Lghani Menhour
email: lghani.menhour@univ-reims.fr

Brigitte D'andr Éa-Novel
email: brigitte.dandrea-novel@mines-paristech.fr

Michel Fliess
email: michel.fliess@polytechnique.edu

Dominique Gruyer
email: dominique.gruyer@ifsttar.fr

Hugues Mounier
email: hugues.mounier@lss.supelec.fr

A new model-free design for vehicle control and its validation through an advanced simulation platform

Keywords: Longitudinal and lateral vehicle control, modelfree control, intelligent P controller (i-P controller), algebraic estimation, ADAS (Advanced Driving Assistance Systems)

A new model-free setting and the corresponding "intelligent" P and PD controllers are employed for the longitudinal and lateral motions of a vehicle. This new approach has been developed and used in order to ensure simultaneously a best profile tracking for the longitudinal and lateral behaviors. The longitudinal speed and the derivative of the lateral deviation, on one hand, the driving/braking torque and the steering angle, on the other hand, are respectively the output and the input variables. Let us emphasize that a "good" mathematical modeling, which is quite difficult, if not impossible to obtain, is not needed for such a design. An important part of this publication is focused on the presentation of simulation results with actual and virtual data. The actual data, used in Matlab as reference trajectories, have been obtained from a properly instrumented car (Peugeot 406). Other virtual sets of data have been generated through the interconnected platform SiVIC/RTMaps. It is a dedicated virtual simulation platform for prototyping and validation of advanced driving assistance systems.

I. INTRODUCTION

The control of the longitudinal and lateral motions of a vehicle has been widely investigated via model-based techniques (see, e.g., [START_REF] Khodayari | A historical review on lateral and longitudinal control of autonomous vehicle motions[END_REF], [START_REF] Manceur | Higher Order Sliding Mode controller for Driving Steering Vehicle Wheels: Tracking Trajectory Problem[END_REF], [START_REF] Menhour | Coupled nonlinear vehicle control: Flatness-based setting with algebraic estimation techniques[END_REF], [START_REF] Nobe | An overview of recent developments in automated lateral and longitudinal vehicle controls[END_REF], [START_REF] Odenthal | Nonlinear steering and breaking control for vehicle rollover avoidance[END_REF], [START_REF] Poussot-Vassal | Attitude and handling improvements through gain-scheduled suspensions and brakes control[END_REF], [START_REF] Villagra | Robust stop-and-go control strategy: an algebraic approach for nonlinear estimation and control[END_REF], and the references therein). It should be however emphasized that obtaining a "good" mathematical modeling is a difficult task, if not an impossible one, since complex uncertainties and disturbances, like, for instance, frictions, should be taken into account. This is why a first model-free setting [START_REF] Fliess | Model-free control[END_REF] was recently proposed in [START_REF] Menhour | Multivariable decoupled longitudinal and lateral vehicle control: A modelfree design[END_REF]. Although the corresponding numerical results were good, this attempt was suffering from the fact that one of the two flat outputs was depending on some uncertain parameters and from the fact that an accurate tracking trajectory is not guaranteed, especially when the trajectories are characterized by tight bends.

Those tedious features vanish here thanks to a new modelfree approach where:

• the need to exploit the flatness property of a simplified model disappears, • the flat output depending on uncertain parameters is replaced by a simpler and perhaps, more natural lateral deviation.

Our paper is organized as follows. Section II gives a short summary on the model-free control approach. It is exploited in Section III in order to describe a new longitudinal and lateral vehicle control. Section IV displays several numerical simulations, first by using real data from a 10DoF properly instrumented Peugeot 406 vehicle model, then thanks to the interconnected platforms SiVIC and RTMaps. This realtime simulator provides an efficient tool to replace an actual system by a virtual one. It allows advanced prototyping and validation of the perception and control algorithms with quite realistic models of the vehicle, the sensors and the environment. Some concluding remarks may be found in Section V.

In this paper, the following variables and notations, with their meaning will be used:

• V x , V y : longitudinal and lateral speeds in [m/s],

• ψ: yaw angle in [rad],

• ψ: yaw rate in [rad/s],

• T ω : acceleration/braking torque in [Nm],

• δ : steering wheel angle in [deg],

• L f : distances from the CoG to the front axle in [m],

• L r : distances from the CoG to the rear axle in [m],

• I z : yaw moment of inertia in [Kg.m -2 ],

• g: acceleration due to gravity [m/s 2 ],

• m: vehicle mass in [kgm 2 ].

II. A SHORT SUMMARY OF MODEL-FREE CONTROL 1

Model-free control was already applied and used quite successfully in a lot of various concrete examples (see the references in [START_REF] Fliess | Model-free control[END_REF], [START_REF] Fliess | Stability margins and model-free control: A first look[END_REF]). For obvious reasons let us insist here on its applications to intelligent transportation systems: see [START_REF] Abouaïssa | Freeway ramp metering control made easy and efficient[END_REF], [START_REF] Choi | Model-free control of automotive engine and brake for Stop-and-Go scenarios[END_REF], [START_REF] Villagra | Robust stop-and-go control strategy: an algebraic approach for nonlinear estimation and control[END_REF], [START_REF] Villagra | A comparison of control techniques for robust docking maneuvers for an AVG[END_REF], and [START_REF] Menhour | Multivariable decoupled longitudinal and lateral vehicle control: A modelfree design[END_REF]. This last reference was briefly discussed in Section I.

A. The ultra-local model

Replace the unknown SISO system by the ultra-local model:

y (ν) = F + αu (1)
where

• ν ≥ 1 is the derivation order,

• α ∈ R is chosen such that αu and y (ν) are of the same order of magnitude, • ν and α are chosen by the practitioner. Until now from our knowledge, in the context of model-free control, the example of magnetic bearings [START_REF] De Miras | Active magnetic bearing: A new step for model-free control[END_REF] with their low friction, provides the only instance where the order ν = 2 is necessary. Some comments and assumptions on F can be done:

• F is estimated via the measurements of the control input u and the controlled output y, • F does not distinguish between the unknown model of the system and the perturbations and uncertainties.

B. Intelligent controllers

Set ν = 2 in Equation ( 1):

ÿ = F + αu (2)
The corresponding intelligent Proportional-Integral-Derivative controller, or iPID, reads

u = - F -ÿd + K P e + K I edt + K D ė α (3)
where • y d is the reference trajectory,

• e = y-y d is the tracking error and y d is a desired signal,

• K P , K I , K D ∈ R are the usual gains. Combining Equations ( 2) and (3) yields ė + K P e + K I edt + K D ė = 0 where F does not appear anymore. Gain tuning becomes therefore quite straightforward. This is a major benefit when compared to "classic" PIDs. If K I = 0 we obtain the intelligent Proportional-Derivative controller, or iPD,

u = - F -ÿd + K P edt + K D ė α (4)
Set ν = 1 in Equation ( 1):

ẏ = F + αu (5)
The corresponding intelligent Proportional-Integral controller, or iPI, reads:

u = - F -ẏd + K P e + K I edt α (6)
If K I = 0 in Equation ( 6), we obtain the intelligent proportional controller, or iP, which turns out until now to be the most useful intelligent controller:

u = - F -ẏ * + K P e α (7)
C. Algebraic estimation of F F in Equation ( 1) is assumed to be "well" approximated by a piecewise constant function F est . According to the algebraic parameter identification developed in [START_REF] Fliess | An algebraic framework for linear identification[END_REF], [START_REF] Fliess | Closed-loop parametric identification for continuous-time linear systems via new algebraic techniques[END_REF], where the probabilistic properties of the corrupting noises may be ignored, if ν = 1, Equation (5) rewrites in the operational domain (see, e.g., [START_REF] Yosida | Operational Calculus[END_REF])

sY = Φ s + αU + y(0)
where Φ is a constant. We get rid of the initial condition y(0) by multiplying the both sides on the left by d ds :

Y + s dY ds = - Φ s 2 + α dU ds
Noise attenuation is achieved by multiplying both sides on the left by s -2 . It yields in the time domain the realtime estimation

F est (t) = - 6
τ 3 t t-τ [(τ -2σ )y(σ ) + ασ (τ -σ )u(σ )] dσ (8)
where τ > 0 might be quite small. This integral may, of course, be replaced in practice by a classic digital filter. See [START_REF] Join | Intelligent" controllers on cheap and small programmable devices[END_REF] for a cheap and small hardware implementation of our controller. The extension to the case ν = 2 is straightforward.

III. APPLICATION TO A VEHICLE CONTROL

Select, in order to avoid any modeling problem, the following input and output variables:

1) the acceleration/braking torque u 1 = T ω and the longitudinal speed y 1 , 2) the steering wheel angle u 2 = δ and the lateral deviation y 2 .

Newton's second law yields then the two local models:

longitudinal local model: ẏ1 = F 1 + α 1 u 1 (9) lateral local model: ÿ2 = F 2 + α 2 u 2 (10)
Note the following properties:

• Equations ( 9)-( 10) seem decoupled, but the coupling effects are included in the terms F 1 and F 2 . • Equation ( 10) is an order 2 formula with respect to the derivative of y 2 .

For Equation (9) (resp. ( 10)), the loop is closed by an iP (7) (resp. iPD (4)).

IV. SIMULATIONS WITH ACTUAL DATA

The simulations are carried out firstly with Matlab using a 10DoF instrumented Peugeot 406 car as in [START_REF] Menhour | Multivariable decoupled longitudinal and lateral vehicle control: A modelfree design[END_REF], and secondly thanks to the SiVIC 2 simulator [START_REF] Gruyer | A new generic virtual platform for cameras modeling[END_REF], [START_REF] Gruyer | SiVIC, a virtual platform for ADAS and PADAS prototyping, test and evaluation[END_REF], [START_REF] Vanholme | Fast prototyping of highly autonomous cooperative driving system for public roads[END_REF], [START_REF] Gruyer | Simulation of vehicle automatic speed control by transponder equipped infrastructure[END_REF] interfaced with RTMaps platform3 .

Figures 1, 2 and 3 demonstrate that our new modelfree setting gives quite satisfying results, even better than the ones obtained in [START_REF] Menhour | Multivariable decoupled longitudinal and lateral vehicle control: A modelfree design[END_REF] with flat outputs. It should be noticed that the test track which has been considered implies strong lateral and longitudinal dynamical requests. This track involves different types of curvatures linked to straight parts, and all these configurations represent a large set of driving situations. Figure 1 shows that the MFC (model-free control) produces accurate enough behavior for autonomous driving applications. According to the results displayed on Figure 2, the lateral error is less than 2 cm. Concerning the yaw angle output, the resulting error is limited to 0.5 deg. Finally, Figure 3 shows that the control signals computed from the MFC strategy are quite closed to the actual ones provided by the driver along the track. sistance systems. These studies generally take into account an ego vehicle perception and the corresponding vehicle maneuvers (e.g. braking and accelerating). However, in many situations an ego perception is no longer sufficient. Additional information is needed to minimize risk and maximize the security of driving. This additional information requires additional resources which are both time-consuming and expensive. It therefore becomes essential to have a simulation environment allowing to prototype and to evaluate extended, enriched and cooperative driving assistance systems in the early stage of the system design. A virtual simulation platform has to integrate models of road environments, virtual embedded sensors (proprioceptive, exteroceptive), sensors on the infrastructure and communicating devices, according to the laws of physics. In the same way, a physics-based model for vehicle dynamics coupled with actuators (steering wheel angle, torques on each wheel) is necessary. SiVIC meets these requirements and is therefore a very efficient tool to develop and prototype a high level autonomous driving system with cooperative and extended environment perception.

In its current state, this platform includes several types of exteroceptive and proprioceptive sensors, thus communication media. The exteroceptive sensors are mainly the cameras, the laser scanner, and the RADAR. The proprioceptive sensors involve odometers and Inertial Navigation systems. Then communication sources for cooperative systems include both 802.11p communication media and beacon (transponder). For all this sensors and medias, it is possible in real time and during the simulation stage to tune and to fix the sampling frequency and the intrinsic and extrinsic parameters. Moreover, several modes of operating are available and can be modified during the simulation: "Off" and "On" to switch on or switch off a sensor. "Record" in order to collect data in a file, "RTMaps", "DDS", and "Matlab" to send sensor data in external applications. Some examples of the rendering of these sensors are shown in Fig. 4. 2) RTMaps platform: RTMaps is a software which has been originally developed at Mines ParisTech by B. Steux [START_REF] Steux | RTMaps, un environnement logiciel dédié la conception d'applications embarquées temps-réel. Utilisation pour la détection automatique de véhicules par fusion radar/vision[END_REF]. 4 This platform has been developed for the real-time, multi-sensors, advanced prototyping. Its main goal is to manage and to process a great number of raw data flows like images, laser scanner, GPS, odometric, and INS raw data. The algorithms, which can be applied to the sensor data, are involved in several dedicated image processing and multisensors fusion libraries (RTMaps packages). Once these data are recorded and processed, it is very easy to replay them. This type of architecture gives a powerful tool in order to prototype embedded ADAS with either informative outputs or orders to control vehicle dynamics. At each stage, the sensor data and module outputs are time-stamped for an accurate and a reliable time management.

3) SiVIC/RTMaps: an interconnected platform for efficient ADAS prototyping: The interconnection of SiVIC with RTMaps brings RTMaps the ability to replace real-life data by simulated data. Moreover, these interconnected platforms provide a solid framework for advanced prototyping and validation of the control/command and perception algorithms. Indeed, this coupling fully and very effectively allows developing SIL applications (Software In the Loop) including virtual prototypes of vehicles with their proprioceptive and exteroceptive embedded sensors. The real-time virtual data coming from vehicles and sensors modeled in SiVIC are sent to RTMaps. In RTMaps platform, these data can be used as inputs for perception algorithms and control/command modules. Similarly, orders can be sent from RTMaps to virtual vehicles used in SiVIC in order to control them. This chain of design is very efficient because the algorithms developed in RTMaps can then be directly transferred as micro-software on real hardware devices. Therefore, the simulation model can be considered very close to reality (real vehicles, real sensors). The different types of data handled by this interconnection library are shown in Fig. 5.

Several mechanisms have been implemented and tested. The best solution is clearly the optimized FIFO method 4 It is now edited by the company Intempora. which allows the transfer of a great number of data in a short time. It is a very critical functionality in order to guarantee a real-time link between SiVIC and the perception/data processing/control algorithms. In order to correctly manage time, a synchronization module is available. This synchronization allows providing a time reference from SiVIC to RTMaps. Then RTMaps is fully synchronized with SiVIC components (vehicle, pedestrian and sensors). The SiVIC/RTMaps simulation platform also enables to build reference scenarios and allows evaluating and testing of control/command and perception algorithms. In fact, the SiVIC/RTMaps platform constitutes a full simulation environment because it provides the same types of interactivity found on actual vehicles: steering wheel angle, acceleration/braking torques, etc.

From the different modules and functionalities available in both SiVIC and RTMaps platform, we have implemented a complete operational architecture in order to test and to evaluate the Model-Free controller with a real time generated reference. In this architecture, shown in Fig. 6 and Fig. 7, SiVIC provides the environment and complex vehicle modeling. Then data coming from a vehicle observer are sent towards RTMaps platform by using a dedicated interface library. In RTMaps, we take into account these car observer data in order to calculate the longitudinal and lateral control inputs. Then, these inputs are sent back to SiVIC's vehicule and more specifically to the virtual actuators. In this architecture, it is also possible to add an event management to apply some constraints in the simulation (obstacle appearance, vehicle parameter modification, ...), and road side beacons to provide speed limit for different areas. The real time software implementation is presented in Fig. 6.

V. CONCLUSION

For the last past decade, the development of autonomous driving applications is become a key issue for the road transportation domain. In order to solve this problem, a lot of studies and works have been proposed. A great part of these works request an accurate reference and a complex modeling of the system evolution. Unfortunately, the use of a complex model needs the knowledge of both a large quantity of parameters and their operating domain. Often, obtaining these values requests the implementation of expensive experimental means. In this paper, we propose a new modelfree approach which takes into account only the outputs signals in order to assess a control law. In application on two different data bases (actual and virtual), this new modelfree controller shows that important questions about vehicle control could be efficiently processed with rather elementary and simple tools, which do not necessitate furthermore any complex modeling. In the first data base, actual reference data coming from a Peugeot 406 car has been applied and provide accurate enough results in order to be useful in autonomous driving applications. A second virtual data base has been generated with the SiVIC/RTMaps platform. In the SiVIC platform, an accurate reproduction of the Satory's test tracks is available. Moreover, a complex modeling of the car dynamics is provided. We have interconnected this virtual environment with RTMaps platform in order to obtain a SiL (Software in the Loop) architecture allowing to validate our model-free approach. In this second case, even with very strong curvatures, the results are relevant and accurate.

In future works, we would like to investigate the impact of sensor and observer failures on this method. With this new study, we will confirm that the model-free control might also be robust enough in different types of troubles and noises (see [START_REF] Fliess | Model-free control[END_REF], [START_REF] Lafont | Model-free control and fault accommodation for an experimental greenhouse[END_REF]).

Remark 2 . 1 :

 21 In all the existing concrete examples ν = 1 or 2

Fig. 1 .Fig. 2 .Fig. 3 .

 123 Fig. 1. Reference trajectory versus the closed-loop simulated trajectory

Fig. 4 .

 4 Fig. 4. Some exteroceptive types of sensors in SiVIC

Fig. 5 .

 5 Fig. 5. SiVIC/Types of data managed between SiVIC and RTMaps

4 )Fig. 6 .Fig. 7 .

 467 Fig. 6. Real time implementation of the model-free control with interconnected platforms RTMAPS/SiVIC

Fig. 8 .Fig. 9 .

 89 Fig. 8. Reference trajectory versus the simulated closed-loop trajectory

Fig. 10 .

 10 Fig. 10. Control inputs: Wheel torques and steering angles control signals

Fig. 11 .

 11 Fig. 11. Tracking errors on longitudinal speed and lateral deviation

See[START_REF] Fliess | Model-free control[END_REF] for more details.

SiVIC is a professional software of CIVITEC (http://www.civitec.com).

RT-Maps is developed by Intempora (http://www.intempora.com).

This work was partially supported by the French national project IN-OVE/ANR 2010 BLANC 308.


Mr Sávio

Francis De Melo

Sávio Francis De Melo

PhD; Jean Letouzey

PhD Jean-Luc Rudkiewicz

PhD André Danderfer

PhD Dominique Frizon De Lamotte

Mark Rowan
email: mgrowan@frii.com

Bruno Vendeville
email: bruno.vendeville@univ-lille1.fr

Ph.D Chang H Kiang

Ph.D John R Underhill

Structural modelling based on sequential restoration of gravitational salt deformation in the Santos Basin (Brazil

Keywords: Salt tectonics, section restoration, Santos Basin, passive margin, South Atlantic, deep offshore

Structural restoration and basin modelling tools enable to evaluate complex sedimentary basins such as the ones extending along the South Atlantic Brazilian margin. Several structures result from a complex 3D evolution and most commercial algorithms usually consider vertical backstripping solutions, even when the basin evolution is controlled by gravitational instabilities and horizontal tectonic transport. Salt tectonics actually, promotes lateral gliding of the overlying sedimentary pile, whereas poor paleo-bathymetric data increase uncertainty and difficulty of any restoration. Crosssections restoration is proposed, at first, to establish an easier understanding of the 3D geological complexities and to provide guidelines to handle more complex solutions. Two sections extending from the platform to deep waters of the Santos Basin, south-eastern offshore Brazil, have been chosen in areas where salt tectonics is simple enough to be solved by 2D restoration. These sections comprise both extensional and compressional deformation. Regional settings were important to establish the constraints applied on basic boundary conditions such as the overall paleo-bathymetry, the isostatic regional compensation, the salt volume control and the overall aspects related to structural style. Many restoration methods (simple shear, flexural slip and free methods) were used to restore the sedimentary deformation, including the salt gravity gliding. The 2D restoration results are consistent with five major sequences of sedimentary evolution: (1) the mechanical brittle pre-salt deformation, (2) the significant and fast salt deposition, (3) the initial post-salt deformation with predominant rafting tectonics, (4) the Late Cretaceous progradation sequence and coeval compressional evolution of minibasins, and (5) the Cenozoic sequence with less intense salt tectonics. A 1D subsidence analysis based on the 2D restored results is shown as a useful restoration control tool. The 1D results suggest a general proximal to distal filling controlled by salt tectonics. They also allow further discussion about areas with large horizontal gravity salt gliding.

Introduction

Salt tectonics is one of the most complex deformation processes operating in sedimentary basins. For instance, there is no unique nor simple solution to restore complex structural sections involving salt tectonics. Most current methods of sequential restorations, however, are based on geometrical approaches imposed to the geological events. Several gross and poorly controlled simplifications are generally required to simulate such mode of deformation, not really integrated with geological process and properties, limiting applicability and effectiveness of the restoration methods.

The study area of the present work in the Santos Basin was intensely deformed by salt tectonics. This passive margin basin constitutes the southernmost prolific petroleum basin of the South Atlantic Ocean which was developed over stretched continental crust in eastern offshore Brazil (Fig. 1). The deep offshore part -close to the study area -constitutes a new frontier for petroleum exploration. The wide bathymetric expression of the Santos Basin was developed over a thick salt layer, a fundamental element to the evolution of the basin history. Considering differential properties like density and compressibility between evaporites and other sediments, numerical tools are needed to control decompaction restoration and flexural isostatic compensation.

Several authors such as [START_REF] Guerra | Role of halokinesis in controlling structural styles and sediment dispersal pattern in the Santos Basin, offshore SE Brazil[END_REF], [START_REF] Rouby | Least-squares Palinspastic Restoration of Regions of Normal Faulting -Application to the Campos Basin (Brazil)[END_REF] and [START_REF] Szatmari | Salt Tectonics in the southern Brazilian margin (Tectônica de sal na margem sudeste brasileira)[END_REF] have discussed the basin evolution using restoration methods. [START_REF] Cobbold | Reativation of an obliquely rifted margin, Campos and Santos Basin, Southeastern Brazil[END_REF], [START_REF] Meisling | Segmentation of an obliquely rifted margin, Campos and Santos basins, southeastern Brazil[END_REF] and other authors also interpreted the complex thin-skinned deformation above the Aptian salt in this basin using structural analyses and regional interpretation. More recently, a failed sea floor spreading in the southern portion, an outer high located over the São Paulo Plateau and the overall basement compartmentalization of the basin evolution were described in several papers and presentations such as [START_REF] Braga | Magneto-Structural Imaging (MSI) and Regional Basement of the Santos Basin, Brazil[END_REF], [START_REF] Carminatti | New exploratory frontiers in Brazil[END_REF] and [START_REF] Scotchman | A failed sea-floor spreading centre, Santos Basin, Brasil[END_REF].

In this work, a comprehensive restoration technique based on data and tools integration to minimize the strong impact of simplifications on basin evolution results is applied. The workflow also counts on geologic models in order to guide and to constrain the restoration assumptions. It marks the structural modeling character of this work: not just a technique application but an idea development.

A relatively simple 2D workflow based on classical backwards cyclic steps is carried out here: (1) isostatic flexural response to unloading and decompaction; (2) modular fault-related restoration to fit a paleo-bathymetric constraint (a morphologic model supported by well and seismic data); and (3) adjustments in the salt layer, under conservative volume, integrating the bathymetric and isostatic results.

Complementing, the 2D restoration is revisited through 1D complementary analysis, which can be used as a calibration modeling tool, producing more consistent structural scenarios. The workflow developed in the present work intends to be the most rigorously integrated and interlaced as possible, marked by suitability or rightness of the tools and methods aplied. It could be applicable in other basins and complexes situations.

*Manuscript

Click here to view linked References 1 2 3 4 5 6 7 8 9

Geological setting

The Santos Basin constitutes a good example of continental drifting. It results from an asymmetrical partition of the Gondwanian "super-continent" whereby the Brazilian marginal basin became wider than its conjugate African basin. The Santos Basin extends over 352,000 km2 down to 3,000 m water depth. The current knowledge of its architecture comes from just over one hundred wells and numerous 2D and 3D seismic surveys. It is bounded in the northeast by the Cabo Frio High and in the southwest by the Florianópolis Platform (Fig. 1). The studied area outlined by the red polygon covers 6,000 km2.

Stratigraphy

The Santos Basin development can be described by successive evolutionary phases, including its pre-rift evolution, and subsequent rifting and drifting episodes. The stratigraphic description presented herein (Fig. 2) is in agreement with the general description of [START_REF] Carminatti | New exploratory frontiers in Brazil[END_REF] and the stratigraphic chart proposed by [START_REF] Moreira | Santos Basin (bacia de Santos), in Stratigraphic charts (Cartas estratigráficas)[END_REF]. A maximum sedimentary thickness of approximately 12,000 meters was deposited in the Santos Basin depocenters [START_REF] Pereira | Santos Basin: perspectives of a new petroleum province in the Southeastern Brazilian continental platform (A Bacia de Santos: perspectivas de uma nova província petrolífera na plataforma continental sudeste brasileira)[END_REF].

The basin opening started about 135 Ma ago, with a 20 Ma-long period of continental breakup and rifting [START_REF] Moreira | Santos Basin (bacia de Santos), in Stratigraphic charts (Cartas estratigráficas)[END_REF][START_REF] Pereira | Stratigraphy of the Santos Basin: sequences analysis, depositional systems and litho-stratigraphic revision (Estratigrafia da Bacia de Santos: Análise das sequências, sistemas deposicionais e revisão lito-estratigráfica)[END_REF][START_REF] Pereira | Santos Basin (Bacia de Santos)[END_REF]. A thermal intracratonic dome developed in the Late Jurassic. Its collapse and coeval rifting occurred in the Early Cretaceous, leading to the opening of the South Atlantic Ocean [START_REF] Williams | Seismic stratigraphic framework and depositional sequences in the Santos Basin, Brazil[END_REF].

Pre-salt sequences of syn-rift and post-rift phases are included in the Guaratiba Group. The syn-rift sequence is composed of significant basaltic volcanism followed by continental sedimentation in half-grabens formed by block rotation and faulting processes. A major unconformity separates the overlying post-rift Late Aptian sequence, which was deposited at a time when the fault system was less active than during the deposition of older units. The Late Aptian sequence is composed of carbonates and shales typical of a transitional environment from continental to shallow marine.

Although [START_REF] Moreira | Santos Basin (bacia de Santos), in Stratigraphic charts (Cartas estratigráficas)[END_REF] postulated a post-rift stratigraphic position to this package, in disagreement with previous authors such as Pereira and Feijo (1994), this controversy has no implication on the restoration approach carried out here.

The Aptian Salt sequence recorded by the Ariri Formation is about 2,500 m thick on average. This salt formation was quickly and unconformably deposited above the Aptian syn-rift limestones during the transition from continental to oceanic conditions. It extends across the West African and Brazilian continental lithospheres (Karner and Gamboa, 1 2 3 4 5 6 7 8 9

2007), and was deposited under a high sedimentation rate in the order of 1 km over a period of 500,000 years [START_REF] Dias | Stratigraphic and sedimentological analysis of Aptian stage in part of the eastern margin of Brazil and Malvinas Plateau -Considerations about the first marine incursions and ingressions of the South Atlantic Ocean (Análise sedimentológica e estratigráfica do andar aptiano em parte da margem leste do Brasil e no Platô das Malvinas -References Click here to view linked References 1 2 considerações sobre as primeiras incursões e ingressões marinhas do oceano atlântico sul meridional)[END_REF]. The age of the salt is still controversial. It has been attributed either to an early post-rift phase at the onset of oceanic spreading [START_REF] Davison | Geology and tectonics of the South Atlantic Brazilian salt basins[END_REF][START_REF] Gamboa | Evaporites stratigraphy in the South Atlantic: interpretation of seismic and tectonic-stratigraphic control in the Santos Basin (Evaporitos estratigráficos no atlântico sul: interpretação sísmica e controle tectono-estratigráfico na bacia de Santos)[END_REF][START_REF] Henry | Presalt source rock development on Brazil's conjugate margin: West African examples[END_REF][START_REF] Jackson | Role of subaerial volcanic rocks and mantle plumesin creation of South Atlantic margins: implications for salt tectonics and source rocks[END_REF][START_REF] Marton | Evolution of the Angolan passive margin, West Africa, with emphasis on post-salt structural styles[END_REF] or to a late syn-rift stage, being then the last deposits before the onset of oceanic spreading [START_REF] Karner | Syn-rift regional subsidence across the West African continental margin: the role of lower plate ductile extension[END_REF][START_REF] Ian | Tectonics of passive margin salt basins: crustal structure of the Gulf of Mexico and South Atlantic during salt deposition[END_REF].

The drift phase is subdivided into three major sequences, i.e. the Camburi, Frade and Itamambuca groups (Fig. 2), which record the Albian to Cenomanian sequences, an intervening Late Cretaceous progradation episode, and the Cenozoic sequence, respectively. These subsequent post-salt sequences are deformed by gravity-driven tectonics with nonhomogeneous displacements along the basin [START_REF] Assine | Migration depocenters in the Santos Basin: importance for hydrocarbon exploration (Migração de depocentros na Bacia de Santos: importância na exploração de hidrocarbonetos)[END_REF], mainly due to heterogeneities of the salt thickness and detachment surface, as well as to a progressive tilt of the basement.

The Albian to Cenomanian sequences of the Camburi Group include the first deposits clearly related to the drift evolution after deposition of the evaporites. Proximal siliciclastics, shallow-water limestones in the continental shelf, and marls and shales in the distal basin were deposited during the Albian. The overlying Cenomanian sequence records the onset of a retrogradation pattern which accounts for the major marine transgression in the Santos Basin and culminates with the Turonian anoxic OAE-2 event [START_REF] Arai | Geochemical reconnaissance of the Mid-Cretaceous anoxic event in the Santos Basin, Brazil[END_REF]. Most of the Late Cretaceous siliciclastic progradation sequences were deposited in continental paleo-environments, pushing the continental shelf limits towards the most distal portions of the basin. After a strong erosional episode in the Santos Basin, a basinwide regressive episode gradually shifted the coastal line eastward for about two hundred kilometers near the Cretaceous-Cenozoic boundary, building a wide progradational wedge. The Cenozoic sequences are marked by decreasing salt tectonics and a high frequency of sea level variations.

An important sea-level fall is associated with the Paleocene series which presents thin sedimentation in the central part of the basin, probably due to reduced accommodation space and growth of salt structures [START_REF] Assine | Migration depocenters in the Santos Basin: importance for hydrocarbon exploration (Migração de depocentros na Bacia de Santos: importância na exploração de hidrocarbonetos)[END_REF]. A new progradation cycle during the Early Eocene accounted for the shelf break migration towards the basin, followed by aggradation periods during the Late Eocene. A new transgressive trend developed above an Early Miocene unconformity, recording the largest sea-level change of the Neogene period. The Late Miocene began with a global eustatic fall [START_REF] Gradstein | A geologic time scale 2004[END_REF][START_REF] Moreira | Santos Basin (bacia de Santos), in Stratigraphic charts (Cartas estratigráficas)[END_REF] and erosional events correlated with glaciation periods. The last and most recent sediments in the Santos Basin are evolving from proximal sandstones to distal diamictites and muddy wedges.

Based on the stratigraphic chart of [START_REF] Moreira | Santos Basin (bacia de Santos), in Stratigraphic charts (Cartas estratigráficas)[END_REF], fifteen horizons were interpreted on the 2D seismic sections.

These horizons have been used to build two structural sections (Fig. 3), which are about 120 km long and less than 20 km apart. These sections have been subsequently used as input data for the 2D structural restoration analysis, with special attention to the salt tectonics. The São Paulo Plateau constitutes a major deepwater physiographic feature within the Santos Basin. This wide domain, already studied by many authors [START_REF] Mascle | The marginal Sao Paulo Plateau, comparison with the southern Angolan margin[END_REF][START_REF] Kumar | Geologic history and origin of São Paulo Plateau (southeastern Brazilian margin ), comparison with the Angolan margin, and early evolution of the northern South Atlantic. Initial reports of the Deep Sea Drilling Project[END_REF][START_REF] Cande | Mesozoic seafloor spreading bordering conjugate continental margins of Angola and Brazil[END_REF][START_REF] Guimarães | Gravimetric modelling in São Paulo Plateau southern portion and its geological implications (Modelagem gravimétrica na porção sul do Platô de São Paulo e suas implicações geológicas)[END_REF][START_REF] Demercian | Halokinesis in evolution of the south of Santos Basin from the Aptian to Upper Cretaceous (A halocinese na evolução do sul da Bacia de Santos do Aptiano ao Cretáceo superior[END_REF][START_REF] Cobbold | Reativation of an obliquely rifted margin, Campos and Santos Basin, Southeastern Brazil[END_REF][START_REF] Gomes | The Outer High of the Santos Basin, southern São Paulo Plateau, Brazil: Tectonic[END_REF][START_REF] Scotchman | A failed sea-floor spreading centre, Santos Basin, Brasil[END_REF][START_REF] Carminatti | New exploratory frontiers in Brazil[END_REF], developed over an extensively stretched continental crust still attached to the Brazilian margin. The evolution of this plateau is intricately correlated to the overall dynamics of the South Atlantic margins.

Structural framework

Ductile heterogeneities in the basement framework have controlled the evolution of the basin through time. Long NEtrending lineaments have been mapped onshore, and can also be clearly observed in the offshore by means of magnetostructural imaging, at least as far as the Cretaceous hinge line [START_REF] Braga | Magneto-Structural Imaging (MSI) and Regional Basement of the Santos Basin, Brazil[END_REF]. Reactivations of these lineaments and coeval shear zones controlled both the formation of the coastal ranges (i.e., Serra do Mar and Serra da Mantiqueira) since the Coniacian (e.g., [START_REF] Almeida | The system of continental rift bordering the Santos Basin, Brazil[END_REF], and the compartmentalization of the offshore basin.

Inherited from the initial rifting complexity, an aborted proto-oceanic domain has been described in the southern part of the São Paulo Plateau [START_REF] Carminatti | New exploratory frontiers in Brazil[END_REF][START_REF] Gomes | The Outer High of the Santos Basin, southern São Paulo Plateau, Brazil: Tectonic[END_REF][START_REF] Gomes | The Outer High of the Santos Basin, southern São Paulo Plateau, Brazil: pre-salt exploration outbreak, paleogeographic setting, and evolution of the syn-rift structures[END_REF][START_REF] Meisling | Segmentation of an obliquely rifted margin, Campos and Santos basins, southeastern Brazil[END_REF][START_REF] Scotchman | A failed sea-floor spreading centre, Santos Basin, Brasil[END_REF]. It is observed as a triangular shape of shallower bathymetry in gravity and magnetic maps [START_REF] Mohriak | Salt tectonics, volcanic centers, fracture zones and their relationship with the origin and evolution of the South Atlantic Ocean: geophysical evidence in the Brazilian and West African margins[END_REF].

The NE-trending aborted rift propagated northward, making possible to extend laterally this feature up to coeval pre-salt normal faults in the proximal part of the study area (Fig. 1). Although available or published data are limited in the Santos Basin, we assume that its overall crustal thinning, including this aborted rift branch, is similar to the Lavier and Manatschal's model (2006) involving an H block in front of a V-shaped basin (Fig. 4). This crustal thinning evolution, which is broadly distributed in the upper crust and probably reflected basin compartmentalization by shear zones, has been studied in more details by [START_REF] Zalán | Stretching and thinning of the upper lithosphere and continental-oceanic crustal transition in Southeastern Brazil[END_REF].

The current target for petroleum exploration, known as "the Outer High of the Santos Basin" [START_REF] Gomes | The Outer High of the Santos Basin, southern São Paulo Plateau, Brazil: Tectonic[END_REF] or the "Santos External High" [START_REF] Carminatti | New exploratory frontiers in Brazil[END_REF], is located a bit farther to the southeast of the studied area, in the compressive domain. It is an important basement structure in the central part of the São Paulo Plateau. This regional high hosts the recent oil discoveries and the most important plays of the Santos Basin, with a recovery potential of 60 billion barrels of oil equivalent [START_REF] Carminatti | New exploratory frontiers in Brazil[END_REF][START_REF] Gomes | The Outer High of the Santos Basin, southern São Paulo Plateau, Brazil: pre-salt exploration outbreak, paleogeographic setting, and evolution of the syn-rift structures[END_REF]. In the Santos External High area, beyond the study area, the marine sequence record is relatively thinner, with a thickness in the order of 1,000 meters. As attested by recent wells, Aptian carbonate reservoirs were deposited over this wide basement high in shallow-water marine environments [START_REF] Carminatti | New exploratory frontiers in Brazil[END_REF]. Beyond a shelf break, interpreted as the eastern limit of the carbonate buildup, deeper waters occurred. More restricted and shallow depositional environments are expected to develop west of this paleo-high due to the presence of an older salt layer. The understanding of the calcareous facies succession of the pre-salt sequence of the Santos External High is a major exploration challenge. The Santos Basin is the southernmost Atlantic basin where Aptian evaporites were deposited. Climatic conditions were favorable for salt deposition over the São Paulo Plateau and other basins to the north. These conditions were enhanced by the structural alignment of paleo-highs such as the Florianópolis Platform and the São Paulo Ridge (Fig. 1). The highs acted as an efficient barrier at the southern limits of the basin that blocked the marine water circulation derived from the proto-Atlantic Ocean extending farther south during the Aptian salt deposition. Simultaneously, the Santos External High blocked the marine waters coming from the east. A fast (ca. 0.5 Ma) isostatic subsidence of probably more than 1,000 m was induced by the deposition of the thick salt layer. Nevertheless, the existing tectonic barriers blocked the entrance of the surrounding oceanic waters and kept the basin sufficiently closed to account for salt deposition.

Evaporites can flow like a viscous material when they become loaded by sediments. The salt tectonics occurs between the Cretaceous Santos hinge line in the west and the salt pinch-out in the southeast, close to the São Paulo Ridge. They have been deformed and account for the regional spreading and gliding of the overlying sedimentary cover since the earliest depositional stages of the Santos Basin [START_REF] Demercian | Halokinesis in evolution of the south of Santos Basin from the Aptian to Upper Cretaceous (A halocinese na evolução do sul da Bacia de Santos do Aptiano ao Cretáceo superior[END_REF]. The high post-Aptian accumulation rates above the thick Aptian salt sequence produced a relatively shallow bathymetry over the São Paulo Plateau. During the drift phase, both the salt and its overlying sedimentary cover were intensely deformed, resulting in a convergent radial gliding configuration [START_REF] Cobbold | Radial gravitational gliding on passive margins[END_REF], with increasing contraction from the coast towards the distal highs. The most active tectonic stage was the Late Cretaceous, as a response to the loading of progradation wedges over the thick salt layer.

The Cabo Frio Fault marks the transition from a dominantly extensional to a rather compressive salt tectonic domain [START_REF] Mohriak | Salt tectonics and sedimentation along Atlantic margins: insights from seismic interpretation and physical models[END_REF]. The classical minibasins, developing piggyback of the compressive gravity-driven domain beyond this fault, seems to result from a sedimentary bypass through the slope.

Within the São Paulo Plateau, one of the most significant preserved stratified salt columns is located over the Santos External High [START_REF] Freitas | Evaporite depositional cycles of the Santos Basin: an analysis of cyclostratigraphy data from two wells and seismic traces[END_REF]. This package is not really autochthonous, as it has been laterally displaced above the basal detachment during the development of the underlying basement relief. More rugged features observed on section A-A' can be related to the preexisting structural framework, differentiated between the sections A-A' and B-B' (Fig. 3).

Methods

The restoration procedure presented here is based on the following backwards successive steps: (1) sediments removal and decompaction with isostatic flexural compensation; (2) fault-related and salt movement restoration fitting the paleogeometry to a reference target; (3) final paleo-bathymetric adjustments. Compared with other restoration methods (e.g. 1 2 3 4 5 6 7 8 9 [START_REF] Rowan | A systematic technique for the sequential restoration of salt structures[END_REF], this restoration is a simplified derivation which simultaneously considers a flexural isostatic compensation and a vertical decompaction procedure. In addition, it does not consider any direct control, data about eustasy or thermal cooling. All effects of these processes are compensated in the final paleo-bathymetric calibration. Fault-related and salt movement deformations are restored in traditional handmade transformations considering a conservative mass balance for the sedimentary layers, including the ductile salt, and a defined paleo-geometry (shelf-slope-rise) with a coherent structural style of salt deformation. This restoration solution method is performed on RECON-MS, a Petrobras in-house software.

Backstripping with flexural isostatic compensation -Due to compaction laws, the layer decompaction solution with isostatic correction requires a detailed facies definition along the entire section. Only the salt layer is considered not compressible during the decompaction step. Once the uppermost sedimentary layer is removed, the decompaction of the underlying layers due to the removal of its overburden is a discretized calculation along the section. All the remaining decompacted units are referenced to the base of the removed unit. Once the decompaction is done, isostatic compensation with a crustal flexural deformation component is calculated. This procedure can be found (including improvements) in other specific applications (e.g. [START_REF] Roberts | 2D flexural backstripping of extensional basins: the need for a sideways glance[END_REF]. This isostatic approach needs a supplementary paleobathymetry calibration data to fit the real equilibrium. The magnitude of isostatic flexural deformation depends on the applied sedimentary load as well as on the flexural properties of the crust that undergoes the deformation. An unloading approach considering only a local Airy-type backstripping history cannot approximate regional isostasy [START_REF] Bender | Bidimensional reconstitution of the geologic history of sedimentary basins: theory and its application in the Campos Basin (Reconstituição bidimensional da história geológica de bacias sedimentares: teoria e uma aplicação na bacia de Campos)[END_REF][START_REF] Karner | Spectral representation of isostatic models[END_REF][START_REF] Roberts | 2D flexural backstripping of extensional basins: the need for a sideways glance[END_REF][START_REF] Watts | Tectonic subsidence, flexure and global changes in sea level[END_REF].

The sections length (around 120 km) does not represent the entire sedimentary basin load (which extends over more than 400 km beyond the study area), thus producing a narrower isostatic unloading than it really should be. The post-salt sequence becomes progressively shortened in the study area during the sequential restoration of the salt gravitational gliding, which means a similar loss in the representativity of the load. An additional sedimentary load is required in the sections in order to compensate the loading representativity and further border effects. It is needed to simulate the regional extent of the basin as well as to restore in the initial sections the missing portions of the sedimentary cover and of the initial salt layer, which have been subsequently translated outside of the model. The lateral continuity of the Aptian evaporitic sequence (more than two thousand meters thick) towards the Santos External High [START_REF] Carminatti | New exploratory frontiers in Brazil[END_REF][START_REF] Gomes | The Outer High of the Santos Basin, southern São Paulo Plateau, Brazil: pre-salt exploration outbreak, paleogeographic setting, and evolution of the syn-rift structures[END_REF] (Fig. 5) make this lateral insertion of sedimentary section a reasonable assumption.

Modular restoration

To restore the original features of each section, the applied algorithms retain length or area of layers respecting the volume conservation law. Thus, neither gain nor material loss impacts the resulting geological features over time. Considering dominant ductile deformation for the salt layer and brittle deformation for other sediments, whenever needed, the section has been subdivided every restoration cycle into minor individual modules with a similar deformation process.

These modules are limited by well defined geological elements such as stratigraphic contacts, salt diapirs borders, sea floor and/or normal faults. Each module is restored by geometrical transformations in order to better fit the target geometry (reference paleo-bathymetry) and lateral module boundaries (faults, diapirs or section borders). We have used here the simplest methods to obtain simple restoration solutions. The solution implemented for the simple shear transformations in the software is able to preserve the modules' areas on the 2D restoration results. These shear transformations were used to restore brittle modules in the extensional deformation domain and also in less deformed situations of the distal domain. Flexural unfolding transformations preserving length on the template bed direction and parallel to the unfolding axes were preferentially used to restore most of the folded minibasins modules. Considering that the major deformation is concentrated close to the faults and diapirs flanks, sometimes partial restoration steps were superimposed, increasing shear restoration rates to better restore some intensely deformed borders. Sometimes part of the salt diapir was included in the module to smooth the rugged fault or diapir geometries. All these operations could be similarly reproduced with any commercial restoration software.

In contrast with other brittle sedimentary rocks, the ductile rheology of the salt layer was treated by free adjustment to other restored modules. The salt layer thickness was modified to conform the differential deformation between its overlying and underlying layers. The degree of freedom of this salt operation was established by structural coherence, a factor discussed further below, always respecting the limits of the restored overburden. A constant amount of salt is an approximate hypothesis applied only under this overburden. Along the whole section, it is not a reliable hypothesis for the three-dimensional gravitational gliding of the study area. The lateral "void" created due to the lateral shortening of the restored extensional domain is filled as explained before.

Paleo-bathymetric referential geometry

The 2D restoration approach requires paleo-bathymetric profiles at each incremental step to which the basin-driving subsidence should be adjusted. The Santos Basin is characterized by a wide and shallow continental margin made up of a thick wedge produced by high accumulation rates of sediment gliding above the Aptian salt. This margin has a particular development in the basin -700 km offshoredecreasing the brittle sedimentary thickness over distal portions of the São Paulo Plateau. The margin development allows to interpret an evolution with gradual changes on the shelf / slope / rise geometry, always controlled by highs at the distal positions.

The shelf / slope / rise limits can be recognized by their general characteristics. The continental shelf domain is an extended, flooded and almost flat perimeter of the continent associated with the coastal plain, with a water depth usually 1 2 3 4 5 6 7 8 9 limited to 200 m [START_REF] Pinet | Invitation to oceanography[END_REF]. In the case of the Santos Basin continental shelf, it is exceptionally wide (in the order of 200 km). The shelf ends when the slope gradient abruptly changes at a point called shelf break. This point was quite easy to interpret in the seismic sections for the different post-salt interpreted horizons. Beyond this gradient break, the average gradient of the continental slope is 3°, with a maximum value of 10° [START_REF] Gross | Oceanography: a view of the Earth[END_REF]. The transition to the continental rise is marked by another gradient change at the foot of the continental slope, beyond which a sedimentary pile was still depositing. The topographic gradient of the continental rise is intermediate between the previous domains, in the order of 0.5-1°. In the Santos Basin, it merges with the deeper oceanic part of the abyssal plain through the São Paulo Ridge topography.

The shelf break and the foot of the continental slope were interpreted for each different horizon on the 2D seismic data in the study area (Fig. 6), as well as their general paleo-geometry position through time. These points provide key references for the shelf / slope / rise target geometry during the restoration of modules. The final geometry was ultimately calibrated by the available paleo-environment data from wells. Additional uncertainties can be considered about the proximity and possible similarity of the shelf break point with the axis of the Cabo Frio roll-over fault. The basal points called foot of the continental slope are always located on the hangingwall of the Cabo Frio Fault in the study area.

Every individual decompacted module has been restored to fit the target geometry of the restoration timing as a first approximation. Some difficulties arise to adjust the isostatically decompacted layers to this target geometry. They will be accommodated through the salt layer restoration and, eventually, local isostatic adjustments in the brittle pre-salt set. It is important to remember that both thermal-subsidence and eustatic processes are not considered in the calculations, but they will be compensated by the paleo-bathymetric calibration.

Structural consistency

The most important criterion for the restoration concerns the structural consistency. The structural evolution from salt deposition to present time results from gravity gliding and progradation above a thick and ductile salt layer. The extensional features occur in the proximal parts of the sections, i.e. in the platform and upper slope domains.

Compressive gravity-driven structures and the minibasins development are restricted beyond the toe of the continental slope, where relatively thinner post-salt layers are observed. During the gravity gliding deformation, the thick salt layer gradually becomes more deformed.

Once the layer is locally depleted or welded, either in the footwall of the extensive growth faults, or in the compressive domain below some minibasins, both the overburden and salt thicknesses must be consistent with the paleo-bathymetry.

This must be checked every restored cycle. If erosion features observed on the slope domain are interpreted as a local restriction for accommodation and/or sediment bypass, no major thickness variation would be expected at these positions 1 2 3 4 5 6 7 8 9

in the salt layer restoration. On the other hand, if a thicker layer is deposited after salt withdrawal, either due to local collapse or gravity slide, this shift must also be consistent with the paleo-bathymetry in the salt layer restoration.

If salt thickness variation is required through time, certain features should be avoided, i.e. the successive random-looking opening and closing of salt windows as well the random increase and decrease of the salt thickness. In all these situations, the local subsidence rates applied to brittle layers and deformation rates of the underlying ductile salt layer should be consistent with the bathymetry variation.

Restoration and discussion

Fourteen different restoration outcomes are presented as restoration results for the geological evolution of fifteen interpreted horizons in the two sections, A-A' and B-B'. These results were obtained following the procedure already described above. The older three restoration outcomes are related to deformation of the pre-salt sequence when brittle tectonics was prevalent. They are strongly different from the other eleven restoration cycles which are recording the effects of thermal subsidence and ductile salt deformation. The pre-salt sequence is the first of five major sequences considered in the structural evolution to account for the different observed architectures. The subdivision of the post-salt sequences can be explained by the major factors controlling salt tectonics: the preexisting relief at the salt deposition time and the sedimentation rate.

They provide different conditions of instability for the gravitational gliding and also different ratios of thickness between the salt layer and its overburden through time.These various aspects of salt tectonics have been already well discussed by several authors (e.g., [START_REF] Cobbold | Radial gravitational gliding on passive margins[END_REF][START_REF] Weijermars | Rheological and tectonic modeling of salt provinces[END_REF][START_REF] Lerche | Salt and sediments dynamics[END_REF][START_REF] Garcia | Three-dimensional study of effects of halokinesis in passive margins (Estudo tridimensional de efeitos da halocinese em margens passivas)[END_REF][START_REF] Mohriak | Salt tectonics and sedimentation along Atlantic margins: insights from seismic interpretation and physical models[END_REF][START_REF] Hudec | The paradox of minibasin subsidence into salt: clues to the evolution of crustal basins[END_REF]. The five sequences are described below.

Pre-salt sequence

The quality of the subsalt seismic imagery is not good enough here to solve uncertainties related to the pre-salt layers. In general, the tilted blocks involving the basement and synrift strata beneath the base of the salt were defined only by few faults without any good definition of the dipping attitude of infra-salt series (Fig. 8).

The observed unconformities are not well mapped continuously either, and no data about the target relief for these sequences are available. The restoration for these sequences was strongly marked by rotation and an important extension is observed in the proximal deep basement domain. This latter feature is consistent with the hypothesis of a northward lateral prolongation of the brittle normal structures described earlier farther south in the failed spreading centre (Fig. 1). It seems also possible that this structural low was already formed before the salt deposition time. The geometry at the restored scenario of the pre-salt sequence top predates the conditions to the salt deposition. However, the lack of bathymetric data prevents any secure calibration and therefore, this geometry remains quite speculative, resulting only from the isostatic and structural adjustments applied during the restoration. Ultimately, the pre-Aptian basement architecture is assumed here to have been less deformed than the present-day architecture of the pre-salt layers derived from the interpretation of seismic images.

The Aptian Salt sequence

The salt layer glided progressively toward the deeper centre of the basin, due to gravitational instabilities (Fig. 9). The light pink portion of the salt layer represents the amount its restored movement. In the study area, a very heterogeneous salt layer presents different average thickness in each section: it is around 1,600 m-thick in section A-A' and only about 700 m-thick in section B-B'. A large amount of salt was pushed toward the distal portions of the basin, outside of the study area. However, this salt still must be taken into account when restoring the sections. Due to the strong isostatic compensation response, part of the basement tilting was modified in order to generate enough accomodation space and to restore a more homogeneous salt layer over the preexisting rift geometry. The resulting salt layer thickness is about 2,800 m for section A-A' and about 1,200 m for B-B'. These differences were due the initial rifting geometry but also due to isostatic differential effects in both sections. A very smoothed yet not flat geometry was proposed here for the top of the restored salt layer at its deposition time. Considering the available seismic data and the significant superimposing effects of a continuous salt deformation, it was not possible to interpret any structural feature deforming the Aptian salt before deposition of the clastic and carbonate overburden units.

Albian to Cenomanian sequences

The first post-salt sequences include the deposition of Albian carbonates and part of the Late Cretaceous marine siliciclastics. These sequences involve several fault-separated modules with gaps of several kilometers in both sections, including some uncertainty about their extent in some intermediate modules (Fig. 10). The simply deformed modules document the large magnitude of raft tectonics operating at the onset of halokinesis. The great salt volume associated with a still thin overburden favours a fast gravitational gliding of the latter, resulting in lateral gaps where the Albian-Cenomanian cover was progressively displaced. Different sedimentation domains and paleo-environments were linked with the shelf / slope / rise geometries, respectively. A relatively thick salt layer is interpreted in the shelf / slope portions whereas thin and folded sediments are observed in the rise domain.

The thickness variations interpreted in the seismic data for the Albian and Cenomanian layers show a thick proximal portion developed in continental shelf and slope domains. An underlying thick salt layer provides the initial minimum basin amplitude to accommodate the carbonate shelf development. Thin and folded distal Albian carbonates interpreted as continental rise deposits are clearly restored in their initial folding stage and reconnected at their correct paleobathymetric position (Fig. 11). In the next steps, still before the development of the classical minibasins, they were translated eastward by the rafting tectonics. The carbonates thickness variations resulted in a differential rheology pattern, which controlled the Cabo Frio Fault development. Restoration results suggest that the Cabo Frio Fault evolution is correlated with the progradation of the thicker overburden and the squeezing of the salt towards the thinner portion of the basin located at the local structural high currently observed in the middle of the sections.

Late Cretaceous progradation sequences

During the massive progradation of the Upper Cretaceous, the salt movement has built multiple overburden compartments limited by faults or salt structures (Fig. 12). The proximal area is initially characterized by a thicker post-salt package, already compartmented by diapirs with antithetic tendency in a restricted area behind the foot of the slope. The slope advances as a consequence of the progradation event and seems to control the Cabo Frio Fault development since its onset. Structural and thickness differences among these Late Cretaceous restored outcomes are observed in both sections, denoting the complex evolution of the progradation in the hanging wall of the Cabo Frio Fault. The general antithetic tendency is not clearly noted in part of section A-A'. A significant basinwards retreat of the Cabo Frio footwall is restored and little or no fault gap will remain to be restored in subsequent phases. Major depocenters can be easily noted beyond the continental shelf. The minibasins became more developed during this progradation. Such regional shift of the 1 2 3 4 5 6 7 8 9 sedimentation pattern was already described by [START_REF] Assine | Migration depocenters in the Santos Basin: importance for hydrocarbon exploration (Migração de depocentros na Bacia de Santos: importância na exploração de hidrocarbonetos)[END_REF]. The location of these depocenters is probably controlled by a bypass through a continental shelf blocking against the local structural high, and by a local ramp adjustment in the Cabo Frio Fault. Initial salt windows are formed beneath locally thick post-salt depocenters.

Tertiary sequences

The top and most recent layers are the least deformed (Fig. 13). They present limited deformation compared to the final stages of salt tectonics. These layers were deposited under moderate sedimentation rates, not enough to induce significant thickness variation or salt deformation. The post-salt overburden is already very thick and there are many welding points and salt windows to block the salt gliding.

The Cenozoic evolution was the easiest to restore within the study area. However, the isostatic response shows very limited accommodation space near the slope domain, close to the salt growing structures where local thickness variation and small erosional traces are observed in seismic data (Fig. 14,detail 1). If these constraints point uncertainties about the isostatic parameterization, they also invoke some compression due to squeezed underlying salt structure. The erosion features on the Miocene horizon produce diagnostic roughness on the horizon surfaces that can be smoothed in order not to transfer them downwards. Ongoing activity of fold growth associated with the salt diapirism at the borders of the minibasins beyond the Cabo Frio Fault cause the uplift and erosion of the adjacent flanks of the minibasins (Fig. 14,detail 2).

Isostasy

Applied as lower boundary conditions to the sedimentary layers below the salt during restoration, the calculations for the flexural isostatic compensation consider the entire loads applied to the mantle by the basin infill and crust. A potential crustal weakness in the Santos Basin was considered with values of 5 km for the effective elastic thickness and 2.78 g/cm3 for crustal density along the whole section and during all the geologic time. The crustal thinning can be estimated by horizontal stretching or synrift sedimentary loading as in the models of [START_REF] Mckenzie | Some remarks on the development of sedimentary basins[END_REF], [START_REF] Wernicke | Low-angle normal faulls in the Basin and Range Province: nappe tectonics in an extending orogen[END_REF], or by formation of weak ductile shear zones as in the model of Lavier and Manatschal (2006), but no specific study has been done to measure these parameters that were arbitrarily assigned. These are sensitive parameters. Using them, it is possible to note gentle undulations with amplitudes of up to 50 meters high on the isostatic compensation results, in phase with the paleo-environmental adjustments required to restore the sections. On the other hand, if we use values of 20 km for elastic thickness and 3.33 g/cm3 for crust density, for example, then the flexural isostatic compensation for the removal of the upper layer (the most recent sediments) would be 18 % deeper. In contrast, the heterogeneities of diapirs, 1 2 3 4 5 6 7 8 9

minibasins and growth faults with a wavelength of a few tens of kilometers would not cause any noticeable differential isostasy at the scale of the restored sections. One simplified and homogeneous crust with a single elastic thickness through space and time can also be unrealistic given the basement rheological heterogeneities. Moreover, the crustal elastic thickness could vary with both its physical integrity and with the thermal regime to which it is submitted. Difficulties to set the restored scenario into the bathymetric limits established by data and the isostatic response can be observed on the results, mainly in restoration cycles comprised between Eocene to recent times (Figs. 13 and14). According to the restoration progression in the earlier stages (from Albian to Maastrichtian), even if the salt tectonic is more intense, a thicker salt layer gives more freedom to restore and adjust the restored paleo-bathymetric model. An important limitation of the restoration tool is the fact that no isostatic effect for the repositioned restored sedimentary masses is recalculated. This can be observed in the isostatic magnitude of the restored Cenomanian outcome for section B-B' (Fig. 10) where the isostatic response to the removal of the first progradational deposits (Fig. 12, dark orange layer) is noted in the basal geometry of the restored Cenomanian outcome, without any recalculated effect of the thicker restored salt layer. The more layers are interpreted or interpolated in a section, the more this isostatic deviation could be minimized, i.e., shorter time intervals from one restoration phase to the other represent more frequent repositioning and smaller lateral transfers of restored masses. However, the effect remains in the accumulated result.

Bathymetry

Applied as upper boundary condition to every post-Aptian restoration cycles, the bathymetry model proposes target geometries with low resolution (according to the available data). The uncertainties in the bathymetry model are represented by large intervals of time and wide ranges of water depth (Fig. 15). In the deeper portions and for several restoration cycles which have no data available, the bathymetric model was freely extrapolated. A critical point was found at the evaporites deposition time. The model assumes a preexisting low, not invaded by oceanic waters, since the isostatic effect produced by the thick salt layer requires additional space so that its fast and continued deposition does not create positive relief (there is no salt deposition on mountains). For the older units, deformed under a rifting tectonic regime, there are no paleo-environmental data for calibration and irregular reliefs were produced by the restored rotated blocks. It is not sufficient to draw the preexisting low geometry (Fig. 8). The problem is obvious in the 1D subsidence geohistory graphics discussed ahead. Applied throughout the section to all restored cycles after salt deposition, a solution to the lateral movement of masses due to the salt gliding takes into account different limitations for bathymetry and isostasy in each situation. This handmade solution aims at a structural coherency through time so that there are no observed alternations of thickness or controversial structural inversions. Intense salt deformation starts from an initial scenario with more homogeneous salt thickness, with longer wavelength for domes and diapirs while overlapping clastic sediments partially expel the underlying salt. All positive reliefs of salt were cut and compensated in the restored salt layer. Situations where salt is locally cropping out at the seabed are consistent with clastic sediments flanking laterally the structures which are involved in progressive unconformity and differential compaction processes, and are covered by a cap rock at the top (Fig. 16).

The partial accounting of the evaporite layer for each structure is compatible with the deformation history. A larger initial volume of salt in the proximal part of the section migrates progressively towards the structural high in the section center, pushing massive clastic material to more distal portions. The difference of salt material between the two sections results in a different structural restoration for each one. The salt laterally flowing out in each section is not proportional to the salt existing at present day in the section. It increases from 75 % in the A-A' section to 160 % in the B-B' section. Whereas the amount of salt is 2.4 times greater at the present day in the A-A' section than in the B-B' section, this relationship is only 1.6 times for the Aptian restored outcome, at the initial deformation stage of salt sequence. These variations suggest that the distribution of salt was spatially more homogeneously in the past and the salt layer was more efficiently pushed away in the B-B' section. The restoration solution considered no synchronism between the extension processes in the salt gravity-driven deformation domain and those deforming the layers below the salt. The accumulated extension represents an increase of almost 60% for the section in the package deformed by salt tectonics in the study area. The accumulated extension for the brittle pre-salt domain represents an increase of only approximately 6%. The deformation kinematics is different below and above the ductile salt layer in the study area. They were independent. The salt layer worked as a full detachment. The gravity-driven deformation above this rheological limit showed a more stretched total extension. The results for the brittle deformation domain below this limit are consistent with the assumption of [START_REF] Moreira | Santos Basin (bacia de Santos), in Stratigraphic charts (Cartas estratigráficas)[END_REF]. For these authors, the master faults of the rift phase ceased their activities or suffered rare reactivations after the deposition of Barra Velha Formation (Fig. 2) and this deformation, almost totally produced before the salt deposition, was fully restored during the restoration cycles of the rifting phase.

Geohistory based on 1D modelling

Gravitational mass gliding is not usually considered in basin modelling studies, which rather focus on thermal or subsidence aspects. Subsidence history graphs based on wells or pseudo-wells allow simple and useful evolutionary analysis where some implications and consequences of a large horizontal gravitational mass movement for the petroleum 1 2 3 4 5 6 7 8 9 systems could be observed. In many previous 1D studies, phenomena related to salt deformation were solved by the simple salt thickness variation (diapirism). The restoration results to the spatial deformation of the structures through time gave new dimensions for 1D modelling studies, with new approaches for time and space. The points of a fictive vertical line composing a pseudo-well in the section at present day came from upstream positions in the former restoration outcomes, due to a differential motion controlled by the cumulative amounts of extension through time. On the other hand, a fictive vertical window in the same section position shows how the overburden that glides to downstream situations is progressively replaced by the former neighboring overburden. For instance, the initial overburden that was deposited above this fictive point in Albian times has been moved away, being now replaced by another segment of the overburden which was deposited farther west, due to the ongoing gravitational gliding. These approaches can be differentially applied to calibrate thermal models based, for example, on vitrinite reflectance data from younger layers and to analyze the evolution of a source rock deposited below the salt layer. Built from restored sections results, the subsidence and overburden historical graphs here presented (Fig. 17) replace the traditional image of layers under increasing compaction by layers under tectonic movement. The relevance of the results on thermal effects that can be analyzed with this approach depends on the magnitude of the accumulated lateral movement that the system has undergone. As most of the thermal data are obtained in more recent layers and their lateral shifting due to the gravitational gliding is not so large, no great differences are observed compared to a traditional approach. However, for thermal data obtained in a stretched layer that was moved kilometers away, the difference may be significant as, for example, when the layer is moved from a diapir flank to an overburden position of a source rock kitchen. These graphs include not only the lateral motion of bodies resulting from gravitational gliding by halokinesis but also illustrate a reference evolutionary scenario to constraint various parameters such as bathymetry and isostasy. Even if a bathymetry history was designed as a coherent evolutionary model, some imperfections can be observed through time in a few restoration outcomes, resulting from handcraft restorations of the modules targeting low-resolution bathymetric data.

Without any control for the restoration of the older units, a dry depression is postulated to the pre-salt sequence, prior to the deposition of a thick salt layer, especially when the salt isostatic response is too small to prevent the creation of a positive relief of salt above sea level. Following this transitional isostatic jump provided by salt deposition, a shallow marine deposition took place during the Albian and gradually changed to a scenario of maximum water depth observed at the Turonian. This trend toward restoration cycles involving even deeper waters is reversed by a progradational clastic sedimentation in the Late Cretaceous.

Since then and until the present day, an evolutionary change accounted for the progressive building of the current basin configuration, during a period characterized by slower salt tectonics. The initial restored salt layer is very thick in all graphs. It allows smoothed bathymetry adjustments to all isostatic calculations, considering the salt layer as a compensating element. The major adjustment problems seem to stand out at the transition between the five evolutionary 1 2 3 4 5 6 7 8 9 sequences described before. Even if there is uncertainty about the initial thickness of salt, the restored salt volume in the results seems to be excessive. Assuming a large availability of salt, these 1D graphs suggest that most of the accommodation space created during the salt tectonics is due to the lateral expulsion of salt under the continuous burial of the Santos Basin, providing a good summary of the progradation history (Fig. 17). Pseudo-well 1B shows significant proximal sedimentation easily accommodated in Albian to Cenomanian times; whereas pseudo-well 2A shows Late Cretaceous progradation and pseudo-well 4A shows Cenozoic representative thickness. The clastic progradation from Late Cretaceous imposes greater deformation on the salt layer. Pseudo-wells 1B, 2A and 4A in Figure 17 are positioned in post-salt depocenters (salt windows), from where thick salt layers had been gradually squeezed at different times (Turonian for pseudo-well 1B, top Cretaceous for pseudo-well 2A and Miocene for pseudo-well 4A). In contrast, pseudowell 3B is positioned above a thick salt wall close to the Cabo Frio Fault. This pseudo-well shows the Late Cretaceous evolution of a minibasin, coeval with a progradation event. It also shows that the salt layer underwent a relatively continuous thickening during its lateral gliding away from more proximal areas. Major problems found in these graphs are linked to periods with the higher sedimentation rates: the more intense is the deformation under higher clastic supply, the greater are the difficulties to set bathymetry and isostasy for the restored timing. These graphs represent a good quality control for the restoration process itself. Because the entire restoration process has some intervention from the interpreter, several deviations could be unintentionally introduced in the meantime. The simultaneous visualisation of these 1D graphs can be a useful tool to identify the critical points and to get better results.

Conclusions

The approach integrating structural restoration tools with isostatic control and paleo bathymetric model is very important to the obtained results. The configuration of the transition from rifting to drifting phases is a consequence of the salt tectonics backward restoration.

Aparently, the results help to characterize the general complex framework for the geometry of the salt depositional environment, but they are not conclusive to provide insights about the pre-existing rifting depositional domains and facies.

For the post-salt sequences, deformed by halokinesis, the brittle clastic package developed early in the proximal domains in contrast with the thin sequences of the distal portions, shaped by ductile rheology of the thick salt layer. In the latter domain, these thin sequences either behave as small rafts during early extension or develop a subsequent and continuous compression in the minibasins area.

A conservative salt volume is not a realistic constraint in the study area. A first approximation was provided by the 2D nature of the restoration while salt movements occur in a complex 3D world. In addition, the extrapolated salt brought from distal areas, coherent with regional knowledge, allows a more realistic restoration scenario for both A-A' and B-B' 1 2 3 4 5 6 7 8 9 geological sections. This approach allowed a decoupled restoration where bathymetry controls the sequence above the salt, isostasy controls the package below the salt and the ductile salt layer works as an element of local compensation.

Paleo-bathymetry data and flexural isostasy calculations provide guidelines to restore independent packages above and below the ductile salt layer. Simplified and arbitrary parameters assumed in the restoration processes did not detract from the methodology approach. Recognized problems were produced by handmade interventions during the simple shear and flexural slip operations and also by the lack of isostatic compensation of the lateral movement of the restored modules.

Geohistory 1D analysis established from 2D section restoration results are complementary tools to improve the whole 2D palinspastic process. Inconsistencies produced during restoration steps can be easily observed in these graphs and use again as a new input for further optimization loops. They allow a consistent evaluation of the local bathymetry variation through time. The 1D subsidence graphs confirm that the sedimentary evolution in the study area results from a continuos sedimentary progradation. They illustrate salt welding first in proximal portions and, consequently, salt windows gradually opening over time from these regions to the most distal ones. They also provide a different approach based on the lateral mass movement for 1D thermal modelling.

The simplified 2D restoration approach with independent and interactive bathymetry, isostasy and modules operation controls here presented could provide easy guidelines for new 3D restoration solutions and developments. 1 Fig. 1 -Regional location map outlining the study area (red polygon) including two restored sections (black lines), six available wells (yellow circles) and four studied pseudo-wells (red circles). Notice the aborted spreading center in the southern region, and its northward propagation along a pre-salt fault trend. Its possible continuity within the study area could account for a local crustal thinning anomaly.

Fig. 2 -Simplified stratigraphic chart of the Santos Basin outlining the fiveteen horizons interpreted in the seismic profiles during the study. The major Early Cretaceous progradation event is highlighted between the horizons 03 and 08. [START_REF] Lavier | A mechanism to thin the continental lithosphere at magma-poor margins[END_REF]. Notice the aborted southern spreading center where a hypothetical H block can be interpreted. This hypothetical scenario suggests a strongly thinned crustal thickness beneath the São Paulo Plateau.

Figure 5 -The section A-A' is projected on the more regional section A-B-C modified from [START_REF] Carminatti | New exploratory frontiers in Brazil[END_REF]. In the compressional domain, extending eastwards the study area, the evaporites were removed from the more proximal regions and transported towards more distal portions of the margin as mobile blocks, creating accomodation space for the overlying sedimentary pile.

Figure 6 -The shelf break (white points) and foot of the slope (black points) are shown here for the section B-B'. These critical points have been interpreted for each restored horizon above the salt layer, including the Albian carbonates top (H9). Notice the Cabo Frio Fault which limits the thicker proximal domain from the post-salt minibasins that developed in the more distal domain.

Figure 7 -Example of the first restoration steps showing sequential sketches for the partial results of the section A-A'. Notice two desired anchor points of overlying post-salt layers (salt windows), which are highlighted in the step 3, as well as an exaggerated spacing point of the isostasy response to adjustment of the salt layer remarked in the step 4.

Figure 8 -Restoration outcomes of pre-salt stages applied without paleobathymetric data to sections A-A' and B-B'. Notice the extension restored represent less than 10% from the deformed section. The result mountainous terrain reaching up 3,000 meters high in the section A-A' is consistent with the accommodation space needed for the thick salt layer deposition. The detail 1 highlights an isostatic result locally higher than the referential bathymetry (potential erosion) while the detail 2 highlights a relatively lower isostatic position in the minibasins domain (potential aggradation).

Figure 15 -Paleo-bathymetry model through time based on well data for the platform and slope regions (no data available to the continental rise region). The grey area is a superposition of all well data in each area. The red dashed lines are regional bathymetry models for each region. Colored circles (blue, green and red) show the bathymetry expected for each restored age. Notice the preexisting interpreted depression preceding the deposition of salt.

Figure 7

 7 Figure 7 shows a detailed restoration example of the cyclic applied methodology. These restoration steps include: I) The initial (present day) condition of the section A-A'; II) The decompaction of the most recent layer with flexural isostatic compensation; III) First paleo-bathymetric approximation, indicated by the dashed line based, in this case, on the present day bathymetry which is represented by the blue line. Both lines were superposed on the top of the decoupled post-salt package. This set is decoupled of the pre-salt package, once the salt layer had been suppressed. Small circles show two salt windows that should be preserved; IV) Adjustments of the post-salt package to the top target dashed line by geometric operations opening locally a larger space for the salt layer. A circle shows the least adjusted point; V) Final adjustments required to better replace the initial amount of salt below the post-salt package. This step leads to a completed restoration cycle.

Figure 3 -

 3 Figure 3 -The two geological sections A-A' and B-B' (see location in Fig. 1) are based on fifteen interpreted horizons. The ten layers above the salt are intensely deformed. The Cabo Frio Fault separates extensional and compressive domains. A proximal low and an intermediate high constitute inherited structures, developed before the onset of salt tectonics. Classical minibasins occur in the distal compressional domain.

Figure 4 -

 4 Figure 4 -Schematic block diagram of the Santos Basin adapted from the model of[START_REF] Lavier | A mechanism to thin the continental lithosphere at magma-poor margins[END_REF]. Notice the aborted southern spreading center where a hypothetical H block can be interpreted. This hypothetical scenario suggests a strongly thinned crustal thickness beneath the São Paulo Plateau.

Figure 9 -

 9 Figure9-Sections A-A' and B-B' restored at the salt deposition stage. The obtained scenario shows an original salt layer up to 4,000 meters thick in the section A-A'. The faint pink color represents the amount of salt added in order to restore the salt motion towards distal portions.

Figure 10 -

 10 Figure 10 -Restored profiles of sections A-A' and B-B' for the Albian to Cenomanian stages that shows a climax of the rafting tectonics. The fast extension of the thin Albo-Cenomanian layers is obtained by the underlying salt layer movement, pushed to distal portions by the thick post-salt sediments deposition in the proximal area.

Figure 11 -

 11 Figure 11 -Restoration model for the Albian carbonates. The seismic image shows the present day configuration of the Albian growth structures. The restoration model requires a formerly thicker salt basin (thicker than 2,500 m) to accommodate the observed thickness growing of the carbonate layers.

Figure 12 -

 12 Figure12-The progradation of the Late Cretaceous restored outcomes for sections A-A' and B-B' showing the development of the Cabo Frio Fault (black arrows) in relashionship to the total extention in the study area (red arrows). In association with this diferential lateral deformation, the first salt windows were formed in many compartments.

Figure 13 -

 13 Figure13-Restored outcomes of the most recent layers for sections A-A' and B-B'. These sections show that salt tectonics is no longer active in the proximal domain, and remained relatively quiescent within the more distal domain, developing the minibasins.

Figure 14 -

 14 Figure 14 -First restoration steps showing the decompacted Miocene situation just after the removal of the uppermost layer. The present day in details images is compared with the decompacted scenario of the central image. The decompaction outcome, dependent of the isostatic parameterization, is refered to the present day referential bathymetry (diference in the striped grey area).The detail 1 highlights an isostatic result locally higher than the referential bathymetry (potential erosion) while the detail 2 highlights a relatively lower isostatic position in the minibasins domain (potential aggradation).

Figure 16 -

 16 Figure 16 -Seismic image showing a possible cap rock over the proximal diapirs. Episodes of differential compaction in the post-sal series are observed in the flanks of salt diapirs, surrounding these sub-outcropping structures and delineating local conditions for progressive unconformities.

Figure 17 -

 17 Figure17-Eight graphs based on the restored sections A-A' and B-B' show subsidence and overburden 1D geohistories. The location map provides the pseudo-wells 1B, 2A, 3B and 4A positions. A pseudo-section composed by projected parts shows a continuous progradation from proximal regions to the distal ones from the Albian up to present day.

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Acknowledgments

Fist of all, we would like to thank Petrobras for all support during the present research. We also express our gratitude to Sylvia Anjos, François Roure, Henrique Penteado, Luiz Antonio Freitas and Cláudia Lima who made important contributions to this paper. Our thanks to all the Petrobras E&P petroleum systems geologists, the IFP Energies Nouvelles researchers and the Tecgraf IT support team. This paper would not have been finalized without their support, comments and suggestions during the entire restoration job.

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