Pauline Chenin
email: chenin@unistra.fr

Stefan M Schmalholz

Gianreto Manatschal

Thibault Duretz

Impact of crust-mantle mechanical coupling on the topographic and thermal evolutions during the necking phase of 'magma-poor' and 'sediment-starved' rift systems: A numerical modeling study

Keywords: Investigation and Conceptualization, Writing -Original Draft Conceptualization, Writing -Review & Editing, Resources Conceptualization, Writing -Review & Editing, Funding acquisition rift, necking, topographic evolution, thermal evolution, numerical modeling

We used high-resolution (500 x 250 m) two-dimensional lithospheric-scale thermo-mechanical numerical modeling to unravel the unexpected topographic and thermal evolutions recorded during the necking phase of several rift systems worldwide. Through a systematic analysis we studied how the lithosphere rheology impacts the topographic and thermal evolutions across the entire width of magma-poor and sediment-starved rift systems until their crust is locally thinned to 10 km. We quantified the evolution of topography, uplift and subsidence rates, accommodation and emerged space creation, temperature and surface heat flow for a wide panel of crustal and mantle rheologies to provide an overview of possible rifting behaviors. Extension of a lithosphere for which the crust and mantle are mechanically decoupled by a weak lower crust generates complex morphotectonic evolutions, with the formation of temporarily restricted sub-basins framed by uplifted parts of the future distal margin. Mechanical decoupling between the crust and mantle controls also largely the thermal evolution of rift systems during the necking phase since, for equivalent extension rates and initial geotherms: (i) weak/decoupled lithospheres have a higher geothermal gradient at the end of the necking p hase than strong/coupled lithospheres; and (ii) weak/decoupled lithospheres show intense heating of the lower crust at the rift center and intense cooling of the crust on either side of the rift center, unlike strong/coupled lithospheres. These behaviors contrast with the continuous subsidence and cooling predicted by the commonly used depth-uniform thinning model. Accommodation space in the evolving basins is first generated by vertical crustal velocities and subsequently by horizontal velocities causing the widening of the earlier formed basin. Processes such as strain softening and mantle fertilization have a limited impact on the primary morphology and thermal state of rift systems before the crust is thinned to 10 km but may locally amplify relief and thermal heterogeneities.

1.

Introduction

The formation of sedimentary basins and the subsidence recorded at rift systems have been attributed to lithosphere necking and thinning processes since the early 1970's (e.g. [START_REF] Artemjev | Structure and Isostasy of the Baikal Rift and the mechanism of rifting[END_REF]. [START_REF] Mckenzie | Some remarks on the development of sedimentary basins[END_REF] developed a simple but robust model to explain the subsidence and temperature evolutions of sedimentary basins formed in extensional settings, assuming that lithosphere thinning is instantaneous and uniform with depth (Figure 1a). In this so-called depth-uniform thinning (DUT) model, extension of a lithosphere generates (black curves in Figures 1b and1c): (ia) immediate surface subsidence related to crustal thinning together with (ib) instantaneous geothermal gradient increase without any material heating (the lithospheric material is simply advected upward); subsequently, thermal relaxation results in (iia) progressive surface subsidence as a result of (iib) lithosphere cooling.

The DUT model has been successfully applied to describe the subsidence and thermal evolutions of rift basins that developed over a crust/lithosphere that underwent little thinning, for instance in the proximal domain of rifted margins where the ratio of initial to final crustal thickness  is less than 1.3 [START_REF] White | Magmatism at rift zones: The generation of volcanic continental margins and flood basalts[END_REF][START_REF] Hendrie | Jurassic extension estimates for the North Sea J o u r n a l P r e -p r o o f Journal Pre-proof ?triple junction' from flexural backstripping: implications for decompression melting models[END_REF]. However, [START_REF] Royden | Rifting process and thermal evolution of the continental margin of eastern canada determined from subsidence curves[END_REF] showed that the DUT model cannot explain the subsidence history recorded at dist al parts of rifted margins and argued for differential crust and mantle thinning (i.e. depth-dependent thinning, DDT). Recent data from distal parts of rifted margins provide growing evidence for a complex tectono-thermal evolution during the necking phase of rifting (i.e. when the crust is thinned from 30-35 to ca. 10 km; [START_REF] Sutra | Quantification and restoration of extensional deformation along the Western Iberia and Newfoundland rifted margins[END_REF]. For example, the Tithonian shallow-water carbonates and clays drilled at ODP Sites 901, 1065 and 1069 offshore Iberia suggest that the distal domain of the Iberian margin remained at shallow water depths during advanced stages of rifting [START_REF] Mohn | Structural and stratigraphic evolution of the Iberia and Newfoundland hyper-extended rifted margins : A quantitative modeling approach[END_REF]. This subsidence evolution is schematically represented as the red curve in Figure 1b.

In some rift systems, distal domains show an initial phase of rift-related subsidence, which is followed by a phase of erosion and/or emersion, and subsequently a phase of renewed subsidence. For instance, the Briançonnais domain in the fossil distal European margin of the Alpine Tethys (e.g. Claudel & Dumont, 1999, Figure 1d), the Campos Basin offshore Brazil [START_REF] Lewis | New insights into late synrift subsidence from detailed well ties and seismic mapping, Campos Basin, Brazil[END_REF], the South China Sea (e.g. [START_REF] Lin | Cenozoic stratigraphy and subsidence history of the south china seamargin in the taiwan region[END_REF] and the East India margin [START_REF] Haupert | Upper-plate magma-poor rifted margins: stratigraphic architecture and structural evolution[END_REF] show such a subsidence-uplift/emersion-subsidence evolution. The width of the J o u r n a l P r e -p r o o f Journal Pre-proof karstified/emerged domain in the Briançonnais can be roughly estimated to a few tens of kilometers based on present-day mapping of the corresponding formation. However, the width of the karst varies largely along strike and its estimate depends on the assumptions made on the direction of Alpine compression. The extent of the erosional unconformity is better constrained in the outer hinge of the Campos Basin, where it was mapped over a width of 10-30 km over 120 km along strike [START_REF] Lewis | New insights into late synrift subsidence from detailed well ties and seismic mapping, Campos Basin, Brazil[END_REF]. The subsidence-uplift/emersion-subsidence evolution recorded by these margins is schematically represented by the blue curve in Figure 1b.

The thermal evolution of continental crust during rifting is difficult to assess due to the lack of access to deep crustal levels, especially at present-day rifted margins. Currently, the only clues are thermochronological data from fossil rifted margins exposed in the Alps and Pyrenees. In both cases data indicate a transient but intense syn-rift heating event at the base of the continental crust (prograde metamorphism), which predates the phase of subcontinental mantle exhumation [START_REF] Smye | Rutile U-Pb age depth profiling: A continuous record of lithospheric thermal evolution[END_REF][START_REF] Seymour | Tracing the thermal evolution of the Corsican lower crust during Tethyan rifting[END_REF][START_REF] Hart | Thermal evolution of a hyperextended rift basin, Mauléon Basin, western Pyrenees[END_REF]. In the Alps, this thermal event was dated to 200-179 Ma [START_REF] Beltrando | A crustal-scale view at rift localization along the fossil Adriatic margin of the Alpine Tethys preserved in NW Italy[END_REF], and thus was largely contemporaneous with the necking phase dated between 189 and 179 Ma by [START_REF] Mohn | Cooling History and Exhumation of Lower-Crustal Granulite and Upper Mantle (Malenco, Eastern Central Alps)[END_REF] and between 191 and 185 Ma by [START_REF] Ribes | The syn-rift stratigraphic record across a fossil hyper-extended rifted margin: the example of the northwestern Adriatic margin exposed in the Central Alps[END_REF]. The thermal evolution recorded at the base of the crust in the distal domain of the Alpine and Pyrenean rift systems is schematically represented by the blue curve in Figure 1c. Several processes may account for both delayed subsidence, and even emersion, and a heat pulse at the base of the crust during rifting. These include:

• simple shear-dominated extension (e.g. [START_REF] Wernicke | Uniform-sense normal simple shear of the continental lithosphere[END_REF][START_REF] Lemoine | Ultramafic and gabbroic ocean floor of the Ligurian Tethys (Alps, Corsica, Apennines): In search of a genetic imodel[END_REF], where one lithospheric-scale shear zone causes a lateral offset in crustal and mantle thinning. This process can account for both uplift and transient crustal heating at one distal margin of a rift J o u r n a l P r e -p r o o f system;

• depth-dependent thinning (e.g. [START_REF] Royden | Rifting process and thermal evolution of the continental margin of eastern canada determined from subsidence curves[END_REF][START_REF] Roberts | Subsidence of the Vøring Basin and the influence of the Atlantic continental margin[END_REF][START_REF] Driscoll | Lower crustal extension accross the Northern Carnarvon basin, Australia: Evidence for an eastward dipping detachment[END_REF][START_REF] Kusznir | Continental lithospheric thinning and breakup in response to upwelling divergent mantle flow: application to the Woodlark, Newfoundland and Iberia margins[END_REF][START_REF] Huismans | Depth-dependent extension, two-stage breakup and cratonic underplating at rifted margins[END_REF], where higher lithospheric than crustal thinning results in transient uplift and local heating of t he lower crust during rift-related extension;

• magmatic underplating (e.g. [START_REF] White | Magmatism at rift zones: The generation of volcanic continental margins and flood basalts[END_REF], where addition of hot and low-density material beneath the crust may result in local uplift and heating;

The following processes may explain distal margin uplift but do not account for a transient and/or local heating event:

• flexural processes [START_REF] Braun | A physical explanation of the relation between flank uplifts and the breakup unconformity at rifted continental margins[END_REF][START_REF] Kooi | Lithospheric necking and regional isostasy at extensional basins 1. Subsidence and gravity modeling with an application to the Gulf of Lions Margin (SE France)[END_REF][START_REF] Weissel | Flexural uplift of rift flanks due to mechanical unloading of the lithosphere during extension[END_REF][START_REF] Chenin | Emersion of distal domains in advanced stages of continental rifting explained by asynchronous crust and mantle necking[END_REF], where isostatic movements caused by the thinning of a lithosphere with a significant flexural rigidity result in uplift (or subsidence) of parts of the margin. For instance, flexural rift shoulder uplift is important in numerical models with strain softening (e.g. Svartman [START_REF] Dias | Conjugate rifted margins width and asymmetry: The interplay between lithospheric strength and thermomechanical processes[END_REF][START_REF] Huismans | Depth-dependent extension, two-stage breakup and cratonic underplating at rifted margins[END_REF];

• surface processes, whereby mass redistribution related to erosion and sedimentation causes loading and subsidence or unloading and uplift of specific parts of rift systems (e.g. [START_REF] Burov | Erosion and rheology controls on synrift and postrift evolution: Verifying old and new ideas using a fully coupled numerical model[END_REF], 2003);

• dynamic topography (e.g. [START_REF] White | Magmatism at rift zones: The generation of volcanic continental margins and flood basalts[END_REF][START_REF] Xie | Origin of anomalous subsidence along the Northern South China Sea margin and its relationship to dynamic topography[END_REF], where regions of high-(mantle plumes) or low (subduction-related) temperatures within the asthenospheric mantle cause large-scale and long-lasting uplift or subsidence, respectively;

• removal of the continental mantle lithosphere (i.e. 'delamination') prior to continental breakup (e.g. [START_REF] Esedo | Uplift prior to continental breakup: Indication for removal of mantle lithosphere?[END_REF], where replacement of lithospheric mantle by lower density asthenospheric mantle results in transient, large-scale uplift and heating of the lower crust.

• mineral phase changes (e.g. [START_REF] Kaus | Effect of mineral phase transitions on sedimentary basin subsidence and uplift[END_REF][START_REF] Simon | The effect of mantle composition on density in the extending lithosphere[END_REF], where the density decrease associated with the transition from garnet-to plagioclase-peridotite at relatively low pressure and high temperature leads to uplift of the most distal part of the rift basin during advanced stages of crustal thinning;

• serpentinization (e.g. [START_REF] Reston | Detachment J o u r n a l P r e -p r o o f Journal Pre-proof faulting, mantle serpentinization and serpentinite-mud volcanism beneath the Porcupine Basin, southwest of Ireland[END_REF], where the increased volume and lower density of serpentinized peridotite with respect to fresh peridotite causes uplift in the most distal part of the rift basin;

J o u r n a l P r e -p r o o f However, many of these processes fail accounting for one or several characteristics of the rift systems mentioned above:

• Simple shear-dominated extension may explain asymmetric topographic and thermal evolutions of rift systems since the upper plate is heated and uplifted with respect to the lower plate. However, applied to the necking stage, this model implies highly-localized, simple shear deformation across the lithosphere, which is incompatible with the distributed extension generally observed during the early stages of rifting (e.g. [START_REF] Withjack | Development of the passive margin of eastern North America: Mesozoic rifting, igneous activity, and breakup[END_REF][START_REF] Ball | The spatial and temporal evolution of strain during the separation of Australia and Antarctica[END_REF][START_REF] Beltrando | A crustal-scale view at rift localization along the fossil Adriatic margin of the Alpine Tethys preserved in NW Italy[END_REF];

• Magmatic underplating is accompanied by extensive syn-rift magmatic activity, which are not observed during 'magma-poor' rifting.

• Dynamic topography and delamination of the continental lithosphere induce typically a large-scale uplift (several hundred kilometers in diameters; e.g. [START_REF] Campbell | Large Igneous Provinces and the Mantle Plume Hypothesis[END_REF]; [START_REF] Esedo | Uplift prior to continental breakup: Indication for removal of mantle lithosphere?[END_REF]), which could theoretically result in local erosion depending on the morphology of the margin. However, this process cannot account for the few tens of kilometers wide erosion of the future distal domain observed in the East India, South China Sea and Brazilian margins and in the former European margin of the Alpine Tethys because the adjacent proximal domains, which were made of thick continental crust and thus rested at shallow water depths, escaped erosion during the uplift of the future distal margin [START_REF] Haupert | Upper-plate magma-poor rifted margins: stratigraphic architecture and structural evolution[END_REF][START_REF] Lin | Cenozoic stratigraphy and subsidence history of the south china seamargin in the taiwan region[END_REF][START_REF] Lewis | New insights into late synrift subsidence from detailed well ties and seismic mapping, Campos Basin, Brazil[END_REF][START_REF] Bourbon | Evolution d'un secteur de la marge nord-téthysienne en milieu pélagique: la zone briançonnaise près de Briançon entre le début du Malm et l'Eocène inférieur[END_REF].

• Several numerical models show that flexural processes may produce uplift above sea level around the so-called 'rift shoulders' on either side of the rift basin. However, these uplifts are usually limited to the proximal part of rift systems (e.g. [START_REF] Huismans | Depth-dependent extension, two-stage breakup and cratonic underplating at rifted margins[END_REF][START_REF] Dias | Conjugate rifted margins width and asymmetry: The interplay between lithospheric strength and thermomechanical processes[END_REF], independent on whether or not erosion and/or sedimentation are modeled [START_REF] Burov | Erosion and rheology controls on synrift and postrift evolution: Verifying old and new ideas using a fully coupled numerical model[END_REF], 2003).

• According to [START_REF] Kaus | Effect of mineral phase transitions on sedimentary basin subsidence and uplift[END_REF]; [START_REF] Simon | The effect of mantle composition on density in the extending lithosphere[END_REF]; [START_REF] Reston | Detachment J o u r n a l P r e -p r o o f Journal Pre-proof faulting, mantle serpentinization and serpentinite-mud volcanism beneath the Porcupine Basin, southwest of Ireland[END_REF], the garnet-to plagioclase-peridotite transition as well as the serpentinization processes can account for up to hundreds of meters uplift of distal parts of a rift system. However, these processes are restricted to advanced stages of crustal thinning (i.e. when the crust is less than 10 km thick), and thus cannot account for uplift during the earlier necking phase of rifting.

From the above arguments, it appears that DDT is a process that could account for a J o u r n a l P r e -p r o o f transient uplift limited to the future distal domain during the necking phase of a magma-poor rift system. The characteristics of DDT are essentially controlled by the rheology of the lithosphere [START_REF] Huismans | Rifted continental margins: The case for depth-dependent extension[END_REF][START_REF] Chenin | Necking of the lithosphere : a reappraisal of basic concepts with thermo-mechanical numerical modeling[END_REF], which depends on the lithology and distribution of the different lithospheric materials, as well as on the initial geothermal gradient.

Since the 1980's, many studies have highlighted the impact of the lithosphere rheology on the timing of rifting, as well as on the thermal evolution and final morphology of rift systems (e.g. [START_REF] Co | Modes of continental lithospheric extension[END_REF][START_REF] Bassi | Factors controlling the style of continental rifting: insights from numerical modelling[END_REF][START_REF] Bassi | Relative importance of strain rate and rheology for the mode of continental J o u r n a l P r e -p r o o f Journal Pre-proof extension[END_REF][START_REF] Cloetingh | Role of pre-rift rheology in kinematics of extensional basin formation: constraints from thermomechanical models of mediterranean and intracratonic basins[END_REF][START_REF] Gartrell | Crustal rheology and its effect on rift basin styles[END_REF]. However, a systematic and quantitative analysis of the impact of the initial rheology on the topographic and thermal evolutions of rift systems is lacking to date. In particular, such quantification requires high-resolution numerical models with accurate free surface tracking and up-to-date rheological models, which were only developed over the last decade (e.g. [START_REF] Popov | SLIM3D: A tool for three-dimensional thermomechanical modeling of lithospheric deformation with elasto-visco-plastic rheology[END_REF][START_REF] Thieulot | FANTOM: Two-and three-dimensional numerical modelling of creeping flows for the solution of geological problems[END_REF]Duretz et al., 2016a;[START_REF] Vogt | The role of lateral strength contrasts in orogenesis: A 2D numerical study[END_REF]. Besides, most studies focused on the topographic and thermal evolutions of the rift center, and much less attention was paid to the evolution of surface topography and temperature across the entire width of rift domains (exceptions are [START_REF] Van Wijk | Basin migration caused by slow lithospheric extension[END_REF], their Figure 9; and [START_REF] Watremez | Buoyancy and localizing properties of continental mantle lithosphere: Insights from thermomechanical models of the eastern Gulf of Aden[END_REF], their Figures 4 and5).

Our study aims to provide insight into the variability of the topographic and thermal evolutions of extensional systems in order to explain the particular erosional features and the heat pulse recorded during the necking phase of several rift systems worldwide. We perform a systematic numerical study with high-resolution simulations (i.e. 500 x 250 m resolution in models that include the entire lithosphere thickness and the upper 75 km of the asthenosphere). We consider a simple lithosphere rheological architecture with homogeneous visco-elasto-plastic crust and mantle. To model the mantle lithosphere we use state-of-the-art rheological models, which consist of a combination of diffusion, dislocation and Peierls creep together with pressure-dependent plasticity and elasticity. We focus on the mechanical coupling/decoupling of the lithosphere and associated DDT by testing various crustal and mantle flow laws. Our aims are (1) to quantify the spatio-temporal evolution of topography, uplift/subsidence rates, accommodation/emerged space creation, temperature and surface heat flow; (2) to understand the relation of these evolutions to deeper lithosphere processes such as necking and flexure of the mantle lithosphere; and (3) to evaluate the impact of additional processes such as prominent normal faulting, modeled by strain softening, and mantle fertilization.

J o u r n a l P r e -p r o o f 2.

Model Configuration

We use the two-dimensional finite difference/marker-in-cell thermo-mechanical code MDoodz to model lithospheric extension, which was applied also in [START_REF] Duretz | The importance of structural softening for the evolution and architecture of passive margins[END_REF], [START_REF] Petri | Thinning mechanisms of heterogeneous continental lithosphere[END_REF] and [START_REF] Duretz | Numerical modelling of cretaceous pyrenean rifting: The interaction between mantle exhumation and syn-rift salt tectonics[END_REF]. The model considers visco-elasto-plastic incompressible deformation, strain-rate-, stress-and temperature-dependent rheologies and thermo-mechanical coupling by shear heating. We apply a diffusion-type erosion-sedimentation model with a

diffusion coefficient K = 5.0  10 6  m 2  s 1
 . Unless stated otherwise we do not apply strain softening or mineral phase changes.

The model domain (Figure 2) is 300 km-wide and 200 km-deep with a resolution of 500 m horizontally and 250 m vertically. The top boundary is a free surface (Duretz et al., 2016a), while free slip is applied to the left, right and bottom boundaries. Horizontal velocities ( v ) at both vertical model sides are in the order of 1 cm  yr 1  . These velocities are adjusted by the current model width ( W ) to generate a constant bulk extension rate (  ) of 1  10 15

 s 1  ( = 2 / vW  ).
The model surface topography is a material interface defined by a high-resolution Lagrangian marker chain, which is displaced with the numerically calculated velocity field.

The modeled lithosphere comprises an initially 30 km-thick continental crust overlying a 95 km-thick upper mantle and a 75 km-thick adiabatic mantle (see next paragraph). To trigger localization of the deformation, we perturb the initial depth of the crust-mantle boundary with a sinusoidal function having a 2.5 km amplitude and a 300 km wavelength, so that the geometrical perturbation is smoothly distributed over the entire model width. We counterbalance the Moho perturbation by a sinusoidal surface topography of ca. 0.5 km amplitude and 300 km wavelength, so that our models are initially in isostatic equilibrium. [START_REF] Chenin | Necking of the lithosphere : a reappraisal of basic concepts with thermo-mechanical numerical modeling[END_REF] showed that the wavelength of the sinusoidal Moho perturbation has little impact on both the duration of the necking phase and the width/morphology of the necking zones (see first paragraph of their section 4.2). Similarly, using a weak seed instead of a sinusoidal perturbation of the Moho depth has limited effects on the rift evolution (compare figures B4e and B4f in [START_REF] Chenin | Emersion of distal domains in advanced stages of continental rifting explained by asynchronous crust and mantle necking[END_REF]), which is consistent with the conclusions of [START_REF] Huismans | Roles of lithospheric strain softening and heterogeneity in determining the geometry of rifts and continental margins[END_REF].

The temperature is 0 C at the top of the model, 1330 C within the asthenosphere and zero heat flux is imposed to the model vertical sides. The crust has a constant radiogenic heat production of 1  W  m 3  . To mimic adiabatic mantle temperatures, we compute the initia l J o u r n a l P r e -p r o o f

Journal Pre-proof temperature field using an unrealistically large asthenosphere conductivity of 3000 W  m 1   K 1  .

During the simulation, the conductivity is set back to 3 W  m 1   K 1  . This set up results in slow diffusive cooling of the lithosphere-asthenosphere boundary, which has however no significant impact given the short duration of the simulation (  8 My). The initial Moho temperature in the model center is 550 C, consistent with the 550-600 C temperatures at the base of the crust at the onset of the Alpine Tethys rifting reckoned by [START_REF] Mohn | Cooling History and Exhumation of Lower-Crustal Granulite and Upper Mantle (Malenco, Eastern Central Alps)[END_REF].

We investigate the impact of lithosphere rheology by first testing various flow laws for both the crust and the mantle. We distinguish between two Model Series, namely Series D and W. 1). In Model D5+Fertilization, we model the density decrease associated with mantle fertilization by melt impregnation [START_REF] Müntener | Plagioclase peridotites in ocean-continent transitions: Refertilized mantle domains generated by melt stagnation in the shallow mantle lithosphere[END_REF][START_REF] Mccarthy | Ancient depletion and mantle heterogeneity: Revisiting the Permian-Jurassic paradox of Alpine peridotites[END_REF]. To mimic the transition from an inherited harzburgite to a fertile plagioclase peridotite, we decrease the density of the mantle from 3330 to 3200 kg  m 3  (i.e. densities of 'inherited' and 'fertile' mantle according to [START_REF] Chenin | Influence of the architecture of magma-poor hyperextended rifted margins on orogens produced by the closure of narrow versus wide oceans[END_REF])

when the temperature is above 1050 C and the pressure below 1 GPa (equilibration pressure and temperature of the plagioclase peridotite from [START_REF] Müntener | Plagioclase peridotites in ocean-continent transitions: Refertilized mantle domains generated by melt stagnation in the shallow mantle lithosphere[END_REF]). Finally, in Models D5+Softening and D5+Softening CC, we test the impact of intense strain softening by decreasing linearly the internal angle of friction from 30 to 5 and the cohesion from 10 to 1 MPa when accumulated plastic strain increases from 5 % to 20 %, after which both the internal angle of friction and the cohesion remain constant. Strain softening is considered in both the crust and the mantle in Model D5+Softening and limited to the crust in Model D5+Softening CC.

J o u r n a l P r e -p r o o f Journal Pre-proof

We limit our numerical modeling investigations to the stages where crustal thickness remains larger than 10 km because we aim to quantify the evolutions of topography and temperature systematically and in detail during the necking phase of rifting only. [START_REF] Ranalli | 4zMaQ{&}si g=9dvPoO8PX0fBSaHgL0hU68CWyyQ#v=onepage&q=Ranalli[END_REF];

Anorthite 60 from [START_REF] Rybacki | Deformation mechanism maps for feldspar rocks[END_REF]; dry and wet quartz from [START_REF] Ranalli | 4zMaQ{&}si g=9dvPoO8PX0fBSaHgL0hU68CWyyQ#v=onepage&q=Ranalli[END_REF][START_REF] Ranalli | Rheology of the lithosphere in space and time[END_REF]; olivine (dry and wet) dislocation and diffusion creep from [START_REF] Hirth | Rheology of the upper mantle and the mantle wedge: A view from the experimentalists[END_REF]; olivine (dry and wet)

Peierls creep from [START_REF] Evans | The temperature variation of hardness of olivine and its implication for polycrystalline yield stress[END_REF] using the approach from [START_REF] Kameyama | Thermal-mechanical effects of low-temperature plasticity (the peierls mechanism) on the deformation of a viscoelastic shear zone[END_REF]. J o u r n a l P r e -p r o o f 3. and3b); (2) the stronger the crust, the shorter the duration of the necking phase (Figure 3c); ( 3) for comparable crustal rheologies the duration of the necking phase is consistently shorter by 0.6 to 0.9 My in the models of Series W than in those of Series D (Figure 3c); and (4) the stronger the crust, the deeper the 500 and 1300 C isotherms at the end of the simulation, and thus the lower the geothermal gradient (Figures 3d and3e).

Crust

(J  kg 1   K 1  ) 1050 1050 1050 thermal conductivity k (W  m 1   K 1  ) 2.5 3.0 2.0 heat production H (  W  m 3  ) 1.0 0.0 0.5 thermal expansion  ( C 1  ) 3.2  10 5  3.2  10 5  1.0  10 5  compressibility  (Pa 1  ) 1.

Results

Impact of Crustal and Mantle Rheology

In contrast, no systematic trend can be identified between crustal rheology and the maximum surface heat flow at the end of the simulation (Figure 3f). In Model Series W, the maximum heat flow is consistently relatively low (between 170 and 220 mW  m 2  ), regardless of crustal rheology. In Model Series D, the maximum heat flow varies between 190 and 260

2 m W m  
regardless of crustal strength.

The rheology of the mantle impacts the characteristics of rift systems to a variable extent:

when the crust is strong (Maryland diabase or Mafic granulite rheology), the relief of the rift system at the end of the necking phase is larger by ca. 3 km in Series D than in the equivalent models of Series W; however, for weaker crustal rheologies, the relief is relatively similar amongst the equivalent models of the two series (Figures 3a and3b). The rheology of the mantle does not control the depth of the 1300 C isotherm in the rift center at the end of the necking phase, since it is comprised between 30 and 90 km in both Series (Figure 3e). However, the rheology of the mantle impacts the depth of the 500 C isotherm in such a way its depth range is narrower in the models of Series W (8-16 km) than in those of Series D (6-18 km depth; Figure 3d). As the rift basin is deep, the underlying Moho is also deep at the end of the simulation (up to ca.

19.5 km in Model D1; Figure 4a). Crustal thinning to 10 km is completed in less than 4.5 My in the four models (Figure 3c). There is no significant difference in the evolution of models with a strong versus a weak mantle except that the rift basin, and thus the Moho, are slightly shallower in the models with a weaker mantle (basin depth is 7.5 km and 9.5 km in Model W1 and D1, respectively; compare Figures 3a and3b).

Uplift and subsidence rates analysis

The evolution of surface topography can be regarded in terms of vertical-only uplift and subsidence or in terms of creation of accommodation space for water or sediments. Here we use the term uplift/subsidence to refer to the upward/downward vertical movement of the model surface. We use the term accommodation space to refer to created space below sea level, here an area in the 2D model, which is available for potential sediment accumulation. In Figure 5, we analyse the topography evolution (top left panels) of the four evolution-types described in the previous section: for Models D1, D5, W5 and W6, we compare the evolution of accommodation space (bottom right panels) with the horizontal and vertical velocities of the surface (top right and bottom left panels, respectively). Indeed, the creation of accommodation space does not only reflect the vertical velocity of the surface, but also the horizontal velocity of the surface. To illustrate the difference between creation of accommodation space and vertical movement, let us imagine a narrow and deep valley: if this valley is extended with only horizontal velocities perpendicular to the valley axis, then the valley widens and generates accommodation space, without the need of any downward-directed velocity. This distinction between creation of accommodation space and vertical surface motion is important in the following, when we analyse uplift and subsidence rates and relate these rates to the basin formation.

J o u r n a l P r e -p r o o f

Analysis of Model W6 with Multiple Rift Sub-basins. The horizontal velocity evolution of

Model W6 is similar to that of Model D5 (Figure 5d). It starts with a brief phase of distributed extension followed by a 5 My long phase of deformation localized within a 80 km-wide region in the model center (top right panel in Figure 5d). From 5 My onward, deformation localizes rapidly into a 5 km-wide domain of active deformation framed by two rigid blocks that are displaced away from the rift center. Like in Models D5 and W5, subsidence is maximal in the rift center at this stage (bottom left panel in Figure 5d), where it reaches 1.5-2 mm y 1  .

The vertical velocity evolution is largely consistent with both the topographic and accommodation space evolutions during the first 6 My of the simulation (compare bottom and top left panels in Figure 5d). Then, like in Models D1, D5 and W5, the region recording increase in accommodation space becomes wider than the region characterized by downward-directed velocities. Here again, this divergence is a consequence of the widening of the existing central r ift basin.

Accommodation Space and Emerged Area Evolution

Plotting the total accommodation space and emerged area created with time (Figures 6 andA.16) highlights that as much accommodation space as emerged area is created during the necking phase of every models. Three main trends stand out as a function of the crust rheology: W5 and W6) show also an initial (between 1.5 and 3 My) slight decrease in both accommodation space and emerged area. Then, both increase slightly to maximum 40 km 2 . In the two models with the weakest crust (wet quartz crust Models D6 and W6), both accommodation space and emerged area remain less than their initial value. The reason is that the initial model topography (see Figure 2 and section 2) flattens during extension.

Figure 6: Evolution of the total accommodation space (blue curve) and total emerged area (red curve) with time along different models. Accommodation space and emerged area are corrected from the initial topography of the model, so that the graphs display how much additional accommodation space and emerged area are created with time.

Strain Rate and Stress Analysis

To understand which mechanical processes control the different evolutions reported in sections 3.1.2 and 3.1.3, we plot the second invariant of the strain rate tensor and the horizontal deviatoric stress for one model of each category (Models D1, D5, W5 and W6; Figure 7). In Models D1, D2, W1 and W2 the crust and mantle are largely mechanically coupled due to the very thin or inexistent weak ductile lower crust (Figure 2). The panels a-c of Figure 7 show that in Model D1 (like in Models D2 and W1-W3), the crust and upper mantle neck immediately and effectively as a single layer in the model center. The longer duration of the necking phase and the wider width of the rift basin of Model W3 compared to Models D1, D2, W1 and W2 can be explained by the significantly lower stress exponent of its crustal material [START_REF] Bassi | Relative importance of strain rate and rheology for the mode of continental J o u r n a l P r e -p r o o f Journal Pre-proof extension[END_REF]; stress exponent = n 3.1 for the felsic granulite compared to = n 4.7 and 4.2 for the dry Maryland diabase and mafic granulite, respectively; see Table 1).

In Models D3-D6 and W4-W5 where the crust is moderately strong to weak, and thus decoupled from the upper mantle by a weak lower crust, a so-called 'crustal keystone' forms during the early stages of extension (Figures 7d and7g). A keystone is a triangular-shaped piece of crust that remains relatively undeformed between two crustal scale faults/shear zones labelled 'K'

J o u r n a l P r e -p r o o f

Journal Pre-proof in Figure 7 [START_REF] Crosby | Keystone faults[END_REF]; see also the 'H-Block' from [START_REF] Lavier | A mechanism to thin the continental lithosphere at magma-poor margins[END_REF]).

This keystone is subsequently split in two as deformation focuses to the model center, leaving one piece of 15-25 km thick continental crust (so-called 'continental lump' by [START_REF] Chenin | Necking of the lithosphere : a reappraisal of basic concepts with thermo-mechanical numerical modeling[END_REF] The topographic evolution of the Moho depends significantly of the mantle rheology: in models where the mantle is strong (Models D3-D6), the Moho remains deep (ca. 30 km) in the model center during the early stages of extension (see insets in Figures 7d and7e). Consequently, the surface of the keystone records significant subsidence (300-800 m depth) after only 1-2 My of extension. In contrast, in Models W4-W5 where the mantle is weaker, the Moho starts rising in the model center as soon as extension begins (see insets in Figures 7g and7h). Because the crust has not been significantly thinned at this stage yet, the surface of the keystone remains at shallow depth (200-300 m below zero).

Model W6 differs from the other models in that crustal deformation remains largely distributed within the upper crust until 5.5-6 My (Figures 7j and7k). In Model W6, the combination between a small necking amplitude in the weak upper mantle and a thick decoupling lower crust prevents the formation of a keystone in the overlying upper crust (Figure 2). Instead, the lower crust is essentially thinned by pure shear and the four very shallow (less than 200 m deep) basins that are regularly spaced suggest the boudinage of the upper crust. Extension localizes eventually in the second basin to the right, where crustal necking is eventually achieved (Figure 7l).

The evolution of the horizontal deviatoric stress in Models D1 and D5 nicely illustrates the difference between effectively single-layer necking and two-layer necking of the lithosphere.

During extension in Model D1, the stress is first positive (i.e. indicating extension) everywhere in the lithosphere (Figure 7a). With progressive extension the flexural rift shoulder uplift generates stresses that are negative (indicating compression) in the top region of the crust (Figures 7b and7c). During extension in Model D5, stresses are also first positive everywhere in the lithosphere (Figure 7d). However, with progressive extension a significant neck only forms in the upper mantle, while the upper crust deforms in a distributed manner (Figures 7e and7f). Consequently, the flexural uplift only occurs in the upper mantle and associated compressive stresses are J o u r n a l P r e -p r o o f generated only in the upper region of the mantle lithosphere.

Figure 7: top panels: log 10 (second invariant of the strain rate tensor); bottom panels: horizontal deviatoric stress; the white line in each panel represents the Moho. The 'K' label marks the keystone block.

Thermal Evolution

Figures 8 andA.17 display the temperature at the end of the simulation and the relative cooling and heating compared to the initial stage. Figures 9 andA.18 show the surface heat flow with time along the model together with crustal thickness isopachs. These figures highlight that the weaker the crust, (1) the more important the asthenosphere upwelling; (2) the more offset between the initial lithosphere-asthenosphere boundary and the 1300 C isotherm; (3) the larger the differential heating and cooling within the rift zone at the end of the simulation; and (4) the more complex the surface heat flow evolution. (strong crust), the amplitude of asthenosphere upwelling at the end of crustal necking is minor (less than 40 km in Model D1) compared to models with a weaker crust (more than 90 km in Model D6; see Figures 8 andA.17, bottom panels). In all models of Series W, the lithospheric mantle tends to delaminate and drip into the asthenosphere (Figures 8d, 8f and A.17g-l, bottom panels).

In all models, the temperature outside the central rift zone at the end of the simulation remains largely unchanged compared to the initial conditions (Figures 8 andA.17, top panels).

J o u r n a l P r e -p r o o f

Journal Pre-proof Within the rift zone, the bottom part of the crust is consistently heated in the very center of the model, while cooling occurs on either side. Cooling areas are located at the fault corridors controlling the rift shoulders in models with strongest crust (Models D1, D2, W1, W2; see Figure 7). They are located beneath the basins that frame the crustal keystone block in models with a weaker crust (Models D3-D6 and W4-W5). Models D4, D6 and W6 (and to a minor extent Models D3 and W3) show additionally significant cooling of the uppermost crust in the model center (i.e. not necessarily the rift center).

At the end of the simulation, the mantle beneath the rift center, which is usually former asthenospheric mantle, is consistently cooled compared to its initial temperature. Cooling ranges from 5-25 C in models with strongest crust (D1, D2, W1 and W2) to > 100 C in models with a moderately strong to weak crust (Models D3-D6 and W4-W6). Conversely, the mantle on either side of the asthenosphere upwelling is heated by 25-70 C. Differential heating and cooling are generally higher in the models of Series D than in the equivalent models of Series W (Figures 8 andA.17, top panels).

In Models D3 to D6 (strong mantle, moderately strong to weak crust), one piece of mantle in the rift center keeps an elevated temperature with respect to its initial state (see arrows in insets in Figure A.17c-f). Yet, the smooth shape of the isotherm indicates the lack of a significant thermal anomaly. In Models W3-W6, two pieces of mantle keep an elevated temperature with respect to their initial state, one on either side of the rift center (see arrows in insets in Figure A.17i-l). These pieces corresponds to part(s) of the former 'upper mantle keystone', namely a block of subcontinental lithospheric mantle that remained largely undeformed between the two major shear zones that are associated with upper mantle necking. This mantle keystone was heated during the early stages of the simulation as a result of upper mantle necking, which juxtaposed parts of the uppermost mantle against deeper and hotter mantle. At the end of the simulation, the remnant of the initial mantle keystone is framed on its proximal side by the same shallow subcontinental mantle as initially, and on its distal side by deeper mantle that was upwelled during extension. The crustal thickness isopachs of Figures 9 andA.18 highlight that surface heat flow is generally higher in regions of thinned crust. However, surface heat flow cannot be used to determine crustal thickness because: (1) to a given crustal thickness corresponds various heat flows depending on the crust and mantle rheology (Figures 9 andA .18); and (2) deviations between the location of highest heat flow and thinnest crust exist in most models and are more pronounced when the rheology of the lithosphere is weaker (see in particular Models D5 and W5

Surface Heat Flow.

in Figure 9 and Model W6 in

Impact of Mantle Deformation Mechanism, Mantle Fertilization and Strain Softening

Figures 10,A .19, A.20 and A.21 display the results of Model Series D5+ where we tested the effect of the mantle creep mechanisms, mantle fertilization and strain softening. Figure 10a shows that topography at the end of the simulation is largely similar amongst the different models

J o u r n a l P r e -p r o o f

The minimum depth of the 500 C isotherm at the end of the simulation is also largely similar amongst the different models of Series D5+, varying by less than 1 km with respect to Model D5 (Figure 10c). The minimum depth of the 1300 C isotherm at the end of the simulation is more variable, ranging from 38 to 25 km compared to 32 km in Model D5 (Figure 10d). The 1300 C isotherm is deepest at the end of the two simulations where diffusion creep is not modeled (36-37 km) and shallowest in the two simulations where strain softening is modeled Figure 2). One consequence is the slight reduction of the duration of extension required to achieve mantle necking. Consequently, crustal necking is also achieved earlier (6.9 versus 7.3 My; Figure 10b).

J o u r n a l P r e -p r o o f

Diffusion creep provides lower effective viscosities at depth compared to dislocation creep (see Table 1 and [START_REF] Rybacki | Dislocation and diffusion creep of synthetic anorthite aggregates[END_REF]). When diffusion creep is not considered, the duration of the necking phase is longer (7.4 versus 7.3 My; Figure 10b) and the 1300 C isotherm is deeper at the end of the simulation (38 versus 32 km; Figure 10d). Consequently, the surface heat flow at the end of the simulation is lower compared to Model D5 (

J o u r n a l P r e -p r o o f

Journal Pre-proof

Impact of Mantle Fertilization

Model D5+Fertilization has an identical evolution as Model D5 until 5.4 My, which is the onset of mantle fertilization (compare panels a and c in Figure 11). From then onward, the decreased density of the fertilized mantle facilitates uplift and emersion above sea level in the region of the right-hand side continental lump. The emerged area is wider (up to 15 km) than in any other model.

Although we did not model the thermal effects of mantle fertilization (for instance the gain or loss of heat related to crystallization and melting or the heat transport due to melt migration), surface heat flow is higher by 15-20 mW  m 2  at the end of Model D5+Fertilization compared to Model D5 (Figure 12c). This increase in surface heat flow results from the facilitated upwelling of the fertilized mantle due to its decreased density (see shallower 500 C isotherm at the end of the simulation in Figure 10c).

Impact of Strain Softening

Although the general spatio-temporal evolution remains similar amongst the simulations with and without strain softening, the topographic evolution of Models D5+Softening and D5+Softening CC is more symmetrical than that observed in Model D5 (F igures 11a, 11d and 11e). Surface topography is rougher and relief is more pronounced in models where strain softening is modeled due to the generation of prominent normal 'faults'/shear zones (Figure 13).

These 'fault-like structures' are located where diffuse deformation zones occur in simulations without strain softening. The most external 'fault' on either side of the model (NF in Figures 13b and13c and BF in Figures 13e-f and13h-i) sits at the foot of the 'rift shoulder' (RS label in Figures 13a-b, 13e-f and 13h-i) and marks a sharp jump in the topographic height. These faults facilitate uplift. Indeed, rift shoulders reach more than 1.3 km high in models with strain softening, while they do not even reach 1 km in Model D5 (Figure 10a).

Like in Model D5, a crustal keystone forms in the model center of Models D5+Softening and D5+Softening CC (Figure 13). The keystone is thinned symmetrically in models with strain softening, conversely to Model D5. Consequently the model center remains more than 25 km-thick until 5 My in Models D5+Softening and D5+Softening CC, while it is already significantly thinned to less than 25 km at 4 My in Model D5. The thick keystone is transitorily emerged at ca.

J o u r n a l P r e -p r o o f 5.5 My in the center of Model D5+Softening, while uplift close to the 0 km isobath occurs later (at ca. 6.5 My) on the right-hand side of the model (i.e. at the largest continental lump) in Model D5

(compare Figures 11a and11d). The central part of the rift system is also uplifted in Model

D5+Softening CC but it remains below 300 m depth.

In our study, strain softening is the process that has the most impact on the temperature and surface heat flow (compare Figures 12a, 12d and12e). Although the general thermal architecture is comparable between Models D5, D5+Softening and D5+Softening CC, the 1300 isotherm is shallower at the end of the simulation (Figure 10c) and many thermal heterogeneities appear on a local scale (Figures 12d and12e). In both Models D5+Softening and D5+Softening CC, the well-developed 'faults' are sharp boundaries between regions of significant cooling and/or heating. The thermal heterogeneities within the mantle are more pronounced in Model D5+Softening compared to Model D5+Softening CC, however the impact on the sur face heat flow is more pronounced in Model D5+Softening CC (compare top and lower panels of Figures 12d and12e).

Figure 13: top panels: log 10 (second invariant of the strain rate tensor); bottom panels: accumulated plastic strain (%); the white line in each panel represents the Moho. strain soft.: strain softening; K: keystone block; RS: rift shoulder; BF: border fault; NF: necking fault.

Figure 14: Synthetic view of the lithosphere architecture and main areas of cooling/heating w ith respect to initial temperature at the end of the necking stage for the four end-members behaviors deduced from our numerical model results; the lighter the red/blue the lower the heating/cooling.

The graph above each panel shows the schematic topographic evolution at the main rift basin and adjacent continental lumps when applicable. nk: end of the necking phase. The duration of necking is largely controlled by the bulk extension rate (e.g. [START_REF] Chenin | Necking of the lithosphere : a reappraisal of basic concepts with thermo-mechanical numerical modeling[END_REF]. For a bulk extension rate of 10 15  s 1



the necking phase lasts between ca. 3.5 and 8 My.

Discussion

Topographic evolution

In our simulations, we identify four types of rift system topographic and thermal evolutions J o u r n a l P r e -p r o o f depending on there lithosphere rheology (field I, II, III and IV in Figure 14). The topographic evolution of models with a strong crust (Models D1, D2 and W1-W3; field I in Figure 14) is simple because it results from the necking of one single brittle-plastic layer that is comprised of the entire crust and the upper mantle lithosphere. This type of necking has been extensively described for instance by [START_REF] Co | Modes of continental lithospheric extension[END_REF] and [START_REF] Bassi | Relative importance of strain rate and rheology for the mode of continental J o u r n a l P r e -p r o o f Journal Pre-proof extension[END_REF].

The topographic evolution of models with a weak lower crust that decouples mechanically the brittle-plastic upper crust from the brittle-plastic upper mantle is more complex (fields II, III and IV in Figure 14). Such complexities are common in present-day numerical models but only rarely described in detail (e.g. [START_REF] Huismans | Rifted continental margins: The case for depth-dependent extension[END_REF][START_REF] Van Wijk | Basin migration caused by slow lithospheric extension[END_REF]. In our Models D3-D6 and W4-W6, we notice the formation of distal high(s) and sub-basins within the main rift basin at various stages of the necking phase (Figure A.15). These sub-basins and highs form as a consequence of the asynchronous necking of first the upper mantle (strongest layer of the model; see Figure 2) and then the upper crust (second strongest layer of the model; see also [START_REF] Chenin | Necking of the lithosphere : a reappraisal of basic concepts with thermo-mechanical numerical modeling[END_REF][START_REF] Chenin | Emersion of distal domains in advanced stages of continental rifting explained by asynchronous crust and mantle necking[END_REF]). Early necking of the upper mantle triggers the formation of a relatively undeformed crustal keystone (high) framed by two fault corridors (lows). As extension progresses, the asthenosphere starts upwelling beneath the center of the keystone and leads to its splitting in two. The splitting of the keystone forms a new sub-basin framed by two ridges (lumps) of thick continental crust (Models D3 and W3 in Figure 7; see also [START_REF] Chenin | Necking of the lithosphere : a reappraisal of basic concepts with thermo-mechanical numerical modeling[END_REF].

Mantle rheology impacts the topographic evolution of rift syste ms because it controls the depth of the upper mantle necking level [START_REF] Braun | A physical explanation of the relation between flank uplifts and the breakup unconformity at rifted continental margins[END_REF][START_REF] Kooi | Lithospheric necking and regional isostasy at extensional basins 1. Subsidence and gravity modeling with an application to the Gulf of Lions Margin (SE France)[END_REF]. As necking seeds around the strongest layer, which tends to remain horizontal [START_REF] Weissel | Flexural uplift of rift flanks due to mechanical unloading of the lithosphere during extension[END_REF][START_REF] Braun | A physical explanation of the relation between flank uplifts and the breakup unconformity at rifted continental margins[END_REF], initial subsidence is more pronounced in models where the mantle is strong to greater depth (compare graphs of fields II and III in Figure 14 and insets in Figures 7e and7h). As the depth of the mantle necking level determines the magnitude of the Moho overdeepening, it also controls the amplitude of the subsequent flexural rebound when the necked layer tends to recover isostatic equilibrium. The amplitude of this rebound is more important when the magnitude of overdeepening is large and the flexural strength of the lithosphere is high [START_REF] Weissel | Flexural uplift of rift flanks due to mechanical unloading of the lithosphere during extension[END_REF]). In the case of a strong (dry olivine) mantle, the lithosphere has a high flexural strength and the Moho is largely over-deepened with respect to its isostatic position during upper mantle necking. As a consequence, the keystone subsides despite its high thickness (graph of field II in Figure 14). But once the upper mantle has been necked enough to locally loose most J o u r n a l P r e -p r o o f of its strength, buoyancy forces bring the Moho upward, which explains the uplift of the two continental lumps (remnants of the former keystone) observed during late stages of the necking phase in Figure 5b. In contrast, when the upper mantle is weaker, the flexural strength of the mantle is lower and the upper mantle necking level is shallower. As a result, the Moho and the surface of the keystone remain shallower and the amplitude of the upper mantle isostatic rebound is lower (Figures 5c-d and graphs of fields III and IV in Figure 14).

Our models show that the creation of accommodation space during the necking phase of rifting is first mainly controlled by (vertical) subsidence. Then, towards the end of the necking phase, horizontal widening of the rift basin as a result of strong deformation localization becomes the dominant factor of accommodation space creation (see section 3.1.2).

Our results suggest that uplift and emersion are processes as common as is subsidence during the necking phase of rifting. Hence, subsidence is not the dominating topographic response to rifting, as implied by simple one-dimensional thinning models. Additional processes, such as flexure, crustal flow or lateral thermal diffusion, must be considered to predict both uplift and subsidence during rifting. The magnitude and spatio-temporal distribution of accommodation space creation and emersion are controlled by the rheology of the lithosphere (see section 3.1.3).

As already pointed out by [START_REF] Kaus | Effect of mineral phase transitions on sedimentary basin subsidence and uplift[END_REF] and [START_REF] Simon | The effect of mantle composition on density in the extending lithosphere[END_REF], mineral phase changes and/or mantle fertilization may lead to uplift of distal parts of rift systems during advanced stages of extension. Our modeling results suggest that density reduction related to mantle fertilization only can generate enough uplift to cause emersion of future distal regions comprised of relatively thick continental crust already during late stages of the necking phase. This uplift would be further increased when the heat related to melt advection and crystallization would be modeled. The effect of mantle fertilization is maximum in models where asthenosphere upwelling is fast compared to crustal thinning, that is in models with efficient mechanical decoupling between the crust and the mantle. In contrast, no mantle fertilization occurs during the necking phase of mechanically coupled models because the 1050 C isotherm does not reach a depth of less than ca. 30 km during the simulation.

Our models with strain softening can be considered as end-members where the impact of this process is maximal (decrease of the internal angle of friction and cohesion from 30 to 5 and from 10 to 1 MPa, respectively, between 5% and 20% accumulated plastic strain). These models suggest that strain softening has a limited impact on the general architecture and evolution J o u r n a l P r e -p r o o f of the modeled rift systems but significantly impacts the topography on a local scale. Strain softening facilitates differential vertical movements by enhancing localized deformation along fewer shear zones/'faults'. As a consequence, the topographic relief of our models with strain softening should be considered as maximal. However, results of models including strain softening must be interpreted with care because the numerical implementation is mesh-, and thus resolution-dependent. This means that the number of faults and their offset depend on the numerical resolution of the model.

The location of the major 'faults'/shear zones in models with strain softening is similar to that of the diffuse deformation zones in equivalent models without strain softening (Figure 13).

Therefore, the zones of diffuse deformation of our models without strain softening can be interpreted as areas where major faults are likely to develop. Two sets of 'faults' are of particular interest: (1) we term 'necking faults' the outermost major faults that form during the early stages of extension (NF in the lower panels of Figures 13b and13c J o u r n a l P r e -p r o o f

Thermal evolution

Our models show regions of differential cooling and heating in the lithosphere Figures 8 andA.17, while only cooling is predicted by DUT models [START_REF] Mckenzie | Some remarks on the development of sedimentary basins[END_REF]. The thermal structure at the end of the simulation depends predominantly on the rheology of the crust. When the crust is strong and thus largely mechanically coupled to the upper mantle they neck rapidly as one single layer, and thus upwelling of the asthenosphere is only beginning when the necking phase is achieved. In contrast, when the crust is efficiently decoupled from the mantle by a weak lower crust, the earlier necking of the upper mantle triggers upwelling of the asthenosphere while the crust has not started thinning significantly yet. The asthenosphere keeps rising while the crust begins to neck, which accounts for the shallow 1300 C isotherm and consequent high geothermal gradient at the end of the simulation. The same process explains the higher surface heat flow at the end of the simulation of models with a weak crust compared to models with a strong crust (Figures 9 andA .18).

Our models show consistently heating of the lower crust in the rift center and cooling of the crust on either side. Heating of the crust in the rift center is explained by the upwelling of hot (asthenospheric) mantle beneath it. Cooling of the crust on either side is a result of crustal thinning without significant underlying mantle thinning. Both the cooling and heating recorded in the mantle result from conductive heat exchange between the upwelling asthenosphere and the encompassing lithospheric mantle. In our models, cooling of the upwelling asthenosphere is enhanced because thermal convection below the lithosphere is not modeled (see section 2).

The amplitude of the relative heating/cooling within both the crust and the mantle is systematically less in models with a weak mantle (compare cartoon of field I with those of fields II, III and IV in Figure 14; see also Figure 8). Reasons are, on the one hand that the brittle-plastic uppermost part of the mantle is thinner in the weaker wet olivine mantle than in the dry olivine mantle (Figure 2). As a consequence, the necking instability is smaller in models with a wet olivine mantle, which triggers a wider and less pronounced upwelling of the asthenosphere compared to models with a dry olivine mantle. On the other hand, the weaker wet olivine mantle is more sensitive to Rayleigh-Taylor instabilities, which result in the delamination of the lowermost part of the lithospheric mantle into the asthenosphere . Consequently, part of the thermal exchanges occur at depth to the detriment of the shallower part of the lithosphere.

Intense strain softening (internal angle of friction and cohesion reduced from 30 to 5

J o u r n a l P r e -p r o o f and from 10 to 1 MPa, respectively) has a significant impact on the thermal evolution of our models, although we did not associate any modification of the thermal conductivity (or any other thermal parameter) to the formation of faults. In our models, we observe that faults are associated with sharp changes in the relative cooling/heating, especially within the crust. One reason for this is the concentration of shear heating along the fewer and more localized faults, which generates significant heating compared to models devoid of strain softening. As in natural rift systems faults are regions of increased permeability, and thus o f efficient fluid circulation and heat transport (e.g. [START_REF] Pinto | Tracing mantle-reacted fluids in magma-poor rifted margins: The example of Alpine Tethyan rifted margins[END_REF][START_REF] Incerpi | Hydrothermal fluid flow associated to the extensional evolution of the Adriatic rifted margin: Insights from the pre? to post?rift sedimentary sequence (SE Switzerland, N ITALY)[END_REF], we suggest that integrating major faults into basin modeling is necessary to obtain a reliable understanding of the thermal evolution of a rift system.

In models where the crust and the mantle are mechanically decoupled, the asthenosphere reaches a depth of less than 40 km at the end of the necking phase. Partial melting of the asthenosphere may be likely under such conditions in natural rift systems. As melt percolation may substantially modify the thermal state of rift systems, a careful quantification of the gain/loss of heat related to magma crystallization/melting processes and of heat transfers due to melt advection should be undertaken in such cases. A first step was made by [START_REF] Van Wijk | Melt generation at volcanic margins: no need for a plume[END_REF], who estimated the amount of melt produced by decompression melting for comparable model settings. They show that volumes of several hundreds of km 3 may be generated during late syn-rift stages (consistently after 15 My). In our decoupled models, we would expect the onset of melt generation from 5-6 My of extension already in models with a relatively weak crust.

Synthesis: Primary control on Topographic and Thermal Evolution of Rift Systems

Our results show that the rheology of the lithosphere, in particular the efficiency of mechanical coupling between the crust and the mantle, is the dominant parameter controlling both the topographic and thermal evolution of rift systems (Figure 14). Mechanical decoupling between the crust and the mantle favors complex topographic evolution during extension and high geothermal gradients at the end of the necking phase. When studying continental rifting, it is therefore of primary importance to determine the distribution of strong versus weak (decoupling) layers within the lithosphere, which is essentially controlled by: (1) the composition of the crust and mantle; (2) the crustal thickness; and (3) the geothermal gradient [START_REF] Kusznir | The extensional strength of the continental lithosphere: its dependence on geothermal gradient, and crustal composition and thickness[END_REF][START_REF] Burov | The effective elastic thickness (Te) of continental lithosphere: What does it really mean[END_REF]. At present, most studies assume that lithospheric strength is essentially J o u r n a l P r e -p r o o f controlled by dislocation creep, sometimes also by diffusion and Peierls creep flow laws of monomineralic materials derived from experimental data (e.g. [START_REF] Kirby | Tectonic stresses in the lithosphere: constraints provided by the experimental deformation of rocks[END_REF][START_REF] Kohlstedt | Strength of the lithosphere: Constraints imposed by laboratory experiments[END_REF][START_REF] Kusznir | The extensional strength of the continental lithosphere: its dependence on geothermal gradient, and crustal composition and thickness[END_REF][START_REF] Tesauro | Global strength and elastic thickness of the lithosphere[END_REF]. These studies predict that, under a low to moderate geothermal gradient, the strongest layer of the lithosphere is the uppermost mantle, which is consistent with the persistence of mountain ranges on geological time scales [START_REF] Burov | The long-term strength of continental lithosphere: ?Äújelly sandwich?Äù or ?Äúcrème brûlée?[END_REF]. However, [START_REF] Maggi | A re-assessment of focal depth distributions in southern Iran, the Tien Shan and northern India: do earthquakes really occur in the continental mantle[END_REF] noticed that lithospheric seismicity is largely limited to crustal layers, while the upper mantle is essentially aseismic. They concluded that, at least in some places, the lower crust is stronger than the upper mantle.

Geological outlooks

The necking stage is a transient phase of rift evolution. Because it is out of equilibrium both from a thermal and isostatic perspective, it is not preserved in the final margin architecture.

The best insights we have on the necking stage of rifting arise from the sedimentary record and erosional unconformities observed at present-day and fossils rifted margins. However, due to the lack of a continuous geological record by the sediments and/or precise dating of sedimentary deposits in deep-water margins, a comprehensive comparison between the topographic evolution of our models and natural rifted margins is currently impossible. Our models provide a first quantification of the possible topographic and thermal evolutions during the necking phase, which need to be compared to the evolution of calibrated natural examples. This step is not straightforward because seismically well-imaged rifted margins of which the distal domain is calibrated with drill holes are rare or data are proprietary. At this stage, we are only able to discuss primary similarities between our models and natural rift systems.

Models where the crust and the mantle are mechanically decoupled predict a complex topographic evolution and both heating and cooling events during the necking phase, consistent with growing evidence from both field studies and drill hole data. Indeed, the existence of local erosional features at distal rifted margins and/or the record o f a heating event at the base of the crust during rifting suggest that rift systems do neither necessarily experience immediate and progressive subsidence [START_REF] Esedo | Uplift prior to continental breakup: Indication for removal of mantle lithosphere?[END_REF], nor only progressive post-extensional cooling (e.g. [START_REF] Smye | Rutile U-Pb age depth profiling: A continuous record of lithospheric thermal evolution[END_REF][START_REF] Hart | Thermal evolution of a hyperextended rift basin, Mauléon Basin, western Pyrenees[END_REF], conversely to what is predicted by the DUT model [START_REF] Mckenzie | Some remarks on the development of sedimentary basins[END_REF].

Models W4 and W5 predict the keystone to remain less than 200-300 m deep during J o u r n a l P r e -p r o o f approximately half of the necking phase (Figure A.15). This result can be compared to the evolution of the Iberian margin, whose distal domain appears to have remained at shallow water depth (within the photic zone) during early stages of the necking phase in Tithonian-Berriasian time (ca. 145 Ma; [START_REF] Boillot | Rifting of the Galicia margin: crustal thinning and emplacement of mantle rocks on the seafloor[END_REF]Mohn et al., 2014, compare Figure 1b and graph III in Figure 14). This hypothesis remains yet to be tested against calibrated stratigraphic data.

Models D6, D5+Fertilization and D5+Softening can account for the existence of syn-rift erosional unconformities at distal parts of rift systems since part of their initial keystone becomes transitorily emerged after an initial phase of subsidence (Figures 11c and11d). This evolution can be compared with that of the Briançonnais unit during the Early Jurassic necking phase of the former Alpine Tethys. The Briançonnais unit, which is characterized by Early Jurassic karsts (e.g. [START_REF] Claudel | A record of multistage continental break-up on the Briançonnais marginal plateau (Western Alps): Early and Middle-Late Jurassic rifting[END_REF], is interpreted to have initially formed as a keystone and have become part of the distal European margin at the time of breakup [START_REF] Lavier | A mechanism to thin the continental lithosphere at magma-poor margins[END_REF].

The evolution of Models D6, D5+Fertilization and D5+Softening can also be compared with that of the outer Campos Basin hinge offshore the Brazilian margin, where a few tens of kilometers wide erosional unconformity was mapped over 120 km along strike (e.g. [START_REF] Lewis | New insights into late synrift subsidence from detailed well ties and seismic mapping, Campos Basin, Brazil[END_REF]. The fact that the eroded region is linear, of relatively constant width and sub-parallel to the coastline suggests that its origin is structural/tectonic rather than thermal. [START_REF] Lewis | New insights into late synrift subsidence from detailed well ties and seismic mapping, Campos Basin, Brazil[END_REF] interpreted the unconformity to be syn-rift. One of the scenarios for its formation was that part of the outer hinge experienced transitory uplift and emersion during the Aptian, after which the entire outer hinge subsided. They rejected this scenario because they could not find a geological process accounting for ca. 1 km of local uplift followed by 2-3 km of subsidence in the span of 13 My.

Assuming Models D5+Fertilization and D5+Softening explain this behavior, the transitory uplift of the outer hinge would be related to the isostatic adjustment of a former keystone after the necking of the upper mantle.

Due to the lack of access to lower crustal levels, the deep thermal evolution of rift basins and hyperextended rift systems is poorly known. The only direct information come from fossil hyperextended rift systems now exposed in the Pyrenean and the Alpine orogens in Western Europe. Thermochronological data from these systems indicate intense heating events during the necking phase of rifting [START_REF] Smye | Rutile U-Pb age depth profiling: A continuous record of lithospheric thermal evolution[END_REF][START_REF] Seymour | Tracing the thermal evolution of the Corsican lower crust during Tethyan rifting[END_REF][START_REF] Hart | Thermal evolution of a hyperextended rift basin, Mauléon Basin, western Pyrenees[END_REF]. Based on the high geothermal gradients at the end of the necking phase, we suggest that the Pyrenean and Alpine rift systems developed within a lithosphere where the crust and the mantle were J o u r n a l P r e -p r o o f

Journal Pre-proof mechanically decoupled, which allowed for asynchronous necking of first the upper mantle, and then the crust. In the Pyrenees, the widespread occurrence of a pre-rift salt further promoted intra-crustal mechanical decoupling during rifting [START_REF] Duretz | Numerical modelling of cretaceous pyrenean rifting: The interaction between mantle exhumation and syn-rift salt tectonics[END_REF].

According to our model results, surface heat flow could be used as a proxy to localize regions of thinned crust. In particular, two regions of higher-than-average surface heat flow separated by a few tens of kilometers may highlight the boundaries of a crustal keystone prior to significant crustal thinning.

Conclusion

We performed a systematic analysis with a high-resolution thermo-mechanical model to quantify the impact of lithosphere rheology on the topographic and thermal evolutions during the necking phase of extensional systems (i.e. until the crust is thinned to 10 km). Our results confirm that the rheology of the lithosphere has a major control on the topography evolution. We argue that this control arises from: (1) the efficiency of the mechanical decoupling between the crust and the mantle, and thus the delay between crust and mantle necking;

(2) the depth of the necking level(s), and thus the amplitude of the initial subsidence and subsequent isostatic rebound; and (3) the flexural strength of the lithosphere, and thus the re gionality and efficiency of isostatic compensation. When the mantle is strong and the crust weak to moderately strong, extension of the lithosphere results in the formation of several highs and sub-basins within the main rift basin. This architecture differs significantly from the traditional view that, in the absence of several weak inherited structures, extension of the lithosphere produces one single basin that subsides progressively. Adjacent highs and lows are usually characterized by positive and negative vertical velocities, respectively. These differential uplift and subsidence movements can occur over a region of a few tens of kilometers only.

The creation of accommodation space is primarily controlled by (vertical) subsidence during the early stages of rifting. By the end of the necking phase, creation of accommodation space is largely caused by horizontal extension as a result of intense deformation localization at the rift center. Our models show that a comparable amount of accommodation space and emerged area is created during the necking phase of rifting. We conclude that during the necking phase of rifting, uplift and emersion are as common processes as is subsidence. Hence, subsidence is not the dominating topographic response to rifting, as is implied by simple thinning models. The rheology

Figure 1 :

 1 Figure 1: a) Illustration of the depth-uniform thinning model from McKenzie (1978); abbreviations: cont.: continental; lithos.: lithospheric; astheno.: asthenospheric mantle. b) Schematic graph showing the topographic evolution of the distal part of different types of rift systems; c) Schematic graph showing the thermal evolution at the base of the crust in the distal part of different types of rift systems. d) Annotated photograph showing the stratigraphic relationships in the Briançonnais unit (Alps of southeastern France). The Briançonnais unit belonged to the distal European margin of the former Alpine Tethys rift system.

Figure 2 :

 2 Figure 2: Model configuration with depth-dependent stress profile and geothermal gradient at the model center for the different rheologies tested. The right-hand side stress profile zooms on the shallowest 100 km of the lithosphere. Each crustal and mantle material is associated to a bracketed number (from 1 to 6) or letter (W or D), which are used to reference the simulations (for instance Model W1 is made of wet olivine mantle and Maryland diabase crust).

Figure 3

 3 Figure 3 summarizes the surface topography (panels a and b), simulation duration (panel c) and thermal state (panels d, e and f) of Model Series D (dry olivine mantle) and W (wet olivine mantle) at the end of the necking stage. Four systematic trends stand out: (1 ) the stronger the crust, the larger the relief (Figures 3a and 3b); (2) the stronger the crust, the shorter the duration of the

Figure 3 :

 3 Figure 3: a) and b) Surface topography at the end of the simulation (i.e. when the crust is locally thinned to 10 km) of Model Series D (dry olivine mantle) and Model Series W (wet olivine mantle), respectively. c) Necking duration of the different models of Series D (squares) and W (circles); d) and e) Minimum depth of the 500 and 1300 C isotherms, respectively, at the end of the simulation in Model Series D and W; f) Maximum surface heat flow at the end of the

Figure 4 :

 4 Figure 4: Top panels: surface (magenta curve), top basement and Moho topography (black curves) at the end of the necking phase (i.e. when the crust is locally thinned to 10 km). The space between the magenta and top basement curves represents sediments.The horizontal blue line corresponds to the isobath 0 km. The 500 C (and in panels e and f the 1300 C) isotherms are plotted in red. Bottom panels: evolution of surface topography with time along different models. RS: Rift Shoulder.

  and A.15j-l). The central high of Models W4 and W5 remains at a shallow depth of 100-300 m compared to the 1-1.5 km-deep adjacent sub-basins until approximately three quarters of the necking phase. The central high of Models W3 and W4 remains also at shallower depth than the 600 and 300 m-deep distal highs of Models D4 and D5, respectively (Figure4eA.15d and A.15e).During the last quarter of the simulation, the central high is split in two as a new sub-basin forms in its center and subsides rapidly to ca. 2 km depth in Models W4 and W5. At the same time, the two outer sub-basins become shallower (1.1-1.2 km in Model W4, 600-700 m in Model W5).The evolution of Model W6 differs from that of the other models in that four shallow J o u r n a l P r e -p r o o f (100-500 m deep) sub-basins separated by three relative highs ( < 100 m deep) form and persist until 5.5 My (approximately three quarters of the necking duration; Figure A.15l). Extension focuses eventually in the second basin to the right, which reaches only 1 km depth when crustal necking is achieved at 7.4 My. 3.1.1.4 Summary. We identify four types of topographic evolution for the necking phase of a rift system: (1) formation of one single, narrow and deep rift basin that subsides continuously and rapidly (Models D1, D2 and W1-W3); (2) formation of three sub-basins separated by two distal highs within the main rift basin; the distal highs may record transient uplift at various stages of the necking phase (Models D3-D6); (3) formation of two sub-basins separated by one distal high within the main rift basin; subsidence of the distal high is delayed to late stages of the necking phase (Models W4 and W5); and (4) formation of multiple, regularly spaced, shallow rift basins and highs (Model W6).

Figure 5 : 1 . 1 

 511 Figure 5: Top left panels: surface topography with time. Top right panels: surface horizontal velocity (x-direction) with time. Bottom left panels: surface vertical velocity with time. Bottom right panels: topography gradient with respect to time.

  (1) Models with a very strong crust (D1, D2, W1 and W2) show an initial (ca. 0.5 My) slight decrease in both accommodation space and emerged area. Then both increase extremely rapidly to values ranging J o u r n a l P r e -p r o o f from 190 to 350 km 2 (Figures 6a-b and A.16a-b); (2) Models with a moderately strong crust (Models D3, D4, W3 and W4) show also an initial (ca. 1 My) slight decrease in both accommodation space and emerged area. Then, both increase progressively to values ranging from ca. 50 to 125 km 2 (Figures 6c-d and A.16a-b); (3) Models with a weak crust (Models D5, D6,

  on either side of the rift center (Figures7e-f and 7h-i). The splitting of the keystone forms a new sub-basin in the model center, which subsides rapidly during the last quarter of the simulation(Figures 4c, 4, 4f,.

Figure 8 :

 8 Figure 8: Top panels: Difference between the initial and final temperature within the model at the end of the necking phase; temperature difference accounts for diffusion, production and advection of heat. The green lines represent top basement, Moho and initial lithosphere-asthenosphere boundary (the latter is visible on panels c-f only). Bottom panels: Model temperature at the end of the necking phase; the cyan lines represent top basement, Moho and the initial lithosphere-asthenosphere boundary; the dark blue lines represent the 250, 500, 750, 1000 and 1300 C isotherms.

  Figures 9 and A.18 show that surface heat flow is relatively homogeneous outside of the rift basin, with values of 50-70 mW  m 2  . Within the main rift basin, surface heat flows of ca. 100 mW  m 2  are consistently observed from approximately half of the J o u r n a l P r e -p r o o f Journal Pre-proof necking duration onward. In models where one single rift basin forms (Models D1, D2 and W1-W3), the maximum heat flow is located in its center during the entire simulation (Figures 9a, 9b, 9d, A.18a-b and A.18g-i). In the other models, the highest heat flow is consistently recorded first in the two sub-basins that frame the crustal keystone. The highest heat flow remains in the outer sub-basins until the last quarter of the simulation, when the central sub-basin starts to deepen rapidly as the crust is efficiently thinned. From then onwards, the central sub-basin becomes the locus of highest heat flow (Figures 9c, 9e and 9f, A.18c-e and A.18j-k).

  Figure A.18).

Figure 9 :

 9 Figure 9: Surface heat flow with time along the different models. The contour lines represent crustal thickness isopachs: 15 km (black), 20 km (magenta) and 25 km (yellow). CC: continental crust.

of

  Series D5+. The largest deviations with respect to Model D5 (black line) occur when either mantle fertilization (yellow line) or strain softening (violet and red lines) are modeled. The necking duration remains also similar, differing by less than 1 My between the different models of Series D5+. The necking duration is slightly longer in Models D5+No diffusion creep, D5+Softening and D5+Softening CC (7.4 to 8.1 My co mpared to 7.3 My in Model D5) and shorter in the other models (minimum necking duration of 6.9 My in Model D5+No Peierls creep).

( 25 -

 25 26 km). In Models D5+No diffusion & no Peierls creep (blue marker), the 500 C isotherm is shallower by 0.5 km than in Model D5, while the 1300 C isotherm is deeper by 5 km. The maximum surface heat flow at the end of the simulation varies from less than 200 mW  m 2  in Models D5+Fertilization to 235 mW  m 2  in the two simulations where Peierls creep is not taken into account, while it is ca. 215 mW  m 2  in Model D5. However, Figure A.21 highlights that, except from Model D5+Softening CC, the distribution and intensity of surface heat flow is largely similar between Model D5 and the different models of Series D5+ during the three first quarters of the simulations (deviations < 10 mW m 2  ).

Figure 10 :

 10 Figure 10: a) Surface topography at the end of the simulation of Model Series D5+; b) Necking duration of the different models; c) and d) Minimum depth of the 500 and 1300 C isotherms at the end of the simulation; e) Maximum surface heat flow at the end of the simulation.

  Figure A.21b) The thermal architecture at the end of the necking phase is largely similar amongst the models with different mantle deformation mechanisms (Figures12a-b and A.20a-d). In the two models without Peierls creep, there is no piece of mantle showing a relative heating with respect to initial temperature at the end of the simulation. Actually, a so-called 'mantle keystone' did form during the early stages of extension in both models, but because deformation was largely symmetrical, the mantle keystone was disintegrated during extension.Models withoutPeierls creep show a positive anomaly of more than 40 mW  m 2  in the surface heat flow (Figures A.21c-d) and a shallower 500 C isotherm (Figure 10c) at the end of the simulation compared to Model D5.

Figure 11 :

 11 Figure 11: Top panels: surface (magenta curve), top basement and Moho topography (black curves) at the end of the necking phase (i.e. when the crust is locally thinned to 10 km). The space between the magenta and top basement curves represents sediments. The horizontal blue line corresponds to the isobath 0 km. The 500 C (and in panels c-e the 1300 C) isotherms are plotted in red. Bottom panels: evolution of surface topography with time along the model. St rain soft.: Strain softening.

Figure 12 :

 12 Figure 12: Top panels: Difference between the initial and final temperature within the model at the end of the necking phase; temperature difference accounts for diffusion, production and advection of heat. The green lines represent the Moho and the initial lithosphere-asthenosphere boundary. Middle panels: Model temperature at the end of the necking phase; the cyan lines represent the surface topography, top basement, Moho and the initial lithosphere-asthenosphere boundary; the dark blue lines represent the 250, 500, 750, 1000 and 1300 C isotherms. Bottom panels: Difference in the surface heat flow compared to reference Model D5 with time along the model; the contour lines represent crustal thickness isopachs: 15 km (black), 20 km (magenta) and 25 km (yellow in panel a, blue in panels b-e). Strain soft.: Strain softening.

  ). At this stage, the necking faults mark the boundary between the main rift basin and the rift shoulders (RS in the top panels of Figures13b and 13c); (2) we term 'border faults' the outermost major faults in the subsequent frames (BF in the lower panels of Figures13e-f and 13h-i). These 'faults' form later than the necking faults and mark the new boundary between the rift basin and its rift shoulders (RS in the top panels of Figures13e-f and 13h-i). This implies that part of the initial rift shoulders may be integrated to the distal part of the margin as the necking phase progresses, as illustrated in Figures11a, 11d and 11e. This model result has yet to be compared to field observations in order to assess the existence of such an evolution.

J

  o u r n a l P r e -p r o o f of the lithosphere controls the magnitude and spatiotemporal distribution of uplift and emersion during necking, which we quantified in detail in our study.The efficiency of mechanical decoupling between the crust and mantle controls also the geothermal gradient at the rift center at the end of the necking phase. When the crust is mechanically decoupled from the upper mantle, earlier necking of the upper mantle triggers the onset of asthenosphere upwelling beneath an largely un-thinned crust, which results in a particularly high geothermal gradient in the rift center. In this case, partial melting and consequent fertilization of the subcontinental lithospheric mantle by melt impregnation are likely and may lead to increased uplift of future distal parts of the rifted margins. the end of the necking phase; temperature difference accounts for diffusion, production and advection of heat. The green lines represent the Moho and the initial lithosphere-asthenosphere boundary. Bottom panels: Model temperature at the end of the necking phase; the cyan lines represent the top basement, Moho and the initial lithosphere-asthenosphere boundary; dark blue lines represent selected model isotherms. Strain soft.: Strain softening.

Figure A. 21 Figure 1 Figure 2

 2112 Figure A.21: a-l: Surface heat flow with time along the different models. The contour lines represent crustal thickness isopachs: 15 km (black), 20 km (magenta) and 25 km (blue). Strain soft.: Strain softening. J o u r n a l P r e -p r o o f

Figure 3

 3 Figure 3

Figure 4

 4 Figure4

Figure 5

 5 Figure5

Figure 6

 6 Figure6

Figure 7

 7 Figure 7

Figure 8

 8 Figure8

Figure 9

 9 Figure 9

Figure 10

 10 Figure10

Figure 11

 11 Figure11

Figure 12

 12 Figure12

Figure 13

 13 Figure13

Figure 14

 14 Figure14

Table 1 :

 1 Material physical properties and flow law parameters. Flow law parameters for Maryland diabase are from Mackwell et al. (1998); mafic and felsic granulite from

Acknowledgment

This Research was conducted in the framework of the Margins 5 consortium, which involves BP, BHP, CNOOC UK Limited, Conocophillips, Econor, Ecopetrol, HESS, Petrobras, Repsol, Shell, Total, ION, CGG. We thank Nick Kusznir for helpful discussions on this manuscript.

Declaration of interests

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Appendix A. Supplementary Model Results

Figure A.15: Top panels: surface (magenta curve), top basement and Moho topography (black curves) at the end of the necking phase (i.e. when the crust is thinned to 10 km). The space between the magenta and top basement curves represents sediments.The horizontal blue line corresponds to the isobath 0 km. The 500 C (and in some panels the 1300 C) isotherms are plotted in red.

Bottom panels: evolution of surface topography with time along the model.