Adriana Lemgruber-Traby

Nicolas Espurt

Christine Souque

Pierre Henry

Ysabel Calderon

Patrice Baby

Stéphane Brusset

Avenida Luis

Thermal structure and source rock maturity of the North Peruvian forearc system: Insights from a subduction-sedimentation integrated petroleum system modeling

Keywords: Basin modeling, thermal model, petroleum systems, subduction-related basins, North Peruvian forearc system

Introduction

Understanding the thermal history of forearc basin systems is a challenge to better evaluate oil and gas exploration potential in subduction zones. Forearc systems are generally considered as regions with low petroleum potential due to high structural and stratigraphic complexities, polyphase tectonic histories, and depressed thermal regime [START_REF] Hessler | Subduction zones and their hydrocarbon systems[END_REF].

However, the producing Talara Basin, part of the North Peruvian forearc zone, is one of the striking exceptions to this generally held idea, as are the Cook Inlet Basin along the Alaska-Aleutian forearc zone or the Sacramento Basin along the Cascadia subduction zone of the USA [START_REF] Moberly | Forearc and other basins, continental margin of northern and southern Peru and adjacent Ecuador and Chile[END_REF][START_REF] Carozzi | The Talara Forearc basin, NW Peru: Depositional models of oil-producing Cenozoic clastic systems[END_REF]Higley, 2004a,b;[START_REF] Fildani | Geochemical characteristics of oil and source rocks and implications for petroleum systems, Talara basin, northwest Peru[END_REF][START_REF] Harun | The Petroleum system of the Central Burma Basin, on shore Myanmar[END_REF][START_REF] Hessler | Subduction zones and their hydrocarbon systems[END_REF]. Significant hydrocarbon production occurs in these basins [START_REF] Hessler | Subduction zones and their hydrocarbon systems[END_REF]. To better understand the thermal history of the forearc regions and the dynamics of their petroleum systems, we focused on the thermal modeling of the North Peruvian forearc system across the Tumbes-Talara-Lancones basins system (Figure 3.1). The structural architecture and tectonic evolution of this forearc basins system is constrained by considerable surface and subsurface database (including more than 9 000 km of 2D seismic reflection profiles, several 3D seismic blocks and more than 14 500 wells) and exhumation data [START_REF] Fernández | Tumbes and Talara basins hydrocarbon evolution[END_REF][START_REF] Espurt | Deciphering the Late Cretaceous-Cenozoic Structural Evolution of the North Peruvian Forearc System[END_REF]. The North Peruvian forearc system is characterized by a thick Cretaceous to Quaternary siliciclastic succession up to ~10 km thick that extends onshore and offshore. It displays a complex structural and stratigraphic architecture dominated by the accretion or underplating of crustal (continental and oceanic) and sedimentary rocks since the Late Cretaceous times [START_REF] Espurt | Deciphering the Late Cretaceous-Cenozoic Structural Evolution of the North Peruvian Forearc System[END_REF][START_REF] Brusset | Reappraisal of the Tectonic Style of the Talara-Tumbes Forearc Basin: Regional Insights for Hydrocarbon Exploration[END_REF]. The tectonic wedge is formed by structural highs and major forearc depocenters that are synchronously deformed by thrusts, normal growth faults and gravitational instabilities, as well as strike-slip faults. The thermal regime of forearc systems is strongly controlled by the cooling effect of the cold subducting oceanic plate [START_REF] Dumitru | Subnormal geothermal gradients in the Great Valley Forearc Basin, California, during Franciscan Subduction A fission track study[END_REF][START_REF] A; Allen | Basin Analysis. Principles and Applications[END_REF]. The subduction process moves the oceanic crust, from the sea floor to deeper, warmer, conditions. This causes a negative thermal anomaly that engenders the cooling of the overlying rocks of the forearc basins system. Several authors addressed the thermal regimes of subduction areas [START_REF] Peacock | Numerical simulation of metamorphic pressure-temperature-time paths and fluid production in subducting slabs[END_REF][START_REF] Hyndman | Thermal constraints on the seismogenic portion of the southwestern Japan subduction thrust[END_REF][START_REF] Molnar | Temperatures in zones of steady-state underthrusting of young oceanic lithosphere[END_REF][START_REF] Oleskevich | The updip and downdip limits to great subduction earthquakes: Thermal and structural models of Cascadia, south Alaska, SW Japan, and Chile[END_REF]Yoshioka and Murakami, 2007). They developed thermal models and show accurate results, in accordance with the available surface and near surface thermal data and also in coherence with the location of seismogenic zones. However, the existing subduction thermal models address interest to the temperature distribution of the lithosphere at present day, whereas in order to evaluate the thermal influence of the subduction on the petroleum system dynamics, a model needs 1) to focus on the sedimentary basin and 2) to assess the paleo-thermal field during the entire basin history. Yet, the industrial basin modeling software that address these questions are not developed to handle the thermal cooling induced by subduction.

A solution is proposed in this paper to consider the impact of the subduction on the evolution of the source rock maturity through the basin history. The goal of this paper is to present the thermal history of the North Peruvian forearc system using an interdisciplinary approach. For that, the sequentially restored crustal scale balanced cross section previously published in [START_REF] Espurt | Deciphering the Late Cretaceous-Cenozoic Structural Evolution of the North Peruvian Forearc System[END_REF] is used in an integrated petroleum system model that accounts for both the sedimentary and subduction processes. The extensive surface and subsurface data (vitrinite reflectance, thermal gradients and bottom seismic reflectors) available in the region, together with new surface vitrinite reflectance measurements, serve as calibration data for the subsurface model. The structural model was tested and its impact on the thermal maturity of the potential source rocks was analyzed using an adapted workflow in TemisFlow® 2019.1 software, from Beicip Franlab [START_REF] Ungerer | Basin evaluation by integrated two-dimensional modeling of heat transfer, fluid flow, hydrocarbon generation, and migration[END_REF][START_REF] Schneider | A 3D basin model for hydrocarbon potential evaluation: application to Congo offshore[END_REF][START_REF] Willien | AMG preconditioning for sedimentary basin simulations in Temis calculator[END_REF]. The results provide insights to the thermal history of each depocenter, allow to test some of the postulated hypotheses for the origin of the Talara basin's oil accumulations, and can help develop new strategies for future exploration in this region.

Geological and tectonic context

The development of the North Peruvian forearc system is related to the NE-to E-directed (i.e., oblique to perpendicular) post-Jurassic subduction of the Caribbean, Farallon and Nazca oceanic plates beneath the South American continental plate (e.g., [START_REF] Pindel | Tectonic evolution of the Gulf of Mexico, Caribbean and northern South America in the mantle reference frame: an update[END_REF]Figure 3.1a). It is a tectonically active area with shallow and very weak interseismic coupling [START_REF] Villegas-Lanza | Active tectonics of Peru: Heterogeneous interseismic coupling along the Nazca megathrust, rigid motion of the Peruvian Sliver, and Subandean shortening accommodation[END_REF]. [START_REF] Somoza | Late Cretaceous to recent plate motions in western South America revisited[END_REF] divided the Late Cretaceous-Cenozoic convergence history in western South America in three periods. (1) The Late Cretaceous to Early Eocene (~56-47 Ma) period shows a relatively slow (4-5 cm/yr) NE motion of the Farallon plate. (2) The Early Eocene-Oligocene period (~47-28 Ma) is characterized by an almost constant convergence rate of ~9 cm/yr. The Oligocene peak of convergence and a coeval change of subduction direction coincide with the breakup of the Farallon plate into the Cocos and Nazca plates [START_REF] Lonsdale | Creation of the Cocos and Nazca plates by fission of the Farallon plate[END_REF][START_REF] Somoza | Late Cretaceous to recent plate motions in western South America revisited[END_REF], and (3) the Late Oligocene to present period (~25-0 Ma) is characterized by an ENE-trending motion of the Nazca plate with convergence rates decreasing from 15 cm/yr to 7 cm/yr. This period is characterized by the subduction of the Inca Plateau (Gutscher et al., 1999b) and the Carnegie Ridge in the Middle Miocene [START_REF] Daly | Correlations between Nazca/Farallon plate kinematics and forearc basin evolution in Ecuador[END_REF]Gutscher et al., 1999a;[START_REF] Schütte | Geodynamic controls on tertiary arc magmatism in Ecuador: Constraints from U-Pb zircon geochronology of Oligocene-Miocene intrusions and regional age distribution trends[END_REF] and more recently, in the Quaternary, by the subduction of the Sarmiento and Alvarado Ridges [START_REF] Lonsdale | Creation of the Cocos and Nazca plates by fission of the Farallon plate[END_REF][START_REF] Espurt | Deciphering the Late Cretaceous-Cenozoic Structural Evolution of the North Peruvian Forearc System[END_REF]. The age of the subducting lithosphere decreases from ~70 Ma in the Paleocene to ~20Ma at present [START_REF] Sdrolias | Controls on back-arc basin formation[END_REF].

The Tumbes, Talara and Lancones basins are part of the North Peruvian forearc system that extends from the Western Cordillera volcanic arc to the Peru-Chile trench (Figure 3.2). They result from a seaward depocenter shift from the inner Lancones Cretaceous depocenter to the Cenozoic Tumbes depocenter. [START_REF] Espurt | Deciphering the Late Cretaceous-Cenozoic Structural Evolution of the North Peruvian Forearc System[END_REF] used field data, wells, seismic reflection profiles together with apatite fission-track data and thermal history modeling to build a section crossing these three depocenters (Figure 3.2). East of the Talara Basin is the Amotape high, followed by the Lancones Basin. West of the Talara Basin are the Zorritos and Carpitas basement highs, followed by the Tumbes Basin that extends northeast offshore, towards the Progresso Basin in Ecuador. The Tumbes Basin is limited westward by the Banco Peru. accretionary prism. Palinspastic restorations suggest that these depocenters were connected in the past, and the successive episodes of deformation and erosion that took place from Early Eocene to Quaternary were responsible for the basin's partitioning observed today (Espurt et al., 2018). The authors interpreted a regional Early Eocene cooling/exhumation, followed by a Middle to Late Eocene reheating/burial, and then by an Oligocene-Miocene cooling/exhumation (Figure 3.3c), as well as a last stage of cooling/exhumation during Middle Miocene (~15 Ma) for the Amotape High. These exhumation pulses are correlated with major erosional surfaces (Figure 3.4) and locally by growth strata across the forearc system [START_REF] Espurt | Deciphering the Late Cretaceous-Cenozoic Structural Evolution of the North Peruvian Forearc System[END_REF]. These vertical motion stages, as well as these major tectonic deformations in the forearc basins, are related to variations in convergence rates, as well as the plate coupling and the subduction of bathymetric asperities [START_REF] Espurt | Deciphering the Late Cretaceous-Cenozoic Structural Evolution of the North Peruvian Forearc System[END_REF]. The forearc stratigraphy is synthetized in Figure 3.4. The oldest depocenter, the Lancones Basin, involves Cretaceous strata with conglomerates at the base followed by successions of marine sequences, locally associated with small intrusive bodies [START_REF] Jaillard | Stratigraphy and evolution of the Cretaceous forearc Celica-Lancones basin of southwestern Ecuador[END_REF][START_REF] Valencia | Cuenca Lancones: Interpretation geologica[END_REF]. These strata are deformed firstly by NW verging thrust-related anticlines during the Late Cretaceous [START_REF] Jaillard | Stratigraphy and evolution of the Cretaceous forearc Celica-Lancones basin of southwestern Ecuador[END_REF][START_REF] Andamayo | Nuevo estilo estructural y probables sistemas petrolíferos de la cuenca Lanconesg[END_REF][START_REF] Espurt | Deciphering the Late Cretaceous-Cenozoic Structural Evolution of the North Peruvian Forearc System[END_REF], and then by Cenozoic normal faults [START_REF] Valencia | Cuenca Lancones: Interpretation geologica[END_REF][START_REF] Andamayo | Nuevo estilo estructural y probables sistemas petrolíferos de la cuenca Lanconesg[END_REF][START_REF] Espurt | Deciphering the Late Cretaceous-Cenozoic Structural Evolution of the North Peruvian Forearc System[END_REF]. The Amotape High is a prominent range exposing Paleozoic rocks and Triassic intrusions (Figure 3.2). The Talara Basin extends onshore and offshore (Figure 3.1b and Figure 3.2), but only its onshore part is crossed by the studied section. In this northern part, the Talara Basin is currently formed by up to 3.5 km-thick Eocene to Miocene fluvial to deep marine strata deformed by major NE trending, SE dipping listric normal faults connected at depth with the basement (e.g., Carpitas fault zone) [START_REF] Séranne | Evolution tectono-sédimentaire du bassin de Talara (nord-ouest du Pérou)[END_REF]Higley, 2004a;[START_REF] Fernández | Tumbes and Talara basins hydrocarbon evolution[END_REF]). Southward, the thickness of the Talara depocenter reaches up to 9 km. While no Cretaceous strata has yet been identified in its northern part, it has been revealed by exploration wells in the southern onshore-offshore part of the Talara Basin (Talara town and Punta Balcones areas) and in outcrops south of the Amotape High (Figure 3.4b). The offshore Tumbes Basin depicts two stacked progradational sedimentary wedge systems of Eocene to Quaternary sediments up to 11 km thick. The lower wedge consists of a seaward prograding wedge of Eocene-Early Oligocene strata. The upper wedge is formed by Late Oligocene to Quaternary strata deformed by Miocene to present syndepositional growth faults and rollovers. The basement that underlies the Talara and Lancones Basins is composed of the Amotape basement (including Paleozoic sedimentary and metamorphic rocks, as well as Triassic intrusions) whereas towards the trench, the Amotape basement gets thinner, and the Tumbes Basin ends up lying above accreted off-scrapped sediments directly exposed to the oceanic crust (Figure 3.2c;[START_REF] Bourgois | A Review on Tectonic Record of Strain Buildup and Stress Release across the Andean Forearc along the Gulf of Guayaquil-Tumbes Basin (GGTB) near Ecuador-Peru Border[END_REF][START_REF] Espurt | Deciphering the Late Cretaceous-Cenozoic Structural Evolution of the North Peruvian Forearc System[END_REF].

Petroleum systems overview

There are at least 40 oil and/or gas fields documented in the Talara Basin, with a cumulative oil and gas production of 1680 MMBO and 340 BCF, respectively (Higley, 2004a). The rate of exploration success is not published, but amid the gathered dataset of 1118 exploratory wells, at least 45% are reported to be dry holes. The Tumbes Basin is considerably less explored than the Talara Basin and has a discovery rate of 30% [START_REF] Higley | The Progresso Basin Province of Northwestern Peru and Southwestern Ecuador: Neogene and Cretaceous-Paleogene Total Petroleum Systems[END_REF]. The central part of the Talara Basin is its most proliferous area, concentrating the oil fields. In our study area, in the northern Talara Basin and the onshore Tumbes Basin, mostly gas fields are present, sometimes associated with oil. The density of Tumbes and Talara oils varies from 18 to 48 °API. Geochemical analyses indicate they present different degrees of biodegradation, but were all originated from a same type of source rock, with probably at least two migration pulses (Higley, 2004a;[START_REF] Hessler | Subduction zones and their hydrocarbon systems[END_REF]and references therein). The Cretaceous source rocks of the Muerto and Redondo Formations (deep marine black shales with type II, II/III kerogen; Figure 3.4 and Figure 3.5) have sufficient organic matter content (1-4.5% TOC) and thermal maturity to be considered active source rocks in the Talara Basin, where they are present [START_REF] Fernández | Tumbes and Talara basins hydrocarbon evolution[END_REF]Table 3.1). These Cretaceous source rocks were considered as the main source of the petroleum present in the area (Higley, 2004a and references therein). But geochemical analyses using molecular biomarker analysis from oil samples and Cretaceous potential source rocks failed to establish a direct correlation between oil and source [START_REF] Fildani | Geochemical characteristics of oil and source rocks and implications for petroleum systems, Talara basin, northwest Peru[END_REF]. The main point for this lack of correlation was the presence of Oleanane and other age-discriminant biomarkers that point towards a Tertiary marine source for the analyzed oils. The Oligocene-Miocene Heath potential source rock or an equivalent interval in the Talara Basin, was then identified as the probable source for the analyzed oils [START_REF] Fildani | Geochemical characteristics of oil and source rocks and implications for petroleum systems, Talara basin, northwest Peru[END_REF]. Marine shales of the Oligocene-Miocene Heath Formation have been observed in the Tumbes Basin in wells and in outcrops along the coast, with fair potential (up to 1.85% TOC) and composed predominantly by terrestrial organic matter (Figure 3.4 and Figure 3.5; Table 3.1). This potential source rock is immature where sampled (Table 3.1Table 3.2; [START_REF] Fernández | Tumbes and Talara basins hydrocarbon evolution[END_REF] but is expected to have generated hydrocarbon at deeper parts of the depocenter [START_REF] Fildani | Geochemical characteristics of oil and source rocks and implications for petroleum systems, Talara basin, northwest Peru[END_REF][START_REF] Fernández | Tumbes and Talara basins hydrocarbon evolution[END_REF], where it is likely richer. It is worth noting that the Muerto Formation samples used in these geochemical analyses did not have good source rock characteristics [START_REF] Fildani | Geochemical characteristics of oil and source rocks and implications for petroleum systems, Talara basin, northwest Peru[END_REF]. Alternative explanations for the Oleanane presence in the Talara oils are the acknowledgment of a younger, Upper Cretaceous, age for the Muerto Formation [START_REF] Fernández | Tumbes and Talara basins hydrocarbon evolution[END_REF] or the occurrence of locally potential Tertiary source rocks (Higley, 2004a and references therein). The available TOC measurements and pyrolysis data indicate also a locally fair source rock potential for Eocene Talara shales [START_REF] Fernández | Tumbes and Talara basins hydrocarbon evolution[END_REF]Figure 3.3 and Figure 3.4;Table 3.1). The migration mechanism is also still debated [START_REF] Hessler | Subduction zones and their hydrocarbon systems[END_REF]. The hypothesis of hydrocarbon generation from the Oligocene-Miocene source rock in the offshore Tumbes depocenter [START_REF] Fildani | Geochemical characteristics of oil and source rocks and implications for petroleum systems, Talara basin, northwest Peru[END_REF] Several good quality reservoirs are present throughout the Talara Basin stratigraphic sequences (Figure 3.4). The main reservoirs are Eocene sandstones interbedded with shale seals [START_REF] Fernández | Tumbes and Talara basins hydrocarbon evolution[END_REF]. In the Tumbes Basin, potential good quality reservoirs are present from the Oligocene Mancora to the Pliocene-Quaternary La Cruz Formation. The primary reservoirs are the Miocene marine sandstones of Zorritos Formation [START_REF] Fernández | Tumbes and Talara basins hydrocarbon evolution[END_REF]. The predominant structural trap type of the Talara Basin comprises tilted fault blocks, controlled by listric basement faults and gravitational cover structures [START_REF] Fernández | Tumbes and Talara basins hydrocarbon evolution[END_REF].

Thermal calibration

Vitrinite reflectance (Ro) data and present-day geothermal gradient data are presented in Figure 3.3a and in Table 3.1 and Table 3.2. Part of these data is projected onto the studied cross section in Figure 3.3b. These data were used to update the structural and kinematic model of [START_REF] Espurt | Deciphering the Late Cretaceous-Cenozoic Structural Evolution of the North Peruvian Forearc System[END_REF] and assure the calibration of the presented thermal model.

Information concerning the presence of bottom seismic reflectors was also gathered and used to verify the model calibration in areas where no direct measurement is available.

Ro data

The Ro is a sensitive geothermometer that indicates the organic matter maturity of the rocks in sedimentary basins and can be used with caution to reconstruct the amount of burial/erosion (e.g., [START_REF] Kamp | Thermal history analysis by integrated modelling of apatite fission track and vitrinite reflectance data: Application to an inverted basin[END_REF][START_REF] Espurt | A scenario for late Neogene Andean shortening transfer in the Camisea Subandean zone (Peru, 12° S): implications for growth of the northern Andean Plateau[END_REF]. The Ro value is a function of the kinetic transformation of organic matter, commonly associated with temperature increase during burial [START_REF] Sweeney | Evaluation of a simple model of vitrinitereflectance based on chemical kinetics (1)[END_REF][START_REF] Peters | Applied Source-Rock Geochemistry[END_REF]. We present 57 Ro measurements in shale outcrops of the Paleozoic-Late Miocene sedimentary succession from the North Peruvian forearc system (Figure 3.3 and Table 3

Present day temperatures and geothermal gradients

The bottom hole temperatures (BHT) measured in 44 onshore wells were gathered from well log files. The wells located close (<10km) to the modeled section were used to support its present day thermal calibration. Additionally, the geothermal gradients were calculated using a 25°C surface temperature (Figure 3.

Bottom seismic reflectors

The presence of methane hydrate in the Peruvian margin has been identified by Ocean

Drilling Program Leg 112 along Central and South Peruvian margin (8-13°S) [START_REF] Kvenvolden | Gas hydrates of the Peruvian outer continental margin[END_REF]) and interpreted by [START_REF] Auguy | Seismic evidence of gas hydrates, multiple BSRs and fluid flow offshore Tumbes Basin, Peru[END_REF] through the observation of bottom simulator reflector (BSR) at the vicinity of Banco Peru, close to the trench. The presence of BSR is restricted to an area south and southwest of Banco Peru, at water depths deeper than 110m. In the inner slope of Banco Peru, i.e., inside the Tumbes-Progresso basin, no BSR is observed. [START_REF] Auguy | Seismic evidence of gas hydrates, multiple BSRs and fluid flow offshore Tumbes Basin, Peru[END_REF] estimated the temperatures at the BSR depths using pressuretemperature curves for seawater-methane hydrate stability. The derived geothermal gradients range from 10 to 50°C/km, with an average value of 26°C/km.

Methodology: petroleum system modeling in a subduction setting

Traditional basin and petroleum systems modeling tools simulate the thermal evolution of sedimentary basins, but they are not built to take into account the cooling effect associated with the oceanic lithosphere subduction. These models calculate the temperature and maturity evolution according to the sediments' thermal properties (e.g. thermal conductivity and heat capacity), deposition history and thermal boundary conditions. The boundary conditions are usually the temperature at the sediments' surface and either a geothermal gradient or a bottom boundary condition, that can be a basal heat flow or a crustal model with a fixed temperature at the base of the lithosphere. Relatively few petroleum systems modeling studies in forearc or subduction-related basins have been published. In most of them [START_REF] Lutz | Petroleum Systems of the Simeulue Fore-arc Basin off Sumatra, Indonesia[END_REF][START_REF] Schultz | Evaluating the thermal history of the Los Angeles Basin through 3-D basin and petroleum system modeling[END_REF] Burgreen-Chan and Graham, 2018), the bottom boundary condition is an inferred basal heat flow, applied at the base of the sedimentary basin, that may vary spatially and temporally in order to fit the basin's thermal data. Typical basal heat flow values for forearc basins range between 20 to 40 mW/m 2 according to [START_REF] A; Allen | Basin Analysis. Principles and Applications[END_REF]. Most of the basal heat flow values defined during the subduction phase in the available studies are in accordance with this definition. Nevertheless, some locally higher or lower heat flow values are sometimes necessary to explain the thermal anomalies observed in the available data [START_REF] Lutz | Petroleum Systems of the Simeulue Fore-arc Basin off Sumatra, Indonesia[END_REF][START_REF] Schultz | Evaluating the thermal history of the Los Angeles Basin through 3-D basin and petroleum system modeling[END_REF][START_REF] Burgreen-Chan | Petroleum system modeling of the East Coast Basin, Hawke Bay, New Zealand[END_REF]. In areas where few data are available and/or the sedimentary basin architecture is heterogeneous, using the basal heat flow as boundary condition is a source of high uncertainty for petroleum systems.

In the crustal model approach, the lithosphere thermal properties, structure, and the temperature at its base are defined [START_REF] Ungerer | Basin evaluation by integrated two-dimensional modeling of heat transfer, fluid flow, hydrocarbon generation, and migration[END_REF][START_REF] Baur | Basin modeling meets rift analysis -A numerical modeling study from the Jeanne d'Arc basin, offshore Newfoundland, Canada[END_REF][START_REF] Roussé | Integrated Stratigraphic and Petroleum system Modeling Study of Southern upper Rhine Graben[END_REF]. The calculation of the thermal model is then performed from the base of the lithosphere to the top of the sedimentary basin, integrating their geometrical evolution and thermal properties. In this case, the basal heat flow and the thermal gradients are obtained as model results, accounting for the thermal insulation caused by the deposition of cold sediments (blanketing effect). This coupled (sediment-basement) approach was used in this study. Additionally, the thermal cooling engendered by the subduction was replicated using advective heat transfer in the oceanic lithosphere, as often used in subduction thermal models [START_REF] Peacock | Numerical simulation of metamorphic pressure-temperature-time paths and fluid production in subducting slabs[END_REF][START_REF] Hyndman | Thermal constraints on the seismogenic portion of the southwestern Japan subduction thrust[END_REF][START_REF] Oleskevich | The updip and downdip limits to great subduction earthquakes: Thermal and structural models of Cascadia, south Alaska, SW Japan, and Chile[END_REF][START_REF] Marcaillou | Thermal segmentation along the N. Ecuador-S. Colombia margin (1-4°N). Prominent influence of sedimentation rate in the trench[END_REF].

Subduction thermal structure and models

The downward motion of the subducting lithosphere brings sediments and water to deeper regions where temperature and pressure are higher. These changing conditions trigger physical and chemical reactions associated with mineral dehydration and melt generation, and consequently strong earthquakes and volcanic eruptions [START_REF] Stern | Subduction Zones[END_REF][START_REF] Syracuse | The global range of subduction zone thermal models[END_REF].

Since these physical and chemical processes occur in precise ranges of temperature-pressure coupling, a good understanding of the thermal structure of subducting lithosphere is crucial to define the updip and downdip limits of a seismogenic zone [START_REF] Marcaillou | Thermal regime from bottom simulating reflectors along the north Ecuador-south Colombia margin. Relation to margin segmentation and great subduction earthquakes[END_REF].

McKenzie (1969) proposed the first analytical solution to this problem. He tried to predict how quick the slab would warm up while going down in a mantle that was not affected by the subduction. Even though [START_REF] Mckenzie | Speculations on the Consequences and Causes of Plate Motions[END_REF] used an oversimplified solution, when using the conductive and advective terms of the energy equation in steady state he managed to suitably address the main processes governing the thermal evolution of the slabs [START_REF] Leng | Geodynamic modeling of thermal structure of subduction zones[END_REF]. Since them, several thermal models have been proposed, all using the energy conservation equation, and getting more complex and realistic as the numerical/ computational capacities increased.

The energy conservation equation for heat transfer commonly used is:

( ) Equation 3.1
Where ρ is the density, c p is the heat capacity, T is the temperature, t is the time, k is the thermal conductivity. The velocity vector, represented by v, takes into account the convergence rate and the dip of the slab, and Q is a volumetric heat production, that may include radiogenic heat production or shear heating, for example. [START_REF] Peacock | Thermal and petrologic structure of subduction zones[END_REF] observed that the downward advection of the oceanic lithosphere dominates the thermal structure of the lithosphere. The main factors that control the thermal structure of the lithosphere are thus the age of the lithosphere, which determines the initial temperature of the incoming lithosphere (the younger the lithosphere, the hotter it is), and the subduction velocity vector, which depends on the convergence rate and the slab geometry. In a lesser degree, shear heating, fluid migration, radiogenic heat production, mantle wedge convection and enthalpies of metamorphic reactions may also affect the temperature field. The effect of sedimentation is often neglected. [START_REF] Hyndman | Thermal constraints on the seismogenic portion of the southwestern Japan subduction thrust[END_REF] identified that the sedimentation rate above the incoming plate could have an influence in the modeled temperatures. Later, [START_REF] Marcaillou | Thermal segmentation along the N. Ecuador-S. Colombia margin (1-4°N). Prominent influence of sedimentation rate in the trench[END_REF] included the effects of sediment compaction in a 1D thermal model of the incoming lithosphere, which was later used as a lateral thermal boundary condition in a 2D model. The compaction was used to calculate the appropriate thermal conductivity of the sediments, taking into account the sediment's porosity evolution. [START_REF] Langseth | Contrasting geothermal regimes of the Barbados Ridge accretionary complex[END_REF] identified that the surface heat flow is lower when the sediment thickness is higher due to the blanketing effect [START_REF] Lucazeau | The blanketing effect of sediments in basins formed by extension: A numerical model. Application to the Gulf of Lion and the Viking graben[END_REF]. This is caused by the arrival of great thickness of cool sediments over a small time period (high sedimentation rate). Nevertheless, no subduction thermal model to date seems to take the blanketing effect into account, mainly because this effect is only observed in shallow depths and/or close to the trench, and not in the core of seismogenic zones.

Integration of the subduction cooling in TemisFlow basin modeling software

The thermal modeling presented in this paper was performed with TemisFlow® commercial petroleum system modeling software [START_REF] Ungerer | Basin evaluation by integrated two-dimensional modeling of heat transfer, fluid flow, hydrocarbon generation, and migration[END_REF][START_REF] Schneider | A 3D basin model for hydrocarbon potential evaluation: application to Congo offshore[END_REF][START_REF] Willien | AMG preconditioning for sedimentary basin simulations in Temis calculator[END_REF] using its Visco calculator [START_REF] Agelas | Calcul de la température dans le logiciel Visco3D. Mise en oeuvre du O-schéma[END_REF]. In this calculator, the heat conservation equation ( (

) (∑ ( ⃗⃗⃗⃗ ) ( ) ⃗⃗⃗ ⃗⃗⃗⃗⃗⃗⃗⃗⃗⃗ ) Equation 3.
2) takes into account conductive and advective heat flow, as well as radiogenic heat production, the heat transfer related to sediment deposition or erosion, and the heat engendered by fluid volume variation due to hydrocarbon generation:

( ) (∑ ( ⃗⃗⃗⃗ ) ( ) ⃗⃗⃗ ⃗⃗⃗⃗⃗⃗⃗⃗⃗⃗ )

Equation 3.2

Where:

-ρc b the heat capacity of the saturated porous media -λ b its thermal conductivity, which depends on the porosity, saturation and the thermal conductivity of the phase.

-q h is the heat source linked to the sediment deposition or erosion, considering that the sediments are deposited with the same temperature as the top of the basin and that the eroded sediments take with them an amount of heat proportional to its temperature; -q r is the radioactivity heat source;

-q oh is the heat source due to the fluid volume variation by hydrocarbon generation.

-α is a phase identification index with the following convention: w for water, o for the hydrocarbon liquid phase and g for hydrocarbon vapor phase;

-Φ is the porosity;

-ρα, Sα and cα the density, saturation and heat capacity of phase α, respectively;

-⃗⃗⃗⃗ is the velocity of phase α, obtained from Darcy law generalized in function of pressure Pα of phase α:

⃗ ⃗ ( ⃗ ⃗ ⃗ ⃗ ) ̿ ( ⃗⃗⃗⃗⃗⃗⃗⃗⃗⃗ ⃗ ) Equation 3.3
With, in addition, ⃗ ⃗ is the Darcy velocity, µ α the viscosity of phase α, kr α its relative permeability, and ̿ the intrinsic permeability of the porous media.

Since the grid of a TemisFlow® model can only move vertically when using its Visco calculator, the only lateral displacement and associated advection is related to the phase α. In the lithosphere layers of the presented model, where no oil and gas generation is simulated, the α corresponds the water phase (S w =1) and all the horizontal advection is then associated to the water displacement ( ⃗ ⃗ ⃗ ⃗

).

In order to use the water displacement to mimic the subduction cooling, equation 4 needs to be met:

⃗⃗⃗⃗⃗⃗ ⃗⃗⃗⃗⃗ Equation 3.4
Where OL corresponds to the subductiong oceanic lithosphere.

Consequently, the darcy velocity of the water phase needs to be :

⃗⃗⃗⃗⃗ ⃗⃗⃗⃗⃗⃗ Equation 3.5
The water horizontal displacement within the oceanic lithosphere was induced applying an overpressure in one of the section's lateral borders and defining the opposite border as "open", via the TemisFlow lateral boundary condition tool.

The Talara-Tumbes-Lancones Basins reference thermal model

The two-dimensional TemisFlow® thermal model of the North Peruvian forearc system was performed along the 213 km-long, sequentially restored, balanced cross section of Espurt et al. (2018). This kinematic model has been updated (see below) with a new thermal dataset presented in this study (Figure 3.3). The thermal model takes into account the successive paleobathymetries, the thickness (and timing) of the eroded sediments, and the slab geometry from the updated kinematic model (Figure 3.6b). This section crosses the different forearc units described above, from the inner Lancones Basin to the trench. Nevertheless, some simplifications were necessary due to the type of grid (vertical shear) used in the TemisFlow® Visco Model (Figure 3.6b). For instance, the imbrication of thrust sheets that generated the Banco Peru structure was approximated by layer thickness variations. A 60 km-thick oceanic lithosphere was defined for present day and varied in time (Figure 3.6c), taking into account the age of the Farallon (Nazca) oceanic lithosphere [START_REF] Sdrolias | Controls on back-arc basin formation[END_REF] and the relation between the lithosphere thickness and the crust age [START_REF] Mckenzie | Thermal structure of oceanic and continental lithosphere[END_REF]. As previously mentioned, (1) the grid used for this thermal model is a vertical shear one, (2) the cooling engendered by the subduction is represented by the advective term of the heat conservation energy equation, and (3) the oceanic lithosphere displacement was modeled using a fluid circulation inside its layer's cells. The flow velocity was defined applying a pressure gradient at the model borders. At the oceanic plate border an overpressure was applied, directing a flow towards the southeast border, which was set to be open (pressure=hydrostatic). The magnitude of the applied overpressure was selected to best represent the convergence rates defined by [START_REF] Somoza | Late Cretaceous to recent plate motions in western South America revisited[END_REF] taking into account the trench, convergence and section directions (Supporting Information Figure 3.S1 and Table

3.S.1)

. There are some restrictions in using this functionality, primarily because it is not possible to control and change the flow rate within the section. The flow rate was chosen in order to represent the convergence rate projected at the Tumbes depocenter, where the sediments directly overlie the oceanic plate and where subduction cooling is expected to have a higher impact on the sedimentary basin.

The model thermal boundary conditions are the temperature at the base of the lithosphere and the paleo surface temperature at top. The basal temperature was defined as 1333°C constant throughout the study area and basin history. The paleo-surface temperature was estimated from the Early Cretaceous to present-day, according to the basin paleo location climate and bathymetry. The paleolatitude of the study area was estimated using paleolatitude.org (version 2.1) taking into account [START_REF] Torsvik | Phanerozoic polar wander, palaeogeography and dynamics[END_REF] paleomagnetic reference frame. The local paleotemperatures, as well as the pole paleo-temperatures were estimated after [START_REF] Wygrala | Integrated study of an oil field in the southern Po Basin[END_REF].

Finally, the paleo-surface temperatures were defined considering that: (1) from sea level to 200 m water depth, the water temperature is equal to the sea level temperature;

(2) at 1500 water depth and below the water temperature is the same as the pole temperature; (3) between 200 and 1500 m of water depth, the water temperature decreases linearly; (4) above the sea level, the air temperature decreases at a -6,5°C/km rate [START_REF] Yan | Mapping the Thickness of the Gas Hydrate Stability Zone in the South China Sea[END_REF][START_REF] Hantschel | Fundamentals of Basin and Petroleum Systems Modeling[END_REF].

The model thermal maturity was calculated using the BasinRo kinetic model (Nielsien et al., 2017), which is a time-temperature vitrinite reflectance thermal model that uses Arhenius rate constants [START_REF] Burnham | A chemical kinetic model of vitrinite maturation and reflectance[END_REF]) calibrated with basin and laboratory data. The BasinRo vitrinite is obtained as result of the thermal model, allowing the calibration with the available vitrinite measurements (Table 3.1 andTable 3.2; see chapter 3.2.4). We chose to use the BasinRo kinetic model over the more usual EasyRo model [START_REF] Sweeney | Evaluation of a simple model of vitrinitereflectance based on chemical kinetics (1)[END_REF] because it matches geological data better, especially for thermal maturity lower than 2%Ro [START_REF] Schenk | Sensitivity analysis of thermal maturation of Alaska North slope source rocks based on various vitrinite models[END_REF], like is the case of the available Ro measurements used for calibration.

For numerical reasons, the continental crust was divided into five layers, the oceanic crust in three layers, and the lithospheric mantle in 10 layers. On the top of the oceanic crust, one "thin" (500 m-thick) layer of off-scraped sediments was created. One petrophysical facies was assigned for each layer (Supporting Information Table 3.S.2). The facies assigned to the continental crust and oceanic lithosphere were defined as incompressible. The compaction curves for the sedimentary facies are presented in Figure 3.S2 (Supporting Information). The density and main thermal parameters for all assigned sedimentary facies, oceanic lithosphere and water are presented in Table 3.S.3 and Table 3.S.4 (Supporting Information). The grid cells have an average horizontal size of 280 m. One additional large (5 km) cell was added at each border of the model in order to avoid border effects that could be propagated inside the section due to the advection.

Thermal modeling results

The thermal modeling of the North Peruvian forearc system, calibrated with the above mentioned data and including the subducting oceanic lithosphere (chapter 3.2.5.3, Figure 3.6), is presented in Figure 3.7b. The complete thermal evolutionary model is presented in Figure 3.8. We also present a thermal model using the basal heat flow history used in previous studies [START_REF] Fernández | Tumbes and Talara basins hydrocarbon evolution[END_REF] as bottom boundary condition (Figure 3.7a). This model appears to give accurate results in the Talara Basin, where plenty calibration data are available, but overestimates considerably the thermal maturity in the Tumbes Basin, while underestimating it in the Lancones Basin. Since the available data set consists mainly of single point measurements scattered across the study area, the calibration was made rather spatially than vertically along the wells.

In the Talara Basin, the calibration of both models could only be achieved by adding around 3 km of post-Eocene erosion (Figure 3.6) to the initial structural restoration proposed by [START_REF] Espurt | Deciphering the Late Cretaceous-Cenozoic Structural Evolution of the North Peruvian Forearc System[END_REF]. In fact, the Ro values in the Late Eocene-Oligocene rocks of the Carpitas High area suggest post-Oligocene subsidence and heating under Late Oligocene-Miocene rocks (Heath and Zorritos Formations). We propose that this burial is followed by an erosional event preceding the deposition of the Middle Miocene Cardalitos Formation as revealed by subsurface data [START_REF] Fernández | Tumbes and Talara basins hydrocarbon evolution[END_REF][START_REF] Espurt | Deciphering the Late Cretaceous-Cenozoic Structural Evolution of the North Peruvian Forearc System[END_REF][START_REF] Brusset | Reappraisal of the Tectonic Style of the Talara-Tumbes Forearc Basin: Regional Insights for Hydrocarbon Exploration[END_REF]. This erosional event mainly recorded near the coastal zone may be controlled by changes in the Nazca subduction dynamic/Andean orogenic building or by the subduction of a buoyant asperity like the Inca Plateau (Gutscher et al., 1999b). A Middle Miocene uplift has been also described southward in the Trujillo forearc zone by [START_REF] Prudhomme | Western thrusting and uplift in northern Central Andes (western Peruvian margin)[END_REF] related to the subduction of the Nazca ridge. Analyzing the model results, we observe that each depocenter has a different thermal history.

The influence of the subduction cooling increases toward the trench where the continental crust gets thinner. The present day basal heat flow values in the Lancones Basin are around 60 mW/m 2 . The thick continental crust that lies under the Lancones Basin partially isolates it from the subduction cooling. The present day basal heat flow decreases to 40 mW/m 2 in the Talara Basin and may be as low as 20 mW/m 2 in the Tumbes Basin, where the high recent sedimentation rate also generates a cooling effect (blanketing effect). At the trench, where the sedimentation rate is lower, the average present-day heat flow is 70 mW/m 2 , in consistence with a 20 Myr old oceanic crust, and the average geothermal gradient is 25°C/km, in accordance with [START_REF] Auguy | Seismic evidence of gas hydrates, multiple BSRs and fluid flow offshore Tumbes Basin, Peru[END_REF]. In this region, the thermal structure is mainly influenced by the oceanic lithosphere age (that may be translated into its thickness, and vice versa). The geothermal gradients follow the same trends observed for the basal heat flow in each depocenter. They are hotter in the Lancones Basin (25-35°C/km) and colder in the Tumbes Basin (~18°C/km). In the Talara Basin the geothermal gradient is higher close to the Carpitas high and to the Cabeza de Vaca fault system (25-28°C/km) and lower in its depocenter (18°C/km).

The modeled thermal structure and history of the three depocenters are also related to the changes in subduction rate and direction during the forearc deposition, and to the timing and amplitude of the erosional events. The influence of the subduction cooling is minor during deposition in the Lancones Basin until 28 Ma, when the convergence rate starts to increase in relation with the Farallon plate break-up. The maximum temperatures in the Lancones Basin are reached around 37 Ma, which also corresponds to the maximum burial depth in the depocenter (Figure 3.7 andFigure 3.8). After this period the thermal maturity of this depocenter remained overall stable. The Cretaceous potential source rocks of the Lancones Basin have reached the gas generation window (Ro>1.35%) during the Oligocene, when the maximum burial of 8.5 km was reached [START_REF] Espurt | Deciphering the Late Cretaceous-Cenozoic Structural Evolution of the North Peruvian Forearc System[END_REF]. This period corresponds also to the maturity timing observed at the eastern border of the Talara Basin, close to the Amotape High, where the model shows that Since the erosion is not uniform in this depocenter, the present depth of the rocks that have reached the oil generation window (Ro=0.6%) depends highly on the amount of erosion.

In the offshore Tumbes depocenter, where the thermal maturity results are calibrated with the Ro measurements of three wells (Table 3.2), the oil generation window is reached only with 6 km of overburden for the Eocene rocks and maybe Oligocene-Miocene rocks. This occurred very recently with the deposition of Late Miocene and Pliocene Cardalitos and Mal Pelo Formations.

Discussion

Understanding the thermal evolution of a sedimentary basin is key to assess its petroleum systems dynamics. When a large data set is available, like in the case of the Talara Basin, it is possible to construct a representative petroleum system model by adjusting its parameters in order to achieve a good calibration with the available data. But in unexplored areas, where the added value of predictive petroleum systems models is higher, the generalization of observations made in similar basins may generate significant misinterpretation, as we showed in Figure 3.7a. A well-established methodology has been integrated, implicitly or not, in most petroleum systems models of extensional basins [START_REF] Ungerer | Basin evaluation by integrated two-dimensional modeling of heat transfer, fluid flow, hydrocarbon generation, and migration[END_REF][START_REF] Baur | Basin modeling meets rift analysis -A numerical modeling study from the Jeanne d'Arc basin, offshore Newfoundland, Canada[END_REF][START_REF] Roussé | Integrated Stratigraphic and Petroleum system Modeling Study of Southern upper Rhine Graben[END_REF], in which the [START_REF] Mckenzie | Some remarks on the development of sedimentary basins[END_REF] model, or variations thereof, is applied to estimate the heat flow at the base of the sedimentary basin in accordance with the lithosphere structure and crustal thinning. But for subduction related basins, no solution was available to date to take into account the subduction cooling in their thermal evolution. In these cases, a low heat flow is usually inferred at the base of the sedimentary basin (Lutz, 2010;[START_REF] Schultz | Evaluating the thermal history of the Los Angeles Basin through 3-D basin and petroleum system modeling[END_REF][START_REF] Burgreen-Chan | Petroleum system modeling of the East Coast Basin, Hawke Bay, New Zealand[END_REF]. In this study, we propose a workflow that integrates the subduction implicitly in the petroleum system model of forearc basins.

The presented integrated thermal model includes the three most important factors that rules the thermal structures of subducting lithosphere: (1) the lithosphere age, (2) the subduction rate and (3) the slab geometry [START_REF] Peacock | Thermal and petrologic structure of subduction zones[END_REF]. Radiogenic heat production is also taken into The workflow presented in this study highlighted the thermal history differences between its three depocenters of the North Peruvian forearc system: Lancones, Talara and Tumbes Basins. Even in these very correlated basins, experiencing the same subduction rates and timing, we observe that their heat flow history is not similar (Figure 3.7 and Figure 3.8). This is mainly due to the presence or absence of the continental crust together with the long-term burial and exhumation history of the prism. The Ro values are very sensitive to burial allowing us to calibrate the structural evolution of the forearc system and then its thermal model through time and space. This is particularly useful when the successive burial and erosion phases takes place without reaching high enough temperatures that can be recorded by apatite fission-track thermochronometry.

The thermal history of the different basins allows some insight into the origin of massive oil accumulations of the Talara Basin fields (Figure 3.9). The two-dimensional characteristics of our model, located North of the main fields, preclude us from making conclusions about the volumetric hydrocarbon balance. But analyzing the maturity timing of the potential source rocks together with the structural development of the forearc system, it is possible to determine the probable origin of these hydrocarbon accumulations. The Oligocene-Miocene Heath source rock, that according to [START_REF] Fildani | Geochemical characteristics of oil and source rocks and implications for petroleum systems, Talara basin, northwest Peru[END_REF], is genetically connected to the Talara oil field, is immature along the modeled section. The long lateral migration hypothesis from the Tumbes depocenter to the Talara fields [START_REF] Fildani | Geochemical characteristics of oil and source rocks and implications for petroleum systems, Talara basin, northwest Peru[END_REF] In the Lancones depocenter, the early and high maturity of the Cretaceous source rocks, and the important uplift and consequent erosion events, do not favor the presence of conventional oil accumulations. Nevertheless, it is possible that some of the generated hydrocarbons might be trapped in low permeability layers.

Conclusion

In this paper, we have proposed a solution model in which the cooling caused by the subduction of the oceanic lithosphere is represented by the advective term of the heat conservation energy equation throughout the basin sedimentation history. This enables the integration of both sedimentary and subduction processes in a TemisFlow thermal model, calibrated to numerous structural and thermal data of the North Peruvian forearc system. The thermal model results give clues to better understand the thermal structure and source rock maturity history of this complex forearc system, involving a poorly understood petroleum system.

The thermal structure and history of a forearc basin is influenced by the same parameters identified by [START_REF] Peacock | Thermal and petrologic structure of subduction zones[END_REF]. However, we show that the exposure of the sedimentary basin to the subducting cold lithosphere (presence or absence of continental crust), the sedimentation rate, and erosions are major factors impacting the thermal maturity along the forearc system. We show an increasing tendency in heat flow, geothermal gradient and thermal maturity from the sea (Tumbes Basin) to the land (Talara then Lancones Basins). In the cold offshore Tumbes Basin residing above the subducting oceanic plate, the Eocene and Oligocene-Miocene source rocks (Talara and Heath shales) can be mature when Cenozoic sediments reach an additional 6 km of burial. This maturation is very recent and occurred after the formation of structural barriers separating the Tumbes and Talara depocenters. In the inner Lancones Basin, a certain preservation from the subduction cooling and early burial led to a high maturity of the Cretaceous source rocks. Therefore, the hydrocarbon accumulations of the Talara Basin were generated locally, at least partially from Cretaceous source rocks, perhaps from intervals or facies not yet analyzed by oil-rock geochemical correlation studies, and Tertiary source rock intervals richer and mature at the Talara Basin's offshore depocenters.

Finally, we conclude that even if the histories of the Tumbes, Talara and Lancones Basins are closely related, their petroleum systems are independent due to their thermal history and maturity timing related to the main geodynamic events.

Acknowledgments

This paper is part of AL-T PhD project at IFP Energies Nouvelles/Aix-Marseille University

Figure 3 . 1 :

 31 Figure 3.1: Geodynamic settings. (a) Map of the Northern-Central Andes showing the study area of Figure 3.2. The base map is produced using elevation data from NASA (National Aeronautics and Space Administration) 30 m ASTER (Advanced Spaceborne Thermal Emission and Reflection Radiometer) GDEM (Global Digital Elevation Model). Plate convergence vector and velocities (mm/yr) are from Gripp and Gordon (2002). Mapping, vector, and velocities (mm/yr) of the continental slivers are from Villegas-Lanza et al. (2016). (b) Location of main depocenters. The location of the balanced and restored cross-section by Espurt et al. (2018), used in this work is shown. The sedimentary basins contours are from PERUPETRO S.A. database. BP: Banco Peru; ZH: Zorritos High; CH: Carpitas High; AH: Amotape High; PH: Paita High; IH: Illesca High; HD: Huacabamba Deflection; SR: Sarmiento Ridge; AR1-2: Alvarado Ridge 1 and 2; GR: Grivalja Ridge; WC: Western Cordillera.

Figure 3

 3 Figure 3.2. (a) Morphology, (b) geological map and (c) structural cross-section (modified after Espurt et al., 2018) of the North Peruvian forearc system. For location, see Figure 3.1. FD: Forearc Depocenter; BPFZ: Banco Peru Fault Zone; TMFZ: Tronco Mocho Fault Zone; CFZ: Carpitas Fault Zone; CVF: Cabeza de Vaca Fault; CAF: Cuzco-Angolo Fault; EFZ: La Encantada Fault Zone.

Figure 3

 3 Figure 3.3. (a) Vitrinite reflectance (Ro) data (Tables 3.1 and 3.2), apatite fission-track (AFT) ages (Espurt et al., 2018) and present geothermal gradients calculated from bottom hole temperature or gathered from well reports in the North Peruvian forearc system. (b) Projection of Ro data along the modeled section. (c) HeFTy (Ketcham, 2005) inverse thermal modeling for Amotape High (Espurt et al., 2018); green and purple fields represent acceptable and good model fits, respectively; the blue line represents the weighted mean path of the model.

Figure 3 . 4 .

 34 Figure 3.4. Synthetic stratigraphy of the North Peruvian forearc system showing the main source and reservoir rocks (modified from Fernández et al., 2005 and Espurt et al., 2018).

  requires a long migration towards the onshore Talara Basin before the segmentation of the two basins. But several authors point towards a preferential vertical migration with limited lateral migration (10-50 km) in the Talara Basin onshore domain(Higley, 2004a and references therein), which is only possible if the hydrocarbon generation occurs locally within the Talara Basin boundaries, and if there is enough structure to capture enough oil to break through vertically. An intermediate alternative is proposed by[START_REF] Fernández | Tumbes and Talara basins hydrocarbon evolution[END_REF], that established a correlation between the location of the oil fields, at structural highs, with the surrounding deep areas, and suggested that the known deep onshore grabens could extend offshore and allow a larger lateral migration.

Figure 3

 3 Figure 3.5. Oxygen Index (OI) versus Hydrogen Index (HI) (Van Krevelen diagram; Espitalité et al., 1985) with the available Rock Eval data (Table 3.1 and Table 3.2; Fernández et al., 2005).

  3). Geothermal gradients presented in exploration reports provided by Perupetro S.A. (Perez Companc S.A., 2000; AIPC, no date) were also collected to help understanding and constraining their variability along the studied area (Figure 3.3). The estimated present day geothermal gradient varies considerably with average values of 18°C/km offshore and 23°C/km onshore. The highest values observed onshore are located along the Cabeza de Vaca, Carpitas and Tronco Mocho fault zones (Figure 3.3a). The lowest onshore gradients are located south of the Carpitas High and north of the Zorritos High, under Quaternary sediments. Offshore, the lowest values correspond to the Cenozoic depocenter of the Tumbes Basin, and an increase is observed southward, when approaching the coast.

Figure

  Figure 3.6. (a) Crustal-scale sequential restoration of the cross section (modified after Espurt et al., 2018). (b) Geometry model defined in TemisFlow. Dashed black line corresponds to the subduction fault. (c) Oceanic lithosphere thickness data (derived from Sdrolias and Müller, 2006; Mckenzie, 2005), and Farallon(Nazca)-South American plate projected convergence rate (Somoza and Ghidella, 2012) through Cenozoic. See Figure 3.1 for section location and Figure 3.2c for legend of the sedimentary units.

Figure 3 . 7 .

 37 Figure 3.7. TemisFlow thermal model results for present-day calibrated with surface vitrinite reflectance (Ro) values. (a) With basal heat flow from previous studies (Fernández et al., 2005). (b) With integrated subduction-sedimentation model. (c) Burial depth, temperature and Ro history extracted from (b) at the bottom of Tumbes, Talara and Lancones Basins. Dashed black line corresponds to the subduction fault. Thin dashed black line indicates the basement-sedimentary basin interface. See Figure 3.1 for section location and Figure 3.6 for model input.

Figure 3 . 8 .

 38 Figure 3.8. TemisFlow thermal model results through Cenozoic time. (a) Temperature results with heat flow (brown line) extracted from the model results at the base of the sedimentary basins along the section. (b) Maturity results (Ro%) with total burial depth (blue line) of the sedimentary units along the section. Thick dashed black line corresponds to the subduction fault. Thick black line indicates the basement-sedimentary basin interface. See Figure 3.1 for section location and Figure 3.6 for model input.

outcropping

  Early Miocene Mogollon Formation may have Ro values equivalent to oil generation (Figure 3.7b). In these zones, the thermal maturity remained nearly constant since the end of the Oligocene erosional event (Figure 3.7 and Figure 3.8).Two episodes of maturity increase are observed in the Talara Basin depocenter(Figure 3.7c) and related to the main burial phases (Figure3.6). The first occurred during the Eocene (49-37 Ma), and the second during the deposition of Late Oligocene-Miocene strata (22-5.8 Ma).

  account, but not the shear heating nor the fluid circulation. It is possible that fluid circulation from the subducting plate through deep-seated faults connected with the slab subduction fault could have been, at least partly, responsible for local thermal anomalies in the basins.Relationships between fluid circulation and rock maturity need to be specified and require further investigation. Downdip variations of frictional properties along the subduction fault of the North Peruvian forearc system through time have been previously speculated byEspurt et al. (2018) to partly explain the development of synchronous upper plate extensional faults and compressional features. The effect of the associated shear heating is neglected in this work and should be investigated in the future.

  implies that the oil migration would have occurred before the separation of Tumbes and Talara Basins and the formation of structural traps formed by the Tronco Mocho fault system. However, in the Tumbes Basin this source rock reached the thermal maturity conditions necessary to generate hydrocarbon only in the deeper parts of the depocenter with the deposition of Pliocene-Pleistocene strata(Figure 3.7 and Figure 3.8), after the Miocene erosion event that separated the Tumbes and Talara Basins(Figure 3.6). Therefore, the assumption of a long lateral migration of oils generated by the Heath source rock in the Tumbes Basin toward the Talara fields is not possible according to our modeling results. Some hydrocarbon generation may have occurred in its deeper parts and migrated toward the coast in the Corvina and Albacora structures, but not sufficiently nor early enough to reach the Talara Basin.The model results are more consistent with the presence of local source rocks in the Talara Basin. The observation of two maturation pulses in the model results fits the interpretation of two migration pulses from geochemical analysis(Higley, 2004a;[START_REF] Hessler | Subduction zones and their hydrocarbon systems[END_REF] and references therein). At the location of the modeled section, the Talara Formation shales reach the oil generation window in the deeper parts of the Talara Basin depocenter. It is then reasonable to deduce that to the south, in the Talara Basin main depocenters, both these Eocene and the Cretaceous potential source rocks might have favorable maturity for oil generation. The model results suggest Cretaceous source rocks remain good candidates for the origin of at least part of the petroleum accumulations of the Talara Basin, and it is possible to conclude that where Cretaceous strata are present in Talara Basin (south of the Mancora city;[START_REF] Fernández | Tumbes and Talara basins hydrocarbon evolution[END_REF], this source rock is mature and has generated hydrocarbon. The presence of age-discriminant biomarkers suggesting a Tertiary source rock might be explained by the absence of Cretaceous strata in the main source rock kitchen, where only Tertiary source rocks would be present and mature. This might be the case at the offshore depocenters of the Talara Basin(Fernandez et al., 2005;[START_REF] Fildani | Geochemical characteristics of oil and source rocks and implications for petroleum systems, Talara basin, northwest Peru[END_REF] Figure 3.9a). Although the model results indicate that the Eocene strata at the base of Tumbes Basin's offshore depocenter are in the beginning of the oil window (Figure 3.7), further studies, assessing the Talara Basin's offshore depocenters, are necessary to validate this hypotheses. .

Figure 3 .

 3 Figure 3.9. (a) Potential source rock kitchens according to the model results. The base map is produced using elevation data from NASA (National Aeronautics and Space Administration) 30 m ASTER (Advanced Spaceborne Thermal Emission and Reflection Radiometer) GDEM (Global Digital Elevation Model). (b) North Peruvian petroleum system events chart based on the model results. Green colors correspond to Cretaceous source rocks; orange to Eocene source rocks and brown to Oligocene-Miocene source rocks.

  and conducted thanks to the Institut de Recherche pour le Développement (IRD)-PERUPETRO S.A. research agreement. The authors acknowledge the use of the MOVE Software Suite granted by Petroleum Experts Limited and thank Claude Gout and Boris Marcaillou for the discussions about the subduction thermal models. We also acknowledge the Associate Editor Johannes Wendebourg, Carolyn Lampe, and an anonymous reviewer for the constructive comments which greatly helped us improve our manuscript. Financial support for field work and analysis came from IFP Energies Nouvelles, IRD (UR 234), CEREGE (internal research grant: Thermal regime and reservoir properties of the Talara-Tumbes forearc basin, North Peru), and the Institut Carnot ISIFoR (Research project: Structural modeling and petroleum simulations in complex zones: insight into the giant petroleum field of the Nord Peruvian forearc).

3. 2 . 11

 211 Figure 3.S1. Calculation scheme for the projection of the subduction convergence (Vc) along the modeled 2D section (Vproj), taking into account the direction of the trench, the section and the convergence. The present day azimuths are presented in the image.

Figure 3 .

 3 Figure 3.S2. Compaction curves for the sedimentary facies used in the model. In hydrostatic conditions the porosity is calculated in function of the depth (light colors lines). When overpressured, the calculation of the porosity takes into account the effective stress (darker colored lines).

Table 3 .1. (next page) Pyrolysis rock eval, Total organic carbon (TOC) and vitrinite reflectance (%Ro) measurements from outcrop samples in the study area. Tmax-Maturity; HI-Hydrogen Index; OI- Classical Oxygen Index; SD-Standard deviation; N-number of particles. Analyses were conducted by Energy Resources Consulting Pty Ltd (Australia)* and LCV (Argentina). LCV data are provided by PERUPETRO S.A..

 3

	Sample name	Longitude (m)	Latitude (m)	Depocenter or structural unit	Stratigraphic age/Formation	Tmax (°C)	HI	OI	TOC (wt%)	%Ro Range	SD	N
	TUM16-1*	538393		Zorritos High	Late Oligocene/Heath	414 152 72	0.85	0.34 0.23-0.42 0.049 25
	TUM16-4*	534301		Carpitas High Late Oligocene/Heath	428 66	31	1.75	0.44 0.34-0.59 0.062 25
	TUM16-7*	534753		Carpitas High Middle Eocene/Talara	444 12	163 0.32	-	-	-	-
	TUM16-8*	540462		Talara	Early Oligocene/Plateritos	426 32	82	0.43	0.65 0.51-0.77 0.066 25
	TUM16-9*	541735		Talara	Early Eocene/Mogollon	438 20	86	0.52	0.55 0.47-0.66 0.060 14
	TUM16-15*	537556		Amotape High Paleozoic/Amotape	490 34	38	0.20	-	-	-	-
	TUM16-16*	512114		Amotape High Early Eocene/Mogollon	440 102 43	0.68	0.68 0.55-0.80 0.062 25
	TUM16-20*	511696		Talara	Early Eocene/Salinas	449 18	91	0.38	0.69 0.59-0.76 0.047 25
	TUM16-21*	506754		Talara	Middle Eocene/Talara	433 93	29	0.70	0.61 0.48-0.73 0.067 25
	TUM16-26*	504466		Talara	Early Oligocene/Mancora	441 51	73	0.20	0.53 0.44-0.66 0.053 25
	TUM16-27*	504268		Talara	Late Oligocene/Heath	430 36	42	0.63	-	-	-	-
	TUM16-28*	506036		Carpitas High Late Eocene/Chira	438 25	99	0.43	0.53 0.44-0.60 0.037 25
	TUM16-30*	505785		Carpitas High Early Oligocene/Plateritos	429 47	102 0.54	0.51 0.42-0.61 0.049 25
	TUM16-33*	506092		Amotape High Paleozoic/Amotape	580 21	55	0.33	1.75 1.57-1.88 0.101 8
	TUM16-34*	506230		Amotape High Paleozoic/Amotape	580 19	24	0.32	1.75 1.58-1.87 0.094 10
	TUM16-35*	506603		Amotape High Paleozoic/Amotape	623 8	64	0.38	1.77 1.62-1.97 0.083 25
	TUM16-37*	499689		Amotape High Paleozoic/Amotape	606 15	85	0.32	1.91 1.76-2.06 0.101 9
	TUM16-48*	538393		Talara	Middle Eocene/Talara	436 370 26	1.13	0.51 0.39-0.63 0.064 25
	TUM-808	533815		Carpitas High Late Oligocene/Heath	413 126 42	1.83	0.42 0.28-1.07 0.030 6
	RoG1	522695		Amotape High Paleozoic/Amotape	-	-	-	-	2.66 2.11-2.99 0.220 32
	RoG2	523110		Amotape High Paleozoic/Amotape	-	-	-	-	2.44 1.98-2.78 0.197 50
	RoG3	523071		Amotape High Paleozoic/Amotape	-	-	-	-	1.71 1.40-2.08 0.200 23
	RoG6	523786		Lancones	Albian/Pananga	-	-	-	-	1.16 1.06-1.23 0.062 6
	RoG7	524892		Lancones	Late Cretaceous/Encuentros	-	-	-	-	1.08 0.91-1.32 0.108 21
	RoE1	554080		Lancones	Late Cretaceous/Encuentros	-	-	-	0.7	1.42 1.15-1.73 0.123 38
	RoE2	554876		Lancones	Late Cretaceous/Encuentros	-	-	-	0.69	1.49 1.28-1.69 0.115 35
	RoE3	555088		Lancones	Late Cretaceous/Encuentros	-	-	-	0.69	1.47 1.25-1.67 0.113 40
	RoE4	555085		Lancones	Late Cretaceous/Encuentros	-	-	-	0.68	1.53 1.32-1.83 0.123 24
	RoE5	554353		Lancones	Late Cretaceous/Encuentros	-	-	-	0.59	1.49 1.27-1.72 0.145 20
	RoE6	554060		Lancones	Late Cretaceous/Encuentros	-	-	-	0.22	1.49 1.32-1.71 0.118 10
	RoE7	554580		Lancones	Late Cretaceous/Jahuay Negro -	-	-	0.39	1.55 1.36-1.78 0.128 20
	RoE8	554819		Lancones	Late Cretaceous/Jahuay Negro -	-	-	0.33	1.54 1.31-1.77 0.163 9
	RoE9	555354		Lancones	Late Cretaceous/Huasimal	-	-	-	0.15	1.79 1.61-1.99 0.143 11
	RoE10	555758		Lancones	Late Cretaceous/Huasimal	-	-	-	0.38	2.05 1.67-2.47 0.184 50
	RoE11	556159		Lancones	Late Cretaceous/Huasimal	-	-	-	0.3	2.07 1.69-2.43 0.199 27
	M4-C1CC	568230		Lancones	Albian/Muerto	-	-	-	0.54	3.62 2.81-4.29 0.503 14
	M6-C266	568191		Lancones	Albian/Muerto	-	-	-	1.6	2.42 2.15-2.77 0.319 3
	GR-01	544333		Lancones	Late Cretaceous/Jahuay Negro -	-	-	-	1.11 0.91-1.28 0.102 16
	RoJP1	545069		Lancones	Late Cretaceous/Huasimal	-	-	-	-	1.28 1.10-1.55 0.129 18
	RoJP2	546150		Lancones	Late Cretaceous/Huasimal	-	-	-	-	1.24 1.08-1.37 0.093 9
	GR-02	544470		Lancones	Late Cretaceous/Jahuay Negro -	-	-	-	1.17 0.97-1.37 0.116 17
	GR-03	545120		Lancones	Late Cretaceous/Encuentros	-	-	-	-	1.12 0.98-1.34 0.109 10
	GR-04	546010		Lancones	Late Cretaceous/Encuentros	-	-	-	-	1.12 0.95-1.39 0.154 8
	GR-05	546409		Lancones	Late Cretaceous/Encuentros	-	-	-	-	1.11 0.89-1.38 0.131 33
	GR-06	547147		Lancones	Late Cretaceous/Encuentros	-	-	-	-	1.32 1.11-1.52 0.102 50
	GR-07	547842		Lancones	Late Cretaceous/Encuentros	-	-	-	-	1.27 1.03-1.48 0.102 50
	GR-08	548950		Lancones	Late Cretaceous/Encuentros	-	-	-	-	1.32 1.15-1.50 0.105 25
	GR-15	543036		Lancones	Late Cretaceous/Jahuay Negro -	-	-	0.31	1.22 1.00-1.39 0.122 18
	SA-1	530004		Lancones	Late Cretaceous/Huasimal	-	-	-	-	1	0.82-1.17 0.100 14
	SA-1A	531342		Lancones	Late Cretaceous/Huasimal	-	-	-	-	1.14 1.03-1.26 0.097 4
	SA-2	529655		Lancones	Late Cretaceous/Jahuay Negro -	-	-	-	1.04 0.90-1.18 0.105 11
	SA-4	530055		Lancones	Late Cretaceous/Jahuay Negro -	-	-	-	1.09 0.90-1.28 0.114 13
	SA-5	529164		Lancones	Late Cretaceous/Encuentros	-	-	-	-	1.01 0.91-1.17 0.068 18
	SA-8	528604		Lancones	Late Cretaceous/Encuentros	-	-	-	-	1.04 0.88-1.25 0.109 18
	SA-9	528515		Lancones	Late Cretaceous/Encuentros	-	-	-	-	0.94 0.78-1.06 0.091 10
	SA-10	527653		Lancones	Late Cretaceous/Encuentros	-	-	-	-	1.06 0.97-1.27 0.082 12
	HUA-1	534973		Lancones	Late Cretaceous/Huasimal	505 35	16	0.6	1.6	1.42-1.79 0.090 50
	OV-3	532580		Lancones	Albian/Lower Muerto	448 142 44	0.71	0.91 0.91-0.91 -	1
	OV-4	532580		Lancones	Albian/Lower Muerto	500 51	49	1.18	0.79 0.79-0.79 -	1

Table 3

 3

.1 and Table 3.2; Fernández et al., 2005).

Table 3 .2. Vitrinite measurements from Tumbes basin wells (cutting) in the study area. See legend in Table 3.1. Data are provided by PERUPETRO S.A..

 3

	Well name	Longitude (m)	Latitude (m)	Stratigraphic age/Formation	Depth interval (mbsl)	%Ro Range	SD	N
	Barracuda 15X-1 538393	9588769 Late Miocene/Cardalitos	2469-2569	0.29 0.21-0.34 0.043 8
	Barracuda 15X-1 534301	9578130 Early-Middle Miocene/Zorritos 4151-4179	0.32 0.26-0.39 0.034 39
	Delfin 39X-1	534753	9575493 Early-Middle Miocene/Zorritos 1774-1856	0.30 0.26-0.35 0.030 9
	Corvina 40-10X	540462	9572069 Late Oligocene/Heath	3008-3027	0.35 0.26-0.41 0.040 14

  .1). The first 15 measures presented in Table 3.1 were analyzed by Energy Resources Consulting Pty Ltd using a Leica MP4500P system with Hilgers DISKUS software and concern only the ones considered to represent the indigenous vitrinite population. The other measurements, provided by Perupetro S.A., were analyzed by LVC. Besides these surface Ro, measurements from four offshore wells in the Tumbes Basin were also provided by Perupetro S.A. (Figure 3.3 and Table3.2).

	The surface Ro data show a clear increasing maturity tendency from sea (Tumbes Basin) to

land (Lancones Basin). Ro data from wells in the shallow offshore Tumbes Basin show immature (0.29-0.35%) Oligocene to Late Miocene rocks with more than 3 km of overburden at present day. In the outcrop area, Oligocene-Early Miocene strata of the Zorritos High show a similar Ro value of 0.34%. Quite mature values (0.53-0.65%) are found in the Late Eocene-Oligocene strata of the Carpitas High. The values increase to 0.69% in the Middle Eocene strata of the Talara Basin center. Cretaceous rocks of the Lancones Basin show higher Ro values ranging from 0.91% to 2.07%. The highest Ro values (2.66-3.62%) are found in Paleozoic rocks of the Amotape High and in lower Cretaceous rocks of the outer part of the Lancones Basin.

Table 3 .S.4. Solid density and main thermal parameters of assigned incompressible facies and water.

 3

	Name	Density	Conductivity	Mass heat	Radiogenic
		[kg/m³]	[W/(m•°C)]	capacity	production
				[J/(kg•°C)]	[µW/m³]
	Upper	2650	3.00	1150	3.00
	continental crust
	Lower	2950	2.00	1030	0.40
	continental crust
	Offscraped	2660	3.00	900	3.00
	sediments
	Oceanic crust	3050	3.00	1082	0.10
	Mantle	3350	3.50	985	0.00
	Advecting fluid	1000		3975