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\DOI{10.5802/crgeos.257}
\datereceived{2023-07-31}
\dateaccepted{2024-03-25}
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\dateposted{2024-05-22}
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%\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

\CDRsetmeta{articletype}{review}

\title{Extension of continental lithosphere in rifted margins: a review
of thinning mechanisms}

\alttitle{Extension de la lithosph\`{e}re continentale dans les marges
passives : une synth\`{e}se des m\'{e}canismes d'amincissement}

\author{\firstname{Julie} \lastname{Tugend}\CDRorcid{0000-0003-3724-7878}\IsCorresp}
\address{Laboratoire G\'{e}osciences et Environnement Cergy (GEC), 
CY Cergy Paris Universit\'{e}, 95000 Neuville sur Oise, France}
\curraddr[J. Tugend]{Commission for the Geological Map of the World,
Paris, France}
\email[J. Tugend]{julie.tugend@gmail.com}

\author{\firstname{Geoffroy} \lastname{Mohn}\CDRorcid{0000-0002-8729-2960}}
\addressSameAs{1}{Laboratoire G\'{e}osciences et Environnement Cergy (GEC),
CY Cergy Paris Universit\'{e}, 95000 Neuville sur Oise, France}

\author{\firstname{Thibault} \lastname{Duretz}\CDRorcid{0000-0001-8472-7490}}
\address{Institut f\"{u}r Geowissenschaften, Goethe-Universit\"{a}t
Frankfurt, Frankfurt, Germany}

\author{\firstname{Benoit} \lastname{Petri}\CDRorcid{0000-0001-7142-0406}}
\address{Institut Terre et Environnement de Strasbourg, Universit\'{e}
de Strasbourg, CNRS, UMR7063, F-67084 Strasbourg, France} 

\author{\firstname{Laetitia}\nobreakauthor\lastname{Le~Pourhiet}\CDRorcid{0000-0001-9495-4742}}
\address{Institut des Sciences de la Terre Paris, ISTeP UMR 7193,
Sorbonne Universit\'{e}, CNRS-INSU, 75005 Paris, France}

\shortrunauthors

\begin{abstract}
{Crustal geometries imaged at rifted margins show contrasted
first-order morphologies (wide and narrow, symmetric or asymmetric
conjugates).
 This contribution aims to review the mechanisms of
continental lithospheric thinning and types of extensional structures
that control the formation of rifted margins. We illustrate, using a
two-layer numerical model (one for the crust and one for the mantle),
how different modes of lithospheric thinning shape the end-member
crustal geometries of rifted margins depending on the initial thermal
conditions and extension rates. As already known, the activation of
narrow or wide modes of lithospheric thinning depends on the
rheological behaviour of the lower crust and its efficiency as a
decoupling layer. Morphologies generated by narrow lithospheric
thinning modes compare well with Atlantic-type rifted margins (e.g.,
Iberia--Newfoundland) while wide lithospheric thinning modes better
apply to marginal seas characterized by higher initial geothermal
gradients (e.g., South China Sea).
 Finally, we also emphasize that
continental lithosphere thinning is depth-dependent, part of which is
transient and cannot easily be measured in natural systems.} 
\end{abstract}

\begin{altabstract}
L'architecture crustale des marges passives imag\'{e}e par les
m\'{e}thodes g\'{e}ophysiques est contrast\'{e}e montrant des
morphologies tant\^{o}t larges ou \'{e}troites, les profils
conjugu\'{e}s pouvant \^{e}tre sym\'{e}triques ou asym\'{e}triques.
Cette contribution pr\'{e}sente les m\'{e}canismes d'amincissement de
la lithosph\`{e}re continentale et les diff\'{e}rents types de
structures extensives qui contr\^{o}lent la formation des marges
passives. L'utilisation d'un mod\`{e}le \`{a} deux couches (une pour la
cro\^{u}te et une pour le manteau),
 permet d'illustrer comment les
diff\'{e}rents modes d'amincissement de la lithosph\`{e}re
fa\c{c}onnent l'architecture premier ordre des marges passives pour
diff\'{e}rents taux d'extension et conditions thermiques initiales.
Comme pr\'{e}c\'{e}demment d\'{e}montr\'{e}, l'activation d'un mode
d'amincissement de la lithosph\`{e}re \'{e}troit/localis\'{e} ou
large/distribu\'{e} d\'{e}pend du comportement rh\'{e}ologique de la
cro\^{u}te inf\'{e}rieure et de son efficacit\'{e} en tant que niveau
de d\'{e}couplage. Les morphologies g\'{e}n\'{e}r\'{e}es par un
amincissement lithosph\'{e}rique \'{e}troit et localis\'{e} sont
comparables \`{a} celles observ\'{e}es dans les marges passives de type
atlantique (par exemple, Ib\'{e}rie--Terre-Neuve).
 Le mod\`{e}le
d'amincissement large et distribu\'{e} s'applique mieux aux mers
marginales caract\'{e}ris\'{e}es par des gradients g\'{e}othermiques
initiaux plus \'{e}lev\'{e}s (par exemple, la mer de Chine
m\'{e}ridionale).
 Enfin, nous soulignons \'{e}galement que
l'amincissement de la lithosph\`{e}re continentale d\'{e}pend de la
profondeur et qu'il est en partie transitoire, une des raisons pour
lesquelles, il n'est pas facile de le mesurer dans les syst\`{e}mes
naturels. 
\end{altabstract}

\keywords{\kwd{Lithosphere thinning}
\kwd{Rifted margins}
\kwd{Depth dependent thinning}}

\altkeywords{\kwd{Amincissement de la lithosph\`{e}re}
\kwd{Marges passives}
\kwd{Amincissement d\'{e}pendant de la profondeur}}

\maketitle

\twocolumngrid

\end{noXML}

\section{Introduction}

{Continental lithospheric thinning is a fundamental process of plate
tectonics associated with the formation of sedimentary basins in
various geodynamic settings including intracontinental rifts and rifted
margins, as well as back-arc domains and post-orogenic contexts 
\citep[see review in][]{Cloetinghetal2013}. Continental lithosphere
thinning can be triggered by several mechanisms such as tectonic
extension, thermal thinning (active mantle upwelling), and mantle
lithosphere delamination and is, hence, not limited to divergent
settings. In this contribution, we offer a synthetic review of some key
conceptual\break models that shifted our understanding of the deformation
modes and mechanisms of continental lithosphere thinning.}

{The tectonic and thermal thinning of the continental lithosphere are
recorded in passive margins during rifting associated with the necking
and breakup of the continental lithosphere. Lithospheric necking is a
mechanical shear instability that occurs in extension
\citep{BraunBeaumont1987,Brun1999,BrunBeslier1996,SchmalholzMancktelow2016,Cheninetal2018}. 
In multi-layered rheological systems like the continental lithosphere,
multiple levels of necking and associated isostatic adjustments
modulate its record in sedimentary basins
 \citep{BrunBeslier1996,Cloetinghetal2013,Duretzetal2016}. The thinning
of the continental lithosphere is achieved during lithospheric breakup,
during which continental extension evolves into the localized accretion
of oceanic lithosphere
\citep{DeweyBird1970,Falvey1974,Heezen1960,McKenzie1978,Whitmarshetal2001}. 
Rifted margins have been and still are key natural laboratories to
answer fundamental questions related to continental lithosphere
thinning such as (1) where and how does the continental lithosphere
thin? (2) what are the deformation modes and mechanisms of lithosphere
thinning?} \looseness=-1

{First kinematic models implying uniform stretching and thinning of the
lithosphere during tectonic extension \citep[e.g.,][]{McKenzie1978}
have been challenged over the years by the improvement of seismic
imaging techniques and other geophysical quantitative analyses in
present-day rifted margins and the study of field analogues in mountain
belts.} 

{The quantification of extension and thinning from seismic data showed
that the amount of extension measured from observed normal faulting is
significantly less than that required to thin the whole crust or
lithosphere \citep[][for reviews]{Reston2007a,KusznirKarner2007}.
This so-called ``extension discrepancy'' is now recognized in many
rifted margins worldwide including the Iberia--Newfoundland margins,
South China Sea, or Woodlark Basin \citep[e.g.,][]{DavisKusznir2004}.
Several explanations have been proposed to account for this extension
discrepancy 
\citep[e.g., see reviews in][]{DavisKusznir2004,Reston2009}.
One suggests that extension
measured from normal faulting is largely underestimated because of
sequential \citep{RaneroPerez-Gussinye2010} or unrecognized multiphase
faulting \citep[e.g.,][]{Reston2005,Reston2007a,Reston2007b,RestonMcDermott2014}.
Alternative explanations suggest that the extension and thinning of the
whole crust and lithosphere exceed that accommodated by the brittle
upper crust
\citep{DriscollKarner1998,DavisKusznir2004,Kuszniretal2005}. This
mechanism is referred to as depth-dependent thinning (DDT) and implies
that the thinning of the continental lithosphere is partitioned with
depth.}


{The increasing acquisition of seismic surveys imaging rifted margins
showed their diverse structural style and crustal structure [Figure~\ref{fig1};
e.g., \citealp{Reston2009,Clercetal2018,Sapinetal2021}]. This
variability is generally interpreted as the result of different modes
of deformation during extension [e.g., narrow or wide rifts,
\citealp{Buck1991}], controlled by the initial conditions such as the
geothermal gradient, the rheological stratification, or structural
inheritance 
\citep[e.g.,][]{LePourhietetal2004,Duretzetal2016,DavisLavier2017,TetreaultBuiter2018},
erosion and sedimentation \citep{BurovPoliakov2001} and variable melt
emplacement during rifting and breakup 
\citep[e.g.][]{WhiteMcKenzie1989,LuHuismans2022}. } {The recognition of
intra-crustal and intra-lithospheric deformation structures remains
challenging solely based on seismic data.} {Intra}{-basement reflectors
are more and more frequently imaged in seismic reflection data and have
convincingly been interpreted as extensional intra-crustal shear zones
\citep[e.g.,][]{Fazlikhanietal2017,Clercetal2015}. However, seismic
reflectors correspond to the impedance contrasts related to variations
in the physical properties of the rocks and their interpretation in
terms of lithologies or deformation processes remains debatable.} 

{Results from the (International) Ocean Drilling Program (I)ODP and
Deep Sea Drilling Program (DSDP) combined to the study of onshore field
analogues in mountain belts have been a game changer in the study of
continental thinning mechanisms. On the one hand,} {direct access to
rocks recording the deformation of the lithosphere showed the key role
of large offset normal faults (i.e., detachment faults) and evidence
for intra-crustal and intra-lithospheric shear zones. On the other
hand,} {ODP legs provided evidence for subcontinental mantle exhumation
in so-called Continent-Ocean Transition (COT) zones of the magma-poor
Iberia--Newfoundland conjugate margins
\citep{Boillotetal1987,Sawyeretal1994,Whitmarshetal2001,Peron-Pinvidicetal2007,Welfordetal2010}. 
Similar evidence for sub-continental mantle exhumation comes from the
study of remnants of rifted margins preserved in the Alps and in the
Pyrenees
\citep{Lemoineetal1987,ManatschalNievergelt1997,Desmursetal2001,LagabrielleBodinier2008,Jammesetal2009}. 
The presence of subcontinental mantle in the COT of so-called
magma-poor rifted margins attests their non-uniform asynchronous
extreme crustal and lithospheric mantle thinning.}

These observations led to the development of an array of conceptual
models aiming to explain continental lithosphere thinning mechanisms in
rifts and rifted margins that are summarized hereafter. After an
overview of the contrasted crustal geometries of rifted margins imaged
by geophysical methods, we present a review of the main extensional
structures identified in rifts and rifted margins. We then propose a
thematic and historical perspective of the different mechanisms and
deformation modes of continental lithosphere thinning. Finally, we
illustrate how these deformation modes depend on different geotherms
and extension rates using a set of simple numerical simulations of
lithospheric extension. Results of these numerical simulations are then
compared to natural examples, if they exist. 

More generally, this review emphasizes the variability and
complementarity in time and space of continental lithosphere thinning
mechanisms during extension and their influence on the morphology of
rifted margins. 

\section{Where does the continental lithosphere thin?}

Continental rifted margins, in contrast to rift systems, record the
complete thinning of the continental lithosphere and its rupture
leading to stable oceanic lithosphere accretion. Thereby, they
represent unique natural laboratories where the final product of
continental lithosphere extension can be observed. Although the crustal
structure of rifted margins can now be imaged at high resolution by
geophysical methods (Figure~\ref{fig1}) (e.g., seismic reflection and
refraction, or gravity and magnetic modelling), their continental
breakup occurred millions of years ago, and they started recording or
recorded post-rift lithosphere thermal cooling. 

{\def\ffigcaption{\label{fig1}}
\xsubfig[t!]{01a}{}
\figcnt
\begin{figure*}
\vspace*{-4pt}
\includegraphics{fig01}
\vspace*{-4pt}
\xcaption{\label{fig1}\ffigcaption}{\fontsize{10}{11.5}\selectfont
Crustal scale profiles across rift basins and
conjugate rifted margins as imaged by refraction seismic data or
modelled from gravity anomalies. This compilation shows the variable
geometry of passive margin crustal structure and crustal domains.
References are indicated above each profile, their location is
indicated on the bathymetric map (after NOAA National Geophysical Data
Center, 2009).}
\end{figure*}}
\setcounter{figure}{1}

\subsection{Crustal structure of rifted continental margins}

Compilations of seismic images and geophysical models show the variable
morphology of rifted margins (Figure~\ref{fig1}) 
\citep[e.g.,][]{Reston2009,Clercetal2018,Sapinetal2021}. This diversity is
commonly interpreted as the result of different modes of extension
operating in the heterogeneous continental lithosphere. Thereby, the
different width of rifted margins is commonly interpreted as the result
of drastically different rheological layering of the continental
lithosphere
\citep{Buck1991,HopperBuck1996,HuismansBeaumont2011,Perez-GussinyeReston2001}. 
Narrow rifts are commonly interpreted as resulting from the necking of
strong layers while the presence of weak lower crust favours lower
crustal flow and de/re-localization of the deformation
\citep{Buck1991}. Contrasted crustal geometries are observed between
rifted margin examples but also between conjugate profiles
(Figure~\ref{fig1}). Quantifications of crustal and lithosphere
thinning mechanisms are therefore even more revealing if they are
derived from the analysis of conjugate rifted margin profiles. For this
reason, in our compilation, we present conjugate sets of passive margin
examples derived from seismic refraction and gravity datasets
(Figure~\ref{fig1}).

The crustal structure of rifted margins (Figure~\ref{fig1}) is shaped by
thinning mechanisms during extension, but also depends on the volumes
of magma emplaced before, during and after the breakup. The inferred
amount of magmatism and its timing of emplacement and extrusion
relative to crustal thinning have therefore been used to characterize passive
margin morphologies \citep{WhiteMcKenzie1989,Tugendetal2020}. In the
case of so-called magma-rich rifted margins (also referred to as
volcanic margins) where large volumes of magmatic rocks intrude the
continental lithosphere and/or where 
an early onset of magmatism occurs relative to continental crustal thinning
\citep{Tugendetal2020}, the imaged crustal structure does not
only result from thinning processes (Figure~\ref{fig1}a/b). Hence, although
magma-rich rifted margins also record lithosphere thinning, the
mechanisms at play and \mbox{quantifications} of continental lithosphere
thinning cannot always easily be investigated and are debated 
\citep[e.g.,][]{Eldholmetal1995,Geoffroyetal2015}. Rifted margins that record
extreme crustal thinning to 15--10 km thick or less prior to melt
extraction [i.e., magma-poor rifted margins,
\citealp{Reston2009,Tugendetal2020}; marginal basins,
\citealp{Larsenetal2018,Mohnetal2022}] appear like the best examples to
study and quantify lithosphere thinning mechanisms during rifting
(Figure~\ref{fig1}c--t). In such examples, the observed crustal
structure more straightforwardly depends on the extensional deformation
modes operating during rifting and breakup. Many passive margins record
polyphase rifting events prior to breakup as a result of distinct
periods of extension, each one possibly having a different direction of
extension
 \citep{Bellahsenetal2006,Leroyetal2012,FrizondeLamotteetal2015}. In
such cases, quantification of thinning mechanisms from rifted margin
crustal structure can only be done if the amount of extension from each
phase can be analyzed. 

{\advance\baselineskip by -.2pt
\subsection{Domains of crustal thinning}\label{sec1.2.}

Despite the obvious diversity of rifted margin geometries
\citep{Reston2009,Clercetal2018,Sapinetal2021} (Figure~\ref{fig1}) similar
crustal domains can usually be identified corresponding to different
magnitudes of crustal thinning (Figure~\ref{fig1}).

Onset of significant crustal thinning from a ${\sim}$35--30 km thick
crust (i.e., pre-rift continental crust thicknesses) to a less
than~${\sim}$15--10 km thick crust is marked by a deepening of the top
basement and rise of the Moho that shape a necking of the continental
crust \citep{Thinonetal2003,OsmundsenEbbing2008,
Mohnetal2012,Peron-Pinvidicetal2013,Tugendetal2015,Nonnetal2017}. 
{The crustal geometry of so-called necking zones or necking domains
hence contrasts with the roughly parallel geometry of the top basement
and Moho observed in proximal domains where only a little crustal
thinning occurs. Onset of the deepening of the top basement and rise of
the Moho may be spatially offset (e.g., Figure~\ref{fig1}l/p/r), in which case,
the complete length of the necking domain [i.e., taper length in
\citealp{OsmundsenRedfield2011}] is defined with uncertainties and can
be underestimated.} 

Necking domains commonly extend over distances ranging from
${\sim}$25~km (i.e., Porcupine basin, Figure~\ref{fig1}c) to
${\sim}$100~km (i.e., Moroccan rifted margin,\break Figure~\ref{fig1}l;
Rockall basin, Figure~\ref{fig1}d) \mbox{defining} a \mbox{relatively}
abrupt crustal neck \citep{Mohnetal2012}. Crustal thinning can be more
progressive or associated with a pinch-and-swell crustal structure of
the rifted margin, also resulting in wider (up to ${\sim}$200 km and in
some cases more than 300 km wide) loosely defined necking domains
(e.g., Galicia margin, Figure~\ref{fig1}h; South China Sea rifted
margins, Figure~\ref{fig1}m--o; Alarcon segment of the Gulf of
California, Figure~\ref{fig1}q). The geometry of passive margin necking
zones is thus extremely variable (Figure~\ref{fig1}). Their style may
vary along strike [e.g., Gulf of California rifted margins:
Figure~\ref{fig1}p--r; Norwegian margin:
\citealp{OsmundsenRedfield2011}]. Conjugate rifted margins and basins
can have relatively symmetric (Figure~\ref{fig1}d/i--j) or largely
asymmetric crustal necks [e.g., Figure~\ref{fig1}c/g--h/s--t; Parentis
basin: \citealp{Tugendetal2015}].

Most of the rifted margin crustal thinning is accommodated in necking
zones. However, many passive continental margins undergo a final
crustal thinning (from ${\sim}$10 km thick crust to 0) prior to oceanic
lithosphere accretion, in usually loosely defined
continent-ocean-transitions (COT). COT, where defined, are
characterized by severely thinned continental crust (less than 15--10
km thick) that can be associated to windows of exhumed lithospheric
mantle in-between the necking and oceanic domain (Figure~\ref{fig1}).
Domains of hyper-thinned continental crust
\citep{Tugendetal2014,Tugendetal2015}, also referred to as the neck
area \citep{Thinonetal2003}, hyper-extended
\citep{Peron-Pinvidicetal2013} or coupled domain \citep{Sutraetal2013}
show a relatively parallel top basement and Moho geometry that
progressively converges seaward to form a continental crustal wedge
(Figure~\ref{fig1}). Exhumed mantle domains are not systematically observed, in
which case hyper-thinned crust is found adjacent to the oceanic crust
in a sharp transition 
\citep[e.g.,][]{Nirrengartenetal2020,Mohnetal2022}
(Figure~\ref{fig1}m/n/o/p/q).
Evidence for exhumed mantle domains is usually indirectly constrained
from geophysical criteria, in the absence of drilled or dredged mantle
rocks as part of the top basement as recovered in the
Iberia--Newfoundland
\citep{Boillotetal1980,Boillotetal1987,Sawyeretal1994} or East
Antarctica margins \citep{McCarthyetal2020}. 

The width of COT shown by our compilation is variable (from
${\sim}$20~km to ${\sim}$250~km) \citep[see also][]{Cheninetal2017}.
Where hyper-thinned or exhumed mantle domains can be distinguished,
this diversity seems mostly related to the variable width of the
inferred exhumed mantle domain, while the width of the hyper-thinned
domain is commonly narrow (${\sim}$25--50 km wide) and rarely reaches
${\sim}$100 km wide [Figure~\ref{fig1}k/i/r; Gabon rifted margin:
\citealp{Clercetal2018}]. It is worth noting that the width of
hyper-thinned and exhumed mantle domains and more generally of COT is
not necessarily comparable between conjugate profiles, except perhaps
in the case of marginal sea basins examples like the South China Sea
(Figure~\ref{fig1}m/n/o) or Guaymas and Alarcon segments of the Gulf of
California (Figure~\ref{fig1}p/q).

\vspace*{-3pt}
\section{How does the continental lithosphere thin?} \label{sec2.}

{The} {diverse morphologies of} {rift basins and rifted margins}
{(Figure~\ref{fig1}) suggest that different} {deformation modes and mechanisms
can operate to thin the continental lithosphere generating different
geometries of extensional structures. By analysing the crustal
structure imaged by geophysical methods} {(Figure~\ref{fig1}) and exposed
rift-related structures onshore}, {it is possible to quantify
continental crustal thinning from the continent to the ocean and the
role of the different types of extensional structures in accommodating
lithosphere thinning.}

\vspace*{-3pt}
\subsection{{Extensional structures in rifted margins}}\label{sec2.1.}

{The thinning of the continental lithosphere is accommodated by an
array of extensional structures with various geometries, active at
different depths and periods of the rift evolution as well as
rheological conditions. The recognition of extensional structures in
present-day rifted margins is usually limited to those accommodating
brittle deformation of the upper crust.} {Intra}{-basement reflectors
are now also frequently identified thanks to the increasingly higher
resolution of seismic reflection imaging techniques. Although
convincing, their interpretation as extensional intra-crustal shear
zones \citep[e.g.,][]{Fazlikhanietal2017,Clercetal2015} or in terms of
lithologies or deformation process remains debatable. To lift these
ambiguities, it is critical to complement these indirect observations
with field observations either in onshore extensional systems
\citep{Jolivetetal2010,Fossen2010} or in fossil remnants preserved in
orogenic systems
\citep{HandyZingg1991,BissigHermann1999,Mohnetal2012,Petrietal2019}.
In the latter case, the identification and description of \mbox{extensional}
structures rely on our capability to distinguish pre-orogenic
(rift-related) from younger orogenic structures
\citep{Tugendetal2015,Mohnetal2022}.} 

\subsubsection{{High and low-angle normal faults}}\label{sec2.1.1.}

{Brittle extensional deformation of the uppermost basement is commonly
accommodated by} {\textit{high-angle normal faults}} {which control the
formation of classical rift basins like horst and graben or half-graben
in extensional settings. These extensional structures show either
planar or listric geometries and are associated or not with block
rotation. Each fault only accommodates a limited amount of lithosphere
thinning. It should, however, be noted that many faults may be below
the resolution of} {seismic imaging and hence accommodate more
extension than that imaged in tilted blocks a situation referred to as
distributed or subseismic faulting \citep{MarrettAllmendinger1992}.} 

{Nowadays, an increasing number of studies highlights the importance of}
{\textit{low-angle normal faults}} {(apparent dip
${<}$30--45\textdegree) in accommodating extensional deformation. Also
often referred to as long offset normal faults \citep{Bradyetal2000},
extensional detachments \citep{Listeretal1986} or top basement
detachment faults \citep{Holkeretal2003}, they can accommodate large
displacements (${>}$10s of kilometres) and exhume deep basement rocks
in their footwall
\citep{Wernicke1981,Gautieretal1993,Jolivetetal2010,Whitneyetal2013,Tugendetal2015}. 
Observations of low-angle normal faults active at ${<}$30\textdegree{}
have triggered numerous debates. Their fault dip is lower than the
45--60\textdegree{} dip of normal faults predicted by fault mechanics 
[\citealp{Anderson1951}, see the review of \citealp{Collettini2011}].
For a long time, these structures were thought to result from the
passive rotation of former high-angle normal faults that become
inactive once their dip becomes significantly low (${<}$30\textdegree). 
This rolling hinge model, notably proposed by \citet{Buck1988}, or
\citet{WernickeAxen1988} based on field evidence, has been successfully
modelled \citep{Brunetal1994,Lavieretal1999}. However, the existence of
low-angle active normal faults in the Gulf of Corinth
\citep{Rigoetal1996} or in the Woodlark basin \citep{Abers2001} remains
enigmatic. Several hypotheses have been proposed to explain normal
faults active and even formed at a low-angle including, stress rotation
\citep{Melosh1990}, \mbox{phyllosilicate} formation at the brittle--ductile
transition \citep{Gueydanetal2001}, the reactivation of dipping
lithological heterogeneities in a nappe stack
\citep{LePourhietetal2004,Huetetal2011b} or their neoformation\break
formation under a compaction regime \citep{Lecomteetal2011,Lecomteetal2012}.} 
}

{Both models for the formation of low-angle normal faults (i.e.,
%rolling hinge vs.\ detachments
rolling hinge vs. detachment) are supported by observations in rifts
and rifted margins but their involvement in accommodating continental
lithosphere thinning may differ from one extensional system to the
other. The formation of necking zones (Figure~\ref{fig1}) has been
associated with the development of long-offset low-angle normal faults,
exhumation of continental basement and crustal thinning in many rifted
margin examples 
\citep[e.g.,][]{OsmundsenEbbing2008,Mohnetal2012,Tugendetal2015,Gressethetal2023}.
Top basement detachment faults are also commonly described in
magma-poor COTs of rifted margins, where they are associated with the
exhumation of lower crustal rocks and lithospheric mantle, after
complete embrittlement of the continental crust
\citep{Perez-GussinyeReston2001}. The presence of such structures 
%%check
is confirmed by IODP drilling results in the Iberia--Newfoundland
margins \citep{Manatschaletal2001} and from field observations in the
Alps \citep{Lemoineetal1987,FroitzheimEberlli1990,Manatschal2004} or
Pyrenees \citep{Jammesetal2009,Lagabrielleetal2019}. In marginal seas,
low-angle normal faults commonly form core complex geometries
associated with the exhumation of deep crustal rocks and emplacement of
syn-kinematic magmatism [Woodlark Basin and Papua New Guinea:
\citealp{Abers2001}; Thailand: \citealp{Morley2014}; South China Sea:
\citealp{Dengetal2020}]. They are not necessarily associated with
localized crustal thinning, in which case they are observed in diffuse
necking zones (South China Sea rifted margin, Figure~\ref{fig1}m/n/o).
Normal faults active at low angle are also present in COTs of marginal
seas where they have been shown to control the latest stage of
continental breakup  [\citealp{Mohnetal2022}; Woodlark Basin:
\citealp{TaylorHuchon2002}]. The geodynamic setting of marginal seas,
including a high geothermal gradient, fast extension rate, and numerous
inherited thrust faults seems to favour the formation of low-angle
normal faults in the continental basement \citep{Mohnetal2022}.
Specifically, the occurrence of former nappe stacks may enhance the
development of such structures
\citep{LePourhietetal2004,Huetetal2011b}.} 

\subsubsection{{Ductile extensional shear zones}}\label{sec2.1.2.}

{In contrast, the identification and interpretation of extensional
structures accommodating continental lithosphere thinning at depth
remain more problematic. Despite the increasing resolution of seismic
reflection images, such structures are not easily observed, and their
interpretation remains ambiguous. Below the brittle upper crust,
extensional deformation has been interpreted as accommodated by ductile
deformation, possibly associated with lower crustal flow
\citep{Buck1991} or localized along sets of extensional shear zones
\citep{Reston1988,BrunBeslier1996,Huetetal2011a,Huetetal2011b}.} 

{Extensional shear zones in the crust and the mantle that localize
strain during continental lithosphere thinning have been identified and
described in several fossil rifted margins sampled in mountain belts
such as the Alps
\citep{BissigHermann1999,Mohnetal2012,KaczmarekMuntener2008}, Pyrenees}
\citep{Aumaretal2022,Odlumetal2019}, {and the Betic-Rif belt
\citep{Gueydanetal2015,Frascaetal2016,Bessiereetal2021}.} {Field
observations show high- to low-angle ductile shear zones active in
amphibolite to greenschist facies conditions accommodating the
exhumation and juxtaposition of different levels of the continental
lithosphere
\citep{BissigHermann1999,Mohnetal2012,Frascaetal2016,Petrietal2019}.
Some of these shear zones show low- to high-angle dips while others are
sub-horizontal and are therefore interpreted as d\'{e}collements. This
association of low- to high-angle dipping shear zones and
sub-horizontal d\'{e}collements can lead to a heterogeneous thinning.
This can result in the omission of specific layers of the continental
lithosphere and juxtaposition of the upper crust against serpentinized
mantle or lower crust for example \citep{Frascaetal2016,Petrietal2019}.
Such a process has been interpreted by \citet{Petrietal2019} as related
to extraction tectonics that accommodate the thinning of continental
lithosphere from the necking to the hyper-thinned\break domain.} 

{Extensional mantle shear zones have also been identified in the upper
mantle in former COTs preserved in the Alps [Lanzo massif:
\citealp{KaczmarekMuntener2008,KaczmarekTommasi2011}] or the Betic-Rif
belt [Ronda or Beni Bousera massifs:
\citealp{Afirietal2011,Precigoutetal2013,Gueydanetal2015}]. These shear
zones have been compared to possible analogous structures observed on
seismic reflection data in present-day rifted margins
\citep{Gillardetal2019}. Field observations from these COTs report
large scale, high-strain mantle shear zones that initiated at high
temperature (approximately 1000~\textdegree C) and are interpreted to
be active during the final rifting phase. These shear zones, as shown
in the case of the Lanzo massif, can act as a permeability barrier
below which mafic magma preferentially crystallize
\citep{KaczmarekMuntener2008}.}

\subsection{{Measuring continental lithosphere thinning}} \label{sec2.2.}

{Spatial variations of the crust and lithosphere thicknesses define the
geometry of rift basins and conjugate rifted margins and indicate how
much stretching and thinning has been accommodated in the continental
lithosphere during rifting. Strain can be measured from variations of
rifted margin crustal structure in terms of a stretching} ({${\beta}$})
{or thinning factor} ({${\gamma}$}{) at the scale of the upper crust,
whole crust, or whole lithosphere using different methods  
\citep[see review in][]{DavisKusznir2004}.} 

The stretching factor can be measured in terms of horizontal extension
(initial length is $l_{0}$ {and length after
extension is} $l$): 
{\begin{equation*}
\beta =\frac{\mathrm{l}}{l_{0}}
\end{equation*}}\unskip

{The stretching factor can also commonly be defined as the} {ratio of
the initial thickness of a layer} ($T_{0}${) to the present-day
thickness of that layer} ($T_{\mathrm{now}}${). Lithospheric thinning will
eventually trigger decompression melting, resulting in the emplacement
of magmatic additions and crustal thickening. If} $T_{\mathrm{ma}}$ {is the
thickness of magmatic additions resulting from decompression melting,
the stretching factor can be calculated as:} 
{\begin{equation*}
\beta =\frac{T_{0}}{T_{\mathrm{now}}-T_{\mathrm{ma}}}
\end{equation*}}\unskip

{The thinning factor is directly related to the stretching factor. It
ranges from 0 (no thinning or extension) to 1 (infinite} {${\beta}$}
{value, i.e., complete thinning) and is often more convenient to
represent graphically.} 
{\begin{equation*}
\gamma =1-\frac{1}{\beta }
\end{equation*}}\unskip

{The amount of brittle extension accommodated by the upper crust can be
determined by measuring the horizontal displacement of faults
interpreted in seismic profiles (fault heave summation method). Using
this method, it is important to} {recognize low-angle top basement
normal faults in seismic data to determine accurately the stretching
factor derived from fault heave summation as pointed out by 
\citet{Gomez-Romeuetal2020}.} {Stretching and thinning factors for the whole crust
can be determined if the crustal geometry down to the Moho can be
imaged or modelled; the initial crustal thickness required in the
calculation is typically inferred from adjacent unthinned regions. The
magnitude of lithospheric thinning cannot be directly measured from the
present-day lithosphere structure of passive margins as they at least
partly recorded post-rift ``thermal'' subsidence \citep{McKenzie1978}.
Post-rift thermal subsidence as recorded in the stratigraphy of rifted
margins can, however, be modelled in reverse to determine the whole
lithosphere stretching or thinning following the method described in} 
{\citet{Robertsetal1998}}. {The calculation of these equivalent whole
lithosphere stretching or thinning factors, however, assume that
uniform stretching and thinning occurred \citep{DavisKusznir2004}.}
%uniform stretching and thinning occurred 

\subsection{{Mechanisms and deformation modes of continental
lithosphere thinning}}\label{sec2.3.}

{Different conceptual models have been proposed to explain how the
continental lithosphere thins during extension depending on the}
{geometry of rift basins and type of extensional structures
(Figure~\ref{fig2})}. {They are either based on} {field
observations
\citep[e.g.,][]{WernickeAxen1988,Lemoineetal1987,Manatschal2004,Mohnetal2012}; 
geophysical data
\citep{Reston1988,Reston2007a,Reston2007b,DriscollKarner1998,RaneroPerez-Gussinye2010}, 
or analogue and numerical simulations
\citep{McKenzie1978,BrunBeslier1996,
BurovPoliakov2001,NagelBuck2007,LavierManatschal2006,HuismansBeaumont2011}.} 

\begin{figure*}
{\vspace*{-4pt}}
\includegraphics{fig02}
{\vspace*{-4pt}}
\caption{\label{fig2}Review of the main deformation modes and
mechanisms of continental lithosphere thinning. (A) Uniform pure shear
model \citep[after][]{McKenzie1978}; (B) Simple shear model 
\citep[after][]{Wernicke1995}; (C)~Boudinage [upper crust after
\citealp{ClercLagabrielle2014}, lower crust after \citealp{Reston1988};
mantle after \citealp{BrunBeslier1996}]; (D) Extraction 
\citep[after][]{Mohnetal2012}; (E) Lower crustal flow; (F) Polyphase faulting
\citep[after][]{Reston2009}; (G) Sequential faulting 
\citep[after][]{RaneroPerez-Gussinye2010}; (H) Upwelling divergent flow 
\citep[after][]{KusznirKarner2007}; (I) Active mantle upwelling [after
{\citealp{Huismansetal2001}}].}
%{Huismans and Beaumont, 2001}].}
{\vspace*{-4pt}}
\end{figure*}

{Different mechanisms and deformation modes have been defined based on
the initial conditions of the continental lithosphere, including
crustal and lithospheric thickness, lithological or thermal structure,
and structural inheritance \citep[e.g.,][]{Ruppel1995}. Consequently,
these mechanisms are dependent on the initial lithospheric rheological
stratification. Because lithosphere rheology may evolve during rifting
\citep{Perez-GussinyeReston2001}, a deformation mode can be activated
during early or later rifting stages only and different thinning
mechanisms can operate at different levels of the lithosphere.} 

\subsubsection{{Uniform continental lithosphere thinning}}\label{sec2.3.1.}

{The first models assumed that the entire continental lithosphere is
thinned by uniform pure shear\break extensional deformation
(Figure~\ref{fig2}A). This mechanism and its consequences for the
thermal and \mbox{subsidence} evolution of sedimentary basins were first
quantified by \citet{McKenzie1978}. The pure shear deformation model
supposes a homogeneous thinning of the continental lithosphere by a
stretching factor (${\beta}$, see Section~\ref{sec2.2.} for calculation
methods). Instantaneous stretching and thinning of the continental
lithosphere create space into which the asthenosphere passively rises.
Crustal thinning results in subsidence while the passive rise of the
asthenosphere generates a thermal uplift, the resultant of both effects
being referred to as} {\textit{initial subsidence or tectonic
subsidence}}. {After thinning, the thermal perturbation of the
lithosphere is predicted to cool conductively with time generating a
slower phase of subsidence, the so-called} {\textit{thermal
subsidence}}. {It should be noted that in the initial uniform pure
shear model of \citet{McKenzie1978}, the lithosphere is assumed to
deform as a continuum rather than by faulting.}

{Despite its simplicity, the formulation of the pure shear model of
\citet{McKenzie1978} has been extensively applied to successfully
predict the subsidence or heat flow evolution of intracontinental rift
basins [e.g., the Gulf of Suez: \citealp{Steckleretal1988}; the Kenya
Rift and the North Sea: \citealp{Kuszniretal1995}; the Jeanne d'Arc
Basin: \citealp{Kusznir1991}]. This model is, however, unable to
predict some of the observations made at distal rifted margins,
including the presence of domains of exhumed mantle in some COT
(Figure~\ref{fig1}). As a result, its applicability to rifted margins recording
an extreme thinning of the continental lithosphere has been widely
discussed \citep[see][for
reviews]{DavisKusznir2004,KusznirKarner2007}.}

\subsubsection{{Depth Dependent continental lithosphere Thinning (DDT)}}\label{sec2.3.2.}

Extension and thinning have been measured extensively on the scale of
the lithosphere, of the whole crust and of the upper crust (from fault
heave summation) in many rifted margins worldwide  \citep[see review
in][]{DavisKusznir2004}. The results showed that the amount of
extension that could be measured from brittle faulting in the upper
crust was by far insufficient to balance the amount of thinning deduced
at the scale of the whole crust or lithosphere
\citep{DavisKusznir2004,Reston2007a}. One explanation invoked for this
identified ``extension discrepancy'' is that the thinning of the
continental lithosphere is depth dependent: the different levels of the
lithosphere (upper/lower crust and mantle) record different magnitudes
of thinning in space and time \citep[see][for
reviews]{Reston2007a,Reston2007b, DavisKusznir2004,KusznirKarner2007,
HuismansBeaumont2014}. The concept of depth-dependent lithosphere stretching or 
depth-dependent lithosphere
thinning (DDT) has been introduced in the 80s based on offshore
[Eastern Canada margin, \citealp{RoydenKeen1980}] and onshore [Basin
and Range, \citealp{Wernicke1995}]
case studies. Over the past decades,
numerous models involving DDT of the lithosphere have been proposed
based on offshore and/or onshore datasets. \looseness=-1

\paragraph{Non-uniform (decoupled) pure shear}

{The non-uniform pure shear model has initially been developed as an
attempt to explain that quantifications of thermal subsidence were
greater than predictions derived from crustal thinning only
\citep{RoydenKeen1980}. The non-uniform pure-shear deformation model is
a variation of the \citet{McKenzie1978} pure shear model, which
incorporates the possibility of depth-dependent extension or thinning
\citep{RoydenKeen1980}. The non-uniform pure shear model considers that
the lithosphere is constituted of layers with distinct mechanical
behaviours that will not deform homogeneously under stress 
\citep[e.g.,][]{RoydenKeen1980,SclaterChristie1980}.
As a result, different
amounts of thinning are recorded above and below a decoupling horizon
separating the brittle crust from ductile mantle; subsidence depends on
the relative magnitude of thinning recorded by the two layers
\citep{RoydenKeen1980}. Despite its value to explain observations, this
model implies that different amounts of extension are accommodated in
the crust and mantle, which creates a problem to balance extension in
2D if the volume of mantle melt production is not considered
\citep{RoydenKeen1980}.} \looseness=-1

\paragraph{Simple shear deformation model}

{An end-member of DDT is the simple-shear lithosphere extensional model
\citep[e.g.,][]{Wernicke1995,WernickeAxen1988,Listeretal1991}
involving the activity of a major low-angle normal fault (i.e.,
detachment fault) cutting across the entire continental lithosphere
(Figure~\ref{fig2}B). This structure will produce two asymmetric margins with an
upper and a lower plate. Extensional deformation will be nonuniformly
distributed across the future rifted margins with a lateral shift
between the location of extreme continental crust and lithospheric
mantle thinning. This has implications\break for both syn- and post-rift
subsidence evolution between the upper and lower plates. However, the
identification of upper and lower plates based on their subsidence
evolution in mature systems has proven to be problematic due to
important lower crust ductile extension and unrecognized normal
faulting. Such a situation was referred to as the ``upper plate paradox''
by \citet{DriscollKarner1998}, implying that both margins appear as
upper plates from their subsidence.} 

{The simple-shear deformation model was invoked to explain the
formation of several rifted margins such as the North Biscay margin
\citep{LePichonBarbier1987} or the Alpine Tethys ones
\citep{Lemoineetal1987}. However, the original model implied that a
low-angle normal fault can cut through the whole lithosphere, a
situation that is plausible under extreme rheological conditions.
The simple-shear deformation is commonly suggested to control the formation
of some rifted margins but during the latest stage of rifting, once the
crust is significantly thinned and embrittled
\citep{Perez-GussinyeReston2001,Manatschaletal2001}.} 

\paragraph{Boudinage}

{The mechanical layering of the continental lithosphere is now commonly
represented by at least four layers alternating strong (brittle) and
weak (ductile) behaviours \citep{BrunBeslier1996}. Thinning of
multi-layered lithosphere is not accommodated by either pure- or
simple-shear deformation and generates a complex and heterogenous
strain pattern.} 

{Extension of a mechanically layered lithosphere triggers structural
instabilities and softening accommodated by localized necking and
boudinage of strong layers (Figure~\ref{fig2}C/D)
\citep{BrunBeslier1996,Mohnetal2012,Duretzetal2016,Clercetal2018}.}
{The disruption of competent layers is accommodated by shear zones
acting as d\'{e}collements in weak layers. Boudinage was initially
inferred to occur in the deeper parts of the crust}
{\citep{Reston1988} and/or in the upper mantle 
\citep[e.g.,][]{BrunBeslier1996}. Boudinage of the upper crust was also
suggested in examples inferred to have high thermal gradients and
involving thick sedimentary layers \citep{Clercetal2018} or
sediment/basement decoupling along salt layer
\citep{ClercLagabrielle2014}.} 

\paragraph{Extraction tectonics}

{In addition to the boudinage of strong layers, recent studies also
highlighted the efficient role of extraction tectonics in accommodating
continental lithosphere thinning based on field evidence and numerical
simulations  \citep{Mohnetal2012,Duretzetal2016,Petrietal2019}.
Extraction mechanisms occur in relation to the necking of competent
layers. The necking or boudinage of strong layers results from strain
localization along conjugate shear zones with opposite senses of
displacement. With extension, strong layers will be coherently
disrupted leaving behind an extraction fault or shear zone where most
of the strain accumulated.} 


{Extraction mechanisms appear critical during the necking of the
heterogeneous lithosphere (Figure~\ref{fig1}). Necking of the
lithosphere results from the activity of conjugate large-offset normal
faults interacting with anastomosing shear zones acting as
d\'{e}collement levels at mid-crustal levels or deeper
(Figure~\ref{fig2}D) 
\citep{Mohnetal2012,Duretzetal2016,Petrietal2019}. During extension,
weak ductile layers localize most of the deformation, resulting in
vertical ductile thinning. Meanwhile, strong levels are laterally
extracted towards the rift axis, forming the distal domains of rifted
margins. As a result, distal domains predominantly retain strong levels
and may preserve variable basement composition after extraction
tectonics, depending on the initial heterogeneities 
\citep{Petrietal2019}.} 

\paragraph{DDT: the key role of the behaviour of the lower crust}

{At first order, the lower continental crust corresponds to the 10--17
km thick layer above the Moho. Although heterogenous and including
various lithologies (felsic and/or mafic), it is often considered as a
simple and uniform layer whose behaviour varies from strong, brittle or
highly viscous  \citep{Jamtveitetal2016}, to weakly viscous, in which
case it can flow \citep{Buck1991} and form a ``channel flow'' 
\citep{BlockRoyden1990,HuismansBeaumont2011,Bruneetal2014}. Geological
models for the lower crust during rifting can be divided into two
members depending on the non-flowing or flowing behaviour of the lower
crust. The behaviour of the lower crust is directly related to the
initial parameters of the rift system (e.g., thermal state, various
inheritance) and can evolve during the development of extension through
rheological softening mechanisms (temperature increase, occurrence of
fluid/melt, grain size reduction along deformation\break zones).} 


{On the one hand, the extension of the non-flowing lower crust is
interpreted as being accommodated by a series of distributed shear
zones. This mode of deformation was recognized on several reflection
seismic profiles  \citep{Reston1988,Clercetal2015}, where reflective
bands showing sigmoidal geometries were interpreted as localized shear
zones accommodating lower crustal boudinage (Figure~\ref{fig2}C). Additionally,
it was confirmed through field observations in the Southern Alps, which
preserve a section of lower crust from the former Jurassic Adriatic
margin 
\citep{HandyZingg1991,Mohnetal2012,Petrietal2019,Simonettietal2021}.
There, several syn-rift Jurassic shear zones delimit sections of
Paleozoic basement unaffected by rift-related deformation.} 


{On the other hand, several studies have emphasized the importance of
lower crustal flow during extension \citep[e.g.,][]{BlockRoyden1990,
Buck1991,HopperBuck1996,HuismansBeaumont2011,Huetetal2011a, Bruneetal2014}.
Crustal thickness variations during thinning generate horizontal
pressure gradients at the base of the crust. These pressure gradients
can drive ductile lower crust, if its viscosity is sufficiently low, to
flow into areas of localized upper crustal thinning (Figure~\ref{fig2}D) 
\citep[e.g.,][]{Artyushkov1973}.
This mode of deformation initially referred to as the
core complex mode by \citet{Buck1991} involves a very weak lower crust
so that the strain in the lower crust remains homogeneously distributed
over a broad area.  \citep{Buck1991,HopperBuck1996}.
Lower crustal
flow is a mechanism commonly associated with the formation of
metamorphic core complexes in post-orogenic settings 
\citep[][and reference therein]{Whitneyetal2013} or marginal basins
[Gulf of Lion: \citealp{Jolivetetal2015}; South China:
\citealp{Dengetal2020}] both of which are characterized by
high-geothermal conditions.}

\subsubsection{{Extensional faulting}}\label{sec2.3.3.}

\paragraph{Sequential faulting}

{Sequential faulting has been proposed as a solution to explain the
extension discrepancy and asymmetry observed at some rifted margins
(Figure~\ref{fig2}E) \citep{RaneroPerez-Gussinye2010}. This deformation model is
derived from observations in Iberia--Newfoundland rifted margins and
suggests that crustal thinning is controlled by the activity of
Andersonian-type extensional faults} { \citep{Anderson1951}}. {Each
fault locks after a rotation to ${>}$30\textdegree} {and is replaced
by a new one formed in the hanging wall of the locked fault.
Consequently, each new fault forms in a previously thinned hanging
wall, explaining why total crustal thinning exceeds that predicted by
faulting at the same location, thus creating an apparent} {extension
discrepancy.}

\paragraph{Polyphase faulting}

{Alternative explanations for the ``extensional discrepancy'' observed
at rifted margins suggest that the amount of extension measured from
upper crustal brittle faulting is largely underestimated in seismic
interpretations. Extension may notably go undetermined because of
complex crosscutting relationships generated by polyphase faulting
[Figure~\ref{fig2}F,
\citealp{Reston2005,Reston2007a,Reston2007b,Reston2009,RestonMcDermott2014}].
This mechanism, derived from observations from the Iberia--Newfoundland
rifted margins and introduced by \citet{Reston2005} aims to explain the
latest stages of thinning once the continental crust has become
embrittled. Polyphase faulting contrasts with the sequential faulting
mechanism and does not imply a migration, but rather a focusing of
extensional deformation at the location of the future continental
breakup. This mechanism implies successive phases of faulting: a first
generation of fault forms, rotates to low angle and locks; then another
generation of fault forms, cuts through the previous one, and so on.
Complex fault intersections could then be generated and be difficult to
identify on seismic profiles  \citep{Reston2005, Reston2007a,Reston2007b,
Reston2009,RestonMcDermott2014,Naliboffetal2017}.} 

\subsubsection{{Active upwelling}}\label{sec2.3.4.}

{Mantle dynamics can also play an active role during continental
lithosphere thinning, which is often triggered by flow instabilities
induced by viscosity contrasts, thermal and melt buoyancy forces
(Figure~\ref{fig2}H/I). The degree of active upwelling or buoyancy can be
quantified by the ratio between extension} ({\textit{Vx}}{) and axial
upwelling rates} ({\textit{Vz}}{)  \citep{Batchelor1967,Braunetal2000}
as defined in the upwelling divergent flow model (Figure~\ref{fig2}H) 
\citep{DavisKusznir2004,KusznirKarner2007}.
Upwelling divergent flow
may be focused on the lower lithosphere, generating small-scale
convection that contribute to thinning the mantle lithosphere
(Figure~\ref{fig2}I)} { \citep{Huismansetal2001}. } {Dynamic models predict that
small-scale convection in} {the mantle lithosphere} {can arise in the
latest stages of rifting, inducing a \mbox{transition} from passive to active
mantle upwelling} { \citep{Huismansetal2001}.} {Thermal anomalies in
the mantle are particularly prone to triggering diapiric instabilities
and small-scale convection in the asthenosphere 
\citep{NielsenHopper2004}. However, active upwelling is also a viable
deformation mode in the absence of anomalously hot mantle 
\citep{DavisKusznir2004,KusznirKarner2007,Fletcheretal2009,Jeanniotetal2016}.} 

\section{{What are the parameters controlling the modes of continental
lithosphere thinning?}}\label{sec3.}

{Various mechanisms and deformation modes can operate to thin the
continental lithosphere (Figure~\ref{fig2}). Nevertheless, whether a
deformation mode is activated or inhibited in lithospheric layers
largely depends on the initial rheology and its evolution during
rifting  \citep{Buck1991,Gueydanetal2008,HuismansBeaumont2003,
HuismansBeaumont2007,
HuismansBeaumont2011,Huismansetal2005,LavierBuck2002}. Previous
numerical studies have notably explored the role of parameters such as
lithospheric strength and thermal structure, crustal thickness,
structural inheritance or brittle--ductile mechanisms and extension
rates on the modes of extension during rifting} 
\citep{BeaumontIngs2012,Bruneetal2014,Bruneetal2017,Buck1991,Bucketal1999,Gueydanetal2008,Huismansetal2005,HuismansBeaumont2007, HuismansBeaumont2011,LePourhietetal2004,JammesLavier2016,SvartmanDiasetal2015,TetreaultBuiter2018}.
Most of these parameters and feedback between them also influence the
final morphology of rifted margins (wide {{vs.}}\ {narrow;
symmetric} {{vs.}}\ {asymmetric)}. {It would be beyond the scope
of this review to do an exhaustive parametric study of all these
parameters. Here, we built a set of numerical models only varying two
key parameters to capture to first order the evolution of continental
lithosphere thinning mechanisms over time within the different levels
of the lithosphere.}

\subsection{{Modelling approach and initial configuration}}\label{sec3.1.}

{The presented numerical models were run using the 2D geodynamic
simulation code MDoodz  \citep{Duretzetal2021}. The code is based on
the finite-difference/marker-and-cell technique  \citep{GeryaYuen2003}
which allows to conveniently couple Eulerian thermomechanical numerical
solutions with Lagrangian advection of material properties. The
mechanical and thermal equations are discretized on a staggered grid
and resulting linear systems are obtained via direct-iterative schemes
\citep{Rassetal2017}. Lagrangian markers are advected using a second
order in space Runge--Kutta scheme. The models include a true free
surface based on the staircase discretization and Lagrangian advection 
\citep{Duretzetal2016}. Kinematic boundary conditions are applied to
the left, right and bottom sides of the model domain.} 


{The rheological model is visco-elastic--viscoplastic
\citep{deBorstDuretz2020} (Table~\ref{tab1}). The visco-elastic creep
model includes the power-law effect of dislocation creep. Peierls and
diffusion creep are additionally taken into account in mantle phases
only. A Drucker--Prager frictional plastic model is applied to all
material phases. The latter is supplemented by viscoplastic
regularisation  \citep{Duretzetal2019}, which allows for successful
integration of the rheological models  \citep{Duretzetal2020}. At the
local level, the rheology is integrated using local iterations 
\citep{PopovSobolev2008}. At the global level, force equilibrium is
achieved by applying Newton iterations  \citep{Duretzetal2021}.}


\begin{table*}
\caption{\label{tab1}Thermal and rheological parameters used in
the simulations}
\begin{tabular}{ccccc}
\thead
Lithology & & Crust (Granite) & Mantle/Asthensphere (Olivine) & Units\\
\endthead
$\rho_0$       &  Density & 2800  & 3330  & kg/m$^{3}$ \\
$n_{\mathrm{dis}}$      &  Stress exponent & 3.3  & 3.5  & \\
$A_{\mathrm{dis}}$      &  Pre-exp factor & 3.1623~$\times$~10$^{-26}$  & 1.1~$\times$~10$^{-16}$  & Pa$^{-{n}}{\cdot}$s$^{-1}$\\
$Q_{\mathrm{dis}}$      &  Activation energy & 185.5  & 530  & kJ~$\times$~mol$^{-1}$\\
$V_{\mathrm{dis}}$      &  Activation volume & 0  & 11~$\times$~10$^{-6}$  & m$^{3}{\cdot}$mol$^{-1}$\\

$n_{\mathrm{dif}}$      &  Stress exponent & -  & 1  & \\
$m_{\mathrm{dif}}$      &  Grain size exponent & -  & 3  & \\
$A_{\mathrm{dif}}$      &  Pre-exp. factor & -  & 1.5~$\times$~10$^{-15}$  & Pa$^{-{n}}{\cdot}$m$^{m}{\cdot}$s$^{-1}$\\
$Q_{\mathrm{dif}}$      &  Activation energy & -  & 375  & kJ${\cdot}$mol$^{-1}$\\
$V_{\mathrm{dif}}$      &  Activation volume & -  & $4\times10^{-6}$  & m$^{3}{\cdot}$mol$^{-1}$\\

$q_{\mathrm{pei}}$      &  Peierls parameter & -  & 2  & \\
$\gamma_{\mathrm{pei}}$ &  Peierls  regularisation & -  & 0.1  & \\
$\sigma_{\mathrm{pei}}$ &  Peierls' stress & -  & 8.5  & GPa\\
$A_{\mathrm{pei}}$      &  Pre-exp. factor & -  & 5.7~$\times$~10$^{11}$  & s$^{-1}$\\
$Q_{\mathrm{pei}}$      &  Activation energy & -  & 540  & kJ${\cdot}$mol$^{-1}$
\botline
\end{tabular}
\tabnote{Flow law parameters are taken from \citet{HansenCarter1983}
for the crust, \citet{HirthKohlstedt2004} and \citet{GoetzeEvans1979}
for the lithospheric mantle with regularization from
\citet{Kameyamaetal1999}.
The following parameters are similar for
the crust and the mantle: Expansivity ($\alpha = 3.2\times 10^{-5}$~K$^{-1}$), 
incompressibility ($\beta = 1.5\times 10^{-11}$~Pa$^{-1}$),
shear modulus ($G = 1.0\times 10^{10}$ Pa), friction angle ($\varphi =
30$\textdegree), initial cohesion ($C_{0} = 50$~MPa), final cohesion
($C_\infty = 1$ MPa), reference visco-elastic overstress
($\Delta\sigma = 1.5$ MPa), heat capacity ($C_p = 1050$~J/kg/K),
thermal conductivity ($k = 3$ W/m/K). A grain size of 1 mm is assumed
for the mantle. The governing equations and the detailed model
implementation are stated in \citet{Duretzetal2021}.}
{\vspace*{2pt}}
\end{table*}


{The model domain has a width of 350 km and a height of 170 km. The
latter is discretized using to $910 \times 500$ cells, which provides a
spatial resolution of 380 m along both dimensions. The domain extent
remains fixed throughout the simulations. Material thus flows out of
east and west boundaries and flows in from the south side. The crust
has an initial thickness of 35~km and only consists of a single
material phase (Westerly granite). The mantle also consists of a single
material phase (dry olivine). In order to seed the model, an initial
bell-shaped thermal perturbation is applied in the mantle (amplitude
50~\textdegree C and half-width 30 km). In the following, we investigate
the role of two key parameters: the extension rate (0.25 to 2.3 cm/yr)
and then Moho temperature (450~\textdegree C to 650~\textdegree C). } 


\subsection{{Results of numerical simulations}}\label{sec3.2.}

{For each simulation, we show the initial strength profile and
geotherm, the evolution of the crustal geometry and superimposed modes
of deformation \mbox{(distribution} between elastic, plastic and viscous
rheological behaviours) and strain distribution. Thinning factors for
the crust, mantle and whole lithosphere are also shown to track the
partitioning between the crust and lithospheric mantle thinning and
evolution in space and time of DDT.} 

\subsubsection{{Model NR01---cold Moho temperature and slow extension rate}}\label{sec3.2.1.}

{The model NR01 shown in the Figure~\ref{fig3} is characterized by an
initial cold Moho temperature of 450~\textdegree C and a slow extension
rate (0.25~cm/yr). The initial lithosphere--asthenosphere boundary (LAB)
(1350~\textdegree C) is slightly deeper than 150~km depth\break
(Figure~\ref{fig3}a).}

\begin{figure*}
{\vspace*{-1pt}}
\includegraphics{fig03}
{\vspace*{-1pt}}
\caption{\label{fig3}{Numerical model NR01 illustrates the
development of rifting with initial Moho temperature of 450~\textdegree
C and a constant bulk extension rate of} 
0.333~$\times$~10$^{-15}$~s$^{-1}$. {Left
column represents an enlargement of the model showing the mode of
deformations and their evolution during ongoing extension. The doted
gray and thin white lines represent passive markers. Please note that
the middle one represents the initial plastic elastic to viscous
transition (i.e., brittle--ductile transition) The central column
documents the accumulated von Mises strain ($\openE{}$II). The white contours
show the isotherms in \textdegree C. The right column displays the
thinning factor distribution across the model for the crust, the mantle
lithosphere and the whole lithosphere.}}
{\vspace*{-3pt}}
\end{figure*}

{Extension is initially accommodated by discrete high-angle structures
in the brittle/plastic upper part of the crust and mantle. Strain
subsequently localizes at the rift axis in the uppermost
brittle/plastic mantle after 16\% of the extension
(Figure~\ref{fig3}b). In~the\break crust, strain starts localizing within two
narrow conjugate deformation zones dipping toward the rift axis
delimiting a central ${\sim}$50~km wide graben. Although strain
continues localizing within these conjugate deformation zones, the
future necking zones, little brittle/plastic deformation is recorded in
the central crustal block in between (Figure~\ref{fig3}c) [so-called
H-block: \citealp{LavierManatschal2006} or keystone:
\citealp{Mohnetal2012}]. Increasing extension leads to the boudinage
and distributed necking of the upper brittle/plastic mantle layer at
the rift axis, accommodated by deformation of the ductile/viscous lower
crust of the keystone that becomes heterogeneously thinned after 20\%
of extension. As increasing extension is accommodated within crustal
conjugate deformation zones, increasing crustal thinning is being
recorded in the forming necking zones associated with the exhumation and
embrittlement of deeper crustal levels (see evolution of passive
markers in Figure~\ref{fig3}d). After 26\% of extension, the
deformation\break and thinning of the keystone crustal block intensifies,
associated to transient asymmetric shearing. Crustal thinning of the
keystone leads to its progressive embrittlement and thinning of
ductile/viscous lower crust (Figure~\ref{fig3}e). After 38\% of
extension, only extremely thinned (${<}$10~km) plastic/brittle crust
remains in between the necking zones, underlain by a plastic/brittle
upper mantle layer. Final crustal thinning and crustal separation is
here accommodated in the frictional field (Figure~\ref{fig3}e).}

\subsubsection{{Model NR03---cold Moho temperature and fast extension
rate}}\label{sec3.2.2.}

{The model NR03 shown in Figure~\ref{fig4} is characterized by an initial
cold Moho temperature (450~\textdegree C) and depth of the LAB similar
to model NR01 (Figure~\ref{fig3}) but with a larger extension rate
(2.3~cm/yr)\break (Figure~\ref{fig4}a). } 

\begin{figure*}
\vspace*{15pt}
\includegraphics{fig04}
\caption{\label{fig4}Numerical model NR03 illustrates the
development of rifting with initial Moho temperature of 450~\textdegree
C and a constant bulk extension rate of
$3\times10^{-15}~\mathrm{s}^{-1}$. {Left column
represents an enlargement of the model showing the mode of deformations
and their evolution during ongoing extension. The doted gray and thin
white lines represent passive markers. Note that the middle one
represents the initial plastic-elastic to viscous transition (i.e.,
brittle--ductile transition) The central column documents the
accumulated von Mises strain ($\openE{}$II). The white contours show the
isotherms in \textdegree C. The right column displays the thinning
factor distribution across the model for the crust, the mantle
lithosphere and the whole lithosphere.}}
\vspace*{7pt}
\end{figure*}

{Strain is initially accommodated by discrete distributed high-angle
extensional faults in the brittle/plastic upper part of the crust and
mantle. Similarly to model NR01, strain localizes in the
brittle/plastic upper mantle at the rift axis at 17\% of extension,
associated to the formation of two deformation zones in the crust
delimiting a central ${\sim}$50~km wide graben (Figure~\ref{fig4}b).
Localized boudinage and necking of the brittle/plastic upper mantle
layer occurs after 22\% of extension, with a larger wavelength
ductile/viscous deformation of the lower crust of the keystone compared
to NR01 (Figure~\ref{fig4}c). The forming necking zones already record
intense crustal thinning} ({$\gamma\sim 0.5$ after 22\% of
extension, Figure~\ref{fig4}c), while little brittle/plastic
deformation of the keystone is recorded. Exhumation of deeper crustal
levels and their embrittlement occur in the necking zones but are less
pronounced than in model NR01. After 22\% of extension, strain
localizes in between the necking zones at the rift axis recorded by
brittle/plastic deformation in the upper crust (Figure~\ref{fig4}d).
After 36\% of extension, strain accumulation in the crust at the rift
axis leads to the thinning and cutting of the central keystone block
into symmetric parts (Figure~\ref{fig4}e). Despite the extreme crustal
thinning of the continental crust, it never fully embrittles before
crustal separation (Figure~\ref{fig4}e) in contrast to model NR01\break
(Figure~\ref{fig3}e).} 

\subsubsection{{Model NR07---hot Moho temperature and slow extension
rate}}\label{sec3.2.3.}

{The model NR07 shown in Figure~\ref{fig5} is characterized by a higher
temperature of 650~\textdegree C at the Moho and a low extension rate
(0.25~cm/yr). The initial LAB (1350~\textdegree C) is slightly deeper
than 90~km depth\break (Figure~\ref{fig5}a).} 

\begin{figure*}
\vspace*{5pt}
\includegraphics{fig05}
\caption{\label{fig5}{Numerical model NR07 illustrates the
development of rifting with initial Moho temperature of 650~\textdegree
C and a constant bulk extension rate of 0.333~$\times$~10}$^{-15}$ {s}$^{-1}$.
{Left column represents an enlargement of the model showing the mode of
deformations and their evolution during ongoing extension. The doted
gray and thin white lines represent passive markers. Please note that
the middle one represents the initial plastic-elastic to viscous
transition (i.e., brittle--ductile transition). The central column
documents the accumulated von Mises strain ($\openE{}$II). The white contours
show the isotherms in \textdegree C. The right column displays the
thinning factor distribution across the model for the crust, the mantle
lithosphere and the whole lithosphere.}}
\vspace*{6pt}
\end{figure*}

{Extension is accommodated by distributed discrete high-angle
extensional faults in the brittle/plastic upper crust for 20~Ma. Strain
subsequently localizes in the lithosphere towards the rift axis while
active mantle upwelling is initiated at the \pagebreak base of the lithosphere.
After 38\% of extension, roughly homogeneous thinning is observed
over a 200~km width at the rift axis} {although mantle thinning slightly exceeds
crustal thinning (Figure~\ref{fig5}b). Conductive cooling of the mantle
due to the low extension rate enables the formation of a
plastic/brittle upper mantle layer, subsequently thinned by short
wavelength boudinage associated with ductile/viscous lower crust
deformation (Figure~\ref{fig5}b). A complex pattern of extensional
structures occurs in the brittle/plastic upper crust, suggesting that
several generations of faults formed (polyphase faulting) dipping in
opposite directions. At 41\% of extension, strain localizes in
a narrower region at the rift axis, associated with the formation of two
conjugate shear zones in the crust that delimit a central graben (up to
25~km wide), under which the crust is slightly thicker (Figure~\ref{fig5}c).
Extension and crustal thinning are accommodated by extensional shear
zones within the necking zones, which are associated to the exhumation
of deeper crustal levels (Figure~\ref{fig5}d). Crustal thinning occurs beneath the
central graben at the rift axis, associated with progressive crustal
embrittlement from 44\% to 49\% extension (Figure~\ref{fig5}e). }


\subsubsection{{Model NR09---hot Moho temperature and fast extension
rate}} \label{sec3.2.4.}


{The model NR09 shown in Figure~\ref{fig6} is characterized by Moho
temperature of 650~\textdegree C and depth of the LAB similar to model
NR07 (Figure~\ref{fig5}a), but with a faster extension rate (2.3~cm/yr)
(Figure~\ref{fig6}a). } 

\begin{figure*}
\vspace*{5pt}
\includegraphics{fig06}
\caption{\label{fig6}Numerical model NR09 illustrates the
development of rifting with initial Moho temperature of 650~\textdegree
C and a constant bulk extension rate of 
$3\times10^{-15}~\mathrm{s}^{-1}$. Left
column represents an enlargement of the model showing the mode of
deformations and their evolution during ongoing extension. The doted
gray and thin white lines represent passive markers. Please note that
the middle one represents the initial plastic-elastic to viscous
transition (i.e., brittle--ductile transition). The central column
documents the accumulated von Mises strain ($\openE{}$II). The white contours
show the isotherms in \textdegree C. The right column displays the
thinning factor distribution across the model for the crust, the mantle
lithosphere and the whole lithosphere.}
\end{figure*}

{During the first 10\% of extension, the lithosphere\break records 
low-magnitude homogeneous thinning. As strain accumulates in the mantle,
predominantly viscous deformation occurs within a roughly 150~km wide
region at the rift axis, except for a thin (${\sim}$2 km\break thick)
plastic/brittle upper mantle layer. Simultaneously, multiple zones of
brittle/plastic deformation develop in the upper crust due to its
boudinage, while lower crustal domes gradually form between crustal
boudins (Figure~\ref{fig6}b). The large-scale boudinage of the upper
crust persists until 30\% of the extension, beyond which strain becomes
localized at the rift axis within the mantle (Figure~\ref{fig6}c). At
this stage, several upper crustal boudins have formed recording
brittle/plastic deformation, while deeper crustal levels are exhumed
and embrittled\break in-between. As strain localizes at the rift axis, offset
crustal deformation zones progressively deactivate\break after 30\% of
extension. Subsequently, strain localizes within one of these crustal
deformation zones, nearest to the rift axis, resulting in asymmetric
crustal thinning offset from the rift axis, with one of the crustal
blocks (``boudins'') preserved on one side (Figure~\ref{fig6}d). After
37\% extension, strain localization\break in the crust progressively shifts
to localize above the rising asthenosphere, generating crustal scale
simple-shear deformation. After 42\% extension, extreme crustal
thinning is recorded in the distal margin, without entailing complete
crustal embrittlement (Figure~\ref{fig6}e). } 


\section{Necking and thinning continental lithosphere: synthesis and
discussion}

\subsection{Different modes of lithospheric thinning}

{Different modes of lithospheric thinning exist, shaping end-member
rifted margin crustal geometries, as illustrated by our simulations
(Figures~\ref{fig3}--\ref{fig6}) and previous models 
\citep{Brun2002,KusznirKarner2007,HuismansBeaumont2007,
HuismansBeaumont2011, HuismansBeaumont2014,Bruneetal2014,
Bruneetal2017,SvartmanDiasetal2015,Perez-Gussinyeetal2023}. Here, we
show the distribution between elastic, plastic and viscous deformation
in the crust and mantle for each stage of our models. The flowing or
non-flowing behaviour of the lower crust is controlled by its strength,
which determines its efficiency as a decoupling layer. The strength of
the viscous lower crust depends on both temperature and extension rates
\citep{Brun2002}, evolving during extension: viscous material
strengthens for higher strain rates and weakens with increasing
temperature  [\citealp{Brun2002}, see also review by
\citealp{Perez-GussinyeLiu2022}]. More generally, extensional modes and
final rifted margin morphology are controlled by the presence or
absence of decoupling levels within the lithosphere 
\citep{Buck1991,Huetetal2011a,BrunBeslier1996,Duretzetal2016}.} 


{Our simple two-layer models with only varying initial thermal and boundary
conditions, enable us to reproduce the classical narrow and wide modes
of extension defined by \citet{Buck1991}. Our conditions designed to
evolve into rifted margins do not reproduce the last core complex
mode. This mode would either require higher temperatures at the Moho
(${>}$800~\textdegree C) and thicker initial crustal thicknesses
(${>}$45 km)  \citep{Tireletal2008} or a reversed/post-orogenic
stratification of the lithosphere leading to the presence of a felsic
lower crust  \citep{Huetetal2011a}.}


\subsubsection{{Thinning cold lithosphere: narrow and localized
lithospheric thinning}}\label{sec4.1.1.}


{Thinning in cold and strong lithosphere results in rapid and narrow
strain localization, within conjugate deformation zones in the crust
and viscous mantle (NR01, NR03, Figure~\ref{fig7}).} 

\begin{figure*}
\vspace*{7pt}
\includegraphics{fig07}
\caption{\label{fig7}{Synthetic diagrams showing the 
various
modes of lithospheric thinning and thinning factors during the early
development of necking zones depending on the initial Moho temperature
and extensional rates.}}
\end{figure*}

{Extensional shear zones in forming necking zones accommodate localized
crustal thinning and delimit in their hanging wall a comparatively less
thinned crustal keystone} {(Figure~\ref{fig7}). Although little brittle
deformation is recorded at this stage in the keystone, ductile
deformation is recorded in the ductile/viscous lower crust,
accommodating the boudinage and necking of the brittle/plastic upper
mantle [Figure~\ref{fig2}C, \citealp{BrunBeslier1996}]. Enhanced
conductive cooling generated by slow extension rates will favour the
brittle deformation of the upper mantle and its smaller wavelength
boudinage. Depending on the distributed or localized boudinage of the
upper mantle layer, the crust of the keystone is more or less}
{heterogeneously thinned (compare NR01 and NR03 in Figure~\ref{fig7}),
possibly even thickened by lower crustal flow (Figure~\ref{fig2}E)
according to \citet{Cheninetal2018}. Depending on extension rates and on
crustal thickness heterogeneities in the keystone, final crustal
thinning occurs after the keystone is delaminated during strain
migration towards the rift axis (NR01) or separated in two symmetric
parts enhanced by the coupling between the viscous lower crust and
mantle (NR03) (Figure~\ref{fig8}).}

\begin{figure*}
\includegraphics{fig08}
\caption{\label{fig8}{Synthetic diagrams showing the different
of modes of lithospheric thinning and thinning factors during the late
development of necking zones and distal margins depending on the
initial Moho temperature and extensional rates.}}
\end{figure*}

\subsubsection{Thinning hot lithosphere: wide and distributed
thinning}\label{sec4.1.2.}

{Thinning in hot and weak lithosphere is associated with delayed strain
localization. The weak lower crust is efficient at decoupling between
the brittle upper crust and the mantle, generating a wide rift. Ductile
deformation is dominant during lithosphere thinning, controlled by the
thick viscous lower crust (NR07, NR09, Figure~\ref{fig7}).} 


{Slow extension favours active mantle upwelling in the early stage of
lithosphere thinning (Figure~\ref{fig2}I)  \citep{Huismansetal2001}
associated with a distributed extension and very progressive
lithosphere thinning. Slow extension rates will favour conductive
cooling and formation of brittle/plastic upper mantle layer thickening
toward the rift axis. Boudinage and necking of this layer are associated
to a change from wide to narrow extensional mode, recorded by several
generations of high-angle normal faults in the brittle upper part of
the crust (polyphase faulting, Figure~\ref{fig2}F). Strain localization
at the rift axis occurs as the continental crust is already
significantly thinned (Figure~\ref{fig7}). Two conjugate extensional
shear zones delimit a narrow central graben that is quickly 
separated into two symmetric parts (Figure~\ref{fig8}).} 


{Fast extension is associated with the boudinage of the brittle/plastic
upper crust (Figure~\ref{fig2}C), while ductile/viscous deformation is
dominant underneath. Strain} {is accommodated by the simultaneous
formation of brittle deformation zones in the upper crust separating
weakly deformed crustal blocks, located in a footwall position relative
to extensional shear zones. Crustal thinning between these crustal
blocks is accommodated by the formation of domes of deeper lower
crustal levels, subsequently embrittled} {(Figure~\ref{fig7})}. {Strain
localization in the mantle and in the upper crust is spatially offset.
The coupling between the viscous lower crust and mantle at the rift
axis below one of these crustal blocks will subsequently generate
simple-shear deformation accommodated along a single extensional shear
zone.} 

\subsection{{Rifted margin morphologies and comparison with modelling
results}} \label{sec4.2.}

{Rifted margins show a large variability in width, either related to a
localized crustal thinning or showing smoother crustal thinning over
very large distances. Conjugate profiles either show symmetric or
asymmetric crustal structures (Figure~\ref{fig1}). This diversity
depends on the modes of lithospheric thinning (Figures~\ref{fig7}
and~\ref{fig8}) as shown by numerical and analogue models 
\citep{Brun2002,KusznirKarner2007,HuismansBeaumont2011,
HuismansBeaumont2014,Bruneetal2014,
Bruneetal2017,Perez-Gussinyeetal2023}. Little asymmetry is observed
because the initial and boundary conditions are mostly symmetric 
\citep{Duretzetal2021}.\break Previous numerical studies showed that the
final morphology of rifted margins and the degree of symmetry or
asymmetry largely depend on the feedback between lithosphere strength,
extension rates and applied initial and boundary conditions 
\citep{TetreaultBuiter2018,SvartmanDiasetal2015,Duretzetal2016}.
In addition, the degree of
symmetry or asymmetry is also related to the efficiency of strain and
strain-rate softening processes 
\citep{Gueydanetal2008,HuismansBeaumont2003} as well as structural
inheritance  \citep{LePourhietetal2004,Huetetal2011a,Huetetal2011b,
Petrietal2019,Balazsetal2018} which were not explored in
our study.}


{Although it is challenging to compare numerical modelling results
with natural examples directly, numerical simulations can be used to
understand some stages of the evolution of rifted margins.} 

\subsubsection{{Narrow rifted margins}}\label{sec4.2.1.}


{Narrow lithospheric thinning is commonly observed in relatively
magma-poor Atlantic-type rifted margins (Figure~\ref{fig1}a/l) and in
some segments of the South Atlantic margin 
\citep[e.g.,][]{Peron-Pinvidicetal2017}. Rifted margins typically show a
localized zone of intense crustal thinning ranging between 50~km to
100~km distance (i.e., the necking zone). Crustal thinning in the
necking zones is accommodated by large offset extensional shear zones
(i.e., detachment faults) that exhume} {deeper crustal levels
(Figures~\ref{fig7} and~\ref{fig8}). As deeper crustal levels are
exhumed, they are, however, progressively embrittled (note in
Figures~\ref{fig7} and~\ref{fig8} the
exhumation in the brittle field of the passive marker indicative of the
initial brittle--ductile transition). Detachment faults associated with
the formation of necking zones have notably been identified in remnants
of the Alpine Tethys margins 
\citep{Mohnetal2012,Ribesetal2020,DallAstaetal2022} and in the Pyrenees
\citep{Masinietal2014,Tugendetal2015}. } 


{In the initial stage of lithospheric thinning (Figure~\ref{fig7}),
these detachments delimit a relatively weakly thinned crustal keystone.
This crustal block is subsequently either delaminated or cut in two parts,
determining the symmetry or asymmetry of conjugate distal rifted
margins (Figure~\ref{fig8}). Delamination of this keystone is
associated to the migration of extensional faulting [as expected for
sequential faulting: \citealp{RaneroPerez-Gussinye2010}] and
progressive crustal embrittlement \citep{Perez-GussinyeReston2001}
(NR01, Figure~\ref{fig8}). Conjugate pairs of rifted margins will show
a partly preserved crustal block on one side, while the other one shows
intense faulting. This block can also be separated in roughly symmetric
parts (NR03, Figure~\ref{fig8}) associated with limited or no crustal
embrittlement, in which case both conjugate rifted margins will show a
crustal block preserved in their distal margin.} {The timing of
extensional faulting (Figures~\ref{fig7} and~\ref{fig8}) and the isostatic
evolution  \citep{Cheninetal2018} of this keystone differ from that
recorded in adjacent necking zones with only the earliest and latest
faulting stages being recorded.} {Since this keystone is not
necessarily preserved as such in present-day rifted margins, its
recognition remains interpretative. Delaminated remnants of this
keystone have been interpreted} {in present-day rifted margins [e.g.,
Iberia--Newfoundland: \citealp{Peron-PinvidicManatschal2010};
Angola--Gabon: \citealp{Peron-Pinvidicetal2017}]. Because of its
atypical sedimentary record  \citep{Lemoineetal1987,Mohnetal2010}, the
Brian\c{c}onnais domain of the Alpine Tethys is often considered as a
fossil analogue of this keystone block} \citep{Mohnetal2012}. 


{In summary, the evolution of NR01 is relatively consistent with that
of sedimentary starved magma-poor rifted margins such as
Iberia--Newfoundland  \citep{Sutraetal2013,Mohnetal2015} or from the
fossil Alpine Tethys  \citep{Manatschal2004,Mohnetal2010}. The general
evolution of NR03 is however less realistic because of the high
extension rates from the onset of rifting. Results of the simulations
cannot straightforwardly be compared to natural examples. Such high
velocities from the onset of rifting could potentially occur in 3D in
the case of rifting at the tip of an oceanic propagator 
\citep{LePourhietetal2018,Jourdonetal2020}. }

\subsubsection{{Wide rifted margins}}\label{sec4.2.2.}


{Wide zones of lithospheric thinning are observed in some marginal seas
(e.g., South China Sea: Figure~\ref{fig1}m--o; Alarcon segment of the
Gulf of California: Figure~\ref{fig1}q) that are expected to form in higher
geothermal gradients. Such rifted margins} {typically show a wide zone
(${>}$200~km) of progressive crustal thinning (diffuse necking zones).
Examples such as the South China Sea rifted margins typically show a
succession of rift basins under which the crust is thinned to extremely
thinned that are separated by thicker crustal blocks}
({Figure~\ref{fig1}m/o) 
\citep{Pichotetal2014,Clercetal2018,Nirrengartenetal2020}}. {Such a
situation is comparable to model NR09 characterized by the formation of
upper crustal boudins (Figures~\ref{fig7} and~\ref{fig8}). Between these
boudins, domes of lower crust are observed below rift basins and are
embrittled with increasing exhumation (see evolution of the passive
marker indicating the initial brittle--ductile transition in
Figures~\ref{fig7} and~\ref{fig8}). Exhumation of deep crustal
levels along low-angle extensional faults is documented in
several rift basins of the South China Sea [Liwan basin:
\citealp{Dengetal2020}; Dangerous Ground: \citealp{Liangetal2019}].
Reflective patterns in some of these domes are interpreted as
folds attesting the initial ductile behaviour of the exhumed crust 
\citep{Dengetal2020}. Synchronous basins are formed during upper
crustal boudinage (NR09, Figure~\ref{fig7}), as suggested for the South
China Sea based on stratigraphic correlations 
\citep{Cameselleetal2020}.} 


{In summary, the evolution of NR07 and NR09 shows typical features of a
wide rift \citep{Buck1991}. Rifted margins formed subsequently to wide
rifting modes are observed in some marginal basins of Southeast Asia.
Marginal seas are however generally characterized by high extension
rates as observed in NR09 [Woodlark Basin: \citealp{Abers2001}; South
China Sea: \citealp{Larsenetal2018,Mohnetal2022}]. Such high velocities
likely result from boundary conditions, controlled by adjacent
subduction zones  \citep{Mohnetal2022,Larvetetal2023}.} 

\subsubsection{{Limitations}}\label{sec4.2.3.}


{It should be noted that magmatism or serpentinization processes are
not included in the models. Serpentinization is expected to occur in
magma-poor systems during the latest stage of crustal thinning
controlling the structural style during mantle exhumation 
\citep{Gillardetal2019}. In normal conditions, magma is expected to be
generated for thinning factors of 0.7 or even 0.5, for higher
geothermal gradients. Magmatic rocks would likely be emplaced prior to
or during the latest stage of lithospheric thinning associated with the
formation of a sharp COT adjacent to the oceanic crust as observed in
the South China Sea  \citep{Larsenetal2018,Nirrengartenetal2020}. Onset
of magmatism during earlier stages of crustal thinning could even be
associated with the formation of seaward-dipping\break reflectors.} 

\subsection{{Evolution of depth-dependent thinning and comparison with
rifted margins}}\label{sec4.3.}

{Depth-dependent thinning has previously been recognized in present-day
rifted margins, showing that extensional faulting identified in the
upper crust could not balance the amount of thinning measured at the
scale of the whole crust or lithosphere 
\citep{DavisKusznir2004,Reston2007b}. Based on the increasingly higher
resolution of seismic data, several studies show that most of this}
{\textit{crustal}} {DDT  \citep{SvartmanDiasetal2016} could be
attributed to sub-seismic extensional faulting, non-recognition of
polyphase faulting \citep{Reston2007a,Reston2007b} or of top-basement
detachment faults  \citep{Gomez-Romeuetal2020}.}


{Thinning factors extracted from our models enables us to compare the
evolution through time of the whole crust, mantle and whole lithosphere
thinning. Except for whole crustal thinning factors, these measurements
are not easily obtained in natural systems. Lithosphere thinning in
natural systems is generally approximated from subsidence analysis in
rift basins and do not greatly differ from whole crust thinning factors
where they can be measured  \citep{DavisKusznir2004}. Thinning factors
extracted from our models show an important discrepancy between crustal
thinning and mantle or lithosphere thinning (Figures~\ref{fig7} and~\ref{fig8}) 
[\citealp{HuismansBeaumont2011}; \textit{lithospheric}} DDT in
\citealp{SvartmanDiasetal2016}] that cannot be measured in present-day
margins.


{Lithospheric DDT in narrow rift models is particularly contrasted in
time and space. The early stage of lithospheric thinning is associated to
initially greater crustal than mantle thinning in rift shoulders where
necking zones are progressively formed, while at the rift axis
(location of the keystone), mantle thinning exceeds crustal thinning
(Figure~\ref{fig7}). Part of this DDT is, however, transient and is
partly erased by subsequent crustal thinning (Figure~\ref{fig8}). Hence
at the end of rifting, little depth-dependent thinning is observed
between the crust and mantle/lithosphere in the distal margins.
Lithospheric DDT is also seen in our wide rift models but is either
less pronounced after lithospheric thinning (NR07) or reflects
asymmetric thinning (NR09). } 


{Although difficult to measure in natural systems, lithospheric scale
DDT is predicted by numerical simulations, part is permanently recorded
(rift shoulders, where necking zones form), part is transient (at the
rift axis). Hence, thinning factors measured in present-day margins are
only partly representative of the magnitude and distribution of DDT,
although its consequences for the subsidence evolution will be recorded
in the stratigraphic record.} 


\section{Conclusions and perspectives}


{We reviewed the mechanisms of continental lithospheric thinning and
the associated extensional structures that control the formation of
rifted margins and their observed diverse crustal geometries. Using a
simple two-layer model for the crust and mantle, we illustrate the
spatial and temporal evolution of extensional modes for different
initial thermal conditions and extension rates. Different modes of
lithospheric thinning are highlighted that control the formation of 
end-member rifted margin morphologies observed in natural systems. We show
as previously known that lithosphere thinning is indeed depth-dependent
\citep{DavisKusznir2004,HuismansBeaumont2011, HuismansBeaumont2014},
notably during the formation of rift shoulders and necking zones.
Transient phases of lithospheric DDT are also observed in modelling
results that cannot easily be measured in natural systems.} 


{Here, only the results of 2D numerical simulations are presented and
compared to natural systems. More and more 3D numerical models are
being developed, testing the effect of obliquity or lateral changes in
boundary conditions 
\citep{BruneAutin2013,Ammannetal2018,Duclauxetal2020,Jourdonetal2021},
changes of extensional modes due to propagation 
\citep{LePourhietetal2018,Jourdonetal2020} or changes in polarity and
asymmetry due to inheritance 
\citep{LePourhietetal2017,Balazsetal2018, Neuharthetal2021}.
The development of 3D models and their comparison with natural systems
will certainly continue to enhance our understanding of rifting
processes in the near future.} 

\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*{Acknowledgments}

{\vspace*{-2pt}}

{We thank Fran\c{c}ois Sapin and another anonymous reviewer for their
thoughtful suggestions
and Olivier Fabbri for a careful final revision of the text. 
Our gratitude also goes to N.~J.~Kusznir for our
extensive and enlightening discussions on lithosphere thinning
mechanisms.} 

\nocite{Afilhadoetal2015,
Biarietal2015,
Deanetal2000,
Funcketal2017,
Funcketal2003,
Funcketal2004,
%Gueydanetal2005,
Lauetal2006,
Lizarraldeetal2007,
LoudenChian1999,
Moulinetal2015,
OReillyetal2006,
WhiteSmith2009,
Zeltetal2003}

\back{}

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\section*{Supplementary data}

{\vspace*{-2pt}}

Supporting information for this article is available on the journal's
website under \printDOI\ or from the author.

\CDRsupplementaryTwotypes[application/zip]{supplementary-material}{\cdrattach{crgeos-257-suppl.zip}}

{\vspace*{-2pt}}

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