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\DOI{10.5802/crgeos.253}
\datereceived{2023-02-27}
\daterevised{2023-11-20}
\datererevised{2024-01-05}
\dateaccepted{2024-01-08}
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\begin{document}

\begin{noXML}

%\makeatletter
%\def\TITREspecial{\relax}
%\def\cdr@specialtitle@english{Geodynamics of continents and oceans - A tribute to Jean Aubouin}
%%\def\cdr@specialtitle@french{G\'eodynamique des continents et des Oc\'eans - Hommage \`a Jean Aubouin}
%\makeatother

\title{The Western Alpine arc: a review and new~kinematic~model}

\alttitle{L'arc des Alpes occidentales : synthese et nouveau mod\`{e}le
cin\'{e}matique}

\author{\firstname{Quentin} \lastname{Brunsmann}\CDRorcid{0009-0009-1442-4537}\IsCorresp}
\address{ISTeP, Institut des Sciences de la Terre de Paris, Sorbonne
Universit\'{e}, 4 place Jussieu, 75005 Paris, France}
\email[Q. Brunsmann]{quentin.brunsmann@sorbonne-universite.fr}

\author{\firstname{Claudio Luca} \lastname{Rosenberg}\CDRorcid{0000-0001-6663-3650}}
\addressSameAs{1}{ISTeP, Institut des Sciences de la Terre de Paris,
Sorbonne Universit\'{e}, 4 place Jussieu, 75005 Paris, France}
\email[C. L. Rosenberg]{claudio.rosenberg@sorbonne-universite.fr}

\author{\firstname{Nicolas} \lastname{Bellahsen}\CDRorcid{0000-0003-4264-4552}}
\addressSameAs{1}{ISTeP, Institut des Sciences de la Terre de Paris,
Sorbonne Universit\'{e}, 4 place Jussieu, 75005 Paris, France}
\email[N. Bellahsen]{nicolas.bellahsen@sorbonne-universite.fr}

\shortrunauthors

\begin{abstract}
The arcuate shape of the Western Alps is commonly interpreted to result
from collisional, NW-ward indentation of the Adriatic indenter. The
radial pattern (${\approx}$180\textdegree) of collisional transport
directions is difficult to explain, especially in the southern WNW--ESE
to E--W striking arc segments. A mid-Cenozoic change, from NW- to
W-directed indentation is often proposed, but poorly constrained. Based
on a critical review of conceptual models for the formation of the
Western Alpine arc and associated geodynamic processes, we conclude
that an arcuate structure already exists before the onset of collision.
NW-ward indentation of the Adriatic indenter amplifies this
arc structure by oroclinal bending, but the E--W to ESE--WNW striking,
southernmost segments of the Alpine arc mainly result from distinct
geodynamic processes, other than Alpine convergence in the strict
sense. The southernmost External Zone is mainly inherited from the
Pyrenean orogeny and was weakly reactivated in the Miocene, probably
accommodating very small parts of Africa--Europe convergence since Late
Miocene times. In the Internal Zone, the E--W strike of the Ligurian
Alps is probably associated with 50\textdegree\ counterclockwise
rotation of the northern Apennines.
\end{abstract}

\begin{altabstract}
La forme arqu\'{e}e des Alpes occidentales est g\'{e}n\'{e}ralement
interpr\'{e}t\'{e}e comme \'{e}tant le r\'{e}sultat d'une indentation
collisionnelle vers le NW par l'indenteur adriatique. Le caract\`{e}re
radial (${\approx}$180\textdegree) des directions de transport
collisionnel est difficile \`{a} expliquer, en particulier dans les
segments au sud de l'arc orient\'{e}s WNW--ESE \`{a} E--W. Le passage
d'une indentation orient\'{e}e vers le NW \`{a} une indentation
orient\'{e}e vers l'W au milieu du C\'{e}nozo\"{i}que, est souvent
propos\'{e} mais peu contraint. Sur la base d'un examen critique des
mod\`{e}les conceptuels de formation de l'arc des Alpes occidentales et
des processus g\'{e}odynamiques associ\'{e}s, nous concluons qu'une
structure arqu\'{e}e existait d\'{e}j\`{a} avant le d\'{e}but de la
collision. L'indentation vers le NW de l'indentateur adriatique
amplifie la forme arqu\'{e}e de l'orog\`{e}ne par une flexion
oroclinale, mais les segments les plus m\'{e}ridionaux de l'arc alpin,
orient\'{e}s E--W \`{a} ESE--WNW, r\'{e}sultent principalement de
processus g\'{e}odynamiques distincts, autres que la convergence alpine
au sens strict. La partie la plus m\'{e}ridionale de la Zone Externe
est principalement h\'{e}rit\'{e}e de l'orogen\`{e}se
pyr\'{e}n\'{e}enne et faiblement r\'{e}activ\'{e}e au Mioc\`{e}ne,
accommodant probablement une tr\`{e}s faible quantit\'{e} de la
convergence entre l'Afrique et l'Europe depuis le Mioc\`{e}ne
sup\'{e}rieur. Dans la Zone Interne, l'orientation E-O des Alpes
ligures est probablement associ\'{e}e \`{a} une rotation antihoraire de
50\textdegree\ de la partie Nord des Apennins. 
\end{altabstract}

\keywords{\kwd{Western Alpine arc}\kwd{Structural
inheritance}\kwd{Collisional indentation}\kwd{Adriatic indenter
rotation}\kwd{Gravitational tectonic}}

\altkeywords{\kwd{Arc des Alpes occidentales}\kwd{H\'{e}ritage
structural}\kwd{Indentation collisionnelle}\kwd{Rotation de l'indenteur
adriatique}\kwd{Tectonique gravitaire}}

\maketitle

\vspace*{6pt}

\twocolumngrid

\end{noXML}

\section{Introduction}\label{sec1}

Most mountain belts are characterised by arcuate shapes, whose
amplitude and wavelength vary significantly as a function of different
lithospheric structures and geodynamic processes 
\citep[e.g.,][]{WortelSpakman2000,Schellart2004}.
Such orogens are termed oroclines as
proposed by \citet{Carey1955} to describe mountain ranges whose
structural trend changes along-strike, although later definitions
suggest that this term should only refer to ranges evolving in time
from straight to arcuate axes \citep{HindleBurkhard1999}. Today, the
term orocline is used to characterise arcuate mountain belts whose
shape is acquired by bending an initially rectilinear orogen, as
opposed to the primary arc whose shape is inherited from processes
preceding the formation of the orogen \citep[e.g.][]{YonkeeWeil2010}.

A distinction can be made between arcs which develop in thin-skinned
tectonics, and lithospheric-scale arcs, which affect entire mountain
belts. The former concern mainly foreland chains like the Jura
Mountains \citep{Gehringetal1991, HindleBurkhard1999} or the arcs of Nice
and Castellane in the southern French Alps. These arcs develop by the
propagation of fold and thrust belts in divergent directions above a
level of decollement \citep[e.g.,][]{HindleBurkhard1999}. No
lithospheric-scale bending is associated with these arcs, in contrast
to the arcs of the Apennines \citep{LucenteSperanza2001,
Rosenbaum2014,RosenbaumLister2004a,RosenbaumLister2004b}, the Scotia arc 
\citep{BarkerDalziel1983,Royden1993,Dalzieletal2013}, the Taiwan arc
\citep{HsuSibuet1995,SibuetHsu1997,Malavieilleetal2002,SibuetHsu2004},
or the western Alpine arc \citep{Zhaoetal2016,Kastleetal2020,
Paffrathetal2021,Handyetal2021}, which we therefore describe as
lithospheric arcs.

The latter type of arcs bound most Mediterranean margins 
\citep{Royden1988}, including the Betic-Rif chains, the Apennines, the
Calabrian arc, and the Aegean arc (Figure~\ref{fig1}). Most of them are
associated with a slab roll-back during subduction \citep{Royden1988,
RoydenBurchfiel1989, Rosenbaum2014, RosenbaumLister2004a,
RosenbaumLister2004b,WortelSpakman2000}. 

\begin{figure*}
{\vspace*{2pt}}
\includegraphics{fig01}
{\vspace*{3pt}}
\caption{\label{fig1}Arcuate mountain belts bounding the western
Mediterranean \citep{Tapponnier1977,Handyetal2010,Faccennaetal2014,
VanHinsbergenetal2020, Jolivetetal2020,Jolivetetal2021}.}
{\vspace*{3pt}}
\end{figure*}

The arc of the Western Alps is characterised by a continuous
topographic relief, forming a semi-circular structure, from the
French--Italian Mediterranean coast in the south, to the western Swiss
Alps in the north. This arcuate structure affects all major alpine
tectonic units, but some ambiguity exists in the literature concerning
its southwestern termination. Whereas some authors set it north of Nice
\citep[e.g.,][]{Staub1924,Laubscher1988,Roureetal1989}, others set it
further west, bounding the Rhone and Bresse graben structures, north of
Marseille \citep[e.g.,][]{SchmidKissling2000,KempfPfiffner2004}. In
the following we describe the arc of the Western Alps as the one
coinciding with the entire topographic relief, i.e. extending as far as
the Rhone graben and in the final discussion we argue whether this area
as a whole is correctly described as an Alpine feature in terms of
tectonic\break processes.

The Western Alpine arc is generally interpreted as a syn-collisional
orocline, formed from the Priabonian onwards, by indentation of the
Adriatic \mbox{indenter} into the European plate  
\citep[e.g.,][]{Tapponnier1977,Choukrouneetal1986,RicouSiddans1986,
Vialonetal1989,Plattetal1989, Laubscher1991, Cerianietal2001,
Fordetal2006,Handyetal2010,Schmidetal2017}, in contrast to most other
Mediterranean arcs (Figure~\ref{fig1}), which are inferred to develop
during the subduction \citep{Royden1988}. The semi-circular Western
Alpine arc is characterised by northward tectonic transport in the
North, westward transport in the West and southward transport in the
South (Figure~\ref{fig2}c) \citep{Siddans1979,Choukrouneetal1986,
Plattetal1989,Handyetal2010,Schmidetal2017}. Such radial transport
poses many questions regarding the lateral kinematic compatibility and
deformation mechanisms of this arc. On the one hand, no systematic,
large-scale, along-strike stretching of the orogenic wedge is
documented by structural studies, a process required in order to
accommodate progressive lengthening of the amplifying arc during the
formation of the orocline \citep[e.g.,][]{YonkeeWeil2010}. On the
other hand, indentation experiments \citep{Lickorishetal2002}, designed
to investigate west-Alpine indentation, successfully produce radial
shortening around more than half of the square indenters, but not along
an entire, semicircular arc, if the indentation direction is constant
throughout the experiment. As a consequence, many hypotheses such as
structural/geometrical inheritance of the European margin, change of
direction of Adriatic indentation, rotation of the Adriatic indenter
and other domains of the Alps, are commonly invoked to explain the
strong curvature of structures accommodating shortening all along the
arc \citep[e.g.][]{Vialonetal1989,Collombetetal2002}.

\begin{sidewaysfigure*}
\vspace*{20pc}
\includegraphics{fig02}
\vspace*{-4pt}
\lbcaption{\label{fig2}}{1}{(a) Synthesis of the strike-slip fault described
in the literature in map. White semi-arrow: sinistral strike-slip
movement associated with the northward translation of the Adriatic
indenter between 80--90 and 25--30~Ma \citep{RicouSiddans1986}; grey
semi-arrows: sinistral strike slip movement to the south of the arc and
dextral strike slip movement to the north of the arc associated with a
westward indentation of Adria since the Oligocene
\citep{Laubscher1971,Laubscher1988,Laubscher1991, Lefevre1984,
Ricou1981,Ricou1984,RicouSiddans1986,Ritz1992,
SchmidKissling2000,Pianaetal2009, Pianaetal2021,
Schmidetal2017}; black semi-arrows: numerous strike-slip
faults, dextral and sinistral in the External Zone, and dextral
reactivation of the PFT end the Periadriatic Fault
\citep{Vialonetal1989, SewardMancktelow1994,
Gigliaetal1996, AubourgChabertPelline1999, 
Collombetetal2002,Bauveetal2014,
Balansaetal2022}. (b) Sinistral strike-slip faults inferred to
accommodate the westward indentation of Adria since 35~Ma
\citep{Laubscher1971,Laubscher1988,Laubscher1991, Lefevre1984,
Ricou1981,Ricou1984,RicouSiddans1986, Pianaetal2009, Pianaetal2021,
Schmidetal2017}. (c) Simplified Tectonic map with
tectonic transport direction \citep{Handyetal2010}. {White
arrows}: pre-collisional tectonic transport direction (83--35~Ma);
{Black arrows}: inferred collisional tectonic transport
direction (35--20 Ma).} 
\vspace*{-2pt}
\endfig
\end{sidewaysfigure*}

With the aim of understanding the processes that formed the Western
Alpine arc, in the following we summarise more than a
century of research on this subject and propose a new kinematic model.
This model is based on the critical literature review, but also on a
new analysis of structures in the southernmost External Zone. We show
that the central and northern parts of the Western Alpine arc are most
likely explained by syn-collisional, oroclinal amplification of a
subduction arc, whereas the southern part of this arc results from a
combination of processes including initial oroclinal bending, rotations
controlled by Apenninic slab retreat and Upper Miocene inversion of the
Ligurian margin, and \mbox{asthenospheric} flow around the southern limit of
the European slab, possibly re-orienting crustal structures.\looseness=1

\section{Tectonic setting}\label{sec2}

The Western Alpine arc (Figure~\ref{fig2}a) is a unique feature within
the Alpine chain, which otherwise strikes ENE--WSW from the Eastern to
the Central Alps. In the External Zone, the arc extends from the Jura
mountains in the north to the Nice--Castellane arcs in the south
(Figure~\ref{fig2}a). In the Internal Zone, the arc extends from the
northeastern margin of the Sesia Zone in the north to the Ligurian Alps
in the south (Figure~\ref{fig2}a).

Two major differences characterise the Internal and External Zones in
terms of arc morphology of the Western Alps: (1) Alpine structures in
the Internal Zone result from the subduction and the following
collisional overprint, whereas those in the External Zone only result
from collision [e.g., \citealp{Handyetal2010}, for a summary of
tectonic events in these distinct domains]. (2) The Internal Zone forms
a continuous 180\textdegree\ arc showing a progressive rotation of its
main structures from the Lepontine Dome to the Ligurian Alps
(Figure~\ref{fig2}a). In contrast, progressive rotation of structures
in the External Zone is only observed along an arc of 90\textdegree\ 
between the ENE--WSW structures north of the Central Alps and the N--S
to NNW--SSE striking arc segment, terminating at the
Guillaumes--Castellane Fault (Figure~\ref{fig2}a). South of the Dignes
nappe, the main structures abruptly change to an E--W orientation,
producing an elbow, rather than an arc (Figure~\ref{fig2}a).

Palaeogeographic reconstructions of the Mesozoic western Alpine domain
point to the occurrence of three distinct, pre-Alpine continental
areas separated by two oceanic and/or continental, extended domains
\citep[e.g.,][]{Stampli1993,Froitzheimetal1996,Schmidetal2004,
Agard2021}. 

The southernmost continental area corresponds to {the Adriatic
margin} (Figure~\ref{fig2}a), largely covered by the Molasse in the Po
Plain, and bound to the west by the Ivrea body (Figure~\ref{fig2}a).
The latter is inferred to behave as an indenter during Alpine collision
\citep[e.g.][]{Tapponnier1977,Channelletal1979,Dumontetal2011,
Schmidetal2017}. It is a northern protuberance of the African Plate
\citep{Argand1924,Tapponnier1977,Channelletal1979, Anderson1987}, whose
displacement may partly differ from that of Africa during Neogene time
\citep{vanHinsbergenetal2014}. The more distal part of this Adriatic
\mbox{margin} forms the Austroalpine nappe stack (Figure~\ref{fig2}a), located
to the N and NW of the Periadriatic Fault (Figure~\ref{fig2}a). Below
the Austroalpine nappes lies {the Liguro--Piemont (L--P) Domain}
(Figure~\ref{fig2}a), consisting of oceanic-derived crustal nappes. Its
structurally uppermost units are formed by the barely metamorphic
Helminthoid Flysch, whose basal thrust passed over the more external
Dauphinois domains. {The Brian\c{c}onnais Domain}
(Figure~\ref{fig2}a), lying in the footwall of the L--P Domain,
consists of basement and cover nappes derived from the
north-easternmost part of the paleo-Iberian continent
\citep{Stampli1993} and lying above the {Valais Domain}
(Figure~\ref{fig2}a). The latter is exposed in the outermost part of
the Internal Zone but it completely lacks south of Moutiers
(Figure~\ref{fig2}a). An open debate is still ongoing concerning the
age of the oceanic basement included in its nappes [pre-Mesozoic,
Jurassic, or Cretaceous; e.g.,
\citealp{Loprienoetal2011,Beltrandoetal2012}] and on the nature of the
Valaisan basement as a whole: continental \citep{Massonetal2008},
oceanic \citep[e.g.,][]{Loprienoetal2011}, or hyperextended and rifted
margin  \citep{LeBretonetal2021}. {The European margin} 
(Figure~\ref{fig2}a) with its Palaeozoic basement and Mesozoic cover
are exposed in and around the External Crystalline Massifs (ECM). The
external-most part of the cover is shortened mainly above Triassic or
Liassic d\'{e}collements, forming the subalpine ranges, and the Jura
Mts and deforming the Cenozoic Molasse\break Basin.

The Valais, Brian\c{c}onnais, L--P and Sesia domains form the Internal
Zone of the Western Alps, as opposed to the External Zone, which
corresponds to the European continental margin. The Internal Zone is
delimited to the East by the Periadriatic Fault, which separates the
``Backstop'' (Adriatic indenter) from the orogenic wedge. To the west
and north of the Internal Zone is delimited by the Penninic Frontal
Thrust (PFT; Figure~\ref{fig2}a), which displaces the internal units on
the external ones, from the late stages of the subduction to the early
stages of collision \citep{Cardelloetal2019}. The prolongation of the
PFT in depth coincides with the lower plate-upper plate interface [e.g.
\citealp{Schmidetal2017}; their figure~2]. In the External Zone, the
shape of the arc is underlined by the NE--SW trending ECMs from the Aar
to Belledonne, followed southward by the NW--SE trending ECMs between
Pelvoux and Argentera. This map-scale trend parallels their internal
fabric \citep{Dumontetal2012}, and it is partly tracked by the Digne
Nappe Front (DNF, Figure~\ref{fig2}a) and the Jura Mts in the more
external parts of the Chain (Figure~\ref{fig2}a). 

Alpine orogeny initiates at around 85~Ma \citep[e.g.,][]{Deweyetal1989,
StampfliBorel2002, BergerBousquet2008}, with south- and
southeast-directed subduction of the Austroalpine Sesia slice, as
testified by its HP metamorphism \citep{DalPiazetal1972,Stampli1993}.
This first stage is followed by the subduction of the L--P Ocean, then
by the Brian\c{c}onnais domain, before ending with the Valaisan domain
and part of the distal European margin \citep[e.g.,][]{Deweyetal1989,
StampfliBorel2002, BergerBousquet2008,
LeBretonetal2021}. The transition from the subduction to
collision takes place at around 34~Ma, possibly coinciding with slab
break-off  \citep{vonBlanckenburgDavies1995}, immediately preceding a
pulse of magmatism along the Periadriatic Fault \citep{Rosenberg2004}.
This time is also characterised by the onset of molasse-type basin
deposits in the foreland at 30--34~Ma
\citep{Matteretal1980,Sinclair1997}, slightly preeceding Barrovian
metamorphism in the Internal Zone \citep{Engietal2004,Bousquetetal2008},
and thick-skinned tectonics in the
External Zone  \citep{BurkhardSommaruga1998,
Bellahsenetal2014}.

\section{Processes inferred to form the Alpine arc}\label{sec3}

In the following we critically review the interpretations suggested to
explain the shape of the western Alpine arc, and eventually propose a
new conceptual kinematic model.

\subsection{Structural inheritance}\label{ssec31}

Structural inheritance of the stretched Mesozoic continental margins
may control both tectonic style and morphology of the orogen. Indeed,
variations in the orientation, thickness and rheology of the
lithosphere, inherited from extensional episodes, may significantly
impact collisional deformation \citep[e.g.,][]{Butler2017}.
Inherited structures from Hercynian and post-Hercynian tectonics may
influence both Mesozoic extension, and Alpine shortening. 

\subsubsection{Variscan inheritance}\label{sssec311}

The very first conceptual model invoking pre-Alpine structures to
explain the existence and orientation of the Alpine ones goes back to
\citet{Argand1916}, who suggests that the arcuate shape of the
Western Alps results from the adaptation of the internal alpine domains
to a pre-existing ``Hercynian hemicycle'' during Alpine
convergence. At that time, before the modern definitions of subduction
and continental margins, Argand imagines pre-orogenic crustal-scale
fold sequences, becoming amplified in a ductile crust by convergence
against more rigid obstacles (the External Massifs). \citet{Argand1916}
suggests that Alpine convergence is directed NNW, thus with tectonic
transport almost normal to the front of the chain in the North, but
largely oblique to the margin underlined by the southern ECMs
(Figure~\ref{fig3}a,b). 

{\xsubfig[ph!]{3}{}
\figcnt
\begin{figure*}
{\vspace*{-.8pc}}
\xincludegraphics{fig03}
%{\vspace*{-4pt}}
\xcaption{\ffigcaption}{\fontsize{9.9}{12}\selectfont(a) 
Argands conceptual model of the ``trouble
surge'' \citep[modified from][]{Argand1916}. The most external
discontinuous line is the maximal extension of the internal nappes. The
most internal discontinuous line is the prolongation of the
Periadriatic Fault. The other internal discontinuous lines, at the
southern end of the western Alpine arc, is probably the continuation of
a major thrust in the Internal Zone, maybe between the Brian\c{c}onnais
units and the Helminthoid flysch. The black continuous lines in the
Internal Zone (Penninic nappes) correspond to the trajectory of
structures such as folds. The dashed arrows connect the different
inflection points of these trajectories. (b) synthetic image of the
``trouble surge'' (``d\'{e}ferlement contrari\'{e}'') in the Alpine arc
\citep[modified from][]{Argand1916}. {White arrow}: direction
of push (${=}$direction of the Adriatic indentation); {Black
arrows}: direction of flow. The size of the arrows is proportional to
the amount of flow. (c) Rotation model modified from
\citet{Vialonetal1989}. This model proposes the counterclockwise
rotation of an independent block located NW of the Adriatic indenter.
This fragment of the Adriatic indenter is rotated in order to
accommodate NNW indentation of the remainder of the Adriatic indenter
to the east. (d) Rotation model modified from \citet{Collombetetal2002}
suggesting counterclockwise rotation of about 20 degrees of the
indenter accommodated by dextral reactivation of the PFT and the
Periadriatic Fault. This rotation is accompanied by southward lateral
extrusion of the Internal Zone and numerous dextral strike-slip faults
showing a fan shape in map view. South of the arc, rotation inferred
from paleomagnetic data increases and is interpreted as distributed
sinistral zone (discontinuous lines). (e) Rotation model modified from
\citet{Bauveetal2014} suggesting counterclockwise rotation of the
Adriatic indenter associated with dextral kinematics in the south of
the arc since at least 12~Ma, based on the inversion of structural data
and focal mechanisms from the southern part of the western Alpine arc.
(f) Tectonic deformation sequence in the Mediterranean area \citep[modified
from][]{Tapponnier1977}. This model proposes that the
peri-Mediterranean chains, and notably the Alps, are formed by the
indentation of plastic domains (the European continental margin in the
case of the Alps) by rigid promontories (the Adriatic indenter in the
case of the Alps). We observe that a change of indentation direction,
from NW-ward to westward, occurs between 50 and 10~Ma. (g) Northward
displacement of the Adriatic indenter, followed by westward impingement
(dashed faults), generates successive orthogonal thrust systems and
their associated strike-slip faults 
\citep[modified from][]{RicouSiddans1986}. (h) Retrotranslation of the EW
(horizontal hatching) and the NS (vertical hatching) components of the
Adriatic indenter in the late Oligocene (post-30~Ma) to early Miocene
(16~Ma) modified from \citet{Laubscher1991}. (i)~Palinspatic
reconstruction modified from \citet{Dumontetal2012}. Note the inferred
progressive rotation of Adriatic indenter convergence direction, from
northward to WNW-ward. (j) Motion vectors produced by the interaction
between the Adriatic indenter motion vector and body forces acting
normal to the trand of a mountain belt; the latter should lie within
90\textdegree\ of the Adriatic indenter motion vector 
\citep[modified from][]{Plattetal1989}.  (k) Sandbox experiment showing the
development of an arcuate thrust belt due to diagonal indenter motion 
\citep{Lickorishetal2002}. The plate-motion vector (large arrow) lies
at  33\textdegree\ to the lateral edge of the indenter. The small
arrows represent incremental displacement vectors of material points at
grid intersections. (l) Palaeogeographical reconstructions of the
western Alps during Priabonian and Burdigalian times modified from 
\citet{Fordetal2006}. It consists of a shift from a northward to a
NW-ward indentation around 30~Ma \citep{Fordetal2006}, accommodated in
particular by a sinistral strike-slip southwestern boundary of the
Adriatic indenter. (m) Kinematic restoration of the Alps--Apennines
orogenic system using Gplates reconstruction software 
\citep[e.g.][]{vanHinsbergenetal2014} holding Europe fixed 
\citep[modified from][]{Schmidetal2017}. It implies a shift from a northward
indentation to a WNW-ward indentation between~35 and 25~Ma.}
\end{figure*}
}

The advance of the nappes on the outer ``semicircular slope'' of the
arc, corresponding to the European continental margin, is due to the
push of a rigid edge [``m\^{o}le m\'eridional; m\^{o}le propulseur''; 
\citealp{Argand1916}], nowadays termed the Ivrea Indenter 
\citep[e.g.,][]{Laubscher1971,Tapponnier1977,SchmidKissling2000,
Dumontetal2011, RosenbergKissling2013,
Schmidetal2017}. Only the latest phase of the arc's
development, in terms of its shape, takes place during Alpine orogeny
in the view of \citet{Argand1916}. It corresponds to a relatively small
\mbox{displacement}, bringing the southern (Argentera Massif) and northern
(Aar Massif) ECMs closer to each other, thus slightly increasing the
arc curvature. 

On the base of modern knowledge, the existence of an intact Hercynian
hemicycle is unlikely, \mbox{considering} that this region is the site
of two post-Hercynian oceanic openings (Liguro--Pi\'{e}mont and Valais)
and one subduction. However, palaeomagnetic data from Permian rocks in
the Argentera massif indicate no significant rotation since that time
\citep{Henry1971,BogdanoffSchott1977}. The same is true for the
Mesozoic cover of the ECMs located north of the Argentera Massif
\citep{Henry1992,MenardRochette1992,Crouzetetal1996}. This implies that
the 50\textdegree\ angle between the Hercynian foliations of the Aar,
Mt Blanc/Aiguilles Rouges, Belledonne/Grandes Rousses massifs and those
of the Pelvoux and Argentera already existed in the Permian 
\citep{Westphal1973}. 

A different kind of inherited structure is provided by the ``East
Variscan Shear Zone'' [EVSZ, \citealp{CorsiniRolland2009,
Padovanoetal2012}], corresponding to the southern
edge of the European plate. The EVSZ may affect Alpine tectonics,
particularly by controlling the location and orientation of the
Valaisan basin \citep{Ballevreetal2018,AngrandMouthereau2021}, which in
turn may control the location, distribution and style of deformation of
the Alpine orogen \citep{Bellahsenetal2014}. To conclude, the effect of
these Variscan inherited structures remains hypothetical and their
associated structures (crustal anisotropy, transform plate boundaries)
are not yet well characterised.

\subsubsection{Structures inherited from subduction}\label{sssec312}

Restoring collisional shortening in the External Zone all along the arc
\citep[][and references
therein]{Bellahsenetal2014,Rosenbergetal2021}
shows that the trace of the PFT in map view and the shape of
the foreland basin \citep{Fordetal2006} highlight the existence of a
pre-collisional, Late Eocene ``proto-arc'' [Figure~\ref{fig4};
\citealp{Bellahsenetal2014}]. These results, are consistent with many
Mediterranean subduction systems (Alboran, Aegean, Carpathian,
Apenninic-Calabrian; Figure~\ref{fig1}), whose arcuate shape is
inferred to form during the subduction roll-back 
\citep{Royden1993,WortelSpakman2000}.

\setcounter{figure}{3}

\begin{figure*}
\includegraphics{fig04}
\caption{\label{fig4}(a--d) Palinspastic reconstruction 
\citep[from][]{Bellahsenetal2014} showing the existence of a pre-collisional
proto-arc amplified during Alpine collision. (e) European margin at
Mesozoic time \citep{Bellahsenetal2014} showing extent and position of
Valaisan basin and the existence of a major NW--SE accident structuring
the European margin in the southern part of the present Western Alpine
arc.}
\end{figure*}

Several processes can explain arc formations during subduction. A
break-off at the southwestern end of the slab, resulting in a
southwestward traction decrease, could create a gradient in the amount
of NW-directed roll-back, producing an arcuate \mbox{morphology} prior to the
collision [e.g., \citealp{WortelSpakman2000}, to explain
peri-Mediterranean arcs shown in Figure~\ref{fig1}]. This model is
appropriate for the Alps, because tomographic sections indicate that
the slab is detached everywhere except beneath the central Alps
\citep{Handyetal2021}. Alternatively, tear fault models described for
other orogenic arcs of the peri-Mediterranean belts 
\citep{Romagnyetal2020,Jolivetetal2021} can explain subduction arcs.
Indeed, a NW--SE transform fault along the present-day NE edge of the
Argentera and Pelvoux massifs is inferred to have existed in some
palaeogeographic reconstructions \citep{Handyetal2010,Romagnyetal2020}.

\subsubsection{Pyreneo-Proven\c{c}al inheritance}\label{sssec313}

Pyrenean orogeny takes place between late Santonian--Campanian or early
Palaeocene and Priabonian [${\sim}$85~Ma--35~Ma; \citealp{Staub1924,
Lutaud1924,Siddans1979,PhilipAllemann1982,Tempier1987,
Bertrand1888,Zurcheretal1891,Kilian1892}]. This event, linked to N--S
convergence between Iberian and European plates 
\citep[e.g.,][]{LacombeJolivet2005,Schreiberetal2010,Advokaatetal2014,
VanHinsbergenetal2020} produces the Pyrenean chain, whose EW
structures extend all along the Mediterranean coast from Spain to the
French--Italian border, in the Alpine foreland  [Figures~\ref{fig1}
and~\ref{fig5}; \citealp{Bertrand1888,
Zurcheretal1891,Kilian1892,Lutaud1924,Lemoine1972,Siddans1979,
PhilipAllemann1982,Tempier1987,Balansaetal2022}], where they are termed
Pyreneo-Proven\c{c}al. These structures strike parallel to the
southernmost part of the western Alpine arc, and are partly located
within the latter area. Some of them clearly predate the Eo-Oligocene
Molasse sediments, and are reactivated in the Miocene
\citep{Grahametal2012}. Hence, the question of an Alpine vs Pyrenean
origin of this southernmost segment of the Alpine arc needs to be
discussed. The occurrence, and interference of such Pyrenean and Alpine
structures in the External Zone is described in the following
paragraphs.

\begin{figure*}
{\vspace*{-2pt}}
\includegraphics{fig05}
\caption{\label{fig5}(a) Structural map of the External Zone with major
structures and their inferred relative ages, from
\citet{Balansaetal2022}. Black lines represent sections along which
amounts of Alpine and pre-Alpine shortening are esimated
\citep{Fordetal2006,Bellahsenetal2012,Espurtetal2012,Jourdonetal2014, Bestanietal2015,
Bestanietal2016}. (b) Two-phase model of deformation
for the External Zone \citep{Lemoine1972,Siddans1979}.}
\end{figure*}

In the Diois and Baronnies, in the footwall of the Digne nappe and to a
very small extent in the Digne Nappe itself (Figures~\ref{fig2}a,
\ref{fig5}a), folds and thrusts are oriented E--W, seeming more
compatible with Pyrenean structures than with the sub-Alpine chains,
which are oriented NNW--SSE in this area [Figure~\ref{fig5}a;
\citealp{Lemoine1972,Siddans1979}]. However, in the Nice--Castellane arc
(Figure~\ref{fig5}), at the southern edge of the External Zone, at
least some of the E--W structures, are shown to be active even during
the Miocene \citep[e.g.,][]{Lemoine1972,Siddans1979,Jourdonetal2014,
Balansaetal2022}, hence after the termination of Pyrenean orogeny
[\citealp{Balansaetal2022}; Figure~\ref{fig5}a].

One may wonder if all E--W structures of the southern Dauphinois are not
mere Pyreneo-Proven\c{c}al structures, partly reactivated in the
Miocene, rather than newly formed, late Alpine structures. However, the
absence of exposed post-Eocene units in most of the area makes it
difficult to assess the age of these structures. North-verging folds
and thrusts are attributed to the Pyrenean event by some authors 
\citep[e.g.,][]{Balansaetal2022}, whereas south-verging ones to the Alpine
event s.s., but this discrimination remains rather speculative.

In summary, structural inheritance in the Western Alps may be related
to 3 distinct events: (1) by Mesozoic rifting potentially controlling
the shape of the European continental margin, and/or of the Adriatic
indenter; (2) pre-collisional structures related to the flexure of the
orogenic wedge caused by bending of the subducting slab; (3)
Pyrenean-Proven\c{c}al structures; which affect the southern E--W
segments of the subalpine ranges and in particular the Castellanne arc.
If the latter structures are accepted to be of Pyrenean-Proven\c{c}al
origin, the topographically continuous 180\textdegree\ arc of the
External Zone needs to be segmented into two parts in terms of its
formation processes. Its northern area, drawing a 90\textdegree\ arc
from the E--W orientation in the Central Alps to the N--S to NNW--SSE
orientation south of the Western Alps corresponds to the Alpine arc
s.s., resulting from Adria-Europe convergence. In contrast the
southernmost, E--W striking segment of the arc (Figure~\ref{fig2}a) is
of Pyrenean-Proven\c{c}al origin, formed during the convergence of
Europe and Iberia and their Miocene reactivation. We discuss below
(Section~\ref{ssec36}), which geodynamic causes may induce this
reactivation. 

\subsection{Collisional indentation}\label{ssec32}

Most collisional models of the western Alpine arc (Figure~\ref{fig3})
are based on the idea that the European continental margin deforms in
order to acquire the shape of the more rigid Ivrea indenter. This
hypothesis is based first on the evidence that the amount of shortening
in the Adriatic indenter is small compared to that observed in the
Internal Zone and in the Dauphinois and Helvetic 
\citep[for a review see][]{Rosenbergetal2021}, 
and second, on the fact that the
structural grain of the Internal Zone is parallel to the indenter
boundary, whereas structures within the indenter are not.

The larger strength of the Adriatic indenter is thought to be related
to the occurrence of the strong, sub-vertical slice of mantle rocks of
the Ivrea body, which borders its western edge 
\citep[e.g.,][]{SchmidKissling2000,Schmidetal2017}. This body, imaged by
seismic refraction, seismic tomography, and Bouguer anomaly analyses 
\citep{Giese1968,Berckhemer1969,Gieseetal1970,Fountain1976,
Pauletal2001,Lardeauxetal2006,Diehletal2009,Schmidetal2017},  indents
both the orogenic wedge and the European margin throughout Alpine
collision.

\citet{Tapponnier1977} is the first to propose an indentation model for
the formation of the Alpine arc (Figure~\ref{fig3}f), suggesting
Adriatic indentation in the European margin first towards the North, in
the Lower Cretaceous, and later towards the West, since the Upper
Cretaceous. \citet{Laubscher1991} provides the first indentation model
which attempts to balance in map view displacements related to an
inferred westward convergence of the Adriatic Indenter throughout
Alpine collision (Figure~\ref{fig3}h). \citet{Laubscher1971, 
Laubscher1988, Laubscher1991} notes that the northern boundary of the
``Ivrea mantle wedge'' coincides with the dextral Periadriatic fault
zone [Figure~\ref{fig2}a: the Jorio--Tonale Segment; 
\citealp{Laubscher1991}]. By retro-deforming the western Alpine nappes, he
concludes that this fault accommodates a westward translation of about
300~km of the Adriatic indenter between Oligocene and Lower Miocene. As
a consequence, a similar accident in opposite shear sense needs to
exist to the south of the arc \citep{Laubscher1971, Laubscher1988, 
Laubscher1991}, wich he terms Villavernia--Varzi--Levanto
Line \citep{Laubscher1991}.\looseness=1

More recent models suggesting westward indentation include dextral
strike-slip movements of approximately 100~km, also along the
Periadriatic Fault \citep{Schmidetal1996, SchmidKissling2000,
Rosenbergetal2021}, and sinistral strike slip (Figure~\ref{fig3}i)
along a structurally not yet characterised, nor precisely located zone
in the South of the arc. Different sinistral structures, located in
different areas, are proposed by different authors [Figure~\ref{fig2}b;
\citealp{Laubscher1971,Laubscher1991,Laubscher1996,
Ricou1981,Ricou1984,RicouSiddans1986,Pianaetal2009,
DAtrietal2016,Schmidetal2017, Pianaetal2021}]. The Acceglio--Cuneo Line
(Figure~\ref{fig2}b) of \citet{Schmidetal2017} and the
Villavernia--Varzi--Levanto Line (Figure~\ref{fig2}b) of
\citet{Laubscher1991}, are based on geometric considerations and map
view reconstructions. The sinistral Limone--Viozene Zone
(Figure~\ref{fig2}b), east of the Argentera, or its extension to the
north of the Argentera, in the Gardetta--Viozene Zone
[Figure~\ref{fig2}b; \citealp{Pianaetal2009,DAtrietal2016,
Pianaetal2021}], or the Stura ``corridor'' and the Preit ``scar''
[Figure~\ref{fig2}b; \citealp{Ricou1981,Ricou1984,
Lefevre1984, RicouSiddans1986}], are interpreted on the base of
structural field data. Alternatively, in the southernmost part of the
arc a more distributed sinistral shear zone [Figure~\ref{fig3}d--l;
\citealp{Collombetetal2002}], possibly corresponding to a sinistral
transpressive large-scale zone, as characterised by
\citet{Michardetal2004}, is also suggested. Interestingly, that in the
southern part of the arc the structures drawn by \citet{Argand1916},
describe sigmoidal lines that could be interpreted as the result of
sinistral shearing (Figure~\ref{fig3}a).

Whereas westward indentation, explains an arc shape whose bisector axis
is oriented E--W, and whose inferred displacement directions may be
nearly symmetric about such E--W axis (Figure~\ref{fig5}b), the westward
indentation is not coherent with the Africa/Adria convergence
direction, which is inferred to be directed northward since the
Cretaceous \citep{Deweyetal1989,Faccennaetal2004} based on palaeomagnetic 
data. In order to reconcile the arc shape of the western Alps and its
E--W symmetry axis with an inferred NW-ward directed Adriatic
indentation, several kinematic models consider a change through time
in the convergence direction of the Adriatic indenter. Generally, an
early N--NW indentation in the collision history is followed by a W--NW
one \citep{Tapponnier1977,Fordetal2006,Handyetal2010, 
Dumontetal2012,Schmidetal2017}. Both the direction of indentation and
the age inferred for these direction changes vary from one author to
the other. \citet{Laubscher1971,Laubscher1991,Laubscher1996}, 
\citet{Tapponnier1977} and \citet{Dumontetal2011,Dumontetal2012}
propose a net westward indentation, while  \citet{Mancktelow1992},
\citet{Handyetal2010}, \citet{Schmidetal2017} and 
\citet{Romagnyetal2020} propose a WNW indentation. Alternatively,
\citet{Plattetal1989} and \citet{Fordetal2006} suggest a more
NW-directed indentation direction, as initially shown by
\citet{Argand1916}.

Models suggesting a transition from northward to WNW-ward, or even to
westward indentation favour its onset around 35~Ma 
\citep{Fordetal2006,Dumontetal2012}, or in the Middle Oligocene 
\citep{Cerianietal2001,Schmidetal2017}. 

Based on pressure--temperature--time data and the stratigraphic
evolution of foreland basins around the western Alpine arc, 
\citet{Fordetal2006} propose a two-phase model (Figure~\ref{fig3}l). 
In this model the first phase of inferred southward continental
subduction and accretion of the Penninic nappes in the Eocene takes
place during the northward indentation of the Adriatic indenter. The
second phase of Oligo--Miocene age accommodates NW-directed indentation
\citep{Fordetal2006}. 

Based on chronostratigraphic and metamorphic compilations associated
with structural analysis especially in the westernmost MCE (Pelvoux,
Grandes Rousses and Belledonne massifs, Figure~\ref{fig2}a), 
\citet{Dumontetal2012} suggest a three-step model. This model starts
with N--S convergence during the Pyrenean phase, from late Cretaceous to
Eocene \citep{Michardetal2010,Dumontetal2012} followed by N--S to
NNW--SSE convergence in the Eocene (Figure~\ref{fig3}i). Their third
step is termed ``Oligocene revolution'' \citep{Dumontetal2012}, because
of an inferred change of 90\textdegree\ in the transport direction,
which becomes E--W at the end of the Lower Oligocene. It is after this
revolution that westward indentation would lead to the development of
the western Alpine arc.

However, WNW-ward indentation is difficult to reconcile with
large-scale plate displacements
\citep{Deweyetal1989,JolivetFaccenna2000, Jolivetetal2021}. Throughout
Alpine collision, the African plate, to which the Adriatic indenter is
probably attached, is inferred to move northward and eventually NW-ward
with respect to Europe based on palaeomagnetic data
\citep{Deweyetal1989} and kinematic reconstructions
\citep{JolivetFaccenna2000,Jolivetetal2021}, but not WNW- or westward.\looseness=1

In summary, indentation models face two major problems: (1) assessing
the existence and the amount of displacement accommodated along the
shear zones bounding the indenter, and (2) assessing the indenter
displacement direction(s) and their compatibility both with large-scale
reconstructions and with structures all along the arc. We discuss these
two points below.

(1) If indentation has a significant westward component it must be
accommodated along lateral structures, i.e., nearly E--W striking
dextral strike-slip in the north and sinistral in the south, according
to the conceptual model of Laubscher [Figure~\ref{fig3}h;
\citealp{Laubscher1971,Laubscher1991}]. The ``Jorio--Tonale line''
[Figure~\ref{fig3}h; \citealp{Laubscher1971,Laubscher1991}] is inferred
to accommodate this dextral displacement that extends towards the
western front of indentation along the Rhone-Simplon Fault
(Figure~\ref{fig2}) \citep{Laubscher1971,Laubscher1991,Laubscher1996,
SchmidKissling2000,Fordetal2006,Schmidetal2017}. Bulk displacement is
estimated at 100~km by map-view reconstructions
\citep{SchmidKissling2000}. However, several authors, based on
geomorphological arguments \citep{GarzantiMalusa2008}, and kinematic
compatibility in map scale \citep{Mulleretal2000,Violaetal2001} suggest
that the offset along the Periadriatic Fault does not exceed 40--50~km.
In addition, as described above, no agreement exists yet on the
required sinistral, E--W striking fault, with an equivalent
displacement, accommodating westward indentation at the southern margin
of the indenter. The strongest argument to suggest some 50~km of
sinistral offset along the ACL [Figure~\ref{fig2}b; 
\citealp{Schmidetal2017}] is the apparent offset of the
Brian\c{c}onnais Front across this line. But this line is not described
as a clear discontinuity between the two offset Brian\c{c}onnais
segments and a large part of this apparent offset could result from a
bend in the original structure, i.e. a progressive rotation of the
southern part of the arc during its formation, without a discontinuity
in the PFT.

(2) An outright westward indentation is consistent with many measured
stretching lineations \citep{Malavieilleetal1984,
Choukrouneetal1986, SchmidKissling2000}, with the inferred
westward displacement along the PFT as observed in the Pelvoux and
Belledonne sectors \citep{Cerianietal2001,Dumontetal2012}, and more
importantly with the N--S orientation of the Chartreuse and Vercors
sub-alpine Chains (Figure~\ref{fig2}a) and all other N--S first-order
structures located along the westernmost segment of the arc. 

NW-directed indentation does not provide a satisfying explanation for
the southern segments of the arc, oriented WNW--ESE and E--W. Analogue
models of the western Alpine indentation following a NW-ward
convergence direction [\citealp{Lickorishetal2002};
Figure~\ref{fig3}k] show that fold and thrust belts striking
sub-parallel to the margin of the indenter develop a more or less
continuous arc shape, whose south-western segment strikes NNW--SSE and
bends progressively northward until it reaches an E--W orientation in
front of the E--W margin of the indenter, corresponding to the Central
Alps, thus forming an arc of some 100--110\textdegree\ around the northern
and western margins of the rigid indenter. Therefore, an indentation to
the NW could produce the 86~km of ENE--WSW shortening to the SW of the
arc \citep[][and references therein]{Rosenbergetal2021} compared to
the more than 200~km of SSE--NNW shortening in the central Alps
\citep[][and references therein]{Rosenbergetal2021}. However, this
setting cannot result in the formation of an arc, but not one of nearly
180\textdegree, i.e., including the southern E--W striking segment that
would correspond the southern termination of the Western Alpine arc.
The latter would easily develop with a strong westward component of
displacement \citep[e.g.,][]{Mancktelow1992} or a late
rotation towards such an orientation 
\citep[e.g.,][]{Dumontetal2012,Schmidetal2017}.

Changes in indentation direction from north to west or to WNW 
\citep[e.g.,][]{Dumontetal2012} would result in dramatic slowing of N--S
shortening in the Eastern and Central Alps and an equally dramatic
increase in E--W shortening in the western Alps. However, the NW--SE
shortening in the Jura fold and thrust belt \citep[e.g.][]{Hombergetal1999}
occurred between Serravallian and early Pliocene times 
\citep{Bolligeretal1993, Steinigeretal1996, Kalin1997, 
Becker2000,Bellahsenetal2014}, which is rather incompatible with a
strictly westward indentation since the Oligocene. In addition, bulk
shortening and exhumation of the latter massifs increases from the
Pelvoux to the Aar massifs 
\citep[e.g.,][]{Bellahsenetal2014,Rosenbergetal2021}. Furthermore,
thermochronological data suggest that the Pelvoux External Massif
(Figure~\ref{fig2}a) begins its exhumation before the Mont Blanc
\citep[][and references therein]{Bellahsenetal2014}. Interpolation of
multiple thermo-chronological data \citep{Foxetal2016} suggests that
the higher exhumation rates progress from the Central Alps to the
southern part of the arc of the Western Alps, but larger exhumation of
the Western Alps compared to the Central Alps are only assessed in the
time span of 2--0~Ma \citep{Foxetal2016}, along the Mt Blanc--Pelvoux
NE-striking axis (Figure~\ref{fig2}a), which is perfectly oriented to
accommodate NW indentation. In addition, the northern deformation front
of the Alps, striking from Switzerland to Austria is active as a
N-directed thrust between 15 and 4~Ma \citep{Mocketal2020}, a
displacement that is incompatible with a net westward displacement of
the Adriatic indenter. Therefore, based on the arguments above there is
no evidence to justify a shift from a NW-ward to a westward or WNW-ward
indentation at 35 or 25~Ma. Finally, large westward-directed components
of displacements of the Adriatic indenter pose some severe kinematic
problems if the northeastern part of the Adriatic indenter is also
taken into account. Its northeastern margin also forms an indenter
(Dolomites indenter) and the deformation pattern around it is
incompatible with large displacement components towards the west
\citep{Rosenbergetal2007}. \looseness=1

\subsection{Rotation of the Adriatic indenter}\label{ssec33}

Some studies attempt to overcome the difficulties of linking radial
collisional transport directions (Figure~\ref{fig2}c) with simple,
uni-directional indentation (Figure~\ref{fig3}f--m) 
\citep{Gidonetal1974,Vialonetal1989,Dumontetal2012}, by considering a
rotation of the Adriatic indenter, as inferred from some palaeomagnetic
studies \citep[e.g.,][]{vanHinsbergenetal2014} and GPS data 
\citep{CaporaliMartin2000,NocquetCalais2004, DAgostinoetal2006}. 

\citet{Gidonetal1974} suggests a ``whirlwind origin'' for the West
Alpine arc. He formulates an analogy between atmospheric vortices, and
the morphology of the Alpine arc \citep{Gidonetal1974}. He bases this
analogy on the presence of major dextral faults along the edges of the
chain, corresponding to the PFT and the Periadriatic fault, which would
allow the Adriatic indenter to rotate, sliding along the edge of the
(European) margin \citep{Gidonetal1974}. He also considers that the
pattern of deformation in the External Zone traces a ``fan'' shape in
map view, emphasised by the frontal thrusts of the ECMs in the north,
the DNF (Figure~\ref{fig2}a) in the west and the dextral Bersezio Fault
Zone (BFZ, Figure~\ref{fig2}a), passing into the Argentera Massif in
the south (Figure~\ref{fig2}a). The pole of rotation, would be located
close to Turin (Italy), just as in recent rotation models, based on GPS
data, \mbox{structural,} seismic and \mbox{palaeomagnetic} analyses
\citep{Westaway1990,Ward1994,
Collombetetal2002,NocquetCalais2004, Bauveetal2014}. 

\citet{Vialonetal1989} interpret the syn-collisional southward
transport directions in the southwestern External Zone of the Alps to
activate several inferred dextral, N--S to NE--SW striking faults,
cross-cutting the External Zone (Figures~\ref{fig2}a and \ref{fig3}c).
These dextral faults are arranged in a fan shape around the PFT, which
is itself reactivated as dextral strike-slip fault
[\citealp{Vialonetal1989}; Figure~\ref{fig3}c]. For this reason, the
arc of the Western Alps results, according to \citet{Vialonetal1989},
from a ``ring shear'' model \citep{Mandletal1977}, in which
counterclockwise rotation of a cylindrical block leads to the
development of dextral faults around it. These faults develop in
directions oriented at 45\textdegree\ from the interface between the
block and the outer domain. The authors associate these dextral
strike-slip movements, interpreted mainly according to focal mechanisms
\citep{Frechet1978,MenardFrechet1989}, with the rotation of a block
decoupled from the Adriatic indenter since the Cenozoic and up to the
present day. Under the effect of NW indentation of the Adriatic
indenter, this block would rotate counterclockwise and move towards the
WNW. The existence of this rotating block is no more than hypothetical
because its boundary faults are not documented by field studies and
because no geophysical or structural data support decoupling of such a
block in the NW corner of the Adriatic indenter.\looseness=1

Most of the recent models suggesting rotation of the Adriatic indenter
compare explicitly \citep{Collombet2001} or not explicitly
\citep{Collombetetal2002,Bauveetal2014}, the present morphology of the
arc, the distribution of inferred dextral faults, and in particular
their fan-shaped arrangement, with rotation models such as that of 
\citet{Mandletal1977}. This counterclockwise rotation is inferred to
affect the whole Adriatic indenter and it is extended to the whole of
the Internal Zone by making the tacit assumption that these two parts
of the Alps are strongly coupled (Figure~\ref{fig3}d)
\citep{Collombetetal2002,Bauveetal2014}.\looseness=1 

The model of \citet{Mandletal1977} is tested by analogue experiments
that show the development of weakly overlapping dextral fan-shaped
faults and very arcuate thrusts within sand layers surrounding a
rotating, rigid disk, also covered by sand layers
\citep{Collombet2001}. This model nicely reproduces \mbox{arcuate}
transpressive structures, but they surround the rotating disc all
around its 360\textdegree. Structures around the western part of the
disc could recall the ones of the western Alps, but those surrounding
the eastern half of the disc are far from structures known to exist in
the Alps. Even those analogue models  \citep{Collombet2001} that
replace the disc with a rotating object whose shape is similar to the
present-day Adriatic indenter create a deformation pattern along its
eastern margin that is not consistent with the tectonic pattern of the
Southern Alps. However, the link between indenter rotation and
nucleation of fan-shaped pattern of dextral faults possibly explains
the numerous dextral faults of the western Alps (Figure~\ref{fig2}a).\looseness=1

Based on new and compiled palaeomagnetic data,
\citet{Collombetetal2002} propose a post-Oligocene counterclockwise
rotation of the Adriatic indenter attaining at least 25\textdegree\
since the Miocene, accommodated by dextral strike-slip movements along
the Periadriatic fault and the PFT (Figure~\ref{fig3}c--e).
\citet{Collombet2001} associates the development of dextral strike-slip
along major faults of the External Zone, such as the DNF
(Figure~\ref{fig2}a), with this rotation, as previously suggested by
\citet{Vialonetal1989}. 

Arguments based on the present-day and palaeo-stress fields, on focal
mechanisms of earthquakes and on structural analyses indicate that the
southern part of the arc, particularly in the Argentera region, is
characterised by a transtensional regime marked by N140\textdegree\ 
striking dextral strike-slip faults, inferred to nucleate between 20
and 26~Ma and still active today \citep{Bauveetal2014}, consistent with
the inferred counterclockwise rotation of the Adriatic indenter since
the Miocene \citep{Vialonetal1989,Collombetetal2002}.

GPS data \citep{CaporaliMartin2000,NocquetCalais2004,
Nocquet2012,DAgostinoetal2006}  represent the strongest and
most direct evidence for present-day counterclockwise rotation of
Adriatic indenter. However, these data only show current movements and
their extrapolation backward in time to infer Cenozoic kinematics, is
only possible if independent evidence also indicates the occurrence of
counterclockwise rotation throughout Oligo--Miocene time. Interestingly,
an analysis of palaeomagnetic data compiled for the entire
peri-Adriatic region \citep{Maffioneetal2008} strongly suggests that
the Adriatic indenter has not rotated since the Middle Miocene, thus
questioning all models reported above that involve large
counterclockwise post-Miocene rotation (some 25\textdegree\ 
counterclockwise) [Figure~\ref{fig3}d, 
\citealp{Collombetetal2002}].

Several authors link an inferred change in indentation direction to a
counterclockwise rotation of the Adriatic indenter 
\citep{Plattetal1989,SchmidKissling2000,Fordetal2006,Dumontetal2011,
Schmidetal2017}, with rotation amounts varying according to the
authors, from about 15\textdegree\
 \citep{Plattetal1989,SchmidKissling2000} to 25\textdegree\
 \citep{Collombetetal2002}, or to even larger, not precisely quantified
values \citep{Dumontetal2011}. The driving force of this rotation is
inferred to be the rollback of the Apenninic slab
\citep{Dumontetal2012}. However, such a rollback does not necessarily
induce any rotation of the Adriatic indenter. Indeed, the
counterclockwise rotation of the Apennines through the Neogene is
compensated by southeastward increasing amounts of rollback and of
extension in the upper plate, not by rotation of the Adriatic Plate.
There is therefore no satisfactory explanation nor a robust data set to
support an ``Oligocene revolution'' or a radical change in
indentation direction.

In addition, all models invoking significant rigid body rotations of
the Adriatic indenter around a pole close to Turin are faced with a
major kinematic problem: an eastward progressive increase of northward
displacement of the Adriatic indenter, which is not supported by any
shortening gradient based on structural studies of the Alpine Chain
\citep[e.g.,][]{LeBretonetal2021,Rosenbergetal2021}. If the rotation
pole is set elsewhere, e.g. south of the Po Plain or south of the
Adriatic indenter as in the hypotheses tested by
\citet{VanHinsbergenetal2014b}, large amounts of Neogene extension would
appear in the Ionian Basin, also not corresponding to what is currently
known \citep{VanHinsbergenetal2014b}. Therefore, if any counterclockwise
rotation takes place, it may be limited to approximately 5\textdegree\
as suggested by numerical modelling \citep{LeBretonetal2017}. Larger
counterclockwise rotations of the Adriatic indenter would be attested
by obvious indicators of dextral shear around it. However, apart from
the Periadriatic Fault, dextral faults in the western Alps only
accommodate very modest displacements (Figure~\ref{fig2}a), such as the
Bersezio Fault \citep{Corsinietal2004, Sanchezetal2011}
with displacements not exceeding \mbox{5--10~km.} As~a~consequence, we
conclude that Neogene significant counterclockwise rotation is very
unlikely and does not explain the Alpine arc shape nor the NNE--SSW
displacements in its southern part.

\vspace*{-2pt}

\subsection{Effect of deep-seated mantle flow on crustal
structures}\label{ssec34}

\vspace*{-2pt}

The southern E--W segment of the Alpine arc terminates at the transition
between the Alps and Apennines (Figure~\ref{fig2}a). This segment is
characterised by a crust of normal thickness [\citealp{Pauletal2022};
Figure~\ref{fig6}b] and lies along the transition between the Alpine
slab dipping eastward and the Apenninic slab dipping westward
\citep{Vignarolietal2008,MolliMalavieille2011}. The Apennine slab is
affected by the eastward roll-back, thus extending the European upper
plate during Oligocene times and opening the Liguro-Proven\c{c}al and
Tyrrhenian Basins since 23~Ma 
\citep{Speranzaetal2002, Ferrandinietal2003}, and also causing an
oroclinal flexure in the Apennines
\citep{Speranzaetal2002,RosenbaumLister2004a,RosenbaumLister2004b}.
Numerical models of adjacent, but opposite-dipping slabs suggest that
the lateral margins of these slabs rotate towards a direction that
tends to parallel the dip direction of the slabs themselves, thus
creating a sigmoidal structure at depth
\citep{Kiralyetal2016, Kiralyetal2021}. In the southern Alpine arc this
direction would be approximately E--W. How, and if, such structure is
transferred towards the upper crust is not known nor modeled yet, but
it is likely that the large-scale orientation of the slabs at depth
controls the orientation of the orogenic prism, hence creating
approximately E--W striking structure between the Alpine and Apennine
arcs \citep{Kiralyetal2016}. Irrespective of the interaction between
adjacent slabs, the map scale pattern of SKS anisotropy directions
\citep[e.g. compilation in][]{Kiralyetal2018} indicates an abrupt
change at the southern end of the arc, where N--S directions paralleling
the N--S striking arc segment suddenly become E--W oriented. This change
is inferred to be due to toroidal flow, with mantle flow parallel to
the European slab in the north, and bordering the southern end of the
European slab in the south [Figure~\ref{fig7};
\citealp{Kiralyetal2018}]. 

\begin{figure}
\vspace*{8pt}
\includegraphics{fig06}
\vspace*{10pt}
\caption{\label{fig6}(a) Structural map of the SW External Zone. Thin
lines represent fold axes. (b)~Structural map of the SW External Zone
above coloured layer illustrating Moho proxy map from
\citet{Pauletal2022}. A Moho depth gap striking E--W, located along
the northern part of the Argentera Massif separates structures oriented
N--S to NW--SE, where the crust is thick ({${>}$}55~km), from an area to
the south, where structures are WNW--ESE to E--W and the crust is less
than 40~km thick both in the Internal and External zones. {Red lines:}
Digne nappe frontal thrusts; {Blue lines:} main rivers. DNF: Digne
Nappe Front; GCF: Guillaumes--Castellane Fault; MDF: middle Durance
Fault; PFT: Penninnic Frontal Thrust; VLT: Ventoux-Lure Fault.}
\end{figure}

\begin{figure*}
\includegraphics{fig07}
\caption{\label{fig7}Map-view displacement model of the bending of the
Alpine and Apenninic slabs terminations, after
\citet{Kiralyetal2016,Kiralyetal2018}.  First there is a space between
the E to SE dipping Alpine slab to the North and the W to SW dipping
Apennine slab to the South. This ``slab free'' area is first oriented
NNW--SSE and becomes progressively reoriented WNW--ESE during eastward
retreat of the Apennine slab. Interaction between slabs of opposite
polarity during their retreat bends their edges producing a
lithospheric sigmoidal structure ultimately amplified by mantle flow,
which invades the growing space between the two slabs. The existence of
slab break-off south of the Western Alps arc is suggested by some
numerous 
\citep[e.g.][]{Lippitschetal2003,Kastleetal2020,Handyetal2021,Paffrathetal2021},
but not all authors \citep[e.g.][]{Malusaetal2021,Zhaoetal2016}, thus
it is represented on these diagrams in spite of some doubts. Red
arrows: asthenospheric toroidal flow.}
\end{figure*}

\vspace*{-2pt}

\subsection{Gravitational tectonics}\label{ssec35}

\vspace*{-2pt}

Gravitational processes are often considered as driving forces for the
formation and displacement of Alpine nappes, folds and faults, since
the early works of \citet{Gignoux1948a,Gignoux1948b} and later ones by
\citet{Kerckhove1969}, \citet{MerleBrun1984}, \citet{Labaume1987}, who
suggest that folding and thickening of the Internal Zone cause
gravitational flow, displacing the sub-alpine chains westward. Recent
works suggest that the present Western Alps may be undergoing
gravitational collapse \citep{Sue1998,Sueetal1999,SueTricart2003,
Selverstone2005,Sueetal2007,Larroqueetal2009,LePichonetal2010,
Ranginetal2010}. This process occurs when the gravitational potential
energy in areas of thickened crust exceeds the force exerted by plate
convergence \citep{Dewey1988,JamiesonBeaumont1989,
Reyetal2001,Selverstone2005}. Therefore, thinning of previously
thickened areas allows for a transfer of gravitational potential energy
from the core of the chain to adjacent areas \citep{Selverstone2005}.
Thus, foreland-directed, radial displacement may be triggered by
gravitational processes, which in turn may play a fundamental role in
creating an arc structure. Indeed, based on stretching lineations and
their relative chronology, \citet{Plattetal1989}, suggest that the
Adriatic indenter moves NW-ward, but displacement around the indenter
margin is parallel to the sum of the vectors corresponding to indenter
displacement and to gravitational collapse of the chain
(Figure~\ref{fig3}j). Therefore, bulk displacement deviates from NW
convergence, becoming W-directed and N-directed in the southwestern and
northern parts of the chain, respectively (Figure~\ref{fig3}j). This
interpretation assumes that an arcuate, thickened structure already
exists at the onset of collision and that the rheology of the crust
allows for its collapse.   

Seismo-tectonic studies and structural analyses indicate that the
Internal Zone of the Western Alps is affected by an extensional regime
since the~Pliocene \citep{Sue1998,Sueetal1999,SueTricart2003}. A~switch
from orogen-parallel to orogen-perpendicular extension in the Internal
Zone is inferred to take place during the Pliocene 
\citep{Sueetal2007}, as indicated by the activation of orogen-parallel
normal faults, and extensional re-activation of the PFT, according to
seismo-tectonic and structural analyses \citep{Sue1998,Sueetal1999,
SueTricart2003,Sueetal2007,Larroqueetal2009}. Based on the spatial
distribution of earthquake focal mechanisms, orogen-perpendicular
extension affects the Internal Zone, where the crust is thickened
\citep{Sueetal2007}, and it is contemporaneous with
{orogen-perpendicular}
shortening, and orogen-divergent shortening in the
foreland \citep{Sueetal2007}. 

Recently, the concept of gravitational tectonics has been specifically
applied to the southernmost Alpine arc \citep{LePichonetal2010,
Ranginetal2010}, suggesting that deformation in the Diois-Baronnies
area (Figure~\ref{fig2}a), i.e. its E--W-striking thrusts and associated
folds result from gravity sliding of the Mesozoic cover along Triassic
evaporites. In the subalpine chains and the Proven\c{c}al basin, the
top of the basement is barely affected by shortening of inferred Alpine
age, and seismicity only affects the cover \citep{LePichonetal2010}. An
additional argument supporting the interpretation of gravity collapse
is the absence of any documented convergence between Eurasia and the
Corsica--Sardinia block \citep{LePichonetal2010}, hence the lack of a
plate tectonics process driving N--S shortening. The latter leads to
southward gravity sliding of the cover units along Triassic evaporites
during basement uplift in the Pelvoux Massif \citep{LePichonetal2010,
Ranginetal2010}. 

The exhumation of the Pelvoux massif cannot produce a southward slope
of the basement roof in the Diois and Baronnies (Figure~\ref{fig2}a),
since it lies to the northeast. In addition, no direct evidence of such
a basement flow exists, in terms of structures exposed at the surface
or in seismic sections.

Concerning the seismo-tectonic evidence
\citep{Sue1998,Sueetal1999,SueTricart2003} the structures described are
outcrop-scale, not map scale structures, suggesting that the amount of
arc-perpendicular extension is of minor importance. It might explain
subsidiary Miocene reactivation of E--W Pyrenean structures, as observed
in the Diois, Baronnies, and in the Nice--Castellane arc, but this
process is not expected to create large-scale, first-order structures
that shape the\break Alpine arc.

To conclude, nearly all studies that infer that gravitational processes
shaped, at least in part, the western Alpine arc, assume that
displacements are triggered by lateral gradients of crustal thickness
and topography. Hence, if the radial character of the structures in the
arc were to be related to gravitational processes, a previously arcuate
belt needs to exist. In other words, gravitational processes in the arc
of the Western Alps may be the consequence of the arc shape, not the
cause of its formation.

\subsection{Post-Tortonian N--S shortening}\label{ssec36}

Numerous E--W striking structures in the southernmost part of the arc of
the Western Alps accommodate small amounts of post-Tortonian N--S
shortening (e.g. 1:50,000 geological map, 999, Grasse-Cannes, BRGM),
potentially accentuating its southernmost E--W grain. We discuss below
the possible causes of this shortening.

Seismo-tectonic \citep{Ritz1992,Chaumillonetal1994,
BigotCormieretal2006,Larroqueetal2009, Larroqueetal2012,Larroqueetal2021,
Bauveetal2014}  and bathymetric studies of the Ligurian
sea \citep{Morellietal2022} suggest that the Liguro-Proven\c{c}al
margin is being inverted, since Tortonian times, along ENE--WSW trending
thrusts. Some models link the compressive seismic events offshore with
large-scale structures onshore, reaching into the core of the Alpine
orogen \citep{Larroqueetal2009,BigotCormieretal2006} and exhuming its
European basement in the Argentera Massif \citep{BigotCormieretal2006}.
These processes cause N--S shortening in the southernmost segment of the
arc and may thus reactivate E--W striking Pyrenean-Proven\c{c}al
structures.

The inversion of the Liguro-Proven\c{c}al margin can only start after
the termination of extension of the Liguro-Proven\c{c}al basin, i.e.
after 15~Ma, based on the age of the Corsica--Sardinia block rotation
\citep{Speranzaetal2002, Ferrandinietal2003}. Inversion of the northern
margin of the Liguro-Proven\c{c}al Basin initiates from the
Plio-Quaternary times according to structural studies, seismic profiles
and sedimentological considerations \citep{Ritz1992,Chaumillonetal1994,
Morellietal2022}. Such inversion could be related to Late Miocene N--S
shortening onshore, in the southernmost part of the Alpine arc. The
absolute amount of this post-11.6~Ma N--S shortening is not assessed
yet, however, based on maps and sections, post-Miocene shortening is
between 4 and 14~km only \citep{Jourdonetal2014}. 

Some of these post-Tortonian structures (e.g., the Tr\'{e}varesse
thrust, Figure~\ref{fig2}a) are located far to the west of the Alpine
arc, suggesting that Alpine shortening cannot be the cause of these
displacements. Significant topographic and crustal thickness gradients,
as existing in the southernmost part of the arc (Argentera Massif
region) are absent in the latter area, precluding gravitational processes
as a driving force of N--S shortening. Therefore, the most likely cause
of these few~km of N--S shortening is linked to the geodynamic process
at the origin of the inversion of the Ligurian-Proven\c{c}al margin. 

This interpretation is challenged by GPS data, which suggest that
convergence between Africa and Europe is absorbed to 90\% along the
northern African margin, thus very little is left to induce convergence
between the Corsica--Sardinia block and the European Plate 
\citep{Nocquet2012}. Hence, barely any convergence may exist at present
between Corsica and southern France. However, based on recent datasets
of global satellite system networks, Corsica is inferred to converge
northward towards Europe at a rate of 0.4~mm/yr
\citep{Massonetal2019}, and this motion results in NNW--SSE shortening
north of Corsica. If this rate of convergence was held constant and
extrapolated backward to Tortonian time, some 4~km of N--S shortening
would be required to accommodate it. Similar field-based values are
inferred to correspond to post Tortonian N--S shortening in the southern
part of the Alpine arc and further west 
\citep[e.g.,][]{Jourdonetal2014}.

Alternatively, post-Tortonian N--S shortening is suggested to result
from the activation of large NE dipping thrust faults rooted in the
core of the Alpine orogen \citep{Larroqueetal2009}. However, the
southwestward propagation of an Alpine crustal ramp
\citep{Larroqueetal2009} is hardly compatible with northward or NW-ward
convergence between Adriatic Indenter and European margin (see
Section~\ref{ssec32}), and it is not supported by structural evidence
nor geophysical imaging. 

In summary, no geodynamic process by itself satisfactorily explains the
small amounts [4--14~km in the Castellane arc,
\citealp{Jourdonetal2014}] of N--S, post-Tortonian onshore shortening
observed all along the Ligurian Sea margin, in the Valensole basin and
in the Castellane arc
\citep{Ritz1992,Chaumillonetal1994,BigotCormieretal2006,
Larroqueetal2009, Larroqueetal2012,Larroqueetal2021, 
Bauveetal2014, Morellietal2022}. However, in
spite of the present-day, but only short-term record of GPS data, it
may be argued that even very low convergence rates between
Corsica--Sardinia block and Europe  \citep{Massonetal2019}, may well
induce several km of shortening over the long term (Miocene to
present). This process, conceivably associated with minor gravitational
tectonics, is likely to explain the seismicity \citep{Larroqueetal2016}
and late Neogene reactivation of Pyrenean-Proven\c{c}al structures in
the south of the arc.

\section{New tectonic model}\label{sec4}

In the following we propose a new kinematic model for the formation of
the western Alpine arc that is based on the critical review presented
above and on new views on the structure of the External Zone.

\subsection{Map-view structural analysis of the southern External Zone}
\label{ssec41}

In order to better understand the relationship between the
Pyreneo-Proven\c{c}al belt and the Alpine one, a structural map of the
External Zone, sketched on the base of 42 1:50,000 geological sheets of
the BRGM, is shown in Figure~\ref{fig6} and discussed in the following
paragraphs. This map illustrates the traces of fold axial planes
and thrusts, and to a minor degree strike-slip faults. Although the
structures shown in Figure~\ref{fig6} are aligned to the axis of the
Alpine arc in several areas, this is not everywhere the case.%\looseness=1

In particular, the NE--SW striking Guillaumes--Castellane Fault (GCF,
Figure~\ref{fig2}a), inferred to be a sinistral fault
[Figure~\ref{fig2}a: GCF; \citealp{Ritz1992}] and sometimes termed
Rouaine--Daluis Fault \citep{Sonnetteetal2014,Balansaetal2022}, abruptly
separates areas characterised by differently oriented structures.
Structures strike NNW--SSE to the north of this line, and E--W to the
south (Figure~\ref{fig6}), where they are continuous and parallel to
the Pyrenean-Proven\c{c}al Chain. The NNW--SSE-striking structures
exposed north of the latter line is parallel to structures exposed
further east, in the internal parts of the External Zone and in the
Internal Zone, hence parallel to the trend of the orogen at this
latitude, and they terminate westward along the NNW--SSE striking Digne
nappe thrust (Figure~\ref{fig6}). The transition from the E--W striking
structures and the NNW--SSE ones, forms a discontinuous 90\textdegree\
 elbow rather than a continuous arc.%\looseness=1

In the Baronnies and Diois (Figure~\ref{fig6}a), all structures strike
E--W, sub-parallel to the Pyreneo-Proven\c{c}al chain exposed further
south [\citealp{Balansaetal2022}; their figure~1]. The region between
the southern coast of France and the Diois is affected by
Pyreneo-Proven\c{c}al structures, whose N--S extent is larger than west
of the Salon-Cavaillon Fault (Figures~\ref{fig2}a and \ref{fig5}b). 
Except for minor N--S striking fold and thrusts in the westernmost
Baronnies (located west of the map of Figure~\ref{fig2}a), along the
margin of the Rhone Graben, the entire area between the latter graben
and the Digne Nappe is not affected by N--S striking folds and thrusts
(Figure~\ref{fig6}). Considering that the spatial change in orientation
is abrupt and so clearly defined along the front of the Digne nappe we
interpret it as the western front of the Alpine orogen, which overrides
the Pyrenean-Proven\c{c}al one. In detail, N--S folds can be recognised
structurally in some areas below the Digne Nappe but they are limited
to the immediate footwall and most likely linked to nappe emplacement.%\looseness=1

The Digne Nappe is classically inferred to accommodate SSW-ward
displacement \citep{GidonPairis1986,Faucheretal1988,GidonPairis1992,
Gidon1997,Grahametal2012}, based on the orientation of striae on fault
planes. However, E--W and WSW--ENE-oriented maximum stress axes are
described all along the western front of the Digne thrust
\citep{Ritz1992,LickorishFord1998, Lickorishetal2002,
Balansaetal2022}, and inferred to be both of Miocene and Pliocene age
\citep{Ritz1992}. Similar orientations of shortening axes inferred from
ASM measurements also characterise the western front of the Digne
thrust \citep{Collombet2001,Sonnette2012}. These orientations are
consistent with the NNW--SSE direction of the thrust front,
accommodating WSW-oriented transport. In addition, several large-scale
observations indicate that the main displacement direction is likely to
be close to westward. First, the longest segment of the Digne Nappe
front is oriented NNW--SSE (Figure~\ref{fig6}) and it consists of a
thrust, not a dextral strike-slip fault (as would be expected for the
lateral ramp of a SSW-directed thrust). \mbox{Second,} the internal structures
of the Digne Nappe strike N--S to NNW--SSE (Figure~\ref{fig6}), being
consistent with a major westward component of displacement and the
NNW--SSE striking front. Third, at its southern end, above the Valensole
Basin (Figure~\ref{fig6}) the frontal thrust of the Digne Nappe
separates into different sub-parallel, close to N--S striking segments,
as classically observed at the terminations of large fault planes. E--W
striking thrust planes that could represent the front of a large nappe
do not really exist. Those that strike E--W seem to accommodate
small amounts of shortening and be related to a wide, distributed fold
and thrust zone, which forms the eastern continuation of the
Pyreneo-Proven\c{c}al belt (Figure~\ref{fig6}).%\looseness=1

In summary, we conclude that the Digne Nappe is displaced dominantly
WSW-ward (N255\textdegree), as also suggested by a recent study
\citep{Schwartzetal2017}. Hence, minimum displacements estimated along
NNE--SSW sections \citep[e.g.][]{Grahametal2012,Balansaetal2022} are
likely to be significantly overestimated. Another outcome is that the
afore-described boundary between E--W striking and N--S striking
structures along the Guillaumes--Castellane Fault (Figure~\ref{fig6})
would coincide with a transition between W-directed and S-directed
displacement. Therefore, the transition from NNW--SSE to E--W structures
in the External Zone is abrupt. Continuous, radial, arc-perpendicular
displacements do not exist there, excepted for the areas in the
immediate surroundings of the Argentera Massif. 

\subsection{Interpretation of structures in the southern External
Zone}\label{ssec42}

Interestingly, the abrupt transition described above, between N--S to
NNW--SSE and E--W structures, is located along a NE--SW fault which is
aligned with the southern termination of the crustal root below the
Internal Zone [Figure~\ref{fig6}; \citealp{Pauletal2022}]. The deepest
part of the orogenic wedge strikes N--S to NNW--SSE, parallel to the
orogen axis, from the Argentera Massif northward, and it is interrupted
along a nearly E--W line east of the Argentera massif
(Figure~\ref{fig6}b). South of this line the crust of the Internal-,
and to a minor degree also of the External Zone, is much thinner. This
sudden E--W interruption of the otherwise N--S striking Moho surface
(Figure~\ref{fig6}b), coincides with the southern termination of the
Ivrea body \citep[e.g.,][]{Kisslingetal2006,Schmidetal2017}, which
represents the base and margin of the Adriatic crust. Its southern
termination coincides with the southern termination of the Adriatic
mantle and Adriatic Plate in their upper plate position.

Because no significant extensional faults are known in this area, the
thickness change indicated by the Moho proxy map (Figure~\ref{fig6}b)
must result from significantly smaller amounts of shortening in the
area south of the Argentera Massif. This observation is consistent with
the idea that different tectonic processes acting independently from
one another to shape the NW--SE segment and the internal and external
E--W segments of the arc. Alpine shortening in the strict sense, i.e. in
terms of accommodation of convergence between Adria and Europe,
probably does not affect the area located south of the southernmost
Argentera Massif, namely the E--W segment of the arc. As a consequence,
the complete shape of the arc would result from the juxtaposition of
two distinct structural domains, one located north of the
Guillaumes--Castellane Fault (Figure~\ref{fig2}a) belonging to the Alps
s.s. and one located south of this line belonging to the
Pyreneo-Proven\c{c}al orogen.%\looseness=1

In summary, E--W striking structures extending from the Pyrenees to the
External Zone in the Western Alps, notably in the Castellane arc and
the Baronnies area, are of Pyrenean origin
\citep{Staub1924,Lemoine1972, Siddans1979,Balansaetal2022}, as
indicated by their pre-Eocene--Oligocene age, and by their spatial
distribution of shortening, whose amount a dramatical decrease
towards the Alpine Chain. Thus, in spite of incomplete dating of the
E--W striking structures, the spatial distribution of shortening, the
abrupt transition between E--W and N--S shortening, and the non-parallel
orientation between E--W structures and the axis of the Alpine Chain,
all suggest that Alpine-age shortening in the southern, E--W segment of
the External Zone is kinematically unrelated to Alpine collision s.s.,
i.e. to the accommodation of Adria-Europe convergence. The Neogene
reactivation of these structures is discussed in the paragraphs below.%\looseness=1

The radial character of the inferred Alpine transport directions
[Figure~\ref{fig2}c; e.g., \citealp{Plattetal1989}] is thus limited to
a progressive change from northward- in the Central Alps to W- or
WSW-directed displacements in the Digne nappe (Figure~\ref{fig5}a). In
the External Zone, from the Nice arc to the Vercors
(Figure~\ref{fig2}a), no additional gradual change to SSW- or southward
displacement is observed, but a sudden change from westward or WSW, to
southward.

These arguments and conclusions provide a rationale to the 
different past interpretations on the western extent of the Alpine arc.
Some authors include all the Cha\^{i}nes Subalpines, incorporating
Diois and Baronnies, into the arc of the Western Alps 
\citep[e.g.,][]{SchmidKissling2000,KempfPfiffner2004}, others 
terminate it along the outer boundary of the Castellane arc and Nice arc
\citep[e.g.,][]{Staub1924,Laubscher1988,Roureetal1989}. The present
interpretation differs from all previous ones as it excludes not only
the Baronnies and Diois chains, but also the Castellane--Nice one of the
arc of the Western Alps s.s., i.e. from the arc formed by NW-directed
collision of the Adriatic Indenter and the European margin.

The latter interpretation links the arcuate structure of the External
Zone of the Alps with two distinct processes: (1) an uni-directional
NW-directed indentation of Adria against Europe to form the Central
Alps and the Northwestern Alps (the NW Alps being defined as the
structures striking from the Pelvoux and Dora Maira massifs northward);
(2) a Pyrenean origin for the southern, E--W striking part of the arc,
with some post-Tortonian reactivation, possibly due to the
Europe--Africa convergence, hence associated with the inversion of the
Liguro-Proven\c{c}al Basin.%\looseness=1

\subsection{Building the southern, E--W-striking arc segment in the
Internal Zone}\label{ssec43}

The E--W striking Ligurian Alps underwent a counter-clockwise rotation
of 50\textdegree\ between lower- and mid-Miocene [23~Ma; 
\citealp{Speranzaetal2002}] as indicated by numerous palaeomagnetic
data in the Tertiary Piedmont Basin (Figure~\ref{fig2}a)
\citep{Maffioneetal2008}. This rotation \citep{Maffioneetal2008} is
contemporaneous with an anti-clockwise rotation of the northern
Apennines is linked to an oroclinal flexure of this orogen 
\citep{Speranzaetal1997}. Therefore, the E--W orientation of the Ligurian Alps
likely results from the Apennine flexure rather than from Alpine
collision.

Indeed, the Ligurian Alps are in the hanging wall of the Apenninic
Frontal Ramp (Figure~\ref{fig2}a). Thus N--S shortening recorded in this
northernmost part of the Apennines likely affects the Ligurian Alps and
can explain its E--W orientation. This implies that at present and
during collision, the Ligurian Alps belong to the upper plate of the
Apenninic subduction system and not to the lower plate of the Alpine
orogen.

In addition, the interaction between the southern and northern
terminations of the Alpine and Apenninic slabs, respectively, each of
them migrating away from the other, can result into the lateral bending
that would also rotate them towards an E--W orientation
\citep{Kiralyetal2016,Kiralyetal2018}. The effect of such a toroidal
mantle flow (Figure~\ref{fig7}) on surface structures is not really
described. The implication of this process in the E--W orientation of
the Ligurian Alps is therefore speculative. 

All these processes may explain the E--W orientation of the southern
segment of the Alpine arc, even in the Internal Zone, i.e. east of the
Pyrenean-Proven\c{c}al belt.

\subsection{New kinematic model}\label{ssec44}

In summary, we propose a new kinematic model for the formation of the
Alpine arc, that we describe in the following. 

During Eocene times (i.e., before 35~Ma, Figure~\ref{fig8}a), the
Internal Zone is already arcuate as a consequence of subduction
processes, as indicated by retro-deformation of collisional shortening,
[Figure~\ref{fig4}, \citealp{Bellahsenetal2014}]. This structure is
probably associated with slab retreat, as described by
\citet{Royden1993} and  \citet{WortelSpakman2000} for the development
of all peri-Mediterranean orogenic arcs (Aegean, Alboran, Carpathian,
Apenninic-Calabrian; Figure~\ref{fig1}). Hence, against the vast
majority of the literature \citep{Tapponnier1977, Laubscher1991,
Schmidetal2004, Handyetal2010,Dumontetal2011,Dumontetal2012}
we suggest that shortening linked to Adriatic indentation only
amplifies an already existing arc structure.%\looseness=1

\begin{figure*}
\includegraphics{fig08}
\caption{\label{fig8}Tectonic model of the Alpine collision [modified
from the reconstruction of \citealp{Romagnyetal2020}].}
\end{figure*}

Meanwhile, the Pyrenean-Proven\c{c}al belt produces E--W structures
reaching as far as the Alpine foreland, giving rise to the present-day
E--W arc segments in the External Zone (e.g., Castellane arc). At 35~Ma
(Figure~\ref{fig8}b), Alpine collision leads to the amplification of
the 90\textdegree\ arc in the External Zone, from the Aar to the
Argentera Massifs, as a result of NW indentation of the Adriatic Plate
into the European margin. The southern termination of this arc
corresponds to the Pyrenean-Proven\c{c}al belt in the West (External
Zone) and to the Ligurian Alps in the East (Internal Zone). Several
processes can explain the E--W orientation of the Internal Zone: (1)
between 23 and 13~Ma [\citealp{Maffioneetal2008}; Figure~\ref{fig8}c],
oroclinal bending of the Northern Apennines causes 50\textdegree\ of
counter-clockwise rotation also affecting the Ligurian Alps, as
suggested by palaeomagnetic  data from the Tertiary Piemont Basin
\citep{Maffioneetal2008}, which overlies with a discordant sedimentary
contact the Internal Zone. Such rotations may be linked to N--S
shortening along the Apenninic frontal ramps exposed north of the
Ligurian Alps (Figure~\ref{fig2}a). Alternatively, and/or in addition
to the latter process, counterclockwise rotation of the Ligurian Alps
may follow a deep-seated bending of slab terminations (Alpine and
Apenninic) dipping in opposite directions \citep{Kiralyetal2016}. 

Further West, the E--W striking part of the Alpine arc in the External
Zone records small amounts of Miocene N--S shortening, which can be
dated to post-Tortonian time (Figure~\ref{fig8}d) in several areas. The
exact origin  of this event, reactivating the Pyrenean structures
remains debatable. Based on the arguments presented in
Section~\ref{ssec36}, we suggest that convergence between the
Corsica--Sardinia block and the European margin is the most plausible
cause, despite the small amounts of present-day convergence rates
between these two domains, as shown by analysing datasets derived from
global navigation satellite system \citep{Massonetal2019}. 

\section{Conclusion}\label{sec5}

Rigid indentation of the Adriatic indenter, generally thought to
generate the arcuate shape of the Western Alps cannot explain by itself
the formation of the entire arc, because it cannot create a radial
pattern of displacement, encompassing 180\textdegree. Given the
generally accepted NW-convergence direction during the collision, the
fundamental question concerns the origin of N--S oriented shortening in
the southern part of the arc. The hypothesis of changing convergence
direction through time, from NW- to W, in order to better explain N--S
striking structures and even NW--SE striking ones is not compatible with
the increase in Cenozoic arc-perpendicular shortening from the Western
to the Central Alps, with the existence of significant Miocene and
Pliocene N--S shortening in Central Alps, and even less with Miocene
tectonics of the Eastern Alps. 

Our kinematic model solves this problem by considering that, in spite of
its topographic continuity and its structural continuity in the
Internal Zone, the arc results from distinct geodynamic processes
acting at different times and in different areas. Following the
formation of an arc during subduction, as manifest in the Internal
Zone, NW-directed Adriatic indentation amplifies this arc in its
northern and western parts. In contrast, its southern E--W striking
segment is shaped first (Paleogene) by the eastern termination of the
Pyrenean orogen, and later by post-Tortonian shortening on the European
margin. Also, during the Miocene, the eastern continuation of this
southern segment, namely the Ligurian Alps, are affected by an
Apennines-related counterclockwise rotation. Hence none of these
processes is caused by the indentation of Adria and should not be
considered as part of Alpine collision.

\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}
Mary Ford and Giancarlo Molli are gratefully acknowledged for their
thorough reviews. Olivier Fabbri kindly corrected the revised version
of the manuscript. Michel Faure provided a very efficient and patient
editorial handling.

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