not be considered
homogeneous, the thermal model showed values much closer to those
measured at the soil surface. This model was used to process all the
monthly data acquired since 2012.

\subsection{Geostatistical 3D modelling of ERT images}\label{ssec26}

The first ERT coverage of the 2.5 ha site was conducted over two weeks
from late March to early April 2013. In total, around 20 2D profiles
were acquired from 96 electrodes. These data were exploited and
described for the first time by \citet{Xuetal2016}.

For data acquired in 2016, in the north of the cave, on-site
acquisition took place over a one-week period in June and October. A
total of 11 profiles were acquired for each measurement survey. The
profiles were repositioned in exactly the same place for both surveys.
The electrode spacing was chosen to be of maximum 1~m, in view of the
first measurement survey \citep{Xuetal2016,Xuetal2017} which showed
geological structures with a higher resolution. The 2D images were
acquired from northwest--southeast and southwest--northeast directions
(Figure~\ref{fig1}) to ensure that they were perpendicular to the
geological structures of interest. At least two electrode spacings were
used so that spatial correlations could then be studied for different
distances between points. Indeed, two more profiles with electrodes
spaced 0.5~m from one another were acquired. A total of 26,571 items of
electrical resistivity data were available, with average resistivities
of 161~$\Omega{\cdot}$m in June and 191~$\Omega{\cdot}$m in
October, testifying to an overall drying up of the massif.

Following the inversion of the resistivity images, a 3D model was
constructed using geostatistical methods. The variographic maps
produced for each measurement survey indicate the presence of
horizontal/vertical anisotropy, as well as an N130 direction. This
latter feature corresponds approximately to the contact between the
detrital and limestone formations, and is a known direction in this
region \citep{Verdetetal2020}. An experimental variogram is calculated
for each measurement survey (one in June and one in October). A
theoretical variogram is then fitted to each of the calculated
experimental variograms in the principal directions. The theoretical
model is the sum of three structures based on spherical or exponential
models, the same for both surveys. The range is reached at 1.5~m in the
vertical plane and 9~m in the horizontal plane for a neighbourhood of
10~m, over the two measurement surveys. This shows that the structures
identified do not vary over time. After conclusive cross-validation, 3D
estimation using the ordinary kriging method was carried out using
0.5~m ${\times}$ 0.5~m ${\times}$ 0.5~m cells.

\section{Results of ten years of ERT measurements at the Lascaux site}
\label{sec3}
\subsection{Time-lapse over ten years}\label{ssec31}

Before describing the time-lapse of the electrical resistivity of the
different formations of the Lascaux massif, it is necessary to describe
the hydric context over the ten years. Analysis of the annual rainfall
shows no change over time, with an average of 865~mm/year over the ten
years. The least rainy years are 2014--2015, 2016--2017, 2018--2019 and
2021--2022. The summers, i.e., the periods of foliation with heavy
transpiration of the oaks on the Lascaux site, run from April to
October. The wettest summers recorded are in 2016, 2019 and 2021. The
wettest winters are in 2014, 2016, 2018 and 2020. Precipitation
generally exhibits a significant increase, becoming especially intense
during October, except in September 2020 and in November 2017, before
dropping off sharply from May to June onwards.

The profile presented is the N50, 25.5~m long, shown in blue in
Figure~\ref{fig1}. All the ERT images acquired on this profile since
2012 and after correction for temperature have been analysed using the
HAC method (Section~\ref{ssec24}). This method is used to construct a
dendrogram that groups the data according to their resistivity value
and temporal variations in their resistivity. The dendrogram
(Figure~\ref{fig3}) has been threshold to group the data into five
clusters that we consider sufficiently representative of the
environment. Thresholding into three clusters distinguishes the
clusters according to their depth in the massif: superficial clusters 1
and 3; intermediate cluster 2; and the deepest clusters 4 and 5. A
seven-cluster threshold separates cluster 1 into two clusters according
to depth, and cluster 2 is also divided into two clusters around 25~m
along the\break profile.

\begin{figure}
\includegraphics{fig03}
\caption{\label{fig3}Dendrogram of electrical resistivity values for
profile N50 between 2012 and 2023.} 
\end{figure}

The spatial distribution of the five clusters is shown in
Figure~\ref{fig4} together with the trees identified within a 5~m
radius of the profile \citep{Dayetal2010}. Some of these trees were
felled in November 2016.

\begin{figure}
\includegraphics{fig04}
\caption{\label{fig4}Resistivity blocks by cluster and projection of
trees located within a 5~m radius of the profile.}
\end{figure}

This classification provides statistical values for each cluster. The
median values for each cluster, \mbox{together} with the flow rate measured at
the emergence of airlock~1 and the effective rainfall, are shown in
Figure~\ref{fig5}. The median values for each cluster evolve in the
same way over the 11 years of measurement. Each year, there is an
increase in electrical resistivity in summer (from May to July,
depending on the cluster) and a plateau of lower resistivity starts
from November to January.

\begin{figure*}
\includegraphics{fig05}
\caption{\label{fig5}Evolution of median resistivity for each cluster,
flowrate through airlock~1 and effective rainfall between the beginning
of 2013 and the end of 2023.}
\end{figure*}

As far as low electrical resistivity values are concerned, the plateau
is reached every winter for almost all clusters. In the following
section, we will assume that the values representing the lowest 25\% of
median resistivity (1{st} quartiles) represent the lowest resistivity
values.

The 1{st} quartiles of the median resistivity value are different for
each cluster:

Clusters 1 and 2, corresponding to the levels closest to the surface,
have an identical minimum electrical resistivity (1{st} quartile) of
130~$\Omega{\cdot}$m. Cluster 1 generally extends from the
surface down to 1.3~m and sometimes up to 2.4~m. Cluster 2 is generally
below cluster 1 and down to a depth of 3.7~m.

Cluster 3, located roughly between the surface and 1~m depth, and
mainly between 0.6 and 0.8~m, reaches the highest value of 
213~$\Omega{\cdot}$m.

Cluster 4, deeper and located around cluster 5, has the value of 
105~$\Omega{\cdot}$m.

Cluster 5, located the deepest (between 3.2 and 7~m), has the lowest
value on this profile with 61~$\Omega{\cdot}$m.

The differences in minimum resistivity values between the clusters are
significant, and undoubtedly reflect the nature of the geological
materials from which they are composed and state of weathering that
they have undergone.

As for the maximum median resistivity values, there is no plateau, in
contrast to the minimum values. For all clusters, the maximum
resistivity value is significantly lower in the summer of 2021, which
is associated with a very wet summer.

In detail, each of these five clusters behaves differently in terms of
both amplitude and cycle duration. The amplitude of the medians is very
high for cluster~3, located under the trees, and reaches 
300~$\Omega{\cdot}$m. For superficial clusters 1 and 2, it is 120 and 
60~$\Omega{\cdot}$m, respectively, bearing in mind that cluster 2 is
generally deeper than cluster 1. Concerning the deeper, less resistive
clusters, the amplitude is lower with values of 20~$\Omega{\cdot}$m
and 40~$\Omega{\cdot}$m for clusters 4 and 5, respectively.

The annual cycle of the different clusters shows repeatability over 11
years, even if slight shifts are observed for some of them, depending
on previous rainfall.

Cluster 1, which is the most superficial, generally shows maximum
resistivity in September; but this maximum resistivity was reached in
late October in 2015, 2017 and 2022, which were less rainy years. This
cluster responds fastest after the beginning of the autumn rains. This
cluster reaches the minimum resistivity plateau between December and
January, and remains there for several months. The increase in
resistivity occurs between March and June (for the years 2016, 2019 and
2021).

Cluster 3, which is located mainly below the trees, reaches maximum
resistivity in September and sometimes early October, as it is for
cluster 1. Two years show a maximum reached late in November (2017 and
2022). The start of the minimum plateau is generally reached in
January, sometimes in November (years 2013, 2019, 2020, 2023), i.e.,
one month earlier than cluster 1. The end of the plateau is almost
always in late April or early May, with the exception of March 2020 and
2022.

Cluster 2 is deeper than the previous two. It reached maximum
resistivity in October and November in 2017 and 2022. It often shows a
plateau in the maxima. The start of the minimum resistivity plateau is
reached in February and sometimes in December (2019, 2020, 2021). The
end of this plateau occurs between March (2020), June and sometimes
July (2016, 2019, 2020, 2021). Every year, all cycles are one month
later than the shallower cluster~1.\looseness=1

Cluster 5, which is deeper than cluster 2, also shows annual cycles of
resistivity variation. The maximum resistivity is reached between
October (2013, 2017, 2018, 2019, 2020, 2021, 2023) and December (2015,
2016, 2017, 2022), generally one month after cluster 2. A plateau was
reached over several months in 2016, 2017, 2018 and 2021. Minimum
resistivity is reached between December (2019, 2021, 2022, 2023) and
January (2016, 2017, 2018, 2019, 2021), i.e., slightly before cluster
2. The resumption of significant flow in the airlock~1 emergence occurs
around 15 days after the plateau is reached. These 15 days are related
to the monthly step of ERT's time-lapse measurements. The end of the
minimum resistivity plateau varies between June and July, approximately
one month after cluster 2. For each year, it can be seen that flows
from airlock~1 cease approximately one month before the median
resistivity begins to rise.

Cluster 4, which has a very low amplitude cycle of the resistivity
median, is more difficult to analyse. However, the median values of
this cluster show a slight tendency to increase from 2013 to 2023. The
null hypothesis, i.e., independence of resistivity versus time, is
rejected (Fischer Snedecor test $F=7$, $p$-value ${=}$\ 0.009).

\subsection{3D extension of cluster~5}\label{ssec32}

Time-lapse ERT has revealed resistivity clusters with different
temporal and spatially organised behaviours. In particular, cluster 5,
the deepest, seems to behave synchronously with the water flow measured
in airlock~1. In order to identify the spatial extension of cluster 5
in 3D, a 3D image was constructed using the results of two measurement
surveys:

One in June 2016, a period of low resistivity at depth
(Figure~\ref{fig5}), located in the range of minimum
values of the resistivity median and therefore corresponding to high
water content.

A second in October 2016, a period of high resistivity. Although the
maximum resistivity is reached in December 2016, the measurement
acquired in October still corresponds to a high resistivity value, very
close to that of December. We can therefore assume that this date
reflects a material with a low water content.

\begin{figure*}
\includegraphics{fig06}
{\vspace*{-2pt}}
\caption{\label{fig6}3D view of the north of the cave, with a section
at 185 m NGF. (a) June 2016; (b) October 2016.}
{\vspace*{-2pt}}
\end{figure*}

From the June 2016 3D model (Figure~\ref{fig6}) on the section located
on a 185 m NGF elevation plane, cluster 5 with low resistivity is
clearly visible at the south-eastern end of the N50 measurement
profile. It extends northwards towards the detrital formations. In the
direction of the south, it continues towards the cave's airlock after a
change of orientation roughly east--west at 184~m NGF to arrive at the
right of the airlock~1 emergence at 182.5~m NGF, roughly at the same
altitude as the emergence, which is at 182~m NGF. Another branch
emerges to the north, to the north of the N50 profile. It joins the
first structure at 182.5~m NGF, just before the emergence.

In October 2016, the structures identified above differed very little
from their surroundings. The overall resistivity of the massif
increased, in line with the driest period on the Lascaux site. The
electrical resistivity of the identified structures has risen sharply,
suggesting that the water content has dropped just as sharply, reducing
the resistivity gap between it and the surrounding limestone. In
addition, the northern end of these structures in the limestone
formations also shows an increase in resistivity of the same magnitude
as that measured at profile N50.

Only the formations located beyond the boundary separating limestone
from detrital formations see their resistivity values remain low, with
channelided forms. Some structures, which became more resistive in
October 2016, appear to extend the so-called cluster 5 formations.

\subsection{Effect of tree felling}\label{ssec33}

The Lascaux Hill is marked by extensive forest cover
(Figure~\ref{fig1}). Forest management has been in place since 2013,
and its impact on the unsaturated massif deserves further attention.
Time-lapse surveys conducted over more than 11 years have been resumed
and studied in detail in order to determine the role of trees, mainly
oaks and pines, in the hydric behaviour of the massif 
\citep{Larcancheetal2023,Larcancheetal2024}. Thinning has been carried
out to allow the forest to develop as well as possible, with a view to
preserving the site from the risk of storms. Two felling operations
took place, in November 2016 and January 2021, mainly involving pine
trees. A localised zone under the felled trees within a 5~m radius was
defined around the ERT profile (Figure~\ref{fig4}) and to a depth of
1.2 m. This zone was subsequently analysed, and its median resistivity
is plotted in Figure~\ref{fig7}.

\begin{figure*}
\includegraphics{fig07}
{\vspace*{2pt}}
\caption{\label{fig7}Evolution of the median resistivity under a zone
with a radius of 5 m around the trees and a depth of 1.2~m, from
\citet{Larcancheetal2023}.}
\end{figure*}

The peak electrical resistivity median was significantly reduced in the
summer of 2017, after the trees had been felled in November 2016. This
phenomenon has been observed in all four profiles studied over the last
11 years at the Lascaux site
\citep{Larcancheetal2023,Larcancheetal2024}. No change has been
observed in the winter values. On first analysis, the curves seem to
return to their maximum in summer 2018.

\begin{figure*}
{\vspace*{2pt}}
\includegraphics{fig08}
{\vspace*{2pt}}
\caption{\label{fig8}3D visualization of spatial heterogeneity over the
entire site, classified into seven clusters with the median resistivity
value for each cluster.}
\end{figure*}

\subsection{Influence of karstic massif heterogeneities on heat
propagation to the cave}\label{ssec34}

The electrical resistivity data acquired at this site show that the
massif is highly heterogeneous, in terms of both the dispersion of
resistivity values and their spatial arrangement. These electrical
heterogeneities can be related either to the geological nature of the
formations (Santonian limestone, Coniacian limestone, detrital sandy or
clayey formations) or to the water content of certain structures
resulting from the weathering of detrital limestones. \mbox{Furthermore,}
\citet{Salmonetal2023}, \citet{Lhartietal2025a} showed that heat
\mbox{propagation} through the Lascaux massif could not be simulated with high
accuracy with the diffusivity of a single medium. It therefore appeared
necessary to re-use the data that had been acquired in 2013
\citep{Xuetal2016} on the entire massif in the vicinity of the cave, in
order to take into account the impact of heterogeneities on heat
propagation across the massif \citep{Lharti2023}. The 2013 data have
been subjected to a classification that took all profiles into account
\citep{Lhartietal2023}.  This classification was applied to the 3D
geostatistical model \citep{Lhartietal2025b} having filtered out the
anthropized part of the massif on the site. A representation of these
heterogeneities is shown in Figure~\ref{fig8}. This spatial
distribution was used to estimate thermal diffusivity values for each
cluster, using an inverse resolution methodology. This method is based
on an objective function that depends on the phase shift and damping of
waves measured and simulated thanks to 21 temperature probes placed in
the cave walls at different depths\break (up to 21.5~m).

\section{Discussion}\label{sec4}

The analysis of time-lapse ERT over a period exceeding ten years makes
it possible to interpret differences between the various clusters, both
in terms of extreme values and the time lag between clusters. When
analysing the data, it is essential to consider rainfall variability in
terms of both quantity and seasonality.

We assume a close link between variations in resistivity and water
content, given the very low clay content measured in samples taken from
the site.

First of all, as described above, cluster 4, which varies little over
the course of a year, shows an upward trend in resistivity between 2013
and 2023. The study of the maximum values for each year, assimilated to
the 3{rd} quartile of resistivities of each cluster, reveals a slight
upward trend over the 11-year period for clusters 1 and 3. An exception
to this trend is 2021, which was marked by a very wet summer. This
indicates that the superficial part of the massif tends to dry out in
the summer months. Given that precipitation levels remained constant
throughout the 11-year study period, two potential explanations for
this drying-up phenomenon can be postulated. The first interpretation
can be attributed to tree growth. The growth of the trees and the
increase of diameters over the course of the 11 years could explain the
increase in transpiration. The second interpretation could be related
to the observed increase in the hotter temperatures (3{rd} quartile),
i.e., summer temperatures. Assuming a linear model for the pair of
variables (temperature/time), the null hypothesis H0 (independence of
the variables) must be rejected (Fischer Snedecor test $F=9$, $p$-value
${=}$\ 0.017). Assuming this linearity, the increase in annual
temperatures of the 3{rd} quartile can be estimated at 2.4~\textdegree
C. An increase in summer temperatures likely has the effect of
increasing both evaporation and transpiration.

Considering the 1{st} quartile of the median resistivity of each
cluster as representative of their low resistivity values, we can see
that it is almost constant over the course of several months. The most
\mbox{superficial} clusters, designated 1 and 2, exhibit a resistivity value
of 130~$\Omega{\cdot}$m. This value is notably low for limestone.
This therefore reflects the weathering of limestone and its high
porosity on a macroscopic scale which is linked to the space left
between centimetric platelets. Cluster 3 near the surface shows a much
higher minimum threshold of 213~$\Omega{\cdot}$m. The presence of
trees above this cluster indicates the potential for permanent
exchanges with the surface or filling of the porosity by rootlets.
Cluster 5 exhibits a markedly lower median resistivity than the other
clusters, at 61~$\Omega{\cdot}$m. We can assume that it represents a
more advanced stage of weathering with a higher water content
throughout the year. In the vicinity of the site, the implementation of
excavation has facilitated the observation of sandy passages within the
limestone, a phenomenon that is also evident in the cave in the Sanded
Hall (Figure~\ref{fig2}). Cluster 4 has a significantly lower median
value of 105~$\Omega{\cdot}$m in comparison to the most superficial
clusters, but does not reach that of cluster 5. This suggests that the
weathering process may be less advanced than that observed in
cluster~5.

The cyclical evolution of the clusters exhibits notable differences.
Cluster 1, the most superficial, which extends to a maximum depth of
1.3 m, reaches a minimum resistivity threshold between late December
and early January, i.e., two months after the resumption of rainfall.
The process of drying out, which occurs with the highest resistivity
value, takes place in September and October in years with less
precipitation. This cluster reflects the behaviour of seepage water
over the first metre of the massif. Again, its low resistivity and the
wide range of annual variations indicate a high porosity and
consequently a state of weathering. Visually, small trenches dug to the
south of the site show that the soil contains a lot of organic matter
in the first 0.1 m, followed by small, disjointed limestone platelets
enveloped in silt. As the limestone matrix has a porosity of 5\%
\citep{Verdet2019}, it can only be concluded that this is the result of
macroscopic-scale porosity.

The median resistivity variations in cluster 2, which lies below
cluster 1 and down to a depth of 3.7 m, are approximately half the
amplitude of cluster 1. Furthermore, the maxima and minima of this
cluster always occur one month after the minima and maxima of cluster
1, regardless of the year. The greater depth of this cluster indicates
that the one-month time lag is associated with the time taken for water
to infiltrate the surface environment. This cluster appears to
represent the continuity of the gravity \mbox{infiltration} front, and also
reflects a material that dries out at a slower rate than cluster 1,
exhibiting a lower maxima.

It is noteworthy that the temporal variations in cluster 3, which are
also superficial (between 0 and 1 m, often between 0.6 and 0.8 m),
deviate from the norm. The resistivity is higher than all the other
clusters and the amplitudes are extremely high 
(300~$\Omega{\cdot}$m). The influence of maize roots has been simulated by
\citet{Raoetal2019}, showing that any such impact depends on the size of
the roots and the soil. According to Archie's law, a ratio of degrees
of water saturation of 62\% would be observed between summer and
winter. Furthermore, it reaches a resistivity maximum at the same time
as cluster 1 except in 2017 and 2022, when measurements were taken
following the felling of trees on the site. Cluster 3 responds first,
occurring between December and January, approximately less than one
month before cluster 1. This occurs shortly after the resumption of
precipitation, and the decrease is very abrupt. As this cluster is
located under the trees, it would reflect the impact of the resumption
of precipitation (between September and November) and the concomitant
reduction in leaf activity, particularly oak transpiration. Regardless
of rainfall, the end of the minimum plateau is reached at the end of
April. This period is undoubtedly linked to the resumption of foliation
observed in oaks from early April, accompanied by significant
evaporation a month later when foliage is more developed and the
duration of sunshine is greater. The amplitude of the seasonal cycles
is much greater than in clusters 1 and 2, suggesting greater drying in
summer, linked to tree transpiration. Clearly, the temporal behaviour
of this cluster is closely linked to tree transpiration activity. In
addition, trees are located within a 5 m radius of the profile. This
cluster must be the site of the most active root tissue, in the form of
rootlets, as observed in a trench to the south of the Lascaux site.
\citet{RiederKneisel2023} show
that the high variability of electrical
resistivity is noticeable at a depth of 0.4 m under pines and beeches
in sand and conclude that this variability is due to the influence of
roots. This depth is consistent with the depth of cluster 3 (from 0 to
1 m and especially between 0.6 and 0.8 m) in limestone.

This time-lapse study allowed us to gain a more detailed of the
behaviour of the massif under the felled trees, within a 5 m radius. It
clearly shows a \mbox{decrease} in resistivity under these trees in the summer
following their demise. Transpiration is weakened around the felled
trees, and compensation from the surrounding trees has not yet taken
place, beginning instead in the following summer. This suggests that
the phenomenon of compensation of the other trees, whether linked to
leaf or root enlargement of the remaining trees, is effective after 18
months. The end of this compensation period is more difficult to
estimate, given the temperatures and electrical resistivity of the
superficial clusters between 2013 and 2023. The area studied shows no
increase in electrical resistivity, unlike the superficial clusters
studied previously.

Cluster 4 shows no real annual variation. The most likely analysis of
this cluster is that made by \citet{Rissetal2016}. 
Indeed, detailed
analysis of block resistivity values over the seasons shows a
centripetal flow of water towards cluster 5. The median of this cluster
is therefore not representative of this spatially variable behaviour
but this value increased over the course of the 11 years.

\begin{figure*}
\includegraphics{fig09}
\caption{\label{fig9}3D model of temperature propagation through the
Lascaux massif on 15 May 2014 after eight years.}
{\vspace*{-2pt}}
\end{figure*}

Cluster 5 is unique, with a very low minimum resistivity median of 
61~$\Omega{\cdot}$m and a maximum value of 110~$\Omega{\cdot}$m, i.e.,
applying Archie's formula, a ratio of degree of saturation of 75\%. The
maximum resistivity is reached one month after cluster 2, while the
minimum threshold is reached one month before cluster 2. This cluster
is therefore fed exclusively by gravity infiltration from cluster 2.
What is remarkable is the temporal link with the flow rate measured at
the outlet of airlock~1. The minimum resistivity threshold is reached
almost synchronously with the occurrence of a significant flow,
whatever the year considered, and the decrease in flow occurs about 1
month before the resistivity increases again in cluster 5, suggesting
that the absence of water supply to this cluster and the drainage by
the airlock's source generates this drying out measurable in ERT. In
addition to this temporal link, the spatial location of this cluster at
an altitude slightly higher than that of the spring and which can be
extended, as shown on the 3D model (Figure~\ref{fig6}), suggests that
this is indeed a temporary reservoir that feeds the outlet of the
airlock. The shape of this reservoir has the tortuosity of a karstic
conduit, suggesting that it has been altered in the form of sand. This
type of sandy formation can also be seen both in the Sanded Hall of the
prehistoric cave and in excavation work. Furthermore, a spatial
continuity towards the contact point between the detrital and
calcareous formations, located further north, seems to emerge. The
temporal variation in the shape of this reservoir could point in the
direction of a water flow, which might begin from the contact point
with the detrital formations. This would explain why cluster 5 is not
only fed by the overlying cluster 2. Furthermore, from a conservation
point of view, the extension of this temporary reservoir into the
detrital formations would mean that not only the limestone formations
would have to be protected, which is already the case, but also the
detrital formations. However, the risk of water pollution arriving at
the outlet of airlock~1 is reduced by the fact that water infiltrating
the sandy-clay detrital formations will be filtered as it passes
through the detrital formations and then the weathered limestone
formations. Furthermore, the volume of this reservoir can be estimated
at 880~m$^{3}$ \citep{Verdet2019} based on the geometric data of the 3D
model, i.e., a water volume of 264~m$^{3}$ with a porosity of~30\%.

This study of the site and the previous data have made it possible to
examine the impact of heterogeneities on heat propagation in the
massif. Initial estimates of the thermal diffusivity of the different
clusters that make up the Lascaux massif in the vicinity of the cave
suggest values consistent with knowledge of the geological formations
\citep{Lhartietal2024}. Coniacian limestone is found to present a thermal
diffusivity of $2.2\times 10^{-6}$~m$^{2}{\cdot}$s$^{-1}$; around 
$1\times 10^{-6}$~m$^{2}{\cdot}$s$^{-1}$ for sandy-clay formations and around 
$6\times 10^{-7}$~m$^{2}{\cdot}$s$^{-1}$ for weathered Santonian limestone.
Knowing the thermal diffusivity of each cluster and the temperature at
many points, heat propagation could be simulated across the massif and
into the cave.

Initial simulations show that the decisive role played by the interface
between the Santonian and Coniacian limestones, which, although
sub-horizontal, generates different thicknesses of Santonian limestone,
depending on both the topography of the hill and the influence of
detrital formations. In addition, the considerable disparity between
the thermal diffusivities of these formations affects heat propagation
significantly. In May, the superficial rock mass is influenced by the
cold temperature of winter (Figure~\ref{fig9}) due to the phase shift.
It is therefore clear that heat propagation is faster in the
north-eastern part of the cave than in the southern, superficial part
in May. Generally speaking, taking geophysical and geological
heterogeneities into account results in a thermal front that is neither
horizontal nor parallel to the topography. Temperatures at the cave
wall will therefore differ according to their spatial position. For
example, the right wall of the Great Hall of the Bulls is affected by
the thermal front before the left wall. This effect can also be
observed between the southernmost gallery (Main Gallery), under a
thicker layer of Santonian limestone, which cools at a faster rate than
the easternmost gallery (Painted Gallery), which is also close to
detrital formations \citepalias{Lhartietal2024}.

\section{Conclusion}\label{sec5}

The conservation of decorated caves requires knowledge of the
surrounding environment. This extends from the vegetation to the
adjacent rock, and includes the circulation of water in the massif
itself, as well as external climatic conditions such as changes in air
temperature and rainfall. The phenomena observed and recorded have
long-term impacts and necessitate an understanding of multiple
hydro-climatic cycles.

The Lascaux site has been studied and equipped by microclimatologists
for over 60 years, and has been subjected to geophysical and forestry
research for over 10 and 7 years, respectively. Using all of the
available data gathered through these studies not only makes this
analysis possible in the first place; it also highlights the links
between the various phenomena observed.

This article has shown that ERT can be used to discriminate between
different clusters with similar temporal variations, using statistical
clustering methods such as HCA. It has demonstrated that these clusters
are related to the more or less rapid way in which water circulates in
each of them. A particular cluster is distinguished by its temporal
variations. The spatial extent of this cluster could be determined with
3D surveys carried out at two characteristic dates determined by the
knowledge of the temporal behaviour of this cluster: the periods of
high and low water content of this cluster. The end of the identified
volume is located near the source of airlock~1. The temporal
consistency of the resistivity variations with the flows recorded in
the emergence makes it the temporary reservoir of the source of the
airlock~1.

While water infiltrating the massif plays a direct role in reaching the
decorated walls, whether on the rock art or on the supporting rock, it
also plays a role in the thermo-aeraulic balance of the cave. At
Lascaux, the water temperature is almost always colder than the rock
temperature, but the presence of water also modifies the thermal
diffusivity of the rock mass.

The 3D modelling of ERT data from the massif surrounding the cave
clearly illustrated the close link between electrical resistivity
heterogeneities and the nature of geological formations
\citep{Xuetal2016, Verdetetal2020}. It was therefore essential to study
the effect of these heterogeneities on heat propagation through the
massif surrounding the cave. This geophysical and thermal coupling
proved invaluable. It demonstrated the respective influence of the
different geological formations and showed the close links in this
context between thermal diffusivity and electrical resistivity for the
majority of the materials encountered at the site. However, the effect
of variations in the water content of the various reservoirs has not
yet been modelled, and further investigation in this area would be
beneficial from a conservation perspective.

Furthermore, the ongoing research continues to highlight the impact of
the forest and tree felling on water circulation within the massif,
directly influencing water circulations in the cave. However, the
potential for significant and prolonged disruption to this process may
be more pronounced in the event of a widespread forest die-off, as
might be caused by climatic events such as fires or storms.

The hydro-thermal-air balance at the cave wall is contingent upon the
totality of external events and the massif's capacity to absorb them.
This balance can either favour condensation or precipitation phenomena
or modify the existing flora and fauna in the cave. It thus appears
evident that studies aimed at the conservation of caves must consider
all external events, as well as the entirety of the critical zone.
While this has been demonstrated at the Lascaux site, further studies
of caves in different contexts (open to the public, ventilated, deeper,
etc.) would be beneficial, taking into account the existing body of
knowledge.

\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*{Acknowledgements}

The authors would like to express their gratitude to the French
Ministry of Culture for its financial \mbox{support.} In particular, they wish
to acknowledge the invaluable assistance of Muriel Mauriac, curator of
the Lascaux cave, who provided unwavering support as well as access to
the site.

\back{}

\printbibliography
\refinput{crgeos20241071-reference.tex}

\end{document}
</pre></body></html>