Keywords: interpolation, non-rigid registration, level set

Volume reconstruction is one of the key problems in 3D image rendering and analysis. Inter slice interpolation methods have been widely discussed in the literature and object-based algorithms have been shown to well behave. In this paper, we present a non-rigid registration based strategy to improve the volume reconstruction. A level set evolution technique is proposed to yield the deformation between adjacent slices. A modified bilinear interpolation method is then designed to generate propagating image. A multi-resolution scheme is applied to decrease the computation time and support large deformation. The resulting images show good results on regions enclosing different anatomic structures.

I. INTRODUCTION

EDICAL imaging devices such as CT or MRI generally produce a set of slices in which the dimension of the voxel is not isotropic, i.e. the distance between two successive slices is larger than the distance between two neighboring pixels within a slice. An interpolation technique is thus required to improve the axial resolution between slices before applying any visualization or analysis technique on the data volume.

Many interpolation techniques have been proposed in the literature [START_REF] Grevera | An objective comparison of 3-D image interpolation methods[END_REF][START_REF] Meijering | Quantitative evaluation of convolution-based methods for medical image interpolation[END_REF][START_REF] Thevenaz | Interpolation revisited[END_REF][START_REF] Herman | Shape-based interpolation[END_REF][START_REF] Raya | Shape-based interpolation of multidimensional objects[END_REF][START_REF] Higgins | Shape-based interpolation of tree-like structures in three-dimensional images[END_REF][START_REF] Penny | Registration-based interpolation[END_REF]. They classically fall into two main categories: scene-based and object-based methods. In scene-based methods the interpolation is only based on the image intensities. Let's cite for instance, the nearest neighbor method, the linear one or the spline-based interpolation functions. Comparisons of these methods have been published by Meijering [START_REF] Meijering | Quantitative evaluation of convolution-based methods for medical image interpolation[END_REF] and Thevenaz [START_REF] Thevenaz | Interpolation revisited[END_REF]. They suppose that the pixels used in the original slices, to compute the pixels in the missing slice, belong to the same anatomic structure. This is rarely the case. When the structure shifts considerably from one slice to another (due to a deformation of the structure), the interpolation method produces artifacts on the new created slice. Object-based interpolation methods rely on additional information previously extracted from the slices to guide the interpolation process. The interpolation is Manuscript re Xudong Bao, Danhua Xu, and Limin Luo are with the Laboratory of Image Science and Technology, School of Computer Science and Technology, Southeast University, Nanjing, Jiangsu Province, 210096, China (Bao's e-mail: bao.list@seu.edu.cn).

Christine Toumoulin is with the laboratoire Traitement du Signal et de l'Image, Université de Rennes I, Rennes, F-35000, France, and also with INSERM, U642, Rennes, F-35000, France (e-mail: christine.toumoulin@univ-rennes1.fr).

All of the authors are also in the Centre de Recherche en Information Biomédicale Sino-français (CRIBs) then only performed between pixels belonging to the same anatomic structures on the different slices. Some of these methods performed a preliminary shape matching between the slices prior to interpolation [START_REF] Herman | Shape-based interpolation[END_REF][START_REF] Raya | Shape-based interpolation of multidimensional objects[END_REF][START_REF] Higgins | Shape-based interpolation of tree-like structures in three-dimensional images[END_REF]. This stage involves performing a preliminary segmentation of the structures all over the slices. This task remains difficult and computationally expensive. Other methods involve a preliminary intensity based registration between adjacent slices before interpolating between corresponding positions in each slice [START_REF] Penny | Registration-based interpolation[END_REF][START_REF] Osher | Level set methods: an overview and some recent results[END_REF]. These techniques used the optical flow or mixed intensity and gradient information to match pixels between slices. A lot of non linear registration techniques have been described in the literature [START_REF] Penny | Registration-based interpolation[END_REF].

Level set techniques have been widely discussed to depict curve or surface deformation [START_REF] Osher | Level set methods: an overview and some recent results[END_REF][START_REF] Liao | Level-set-based deformation methods for adaptive grids[END_REF]. The level sets evolve from initial position based on spatio-temporal partial differential equations (PDEs) in distance space. Vemuri, et al. presented a level set based non-rigid registration method [START_REF] Vemuri | Image registration via level-set motion: Applications to atlas-based segmentation[END_REF].

Our volume reconstruction method is based on the object-based scheme and the level set is used to estimate the deformation between slices. A modified bilinear interpolation method is designed for the propagation of gray image. A multi-resolution scheme is applied to optimize the computation and trace the large size deformation. Results are given on brain MRI slices.

II. METHODS

A. Level Set Based Non-rigid Registration Scheme

Osher and Senthian [START_REF] Osher | Fronts propagating with curvature dependent speed: algorithms based on Hamilton-Jacobi formulations[END_REF] presented elementary spatio-temporal PDE

0 ∇ ∂ ∂ = Φ ⋅ + Φ v t , (1)
which converts the level set values (levels) with the velocity field v, where Φ is level set function (distance function). If only the motion on normal direction is taken into account, (1) becomes

0 = Φ ∇ + ∂ Φ ∂ N v t , (2)
where

Φ Φ ⋅ = ∇ ∇ v N v .
Usually, the contours on image plane are mapped to zero level sets in distance space. Because the level sets evolve in higher dimensional space than image plane, the topological change of contours can be easily performed during evolution.

Vemuri et al. defined the distance function Φ to be

Volume Reconstruction Based on Non-rigid Registration

Xudong Bao, Danhua Xu, Christine Toumoulin, and Limin Luo M image gray levels and introduced level set based non-rigid registration method [START_REF] Vemuri | Image registration via level-set motion: Applications to atlas-based segmentation[END_REF]. The registration of two images is given by the evolution of the gray levels of the intensity function from source image I 1 to that of target image I 2 . The velocity of evolution on normal direction is selected as the gray level difference between two images. Then, (2) can be rewritten as [START_REF] Vemuri | Image registration via level-set motion: Applications to atlas-based segmentation[END_REF],

) , ( )) , ( ) ( ( ) , ( 2 t I t I I t I t X X X X ∇ - = , (3)
with I(X,0)=I 1 (X), where X=(x, y) T is the position of pixel, I t (X,t) denotes the increment of image intensities at time t. Suppose that adjacent slices contain similar anatomic structures and same anatomic structures have similar gray levels. Fortunately, the assumption is satisfied for adjacent slices from most tomographic imaging devices. Based on the assumption, the gray level evolution can be equivalently considered as the deformation of source image. A similar approach was presented [10],

)) ( (

)) ( ( ))] ( ( ) ( [ 1 1 1 2 X V X V X V X V I I I I t ∇ ∇ - = , (4)
where V=(u, v) T denotes the displacement vector at X and the operation V(X)=(x-u, y-v) T translates position X at the opposite direction of V. The normalized gradient at the right side of (4) defines normal of evolution. The stable solution of V from (4) registers source image I 1 to target image I 2 .

Because the gradient operation is very sensitive to noise, the image is convolved with a Gaussian filter kernel with standard derivation σ before the gradient operation [START_REF] Vemuri | Image registration via level-set motion: Applications to atlas-based segmentation[END_REF],

α I G I G I I σ σ t + * ∇ * ∇ - = ))) ( ( (
))) ( ( ( ))] ( ( ) ( [ 1 1 1 2 X V X V X V X V . (5)
Positive constant α is selected to stabilize the computation when the denominator is close to zero.

B. Numerical implementation

Malladi et al. presented the numerical implementation of non-linear hyperbolic PDEs in detail [START_REF] Malladi | Shape modeling with front propagation: A level set approach[END_REF]. This numerical scheme can be used in the implementation of Eq. ( 5) except the propagation of the distance image (gray level image). Usually, in numerical implementation of level set equations, the increment of distance function at each position on distance image is computed and then the distance function is simply updated during each iterative step. But, Eq. ( 5) explicitly defines the modification of deformation matrix of image grids from I 1 to propagated image I t instead of the increment of distance function. Thus, the distance image will be updated by deforming I 1 based on the deformation matrix. An appropriate interpolation method has to be adopted to compute the gray levels of discrete image depending on the pixels at twisted grids mapped from I 1 .

For each pixel X' of discrete image I t , a minimal surrounding quadrangle can be found, which four vertices, denoted as X' 1 , X' 2 , X' 3 and X' 4 , are mapped from corresponding pixels X 1 , X 2 , X 3 , and X 4 on image I 1 by deformation matrix, shown as Fig. 1. Based on the assumption that the gray levels of the pixels will not change during deformation, we have I t (X' 1 ) = I(X 1 ), I t (X' 2 ) = I(X 2 ), I t (X' 3 ) = I(X 3 ) and I t (X' 4 ) = I(X 4 ), although the position X' 1 , X' 2 , X' 3 and X' 4 may be not discrete coordinates. The modified bilinear interpolation method is designed to estimate the pixel gray level based on pixels at the vertices of surrounding quadrangle other than rectangle. The scheme is divided into two steps. Firstly, a linear interpolation is applied to left vertices pair (X' 1 and X' 4 ) and right vertices pair (X' 2 and X' 3 ) respectively. Suppose that X' L is the dot on line X' 1 X' 4 closest to X' (in the figure, X' L has the same position with X' 1 ), and X' R is the dot on line X' 2 X' 3 closest to X'. The gray levels at X' L and X' R are respectively interpolated by In numerical implementation the displacement of deformation matrix, ∆V(X, t), is computed by applying the numerical scheme presented by [START_REF] Malladi | Shape modeling with front propagation: A level set approach[END_REF] to Eq. ( 5) during each iterative step. The deformation matrix V is updated by normalized ∆V(X, t) for the stability, i.e.

X X X X X X X X X X L t R L R R t R L L t I I I + + + = . (8)
{ } | ) , ( | max ) , ( ) , ( ) 1 , ( t t t t X V X V X V X V X ∆ ∆ + = + . (9)
Each pixel on original image I 1 is mapped to propagated image plane by deformation matrix V. Then, the discrete propagated image I t is interpolated with presented modified bilinear interpolation method. The iteration will be stopped if the maximum of ∆V is less than a threshold.

A multi-resolution strategy is adopted to reduce computation time and improve the stability of the propagation by applying a coarse-to-fine registration process.

X'

X' 1 X' 2 X' 3 X' 4 X' R (X' L )

C. Volume Reconstruction

The registration depicts the geometric transformation V between slices. The each element of V maps one pixel on slice I 1 to corresponding position on slice I 2 , which is benefited from level set based registration scheme. The linear interpolation of gray levels is taken place between the corresponding pixels on two adjacent slices, which will reduce the artifacts in the boundary area of anatomic structures.

Suppose that the distance between two slices is z, and the interpolated image is d from slice 1. The deformation from slice 1 to interpolating plane, denoted as V d , will be d/z times V, shown as Fig. 2. Let X d be the cross point where line XX' passes through interpolation plane I d . The gray level at X d , denoted I d (X d ), can be decided by linear interpolation between corresponding pixels X and X',

) ( ) 1 ( )) ( ( ) ( 1 2 X X V X I z d I z d I d d - + = . ( 10
)
Each element of deformation matrix V defines a pair of corresponding pixels respectively on I 1 and I 2 , and, then, a pixel, which may locate within coordinate grid, can be evaluated. Based on the pixels, the discrete image on interpolation plane can be obtained by applying presented modified bilinear interpolation method again.

Fig. 2 The registered positions of pixels on slices and interpolation plane

III. RESULTS

In the experiment, three consecutive slices were selected from MRI sequence with 2mm intervals to test the performance of the methods, shown in Fig. 3 (a)-(c). The size of images was 256×256 and the dimension of each pixel was 0.9375mm × 0.9375mm. The middle slice, shown in Fig. 3(b), was removed from the sequence and the image at the position of the middle slice was interpolated based on first and last slices. The difference between the interpolated image and the removed middle slice was analyzed for the evaluation of the methods. All computations were done on PC with P4 2.66GHz CPU and 512M memory, and the program was encoded with Microsoft Visual C++.

The level set based methods were applied to the interpolation. The multi-resolutional registration was applied in three different resolution stages, i.e. 32×32, 128×128 and 256×256 resolution levels. The coarse images were resampled from original slices by averaging pixels within correlative region. We set the standard derivation σ of Gaussian filter in Eq. ( 5) to 1.0 and α to 0.01. The final deformation registered between the first and last images was shown in (e). The linear interpolation was applied between corresponding pixels defined by the deformation matrix and the modified bilinear interpolation method was chosen to get discrete image, shown as (d). All the process took less than 2s. An image of the absolute differences between the interpolated image and the original slice was shown in (f). The mean square root of the difference image was 11.6.

For the comparison, we applied traditional linear interpolation method and [START_REF] Penny | Registration-based interpolation[END_REF] presented methods to the experiment data respectively. The results were shown in (g) and (i) and the images of absolute differences between interpolated images and the original slice were given by (h) and (j), where the differences were normalized to [0,255]. The mean square root of the difference images were 20.9 and 16.2 respectively.

IV. CONCLUSION

We have applied level set based non-rigid registration to volume reconstruction and designed a modified bilinear interpolation scheme applied to the propagation of gray level image in registration process and the estimation of interpolated image. The results indicated that the anatomic structures were well kept on interpolated image.

Fig. 1 .

 1 Fig. 1. Pixel X' and its minimal surrounding quadrangle

Fig. 3 (

 3 Fig. 3 (a) -(c) three consecutive slices from MRI slice sequence with 2mm intervals, (d) the interpolated image between slice (a) and (c) at the position of slice (b) based on the presented method, (e) the displacement field depicting the deformation between (a) and (c), (f) absolute differences between (d) and (b), (g) the interpolated image with linear interpolation, (h) the absolute differences between (g) and (b), (i) image based on method described in [7], (j) the absolute differences between (i) and (b)

Then, the gray level of pixel X' is interpolated from I t L (X') and I t R (X') by


A Azdimousa

A Jabaloy-Sánchez

P Münch

J M Martínez-Martínez

G Booth-Rea

M Vázquez-Vílchez

L Asebriy

J Bourgois

F González-Lodeiro

G Booth- Rea

Martínez -Martínez

Structure and exhumation of the Cap des Trois Fourches basement rocks (Eastern Rif, Morocco)

Keywords: Rif Chain, Cap des Trois Fourches, ductile-brittle detachment fault, U-Pb SHRIMP zircon geochronology

-Introduction

The Eastern Rif Chain (Northwest Africa, Fig. [START_REF] Frizon De Lamotte | La structure du Rif oriental (Maroc). Rôle de la tectonique longitudinale et importance des fluides[END_REF][START_REF] Frizon De Lamotte | Cinématique des chevauchements néogènes dans l'Arc bético-rifain: discussion sur les modèles géodynamiques[END_REF][START_REF] Azdimousa | Lithostratigraphy and structure of the Temsamane unit (eastern external Rif, Morocco)[END_REF][START_REF] Chalouan | The Rif Belt[END_REF][START_REF] Jabaloy-Sanchez | The structure of the Temsamane fold-and-thrust stack (eastern Rif, Morocco): Evolution of a transpressional orogenic wedge[END_REF]. It notably includes the Temsamane area, the Cap des Trois Fourches and the Khebaba massif [START_REF] Frizon De Lamotte | La structure du Rif oriental (Maroc). Rôle de la tectonique longitudinale et importance des fluides[END_REF][START_REF] Frizon De Lamotte | Cinématique des chevauchements néogènes dans l'Arc bético-rifain: discussion sur les modèles géodynamiques[END_REF][START_REF] Azdimousa | Lithostratigraphy and structure of the Temsamane unit (eastern external Rif, Morocco)[END_REF][START_REF] Negro | Tectonic evolution of the Betic-Rif arc: new constraints from 40 Ar/ 39 Ar dating on white micas in the Temsamane units (External Rif, northern Morocco)[END_REF][START_REF] Booth-Rea | Upper-crustal extension during oblique collision: the Temsamane extensional detachment (eastern Rif, Morocco)[END_REF][START_REF] Jabaloy-Sanchez | The structure of the Temsamane fold-and-thrust stack (eastern Rif, Morocco): Evolution of a transpressional orogenic wedge[END_REF] (Figs. 1 and2). The sequences of these areas include metapelitic Paleozoic rocks covered by Triassic greenschists and Jurassic to early Cretaceous marbles and metapelites [START_REF] Frizon De Lamotte | La structure du Rif oriental (Maroc). Rôle de la tectonique longitudinale et importance des fluides[END_REF][START_REF] Frizon De Lamotte | Cinématique des chevauchements néogènes dans l'Arc bético-rifain: discussion sur les modèles géodynamiques[END_REF][START_REF] Azdimousa | Lithostratigraphy and structure of the Temsamane unit (eastern external Rif, Morocco)[END_REF]Negro et al., 2008;[START_REF] Booth-Rea | Upper-crustal extension during oblique collision: the Temsamane extensional detachment (eastern Rif, Morocco)[END_REF][START_REF] Jabaloy-Sanchez | The structure of the Temsamane fold-and-thrust stack (eastern Rif, Morocco): Evolution of a transpressional orogenic wedge[END_REF]. Those rocks are characterized by LT-IP Alpine metamorphic conditions [START_REF] Negro | Exhumation des roches métamorphiques du domaine d´Alboran: étude de la Chaine Rifaine (Maroc) et corrélation avec les Cordillères Bétiques (Espagne)[END_REF][START_REF] Negro | Tectonic andmetamorphic evolution of the Temsamane units, External Rif (northern Morocco): implications for the evolution of the Rif and the Betic-Rif arc[END_REF][START_REF] Jabaloy-Sanchez | The structure of the Temsamane fold-and-thrust stack (eastern Rif, Morocco): Evolution of a transpressional orogenic wedge[END_REF], and by penetrative Alpine ductile deformations. Most of the rocks also were exhumed by a ductile-brittle extensional detachment (see [START_REF] Azdimousa | Lithostratigraphy and structure of the Temsamane unit (eastern external Rif, Morocco)[END_REF][START_REF] Booth-Rea | Upper-crustal extension during oblique collision: the Temsamane extensional detachment (eastern Rif, Morocco)[END_REF][START_REF] Jabaloy-Sanchez | The structure of the Temsamane fold-and-thrust stack (eastern Rif, Morocco): Evolution of a transpressional orogenic wedge[END_REF]. At the present day, those metamorphic outcrops are isolated, making their mutual correlation difficult to disentangle the first order structure of the area that is a basic key point to understand the evolution of the North Africa palaeomargin.

One of the aforementioned outcrops occurs in the Cap des Trois Fourches sector (Figs. 2 and 3), where scarce detailed studies have been performed [START_REF] Guillemin | Carte géologique du Rif, échelle 1/50 000, feuille Melilla[END_REF][START_REF] García-Dueñas | El Despegue extensional de Lahsene y los jirones de serpentinitas del anticlinal de Taryat (Melilla, Rif)[END_REF][START_REF] Sánchez-Gómez | Emplazamiento intracortical y desmembramiento extensional de los cuerpos peridotíticos de Ronda y del Rif (Arco de Gibraltar)[END_REF][START_REF] Michard | The Variscan Belt[END_REF][START_REF] Negro | Tectonic evolution of the Betic-Rif arc: new constraints from 40 Ar/ 39 Ar dating on white micas in the Temsamane units (External Rif, northern Morocco)[END_REF]. The rocks of this specific massif have been tentatively correlated with those of the Internal Rif [START_REF] García-Dueñas | El Despegue extensional de Lahsene y los jirones de serpentinitas del anticlinal de Taryat (Melilla, Rif)[END_REF][START_REF] Sánchez-Gómez | Emplazamiento intracortical y desmembramiento extensional de los cuerpos peridotíticos de Ronda y del Rif (Arco de Gibraltar)[END_REF] or the uppermost and most metamorphosed of the Temsamane metamorphic units: the Ras Afraou unit [START_REF] Michard | The Variscan Belt[END_REF][START_REF] Negro | Tectonic evolution of the Betic-Rif arc: new constraints from 40 Ar/ 39 Ar dating on white micas in the Temsamane units (External Rif, northern Morocco)[END_REF].

Our main aim is to establish the structure of the low-grade metamorphic outcrops of the Cap des Trois Fourches sector in order to determine their tectonic evolution and correlation with the Rifian structures. In order to do so we carried a detailed microtectonic

2.-Tectonic setting

The Rif Chain is an Alpine mountain belt bordering northern Morocco (Fig. 1) that in union with the Betic Chain belt in southern Spain form the Betic-Rif orogen (e.g., [START_REF] Booth-Rea | Contrasting structural and P-T evolutions of tectonic units in the southeastern Betics: key for understanding the exhumation of the Alborán Domain HP/LT crustal rocks (Western Mediterranean)[END_REF][START_REF] Chalouan | The Rif Belt[END_REF]Platt et al., 2013, and references therein).

This orogen was formed during the westward drifting of the Alborán domain [START_REF] Andrieux | La structure du Rif central[END_REF][START_REF] Bourgois | D'une étape géodynamique majeure dans la genèse de l´arc de Gibraltar: L´hispanisation des flyschs rifains au Miocène inférieur[END_REF][START_REF] Balanyá | Les directions structurales dans le Domaine d'Alborán de part et d'autre du Détroit de Gibraltar[END_REF], at the same time as the African and Eurasian plates converged (e.g., [START_REF] Chalouan | The Alpine Rif belt (Morocco): a case of mountain building in a subduction-subduction-transform fault triple junction[END_REF][START_REF] Jolivet | Subduction tectonics and exhumation of high-pressuremetamorphic rocks in the Mediterranean orogens[END_REF] during the Oligocene-Miocene times [START_REF] Chalouan | The Alpine Rif belt (Morocco): a case of mountain building in a subduction-subduction-transform fault triple junction[END_REF][START_REF] Chalouan | The Rif Belt[END_REF].

The tectonic model for these movements in the Western Mediterranean area is controversial, although most of them involve the westwards roll back of a SE-dipping slab of Tethys lithosphere below the Alborán domain (i.e. [START_REF] Rosenbaum | Reconstruction of the tectonic evolution of the western Mediterranean since the Oligocene[END_REF][START_REF] Faccenna | Lateral slab deformation and the origin of the western Mediterranean arcs[END_REF][START_REF] Booth-Rea | Crustal types and Tertiary tectonic evolution of the Alborán Sea, western Mediterranean[END_REF][START_REF] Carminati | Geodynamic evolution of the central and western Mediterranean:.Tectonics vs. igneous petrology constraints[END_REF][START_REF] Chertova | Absolute plate motions and regional subduction evolution[END_REF], while others authors propose delamination or convective removal of the subcontinental mantle lithosphere [START_REF] Calvert | Geodynamic evolution of the lithosphere and upper mantle beneath the Alboran region of the western Mediterranean: constraints from travel time tomography[END_REF][START_REF] Platt | Thermal evolution, rate of exhumation, and tectonic significance of metamorphic rocks from the floor of the Alboran extensional basin, western Mediterranean[END_REF][START_REF] Seber | Geophysical evidence for lithospheric delamination beneath the Alboran Sea and Rif-Betic mountains[END_REF]. Seismic studies have delimited a SE-dipping high-velocity slab within the upper mantle beneath the Gibraltar Arc (i.e. [START_REF] Bezada | Evidence for slab rollback in westernmost Mediterranean from improved upper mantle imaging[END_REF][START_REF] Palomeras | Finite-frequency Rayleigh wave tomography of the western Mediterranean: Mapping its lithospheric structure[END_REF][START_REF] Thurner | Evidence for Ongoing Lithospheric Removal in the Western Mediterranean: Ps Receiver Functions Results From the PICASSO Project[END_REF]Mancilla et al., 2015;[START_REF] Villaseñor | Subduction and volcanism in the Iberia-North Africa[END_REF] that together with geochemical data of volcanic rocks in the region [START_REF] Duggen | Geochemical zonation of the Miocene Alboran Basin volcanism (westernmost Mediterranean): geodynamic implications[END_REF][START_REF] Varas-Reus | Sr-Nd-Pb isotopic systematics of crustal rocks from the western Betics (S. Spain): Implications for crustal recycling in the lithospheric mantle beneath the westernmost Mediterranean[END_REF] and the volcanic arc structure of the East Alboran basin (Booth-Rea et al., in press) favours the subduction/roll-back models.

However, delamination of the subcontinental lithosphere at the edges of the subduction system in the Betics and Rif, coeval to slab rollback, is supported by the geochemical [START_REF] Duggen | Deep roots of the Messinian salinity crisis[END_REF], by tectonic analysis [START_REF] Martínez-Martínez | Active transfer fault zone linking a segmented extensional system (Betics, southern Spain): Insight into heterogeneous extension driven by edge delamination[END_REF], and by receiver function data that show a missing orogenic root under parts of the Betics and the Eastern Rif [START_REF] Thurner | Evidence for Ongoing Lithospheric Removal in the Western Mediterranean: Ps Receiver Functions Results From the PICASSO Project[END_REF]Mancilla et al., 2015). Delamination occurred under the continental orogenic crust inboard of Subduction Transfer Edge Propagator boundaries (STEP, [START_REF] Govers | Lithosphere tearing at STEP faults: response to edges of subduction zones[END_REF] at the northern and southern edges of the Betic-Rif orogen (Mancilla et al., 2015).

M A N U S C R I P T A C C E P T E D ACCEPTED MANUSCRIPT evolution of volcanism
From the Mediterranean coast towards the south, three main structural domains compose the Rif belt (Fig. 1 et al., 2000). Bourgois (1980 a, b) has inferred that this main suture is located north of the Internal Zones in the Betic Chain.

iii) External Rif formed of Mesozoic to Cenozoic sediments and metasediments, and interpreted as the North African passive margin of the Tethys Ocean.

Traditionally, the External Rif rocks have been grouped into three main zones: the Prerif, the Intrarif, and the Mesorif zones (Suter, 1980a, b). The Prerif zone is the outermost zone of the External Rif and is located to the south. It comprises a frontal foldand-thrust belt that deforms thin Jurassic and Lower Cretaceous successions detached from the Paleozoic basement of the Variscan Western Moroccan Meseta ("Rides Prérifaines", see [START_REF] Michard | Elements de Géologie Marocaine[END_REF]Ben Yaïch, 1991;[START_REF] Favre | Géologie des massifs calcaires situés au front Sud de l'unité de Kétama (Rif, Maroc[END_REF]. The "Rides Prérifaines" are overlain

M A N U S C R I P T A C C E P T E D ACCEPTED MANUSCRIPT
6 by an olistostromic complex formed of Paleozoic to Cenozoic blocks in a matrix of Tortonian marls ("Nappe Prérifaine", [START_REF] Levy | Maroc septentrional (chaîne du Rif). Partie B, livret guide des excursions A31.C31[END_REF][START_REF] Vidal | Une interprétation nouvelle des nappes du Prérif central (Maroc) et ses conséquences sur la structure de leur substratum autochtone[END_REF]Leblanc, 1975Leblanc, -1979;;[START_REF] Bourgois | D'une étape géodynamique majeure dans la genèse de l´arc de Gibraltar: L´hispanisation des flyschs rifains au Miocène inférieur[END_REF]Suter, 1980a, b;[START_REF] Feinberg | Les séries tertiaires du Prérif et des dépendances post tectoniques du Rif (Maroc)[END_REF][START_REF] Kerzazi | Etudes biostratigraphique du Miocène sur la base des foraminifères planctoniques et nannofossiles calcaires dans le Prérif et la marge atlantique du Maroc (site 547A du DSDP Leg 79)[END_REF].

The Mesorif zone is formed of allochthonous units with Triassic to Paleogene successions thrusting over autochthonous or para-autochthonous successions culminating with Middle-Upper Miocene turbidites and olistostromes. Those lithological successions are thought to be deposited in proximal areas of the African paleomargin (e.g. [START_REF] Chalouan | The Rif Belt[END_REF]. However, recently [START_REF] Benzaggagh | Oceanic units in the core of the External Rif (Morocco): intramargin hiatus or South-Tethyan remnants?[END_REF] have proposed the existence of ophiolitic massifs indicating the opening of ocean-floor basins within the Mesorif domain.

In the eastern Rif, those Mesorif units correspond to the Temsamane units that underwent ductile deformations and IP-IT metamorphism during Alpine times (see Azdimousa et al., 2007, Jabaloy et al., 2015, andreferences therein).

The Intrarif zone includes the distal units derived from the African paleomargin.

These units crop out immediately beneath the Maghrebian Flyschs and Internal Rif and are characterized by a thick accumulation of sediments with ages ranging from Lower Jurassic to Cretaceous. These sediments underwent ductile deformations that developed under diagenetic to anchizone conditions [START_REF] Andrieux | La structure du Rif central[END_REF][START_REF] Asebriy | Evolution tectonique et métamorphique du Rif central (Maroc): définition du domaine Subrifain[END_REF][START_REF] Asebriy | Structure du Rif externe sur la transversale du Massif de Ketama[END_REF][START_REF] Azdimousa | Histoire thermique du massif de Kétama (Maroc); sa place en Afrique du Nord et dans les Cordillères Bétiques[END_REF][START_REF] Azdimousa | Histoire thermique et surrection du Rif externe et des nappes de flyschs associées (Nord Maroc)[END_REF][START_REF] Azdimousa | Lithostratigraphy and structure of the Temsamane unit (eastern external Rif, Morocco)[END_REF]Vazquez et al., 2013). The Mesorif units include the Ketama unit, overlain by the partly detached Tanger unit, and the Aknoul nappe, totally detached and containing the Upper Cretaceous-Eocene succession. [START_REF] Asebriy | Resédimentation d´âge sénonien dans le Rif central (Maroc): conséquences sur les divisions paléogeógraphiques et structurales de la chaîne[END_REF] have defined the Subrif zone located north of the Prerif zone that includes the Intrarif and Mesorif units as defined by [START_REF] Durand-Delga | Données actuelles sur la structure du Rif[END_REF] and (Suter, 1980a,b). In the Eastern Rif (Fig. 2), the External Rif includes three main sets of tectonic units. From bottom to top, it includes: the Temsamane fold-and-thrust stack, the Tanger-Ketama unit, and the Aknoul unit. [START_REF] Monié | Etude géochronologique préliminaire par la méthode 39Ar/ 40Ar du métamorphisme alpin dans le Rif externe (Maroc). Précisions sur le calendrier tectonique tertiaire[END_REF][START_REF] Negro | Tectonic evolution of the Betic-Rif arc: new constraints from 40 Ar/ 39 Ar dating on white micas in the Temsamane units (External Rif, northern Morocco)[END_REF][START_REF] Jabaloy-Sanchez | The structure of the Temsamane fold-and-thrust stack (eastern Rif, Morocco): Evolution of a transpressional orogenic wedge[END_REF]. [START_REF] Negro | Tectonic evolution of the Betic-Rif arc: new constraints from 40 Ar/ 39 Ar dating on white micas in the Temsamane units (External Rif, northern Morocco)[END_REF][START_REF] Jabaloy-Sanchez | The structure of the Temsamane fold-and-thrust stack (eastern Rif, Morocco): Evolution of a transpressional orogenic wedge[END_REF] have proposed the older Oligocene ages correspond to the metamorphic peak during subduction, and those of the Middle to Late Miocene date the cooling during extensional exhumation of the rocks.

The exhumation of the Temsamane metamorphic rocks took place along a major extensional detachment with tectonic transport towards the WSW that is the so-called Temsamane detachment, separating the Temsamane fold-and-thrust stack in the footwall from the Tanger-Ketama and Aknoul units in the hanging wall [START_REF] Booth-Rea | Upper-crustal extension during oblique collision: the Temsamane extensional detachment (eastern Rif, Morocco)[END_REF]. In turn, the sedimentary Mesozoic cover of the Eastern Moroccan Meseta or their

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prolongation as the Middle Atlas underthrusts the metamorphic Temsamane fold-andthrust stack. In contrast, the structure in the western Rif includes structurally higher rock units with the thick Jurassic marbles and Cretaceous slates of the Tanger-Ketama unit (see [START_REF] Vázquez | Evidence of extensionalmetamorphismassociated to Cretaceous rifting of the North-Maghrebian passive margin: the Tanger-Ketama unit (External Rif, northern Morocco)[END_REF] covering the ophiolitic bodies of the Central Rif [START_REF] Benzaggagh | Oceanic units in the core of the External Rif (Morocco): intramargin hiatus or South-Tethyan remnants?[END_REF][START_REF] Amar | Structure and peridotite of Gibraltar arc southern bloc: gravimetric and aeromagnetic evidences[END_REF], and, in turn, these rocks are overthrust by the Maghrebian Flysch units and the Internal Rif Alboran domain rocks.

Below the Rif Chain, the Moho shows strong differences in depth, ranging from more than 50 km below the western and central Rif to around 24 km below the eastern Rif.

These two structural domains are separated by a steep transition zone [START_REF] Mancilla | Crustal thickness variations in northern Morocco[END_REF](Mancilla et al., , 2015;;[START_REF] Díaz | Constraining the crustal root geometry beneath Northern Morocco[END_REF] located beneath the active Trougout-Nekor Fault-system.

GPS data [START_REF] Vernant | Geodetic constraints on active tectonics of the Western Mediterranean: Implications for the kinematics and dynamics of the Nubia-Eurasia plate boundary zone[END_REF][START_REF] Pérouse | Active surface deformation and sublithospheric processes in the western Mediterranean constrained by numerical models[END_REF] and reorganization of the drainage networks [START_REF] Barcos | Study of relief changes related to active doming in the eastern Moroccan Rif (Morocco) using geomorphological indices[END_REF] have recorded the tectonic activity along this Trougout-Nekor fault system. This sinistral transtensional fault-system [START_REF] Asebriy | Evolution tectonique récente de la zone de faille du Nékor: importance paléogeographique et structurale dans le Rif externe, Maroc[END_REF][START_REF] Barcos | Study of relief changes related to active doming in the eastern Moroccan Rif (Morocco) using geomorphological indices[END_REF][START_REF] Poujol | Active tectonics of the Northern Rif (Morocco) from Geomorphic and Geochronological Data[END_REF] accommodates most of the Present-day Western Rif belt displacement towards the WSW with respect to the stable Nubia [START_REF] Poujol | Active tectonics of the Northern Rif (Morocco) from Geomorphic and Geochronological Data[END_REF].

-Geology of the Cap des Trois Fourches area

The rocks of the Cap des Trois Fourches area extend along the Peninsula of Melilla, a North-South elongated cap on the southern border of the Alboran Sea (northeast of Morocco, Figs. 2 and3) in an open antiform striking NE-SW: the Tarjât (also known as Taryat) anticline [START_REF] Guillemin | Le Néogène post-nappes et le Quaternaire du Rif Nord oriental. Stratigraphie et tectonique des bassins de Melilla, de Kert, de Boudinar et du piémont des Kebdana[END_REF]. The normal left-handed Aït Lahsene fault bounds the NW limb of the Tarjât anticline [START_REF] Brahim | Tectonique cassante et états de contraintes récents au nord du Maroc; contribution à l'étude du risque sismotectonique[END_REF][START_REF] Morel | Evolution récente de l'orogène rifain et de son avant-pays depuis la fin de la mise en place des nappes (Rif, Maroc)[END_REF][START_REF] Asebriy | Evolution tectonique récente de la zone de faille du Nékor: importance paléogeographique et structurale dans le Rif externe, Maroc[END_REF]. [START_REF] García-Dueñas | El Despegue extensional de Lahsene y los jirones de serpentinitas del anticlinal de Taryat (Melilla, Rif)[END_REF] and [START_REF] Michard | Serpentinite slivers and metamorphism in the External Maghrebides: arguments for an intracontinental suture in the African paleomargin (Morocco, Algeria)[END_REF] have recognized two tectonic units in the area:

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-The Tarjât Unit [START_REF] García-Dueñas | El Despegue extensional de Lahsene y los jirones de serpentinitas del anticlinal de Taryat (Melilla, Rif)[END_REF] formed of chloritoid-bearing schists, phyllites, quartzites and marbles that underwent MP-LT metamorphism at around 7-9 kbars and 330-430 ºC during the Oligocene times [START_REF] Negro | Tectonic andmetamorphic evolution of the Temsamane units, External Rif (northern Morocco): implications for the evolution of the Rif and the Betic-Rif arc[END_REF][START_REF] Negro | Tectonic evolution of the Betic-Rif arc: new constraints from 40 Ar/ 39 Ar dating on white micas in the Temsamane units (External Rif, northern Morocco)[END_REF]. This unit overlies a detachment underlined by fragments of chloritites and "serpentinites" [START_REF] García-Dueñas | El Despegue extensional de Lahsene y los jirones de serpentinitas del anticlinal de Taryat (Melilla, Rif)[END_REF][START_REF] Michard | Serpentinite slivers and metamorphism in the External Maghrebides: arguments for an intracontinental suture in the African paleomargin (Morocco, Algeria)[END_REF] that separates it from

ii.-the Taïdant Unit [START_REF] García-Dueñas | El Despegue extensional de Lahsene y los jirones de serpentinitas del anticlinal de Taryat (Melilla, Rif)[END_REF] formed of a thin sequence of shales and greywackes attributed to the Carboniferous. [START_REF] García-Dueñas | El Despegue extensional de Lahsene y los jirones de serpentinitas del anticlinal de Taryat (Melilla, Rif)[END_REF]), and Negro et al. (2007, 2008) have previously described the grey chloritoid-bearing micaschists. These micaschists exhibit mineral associations including chlorite + phengite + quartz ± chloritoid ± paragonite ± kaolinite.

The XMg from chloritoid shows values varying between: 0.08-0.14 (see [START_REF] Negro | Tectonic andmetamorphic evolution of the Temsamane units, External Rif (northern Morocco): implications for the evolution of the Rif and the Betic-Rif arc[END_REF]. They document 7-9 kbars and 330-430 ºC metamorphic P-T conditions for the grey schists at the base of the Tarjât unit. Also, they provide evidences for this metamorphism occurring during the Oligocene. The presence of kaolinite substantiates a retrometamorphic event that occurred during the late Miocene times. The previous studies of the metamorphic rocks discuss if they can be ascribed to the foreland of the Rif Chain (the Eastern Moroccan Meseta, Fernandez Navarro, 1911;Suter, 1980), to the Mesorif zone as the continuation of the outcrops of the Temsamane unit [START_REF] Azdimousa | Lithostratigraphy and structure of the Temsamane unit (eastern external Rif, Morocco)[END_REF][START_REF] Michard | Serpentinite slivers and metamorphism in the External Maghrebides: arguments for an intracontinental suture in the African paleomargin (Morocco, Algeria)[END_REF][START_REF] Booth-Rea | Upper-crustal extension during oblique collision: the Temsamane extensional detachment (eastern Rif, Morocco)[END_REF], or to the Internal Rif [START_REF] García-Dueñas | El Despegue extensional de Lahsene y los jirones de serpentinitas del anticlinal de Taryat (Melilla, Rif)[END_REF][START_REF] Negro | Tectonic evolution of the Betic-Rif arc: new constraints from 40 Ar/ 39 Ar dating on white micas in the Temsamane units (External Rif, northern Morocco)[END_REF].

Late Tortonian to Messinian sediments and volcanoclastics rocks, detached from the underlying metamorphic basement, crop out in the central part of the Melilla peninsula forming the Melilla Neogene basin (i.e. see [START_REF] Roger | 40 Ar/ 39 Ar dating of the pre-evaporitic Messinian marine sequences of the Melilla basin (Morocco): a proposal for some biosedimentary events as isochrons around the Alboran Sea[END_REF][START_REF] Münch | Restriction des communications entre l'Atlantique et la Méditerranée au Messinien : apport de la téphrochronologie dans la plate-forme carbonatée et le bassin de Melilla-Nador (Rif nord-oriental, Maroc)[END_REF]and 2006[START_REF] Van Assen | Messinian astro chronology of the Melilla Basin: Stepwise restriction of the Mediterranean-Atlantic connection through Morocco: Palaeogeography[END_REF]and references therein). The northern and southern tips of the peninsula show two volcanic complexes. The northern Cap des Trois Fourches volcanic

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field exhibits rhyolites and rhyodacites with Tortonian ages (9.8 ± 3 Ma; Hernandez and Bellon, 1985). The southern Gourougou stratovolcano composed of Si-K rich igneous rocks spatially associated with Si-poor, Na-rich lavas was active from 6.69 to 3.37 Ma [START_REF] Duggen | Postcollisional transition from subduction-to intraplate-type magmatism in the Westernmost Mediterranean: evidence for continental-edge delamination of subcontinental lithosphere[END_REF].

4.-Description of rocks

Analytical methods for separation of minerals, chemical analysis, X-ray diffraction (XRD), 40 Ar/ 39 Ar dating on white micas, and SHRIMP U-Pb on zircons are described in the supporting information. The field work in the Cap des Trois Fourches area has revealed the presence of a major ductile fault separating the Tarjât Unit [START_REF] García-Dueñas | El Despegue extensional de Lahsene y los jirones de serpentinitas del anticlinal de Taryat (Melilla, Rif)[END_REF] from the underlying Taïdant tectonic unit formed of very low-grade metamorphic rocks and essentially outcropping at the south-eastern part of the massif.

4.1.-Stratigraphy of the Tarjât and the Taïdant unit

The stratigraphic sequence of the Tarjât unit begins with more than 350 m of grey chloritoid-bearing micaschists interlayered with quartzite layers including orthogneiss bodies, first described in this work.

Orthogneiss bodies outcrop in the northern part of the massif near the road to the lighthouse (Figs. 3,4 and 5A). These are metric lens-shaped bodies several decimetres in thickness. These orthogneiss bodies show borders paralleling the main schistosity of the chloritoid-bearing schists. White layers rich in felsic minerals alternating with light grey layers of white mica and biotite (Fig. 5B) define prominent layering. K feldspar is clearly visible as centimetric porphyroblasts surrounded by the layering (Fig. 5B). The main mineral association includes K feldspar + quartz + muscovite + biotite + rutile.

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The sequence follows up section with a ∼10 meters thick quartzite-micaschist package covered by a brecciated dolomitised yellow marble discontinuous level. This marble always shows overlapping contacts over the above described sequence. The serpentinite bodies previously described in the area (see [START_REF] García-Dueñas | El Despegue extensional de Lahsene y los jirones de serpentinitas del anticlinal de Taryat (Melilla, Rif)[END_REF][START_REF] Michard | Serpentinite slivers and metamorphism in the External Maghrebides: arguments for an intracontinental suture in the African paleomargin (Morocco, Algeria)[END_REF] have been found to be chlorite-rich rocks (chloritites according to [START_REF] Michard | Serpentinite slivers and metamorphism in the External Maghrebides: arguments for an intracontinental suture in the African paleomargin (Morocco, Algeria)[END_REF]. XRD data in sample CTF2 shows the presence of chlorite and quartz (Fig. 6). No serpentine mineral group exist in the bulk XRD patterns. If they exist, the abundance of serpentine mineral is less than 1%. Chlorite is the main phyllosilicate component identified from its characteristic reflections (14.18 Å, 7.08 Å, 4.72 Å and 3.54 Å) that differ from reflections of serpentine minerals (7.29 Å, 4.52 Å and 3.65 Å).

The lithological sequence of the underlying Taïdant Unit [START_REF] García-Dueñas | El Despegue extensional de Lahsene y los jirones de serpentinitas del anticlinal de Taryat (Melilla, Rif)[END_REF] consists of ∼300 meters of green and brown shales interlayered with centimetric to decimetric levels of quartzites.

4.2.-Geochronology

Two samples from the orthogneiss bodies have been collected (AP3-F, C3F; see Fig. 3 for location). Samples were divided into two parts. The first one has been used for major, trace elements and isotopes contents analyses, while the second fraction was used to extract zircons using standard separation techniques. The content in major elements ( a lower intercept at -13.1 +105.4 -13.1 Ma (MSWD = 2.0913) (Fig. 8B). The 8 data with a higher age and more concordance yield a 206 Pb/ 238 U Age = 295 ± 4 Ma (mswd= 1.75) (Fig. 8C).

Sample C3F consists of a white mylonitised augengneiss (see Fig. 5B) with centimetric K feldspar porphyroblasts with σ-structures. Zircons are abundant and euhedral to subhedral bipyramidal prisms with dimensions about 250 to 80 µm of major length and 100 to 50 µm width. Most are brownish translucent crystals. Cathodoluminiscence imaging reveals partial metamictic alteration of most of the small zircons and fracture patterns in several crystals; however, well-defined oscillatory zoning can be imaged in several grains (Fig. 8D). U-Pb measurements on 26 different crystals without metamictic alteration yielded moderate to large concentrations of U (349.5-4142.9 ppm) and Th (67.6-902.9

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ppm) with Th/U = 0.05-0.62 (Table 3S in Supplementary material). The data define also a discordia by Pb loss and common Pb 204 (Fig. 8E). The 11 analysis with higher and more concordant ages yield a 206 Pb/ 238 U Age = 290 ± 5 Ma (mswd= 4.32). All the previous data point to a Sakmarian (early Permian) age for the intrusion of the protoliths of the gneisses. 40 Ar/ 39 Ar determinations in micro-populations (2 to 3 grains) of white mica in mylonitized porphyroclasts from the sample AP3-F (Fig. 8F) yield four disturbed spectra with individual total fusion ages between 195.23 ± 0.77 Ma and 205.88 ± 1.52 Ma (Fig. 9, Tables 4S to 7S in Supplementary material) and a weighted mean age of 202.45 ± 0.98 Ma.

In one replica, we obtained a mini-plateau age with most of released Argon on one step, corresponding to 47% of 39 Ar, of 205.49 ± 1.49 Ma concordant with the total fusion age (205.88 ± 1.52 Ma) (Fig. 9A), and the weighted mean age calculated with all total fusion ages. For all the spectra, the age changes with constant Ca/K, suggesting Ar loss from a homogeneous population (e.g. [START_REF] Negro | Tectonic evolution of the Betic-Rif arc: new constraints from 40 Ar/ 39 Ar dating on white micas in the Temsamane units (External Rif, northern Morocco)[END_REF].

Structure

The different tectonic units of the area are separated by a major ductile shear zone roughly striking NE-SW that bounds the upper Tarjât unit from the underlying Taïdant unit. The shear zone is gently dipping towards the NW or NNW. This main ductile shear zone is nicely exposed just below a long section of the road to the lighthouse (Figs. 3 and4). The main surface is always marked by an iron-bearing carbonate mylonite. The mylonite has a very well defined stretching lineation (L p , Fig. 10A) with trends varying between N50ºE and N80ºE and small dips gently dipping as undulating towards the NE and the SW. The S-C ductile structures related to the major shear zone document a top-tothe-WSW sense of movement (Fig. 10B).

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14

A S c crenulation cleavage (Fig. 10D) associated to a NE-SW trending antiform exhibiting a SE-vergence is bending the main fabric of the upper Tarjât unit (Fig. 10D).

The reverse limb of the antiform is also cut and duplicated by another ductile shear zone striking N50ºE that dips 30 to 40° towards the NW (Fig. 10C). This shear zone is also underlined by an iron-bearing carbonate mylonite, nicely exposed near the 403 m summit (Fig. 10D andE Three major faults bound the horst exhibiting the metamorphic basement of the Cap des Trois Fourches area. It includes the Aït Lahsene Fault, the Râs Izemrân Fault, and the Mersa Taïdant Fault, clockwise (ALF, RIF, and MTF, respectively in Fig. 3).

Towards the northwest, there is the Aït Lahsene Fault, with N50ºE strike and dip of 60° toward the NW (Fig. 3). The Fault exhibits two sets of superimposed striations, one To the east, the coast of the peninsula corresponds to the Râs Izemrân Fault that strikes NNE-SSW and has high dips towards the ESE. This normal fault shows a normal regime with a small left-handed oblique component (Fig. 12C).

The Mersa Taïdant Fault (Figs 3, 4, and 12A) is a normal right-handed brittle fault, which extends from the Oued Amekrane to the coast line cutting across all the aforementioned faults (Fig. 3, 4, 12A). This fault has N110ºE strike and dips to the southwest. On the western border of the massif, another normal fault (Oued Amekrâne Fault, OAF in Fig. 3) striking N155ºE bounds the metamorphic basement from the Neogene sediment. This normal fault following the Oued Amekrâne is dipping 80° to the west.

We have measured several small faults along the trace of the Aït Lahsene, Râs Izemrân, and Oued Amekrâne faults (see Figs. 12D to I) that show both normal and reverse slip kinematics. The right-dihedral method [START_REF] Angelier | Sur une méthode graphique de recherche des contraintes principales également utilisable en tectonique et en séismologie: la méthode des dièdres droits[END_REF] allows us reconstructing the palaeostress axes from fault populations. The σ 1 , σ 2 , and σ 3 axes are trending NNW-SSE, subvertical, and WSW-ENE, respectively. A late open-radius antiform exhibiting an E-W trending axes gently deforms the bedding of the Tortonian rocks together with the basement rock, and probably also the aforementioned faults.

6.-Discussion

The geochemistry of the orthogneisses shows that both major and trace elements have been mobilised during the main metamorphism event that agrees with the later

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metasomatic event producing kaolinite in the metasediments (see [START_REF] Negro | Tectonic andmetamorphic evolution of the Temsamane units, External Rif (northern Morocco): implications for the evolution of the Rif and the Betic-Rif arc[END_REF][START_REF] Negro | Tectonic evolution of the Betic-Rif arc: new constraints from 40 Ar/ 39 Ar dating on white micas in the Temsamane units (External Rif, northern Morocco)[END_REF].

However, the data document that the protoliths of the rocks were peraluminous granitoids, and specifically magnesian ones according to [START_REF] Frost | A geochemical classification of granitic rocks[END_REF] (Fig. 5).

In the silicate Earth-normalised diagrams, they have negative anomalies in Ba, Nb, Sr, Zr, and Ti; and positive anomalies in U, Ta, Pb, and P (Fig. 7), suggesting a crustalderived signature. These rocks have low contents in REE, and also have chondritenormalised enrichment in LREE relative to HREE with negative Eu anomalies (Fig. 7).

The low values of 87 Rb/ 86 Sr (3.002 and 10.241) of the orthogneisses suggests that Rb has been mobilized in these rocks agreeing with the previously mentioned metasomatic event, while the 147 Sm/ 144 Nd (0.166 and 0.169), εNd 335Ma (-3.3 and -4.1) and T DM(Ga) (2.0 and 2.2) suggest a significant crustal component that agrees with the crustal-derived signature.

The obtained U-Pb SHRIMP on zircons ages range from 290 to 295 Ma suggesting a Sakmarian (Early Permian) age for the intrusion of the protoliths of the gneisses.

Intrusive bodies at the origin of the protoliths are probably related to the Late Variscan magmatic event that is reported throughout the entire Variscan Belt (i.e. [START_REF] Bea | La naturaleza del magmatismo de la Zona Centro Ibérica: consideraciones generales y ensayo de correlación[END_REF][START_REF] Casquet | El magmatismo varisco de la Zona de Ossa Morena[END_REF]Pereira et al., 2012) The 40 Ar/ 39 Ar age analyses of muscovite porphyroclasts from the mylonites (AP3-F sample) are very difficult to interpret due to the disturbed spectra of all the replicates.

However, it must be emphasized that the muscovite have retained an uppermost Triassic age at around 202 Ma and have not been re-equilibrated during the later metamorphic events [START_REF] Negro | Tectonic andmetamorphic evolution of the Temsamane units, External Rif (northern Morocco): implications for the evolution of the Rif and the Betic-Rif arc[END_REF][START_REF] Negro | Tectonic evolution of the Betic-Rif arc: new constraints from 40 Ar/ 39 Ar dating on white micas in the Temsamane units (External Rif, northern Morocco)[END_REF][START_REF] Jabaloy-Sanchez | The structure of the Temsamane fold-and-thrust stack (eastern Rif, Morocco): Evolution of a transpressional orogenic wedge[END_REF]. This uppermost Triassic age from the sample AP3-F could be interpreted as a cooling age following the heat anomaly related to the rifting leading to the opening of the Tethys Ocean. Whatever is the possible origin of the heat event, the most likely interpretation is a partial re-opening of the system in relation with fluids circulation during the mylonitisation processes but at an undetermined age. The planar-linear fabric (S p /L p ) generated in a non-coaxial deformation with a topto-the-WSW is present in both situations as the main mesostructures and the subsequent SE verging NE-SW trending major folds (F c ) deforming the fabric. Also, in good agreement are: (1) the IP-LT metamorphic conditions recognized in the uppermost metamorphic unit [START_REF] Negro | Tectonic andmetamorphic evolution of the Temsamane units, External Rif (northern Morocco): implications for the evolution of the Rif and the Betic-Rif arc[END_REF]2008), and (2) the 40 Ar/ 39 Ar ages indicating that the main metamorphic event took place during the Chattian-Aquitanian times (Negro et al., 2008;[START_REF] Jabaloy-Sanchez | The structure of the Temsamane fold-and-thrust stack (eastern Rif, Morocco): Evolution of a transpressional orogenic wedge[END_REF]. [START_REF] García-Dueñas | El Despegue extensional de Lahsene y los jirones de serpentinitas del anticlinal de Taryat (Melilla, Rif)[END_REF] and [START_REF] Sánchez-Gómez | Emplazamiento intracortical y desmembramiento extensional de los cuerpos peridotíticos de Ronda y del Rif (Arco de Gibraltar)[END_REF] agents during Tortonian times. This is in good agreement with the evolution described in the Boudinar basin further west [START_REF] Azdimousa | Géodynamique des bordures méridionales de la mer d´Alboran; application de la stratigraphie séquentielle dans le bassin néogène de Boudinar (Rif oriental, Maroc)[END_REF]Galindo-Zaldivar et al., 2015;[START_REF] Jabaloy-Sanchez | The structure of the Temsamane fold-and-thrust stack (eastern Rif, Morocco): Evolution of a transpressional orogenic wedge[END_REF][START_REF] Achalhi | The late Miocene Mediterranean-Atlantic connections through the North Rifian Corridor: New insights from the Boudinar and Arbaa Taourirt basins (northeastern Rif, Morocco)[END_REF]. The last brittle deformation events have recorded a NNW-SSE compression and a WSW-ENE extension of Messinian age. We therefore suggest that the Cap des Trois Fourches Paleozoic rocks are part of the Temsamane fold-and-thrust stack. This interpretation has been previously proposed by [START_REF] Michard | Serpentinite slivers and metamorphism in the External Maghrebides: arguments for an intracontinental suture in the African paleomargin (Morocco, Algeria)[END_REF][START_REF] Michard | The Variscan Belt[END_REF]. Also, it was considered that the As previously mentioned in the geological setting section, the western and eastern

Similarities with the

Rif exhibit a major contrast in their structural level of tectonic deformation. This is in good agreement with the crustal thickness of both areas that are ~50 km to ~ 24 km, respectively [START_REF] Mancilla | Crustal thickness variations in northern Morocco[END_REF](Mancilla et al., , 2015;;[START_REF] Díaz | Constraining the crustal root geometry beneath Northern Morocco[END_REF]. We infer that the crustal transition step between both domains is located along the active Trougout-Nekor sinistral transtensional system [START_REF] Asebriy | Evolution tectonique récente de la zone de faille du Nékor: importance paléogeographique et structurale dans le Rif externe, Maroc[END_REF][START_REF] Barcos | Study of relief changes related to active doming in the eastern Moroccan Rif (Morocco) using geomorphological indices[END_REF][START_REF] Poujol | Active tectonics of the Northern Rif (Morocco) from Geomorphic and Geochronological Data[END_REF] at subsurface shallower depth. This transtensional zone system that involves the lithosphereasthenosphere boundary at depth is considered as accommodating the Present-day movement of the Western Rif towards the WSW with respect to the stable Nubia (see GPS data from [START_REF] Vernant | Geodetic constraints on active tectonics of the Western Mediterranean: Implications for the kinematics and dynamics of the Nubia-Eurasia plate boundary zone[END_REF]. Thus, forming the southern STEP boundary of the Betic-Rif subduction system. Upward, the active Trougout-Nekor system would be the signature of the crustal step (Fig. 13, location of the cross-section on Fig. 2) at shallower depth. The ductile tectonic deformation identified at the Cap des Trois Fourches together with those recognized in the Temsamane area document a major detachment: the Temsamane detachment system, whose hanging wall moved towards the SW [START_REF] Azdimousa | Lithostratigraphy and structure of the Temsamane unit (eastern external Rif, Morocco)[END_REF][START_REF] Booth-Rea | Upper-crustal extension during oblique collision: the Temsamane extensional detachment (eastern Rif, Morocco)[END_REF][START_REF] Jabaloy-Sanchez | The structure of the Temsamane fold-and-thrust stack (eastern Rif, Morocco): Evolution of a transpressional orogenic wedge[END_REF]. To the west, the active Trougout-Nekor fault system [START_REF] Asebriy | Evolution tectonique récente de la zone de faille du Nékor: importance paléogeographique et structurale dans le Rif externe, Maroc[END_REF][START_REF] Barcos | Study of relief changes related to active doming in the eastern Moroccan Rif (Morocco) using geomorphological indices[END_REF][START_REF] Poujol | Active tectonics of the Northern Rif (Morocco) from Geomorphic and Geochronological Data[END_REF] records a sinistral transtensional movement. This fault system cuts the Temsamane detachment, which is displaced downward by about several km bounding the Ketama unit at depth. At Present

M A N U S C R I P T A C C E P T E D ACCEPTED MANUSCRIPT 20
time, this detachment is active bounding the western Rif at depth that is moving as a whole, being the hanging wall of the system.

The cross section at Figure 13 agrees with the roll-hinge model [START_REF] Buck | Flexural rotation of normal faults[END_REF][START_REF] Hamilton | Detachment faulting in the Death Valley region, California and Nevada[END_REF]and Wernicke and Axen, 1988;[START_REF] Lavier | Self-consistent rollinghinge model for the evolution of large-offset low-angle normal faults[END_REF][START_REF] Platt | Stability and localization of rapid shear in fluid-saturated fault gouge: 2. Localized zone width and strength evolution[END_REF] where the Trougout-Nekor fault system is the active section of the detachment whose hanging wall is moving around 4 mm/year -1 towards the WSW. The Temsamane detachment represents the inactive section of the detachment as previously proposed by

Booth-Rea et al. ( 2012) and Jabaloy et al. (2015). The strong thinning of the crust along the eastern Rif, which occurred since the Late-Neogene is proposed resulting from the Temsamane detachment fault system at the southern edge of the Betic-Rif subduction system.

7.-Conclusions

We present new lithostratigraphic and geochemical data from the Cap des Trois Fourches area. We describe and date for the first time mylonitised orthogneisses derived from Late Variscan magnesian peraluminous granitoids. Their protoliths were subsequently involved into the Alpine orogeny and associated metamorphism. We also redefine the major metamorphic sequences from the area and we clarify their tectonic relationship. We present a new cartography of the area defining the extension of the Taïdant and Tarjât units and their internal tectonic deformations. A major ductile shear zone separates the Upper Tarjât unit from the Lower Taïdant unit. Tectonic deformation kinematics of the shear zone documents a top-to-the-west sense of movement.

Also, we have identified a major ductile-brittle detachment fault with a top-to-thewest sense of movement. We infer this detachment being an eastward prolongation of the respect to stable Nubia [START_REF] Vernant | Geodetic constraints on active tectonics of the Western Mediterranean: Implications for the kinematics and dynamics of the Nubia-Eurasia plate boundary zone[END_REF]. The location of the study area (Fig. 2) is shown. et al., 2015). Velocity data of the GPS sites with respect to stable Nubia in red [START_REF] Vernant | Geodetic constraints on active tectonics of the Western Mediterranean: Implications for the kinematics and dynamics of the Nubia-Eurasia plate boundary zone[END_REF]. Location of Fig. 3 [START_REF] Frost | A geochemical classification of granitic rocks[END_REF]. F) Molar (FeOT +MgO)/(MgO) vs SiO 2 [START_REF] Frost | A geochemical classification of granitic rocks[END_REF]). Th-Tholeiitic; Ca-Calc-alkaline; Alk-Alkaline. from the sample AP3-F. To the left, the replica with a mini-plateau age corresponding to 47% of 39 Ar, of 205.49 ± 1.49 Ma, concordant with the total fusion age (205.88 ± 1.52 Ma). To the right, the three replicas without plateau ages (see text for discussion). In every graphic, the box heights are 2σ.

  1) is characterized by very low-to low-grade metamorphic terranes derived from the Mesozoic Maghrebian palaeomargin cropping out in different isolated sectors along the Mediterranean coast (Frizon de

  40 Ar/ 39 Ar ages on white micas and SHRIMP U-Pb dating on zircons.

  Alborán Domain that is an allochthonous terrain mainly composed by metamorphic and sedimentary rocks exhibiting ages ranging from Paleozoic to Paleogene. ii) Maghrebian Flysch units thrusted southward as tectonic sheets mainly formed of Mesozoic-Cenozoic turbidites. They are commonly interpreted as rocks originating from the main suture of the Tethys Ocean (Durand-Delga

  ). The main fabric of the schists is a planar-linear fabric (S p /L p ) with a schistosity (S p ) and a N50 to N80ºE trending stretching lineation (L p )(Figs. 10 F and G). Ductile S-C and S-C' structures within the schists and gneisses and asymmetric σstructures around K feldspar porphyroblasts in the gneisses indicate deformation in a simple shear regime with a SW transport sense. The lower Taïdant unit exhibits a slaty cleavage with N50ºE strike and dips towards the NW. A pervasive crenulation with an axis trending around N20ºE (Fig. 11) is warping the previous penetrative deformation. The whole structure of the Tarjât and Taïdant units is tectonically superposed over the more metamorphic Tarjât unit by a major ductile-brittle horizontal fault near the sea level (Figs. 3, 4 and 12A). The main surface is marked downwards by brittle fault rocks: fault gauges and carbonated fault breccias (Figs. 12A and B). The striations measured in the fault zone at the base of the unit have NE-SW trends and subhorizontal dips. Cataclastic structures such as S-C structures and crushed clast trails indicate a SW sense of movement of the hanging wall.

  latter one parallel the maximum dip line of the fault. The brittle structures on the fault surface indicate a former left-handed strike-slip sense of movement coeval with of the opening of the Cap des Trois Fourches Tortonian basin, and a younger normal sense of movement imprinting Tortonian pyroclastic layer nearby El Addi (Fig.3).

  Temsamane fold-and-thrust stack include far more than the presence of the chloritoid-bearing Paleozoic IP-LT metamorphic unit. The meso and macrostructures described in this work correlate properly with those previously described in the Temsamane mountain range by Frizon de Lamotte (1985), Frizon de Lamotte et al. (1991), Azdimousa et al. (2007), Booth-Rea et al. (2012) and Jabaloy et al. (2015).

  have ascribed the rocks of the Tarjât Unit to the Sebtide/Alpujarride Complex from the Internal Zones of the belt. Because the Taïdant Unit is in the uppermost structural situation, they have proposed this unit to be part of the Ghomaride/Malaguide Complex of the Internal Zones.[START_REF] Michard | Serpentinite slivers and metamorphism in the External Maghrebides: arguments for an intracontinental suture in the African paleomargin (Morocco, Algeria)[END_REF][START_REF] Michard | The Variscan Belt[END_REF] have provided the same tectonic interpretation for the Taïdant Unit being in the uppermost position. However, instead of proposing any relationship with the Rif/Betic Internal Zones they correlated the Taïdant Unit with the Ketama Unit and the Tarjât Unit to the highest most metamorphic Temsamane Unit (i.e. the External Zone of the Rif)(Michard et al., 2007, their Fig. 8).The horizontal brittle-ductile fault at the base of the Taïdant Unit and outcropping at the sea level strongly resembles the fault rocks association, kinematics and geometry of the Temsamane detachment as described by[START_REF] Booth-Rea | Upper-crustal extension during oblique collision: the Temsamane extensional detachment (eastern Rif, Morocco)[END_REF][START_REF] Jabaloy-Sanchez | The structure of the Temsamane fold-and-thrust stack (eastern Rif, Morocco): Evolution of a transpressional orogenic wedge[END_REF]. More precisely, the Cap des Trois Fourches area is similar to the brittle Ait Amrâne klippen and the Khebaba semi-klippe where IP-LT metamorphic rocks are separated by brittle fault rocks from the lowermost Temsamane units[START_REF] Booth-Rea | Upper-crustal extension during oblique collision: the Temsamane extensional detachment (eastern Rif, Morocco)[END_REF][START_REF] Jabaloy-Sanchez | The structure of the Temsamane fold-and-thrust stack (eastern Rif, Morocco): Evolution of a transpressional orogenic wedge[END_REF]. The Tortonian and Messinian sediments and volcanic rocks covering the subhorizontal detachment fault indicate that this fault was exposed at eroding

  Paleozoic rocks of the Cap des Trois Fourches extend eastwards into the Kebdana range and western Algeria. As a consequence, we consider that the Paleozoic sediments and igneous rocks of the Cap des Trois Fourches together with the along-trending similar units are remains derived from the involved in the Rif belt. These units were involved as tectonic sheets in the External Zone of the Rif, and originated most probably from the Eastern Moroccan Meseta. They have first recorded the Triassic rifting events and then the collision between the Internal Zones of the Rif belt (i.e. the Alborán domain) and the Tethysian margin of the Africa plate during the Cenozoic times.

  the des Cap des Trois Fourches area. We provide new U-Pb SHRIMP zircon ages from the orthogneisses indicating a Sakmarian (Early Permian) age for the intrusion of their protoliths. We also determine 40 Ar/ 39 Ar ages in micro-populations (2 to 3 grains) of white micas from the mylonitised orthogneisses with a weighted mean age of 202.45 ± 0.98 Ma. That age is more probably related to a partial re-opening of the system in relation with fluids circulation during the mylonitisation processes, but at an undetermined age.We propose a model of the crustal structure of the eastern Rif, where the brittle detachment represents the inactive section from an active detachment responsible for the Present-day movement of the central Rif with respect to the eastern Rif and the different crustal thicknesses between both sectors. . and Axen, G.J., 1988. On the role of isostasy in the evolution of normal fault systems, Geology 16, 848-851.

Figure 1 .-

 1 Figure captions:

Figure 2 .

 2 Figure 2.-A) Main geological domains of the Betic-Rif orogenic system surrounding the Alborán Sea.

  Fig. 13 profile.

Figure 3 .-

 3 Figure 3.-Geological map of the Cap des Trois Fourches area. See Figure 2 for location. Red stars

Figure 4 .-

 4 Figure 4.-Geological cross-sections of the Cap des Trois Fourches area. See Fig. 3 for location. Key

Figure 6 .

 6 Figure 6.-X-ray powder diffractogram of the chloritite sample CTF2. See Figure 3 for location.

Figure 7 .

 7 Figure 7.-Silicate Earth-and chondrite-normalized diagrams of the orthogneisses (normalization

Figure 8 .

 8 Figure 8.-A) Cathodoluminescence images of representative analyzed zircons of sample AP3-F. See

Figure 9 .-

 9 Figure 9.-Diagrams of cumulative 39 Ar Percent v. Age (Ma) of white mica mylonitized porphyroclasts

Figure 10 .-

 10 Figure 10.-Mesoestructures from the Tarjât unit: A) upper view of the S p foliation and L p stretching

Figure 11 .-

 11 Figure 11.-Mesoestructures from the Taïdant unit: A) view of the main foliation of the green and

Figure 12 .

 12 Figure 12.-A and B) View of the horizontal brittle-ductile fault and fault gouges outcropping at the

Figure 13 .

 13 Figure 13.-A) Crustal model of the eastern Rif and the transition towards the central Rif area. The

  Figure1

  Fig.3

Table 1S in

 1S Supplementary material) are as follow: SiO 2 ≈ 67-75 wt %, Na 2 O + K 2 O ≈ 7-8 wt %, HREE with negative Eu anomalies (Fig. 8; Table 1S in Supplementary material). The rocks also have low values of 87 Rb/ 86 Sr that are 3.002 and 10.241 with values of 87 Sr/ 86 Sr of 0.707600 and 0.729318, being 87 Sr/ 86 Sr 335 Ma of 0.680488 and 0.693285. The values of

	ACCEPTED MANUSCRIPT
	147 Sm/ 144 Nd are 0.166 and 0.169, with 143 Nd/ 144 Nd values of 0.512401 and 0.512369, being
	M the εNd 335Ma of -3-.3 and -4.1 with a T DM(Ga) of 2.0 and 2.2 (see Table 1S in Supplementary material). Sample AP3-F consists of a leucocratic mylonitised augengneiss. Zircons are A N U S C R I P T abundant and euhedral to subhedral bipyramidal prisms with dimensions about 250 to
	low contents in MgO ≈ 0.14-0.24 wt %, high Al 2 O 3 ≈ 14.7-19.7 wt %. Their protoliths are A C C E P T E D
	peraluminous granitoids (ASI≈ 1.1.-1.2) (Fig. 5C, D, E and F). In silicate Earth-normalised
	diagrams they have negative anomalies in Ba, Nb, Sr, Zr, and Ti, and positive anomalies in

U, Ta, Pb, and P (Fig.

7

; Table

1S

in Supplementary material). These rocks have low contents in REE, and also have chondrite-normalised enrichment in LREE relative to 100µm (Fig.

8A

). Most are brownish translucent crystals. Cathodoluminiscence imaging reveals partial metamictic alteration of several of the small zircons. Well-defined oscillatory zoning can be imaged in most of the grains. U-Pb measurements on 31 different crystals yielded moderate to large concentrations of U (427.0-5869.4ppm) and Th (54.0-489.0ppm) with Th/U = 0.06-0.50 (Table

2S

in Supplementary material). The data define a discordia by Pb loss and common Pb with an upper intercept at 271.2 +17.7 -18.8 Ma, and

.

  The early Permian age for the igneous protoliths also indicates that the metasedimentary sequence of the upper Tarjât Unit has a Carboniferous or older age. The age of the sequence of the lower Taïdant Unit cannot be determined in the Cap des Trois

	ACCEPTED MANUSCRIPT
	2008; Jabaloy et al., 2015) suggest an early Cretaceous age for the green and brown shales
	of the lower Taïdant Unit.
	M A N U S C R I P T
	Fourches area. However, similarities with the early Cretaceous (Aptian-Albian) brown shales and quartzites of the intermediate Temsamane units, together with a similar location A C C E P T E D
	below a chloritoid-bearing Paleozoic IP-LT metamorphic unit (Ras Afrou Unit in the
	Temsamane mountain range and Tarjât unit in the Trois Fourches Peninsula, see Frizon de

[START_REF] Frizon De Lamotte | La structure du Rif oriental (Maroc). Rôle de la tectonique longitudinale et importance des fluides[END_REF][START_REF] Frizon De Lamotte | Cinématique des chevauchements néogènes dans l'Arc bético-rifain: discussion sur les modèles géodynamiques[END_REF][START_REF] Azdimousa | Lithostratigraphy and structure of the Temsamane unit (eastern external Rif, Morocco)[END_REF][START_REF] Negro | Tectonic andmetamorphic evolution of the Temsamane units, External Rif (northern Morocco): implications for the evolution of the Rif and the Betic-Rif arc[END_REF]

Acknowledgements

We acknowledge the financial support of research grants CGL2015-71692-P and CGL2015-67130-C2-1-R from the Spanish Ministry of Economy and Competitiveness (MINECO/FEDER, Spain). This project has received funds from the FP7-Marie Curie Action IRSES-MEDYNA funded under Grant Agreement PIRSES-GA-2013-612572. We want to thank Aitor Cambeses for his help with the geochemistry and geochronology of the orthogneisses, and Fernando Nieto for his help with the adquisition and interpretation of the XRD data.