José Alejandro Franco
email: jafrancov@unal.edu.co

Thomas Cramer

Alexandre De

Oliveira Chaves

Heinrich Adolf Horn

Marc Poujol

Alejandro

; Cramer

Alexandre Chaves

De Oliveira

; Horn

Heinrich Adolf

; Poujol

Geochronology of monazite related to REE, Nb-Ta and U-Th bearing minerals from Mesoproterozoic anorogenic magmatism in the E-Colombian Amazonian Craton: links to mantle plume activity in the Columbia (Nuna) supercontinent

Keywords: monazite, U-Pb and EPMA geochronology, anorogenic magmatism, mantle plume, Columbia (Nuna) supercontinent

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Introduction

Due to their high ionic charge and large ionic radii, Rare Earth Elements (REE) are not easily incorporated within the early-crystallizing silicates (Winter, 2001). Instead, they are enriched in highly differentiated magmatic phases together with other incompatible elements (such as P, K, Rb, U, Th). Despite similar chemical properties, they may be partitioned by either geochemical, mineralogical, and petrological processes in which case they become valuable proxies to study them [START_REF] Henderson | Chapter 1 -General Geochemical Properties and Abundances of the Rare Earth Elements[END_REF].

Generally spoken, Light Rare Earth Elements (LREE) tend to be concentrated in pegmatites and carbonatites, whereas Heavy Rare Earth Elements (HREE) are concentrated in granitic magmas [START_REF] Pirajno | Hydrothermal Processes and Mineral Systems[END_REF].

Monazite is a LREE phosphate with the generalized formula (LnIII, Th) (PO4), where LnIII represents a trivalent light lanthanide, and is part of a complete solid solution with the LREE from La -Ce to Sm. Although present in most rock types, monazite is frequently found as an accessory mineral in low-Ca igneous rocks [START_REF] Itano | U-Pb chronology and geochemistry of detrital monazites from major African rivers: Constraints on the timing and nature of the Pan-African Orogeny[END_REF], instead of apatite and/or bastnäsite mineralization, and in differentiated magmatic phases like granites, syenites and granitic pegmatites. As monazite frequently occurs in colluvial and placer deposits, it is often better studied in these types of deposits than in the magmatic phases where they crystallized (Dill, 2010;Dill et al., 2012).

Elemental analyses of monazite can bring some information on its origin. For example, [START_REF] Itano | REE-Th-U and Nd isotope systematics of monazites in magnetite-and ilmenite-series granitic rocks of the Japan arc: Implications for its use as a tracer of magma evolution and detrital provenance[END_REF] found that the La/Sm ratios in monazite grains from granite and granitic pegmatite and from magnetite and ilmenite magmas were different. This ratio could therefore be used as a good proxy for the type of magma. Although monazite can contain up to 12 wt% ThO2 [START_REF] Mottana | Simon and Schuster's guide to rocks and minerals[END_REF] it is never metamict [START_REF] Montel | The giant monazite crystals from Manangotry (Madagascar)[END_REF] and, such as zircon, usually does not incorporate initial lead when it crystallizes. Therefore, all the Pb comes from the radioactive decay of Th and U, which makes monazite a mineral suitable for U-Th-Pb dating via EPMA (electron probe micro analysis) [START_REF] Itano | U-Pb chronology and geochemistry of detrital monazites from major African rivers: Constraints on the timing and nature of the Pan-African Orogeny[END_REF] as described by [START_REF] Montel | Chemical Electron microprobe dating of monazite[END_REF], [START_REF] Suzuki | CHIME dating of monazite, xenotime, zircon and polycrase: Protocol, pitfalls and chemical criterion of possibly discordant age data[END_REF] and [START_REF] Chaves | Desenvolvimento do método de datação química U-Th-Pb de monazita por microssonda eletrônica na UFMG[END_REF]. This type of analyses should however be used with caution as, in some cases, EPMA dating can fail to resolve different monazite age populations as demonstrated by [START_REF] Poujol | Two-stage partial melting during the Variscan extensional tectonics (Montagne Noire, France)[END_REF]. Their use as geochronometers by means of LA-ICP-MS (Laser ablation inductively coupled plasma mass spectrometry) and EPMA is compiled by [START_REF] Engi | Petrochronology based on REE-Minerals: Monazite, Allanite, Xenotime[END_REF] and [START_REF] Williams | [END_REF].

Crustal-melt rapakivi granites with their characteristic coarse zoned feldspar megacrysts in a finer matrix are probably the result of mantle plume activity [START_REF] Pirajno | Chapter 8.3 Ancient to Modern Earth: The Role of Mantle Plumes in the Making of Continental Crust[END_REF]. In eastern Colombia, several authors have reported ages between 1550 and 1340 Ma for anorogenic rapakivi granites such as the Parguaza, Danta, Matraca and Tabaquen intrusions (e.g. [START_REF] Bonilla-Pérez | Petrography, geochemistry and geochronology of Parguaza granite in Colombia[END_REF][START_REF] Bonilla | Rapakivi magmatism in the middle Inirida Basin, Guainía deparment, Colombia[END_REF][START_REF] Cordani | U-Pb zircon ages of rocks from the Amazonas Territory of Colombia and their bearing on the tectonic history of the NW sector of the Amazonian Craton[END_REF]. In these granites, pegmatitic phases may host monazite, xenotime, columbite-tantalite, Nb-rich rutile as well as U oxides.

For this research, three localities in the E-Colombian Guainía Department were selected (Figures 1 and2): Espina hillsnear the Inírida river LOC (4), San José near the Guainía river LOC [START_REF] Ludwig | User's Manual for Isoplot 3.00 -A Geochronological Toolkit for Microsoft Excel[END_REF] and Barranquillanear the Cuyarí river LOC (6) where Mesoproterozoic pegmatite-related colluvial rock fragments contain centimetric Ti, Nb-Ta, U and Th bearing minerals together with monazite and xenotime. Here we present EPMA and LA-ICP-MS analyses performed on monazite crystals in order to determine their elemental compositions as well as their crystallization ages in order to understand their possible provenance within the western Guiana Shield, i.e. the NW-part of the Amazonian Craton.

Further we discuss pegmatitic phases with Ti, Nb-Ta, U-Th and REE mineralization in relation to the 1550-1340 Ma anorogenic granites found in various parts of the western Amazonian Craton in the light of intra-plate processes associated with mantle plume activity, which may have controlled this magmatism within the Columbia (Nuna) supercontinent.

Methods used

From panning concentrates (pc) more than 20 monazite crystals from each locality were picked and verified using a handheld Bruker Tracer III-V X-ray fluorescence instrument equipped with a Rh-tube and Silicon Drift Detector (SDD), working conditions 15-40kV, 5-10mA, 60-120s exposure time, no filter nor vacuum which together with the S1PXRF software allow to detect all elements heavier than Na (e.g. [START_REF] Magrini | Innovative application of portable X-ray fluorescence (XRF) to identify Göktepe white marble artifacts[END_REF]. Three epoxy resin pucks, labeled LOC (4), LOC ( 5) and LOC (6), each with ~10 crystals, were prepared using buehler epoxy cure2 resin and hardener, polished first with silicon carbide and diamond and then coated with graphite [START_REF] Mange | Heavy minerals in use[END_REF][START_REF] Reed | Electron Microprobe Analysis and Scanning Electron Microscopy in Geology, Electron Microprobe Analysis and Scanning Electron Microscopy in Geology[END_REF]. Scanning electron microscopy (SEM) BSE images of the monazite crystals allowed choosing the most homogeneous zones, free of inclusions or in very low proportion. Their chemical composition was determined using wavelength-dispersive spectroscopy (WDS) in a JEOL JXA-8900 EPMA in the Laboratory of Microanalysis of the Microscopy Center at Federal University of Minas Gerais (LMA-CM-UFMG), Brazil. The reference materials used were Y2O3 (YAG_25K50n), Dy2O3 (DyPO4_25K50n), P2O5 (Monaz_25K50n), SiO2 (ThSiO4_25K50n), Gd2O3 (GdPO4_25K50n), PbO (Crocoi_25K50n), Sm2O3 (REE2_25K50n), ThO2 (ThSiO4_25K50n), Nd2O3 (NdPO4_25K50n), UO2 (UO2_25K50n), Pr2O3 (PrPO4_25K50n), CaO (Ca2P2O7_25K50n), (Ce2O3) (Monaz_25K50n) and La2O3 (Monaz_25K50n). Additionally, 30 monazite crystals up-to-0,5 cm large from LOC [START_REF] Ludwig | User's Manual for Isoplot 3.00 -A Geochronological Toolkit for Microsoft Excel[END_REF] were analyzed. For EPMA dating, from each locality 1 monazite crystal from the polished epoxy pucks was selected, and ages were calculated using U, Th and Pb concentrations [START_REF] Williams | Microprobe Monazite Geochronology : Understanding Geologic Processes by Integrating Composition and Chronology[END_REF].

The EPMA-analyses were performed in 6 to 10 spots per crystal. Standards and quantitative WDS analytical parameters used during monazite analyses are described in [START_REF] Chaves | Desenvolvimento do método de datação química U-Th-Pb de monazita por microssonda eletrônica na UFMG[END_REF]. Overlaps of X-ray peaks between Y and Pb have not been corrected because there was no measurement in PbMa (Lead M alpha), but only in PbMb (Lead M beta). However, to avoid errors in the obtained ages, the interference of ThMz (Thorium M gamma) on the measured UMb (Uranium M beta) had to be corrected, following [START_REF] Scherrer | Monazite analysis; from sample preparation to microprobe age dating and REE quantification[END_REF] in adaptation to the conditions of the LMA-CM-UFMG, as follows [START_REF] Chaves | Desenvolvimento do método de datação química U-Th-Pb de monazita por microssonda eletrônica na UFMG[END_REF]:

U corrected = U measured -(0.006365 x Th measured).
Microprobe chemical U-Th-PbT ages and associated errors were obtained using EPMA Dating software [START_REF] Pommier | EPMA Dating User'Manual, V. 1.01: Age Calculation from Electron Probe Microanalyser Measurements of U-Th-Pb[END_REF] and the average ages were taken through Isoplot/Ex software [START_REF] Ludwig | User's Manual for Isoplot 3.00 -A Geochronological Toolkit for Microsoft Excel[END_REF]. The age equation used is:

𝑃𝑏 = {𝑇ℎ × [exp (λ232T) -1] × (𝑀208 ⁄ 𝑀232 )} + {𝑈𝑐 × [exp (λ238T) -1] × (𝑀206 ⁄ 𝑀238 ) × 0.9928} + {𝑈𝑐 × [exp (𝜆235𝑇) -1] -1] × (𝑀207/𝑀235) × 0.0072}
Where: 238U/(235U+238U) = 0.9928 and 235U/(235U+238U) = 0.0072. Uc (U corrected), Th and Pb are concentrations in ppm; T is the age in Ma; M206, M207, M208, M235, M238, M232 are the atomic masses of 206Pb, 207Pb, 208Pb, 235U, 238U, 232Th; λ232= 0.49475 x 10-4 Ma-1; λ238 = 1.55125 x 10-4 Ma-1; λ235 = 9.8485 x 10-4 Ma-1 [START_REF] Pommier | EPMA Dating User'Manual, V. 1.01: Age Calculation from Electron Probe Microanalyser Measurements of U-Th-Pb[END_REF].

Ages and uncertainties were obtained using EPMA Dating software [START_REF] Pommier | EPMA Dating User'Manual, V. 1.01: Age Calculation from Electron Probe Microanalyser Measurements of U-Th-Pb[END_REF] and age averages were processed using Isoplot 3.75 Excel version [START_REF] Ludwig | User´s manual for Isoplot 3.75 -A Geochronological Toolkit for Microsoft Excel[END_REF][START_REF] Ludwig | User's Manual for Isoplot 3.00 -A Geochronological Toolkit for Microsoft Excel[END_REF].

Beside the U and Pb values, also the other elements were used for unravelling both mineral chemistry and REE-geochemistry and calculate approximate mineral compositions assuming an idealized monazite formula Ln 3+ PO4 and considering all elements as part of the mineral lattice (i.e. not specifying possible inclusions or exsolutions of other phases). For the formulae calculations, mineralogical standard normalization procedures were applied [START_REF] Deer | An Introduction to the Rock-Forming Minerals[END_REF][START_REF] Perkins | Mineralogy[END_REF], i.e. the transformation of the mean oxide wt-% to mole-%, the distribution of the cations to the four anionic O-sites, and the calculation if the cation and anion charges became balanced.

LA-ICP-MS dating has been performed by using aleatory points in all crystals of the three sampling sites LOC (4, 5 and 6) including the same crystals analyzed by EPMA. Analyses were carried out on a single quadrupole Agilent 7700 ICP-MS mass spectrometer coupled to a 193-nm excimer laser system ESI (NWR193UC) in the GeOHeLiS analytical platform of the University of Rennes 1 in France. In the present study, the acquisition time of each analytical spot was set to 80 seconds (20 seconds background followed by 60 seconds with the laser firing). Spots diameters of 8 μm associated with repetition rates of 3 Hz with a laser fluency of 5 J.cm -2 were used. The signal of 204 (Pb+Hg) 206 Pb, 207 Pb, 208 Pb, 232 Th and 238 U masses were acquired. The 235 U signal is calculated from 238 U based on the ratio 238 U/ 235 U = 137.818 [START_REF] Hiess | 238U/235U Systematics in Terrestrial Uranium-Bearing Minerals[END_REF].

Data were corrected for U-Pb and Th-Pb fractionation and for the mass bias by standard bracketing with repeated measurements of the Moacir monazite reference material [START_REF] Gasquet | Miocene to Messinian deformation and hydrothermalism in the Lauzière Massif (French Western Alps): new U-Th-Pb and Argon ages[END_REF]. Data reduction was carried out with the software package GLITTER® (Van Achterbergh et al., 2001). Repeated analyzes of the Manangoutry monazite reference material [START_REF] Paquette | High resolution (5 μm) U-Th-Pb isotopes dating of monazite with excimer laser ablation (ELA)-ICPMS[END_REF] treated as unknown were used to control the reproducibility and accuracy of the corrections and yield a concordia age of 548 ± 6 Ma (MSWD=0.98; n=11). After data reduction, U-Th-Pb Concordia diagrams were constructed with the IsoplotR software [START_REF] Vermeesch | IsoplotR: A free and open toolbox for geochronology[END_REF]. The calculated Concordia ages are quoted with 95% of confidence interval. More information on the analytical protocol in [START_REF] Poujol | Two-stage partial melting during the Variscan extensional tectonics (Montagne Noire, France)[END_REF] and supplementary table in Annex. A.

Geological background

The Guainía Department is located at the northwestern part of the Guiana Shield i.e. a portion of the Colombian part of the Amazon Craton, which extends from the Andean Eastern Cordillera foothills to Venezuela and Brazil and is the least populated and studied area of Colombia. Our geological knowledge of this area is largely based on research conducted in Brazil and Venezuela (e.g., [START_REF] Gansser | The Guiana Shield (S. America) Geological Observations[END_REF][START_REF] Gansser | The Roraima Problem (South America)[END_REF][START_REF] Amaral | Geologia pré-cambriana da região Amazônica[END_REF][START_REF] Gaudette | Geology and age of the Parguaza rapakivi granite, Venezuela[END_REF][START_REF] Almeida | Brazilian structural provinces: an introduction[END_REF][START_REF] Gaudette | Geochronology of the basement rocks, Amazonas territory, Venezuela and Tectonic evolution of the western Guiana Shield[END_REF][START_REF] Bettencourt | Mesoproterozoic rapakivi granites of the Rondo ˆ nia Tin Province , southwestern border of the Amazonian craton , Brazil -I . Reconnaissance U -Pb geochronology and regional implications[END_REF][START_REF] Tassinari | Geochronological provinces of the Amazonian Craton[END_REF][START_REF] Santos | A new understanding of the Provinces of the Amazon Craton based on Integration of Field Mapping and U-Pb and Sm-Nd Geochronology[END_REF], although important studies have been done recently also in Colombia (e.g., [START_REF] Bonilla-Pérez | Petrography, geochemistry and geochronology of Parguaza granite in Colombia[END_REF][START_REF] Bonilla | Rapakivi magmatism in the middle Inirida Basin, Guainía deparment, Colombia[END_REF][START_REF] Bonilla | Petrografía, geoquímica y geocronología U/Pb en circones de rocas ígneas y metamórficas a lo largo del Río Cuiarí en el sur del Departamento de Guainía, Colombia[END_REF][START_REF] Cordani | U-Pb zircon ages of rocks from the Amazonas Territory of Colombia and their bearing on the tectonic history of the NW sector of the Amazonian Craton[END_REF], Ibanez et al., 2011[START_REF] Kroonenberg | The Proterozoic Basement of the Western Guiana Shield and the Northern Andes[END_REF].

According to [START_REF] Santos | Geotectônica dos Escudos das Guianas e Brasil-Central[END_REF], the crystalline basement in the Western Guiana Shield is linked to the Rio Negro geochronological province 1.82 -1.52 Ga (Figure 1). Modified from [START_REF] Santos | Age and autochthonous evolution of the Sunsás Orogen in West Amazon Craton based on mapping and U-Pb geochronology[END_REF].

Enhanced by the PRORADAM program (Galvis Vergara et al., 1979a;Huguett et al., 1979) the complex geological history of Colombia since the Proterozoic has been slowly revealed, with different phases of extension and compression, orogenesis, erosion, sedimentation, metamorphism and emplacement of a wide variety of magmatic rocks. Hallmarks in descriptions represent [START_REF] Celada | Potencial de Recursos Minerales en el Oriente Colombiano: Compilación y Análisis de la Información Geológica Disponible[END_REF] and recently [START_REF] Kroonenberg | The Proterozoic Basement of the Western Guiana Shield and the Northern Andes[END_REF] synthetized the actual geological information of E-Colombia.

Different orogenic episodes in the Guiana Shield have been recognized so far [START_REF] Kroonenberg | The Proterozoic Basement of the Western Guiana Shield and the Northern Andes[END_REF]): the Transamazonian Orogeny (2.26 to 1.98 Ga) in the Eastern margin (as result of the collision with Proto-Africa); the Querarí Orogeny at the Western border between Colombia, W-Venezuela and NW-Brazil; and, in the framework of the Rodinia supercontinent formation, the Grenvillian Orogeny (1.3-1.0 Ga), called Putumayo Orogeny by Ibáñez-Mejía et al. (2011) as revealed by some inliers in the Andes but also eastward by gabbroic intrusions [START_REF] Bonilla Perez | Apatite LA-ICP-MS U-Pb and fission-track geochronology of the Caño Viejita gabbro in E-Colombia: Evidence for Grenvillian intraplate rifting and Jurassic exhumation in the NW Amazonian Craton[END_REF].

In the Guainía Department between the Guaviare River to the north, the Caquetá River to the south, and the Chiribiquete mountain range to the west only very few outcrops have been studied in the past. The oldest rocks seem to be felsic to intermediate metavolcanic rocks along the Atabapo River and parts of the Río Negro River, which Galvis et al. (1979) and [START_REF] Huguett | La Amazonía Colombiana y sus recursos. Geología, La Amazonía Colombiana y sus recursos[END_REF] named "Neises del Atabapo-Río Negro" (see [START_REF] López | Cartografía Geológica y Muestreo Geoquímico de las Planchas 297 -Puerto Inírida, 297 Bis -Merey Y 277 Bis -Amanaven, Departamento del Guainía[END_REF]. [START_REF] Kroonenberg | The Proterozoic Basement of the Western Guiana Shield and the Northern Andes[END_REF] proposed that they do not belong to the Mitú-Complex but rather to the Mid-Paleoproterozoic Caicara Metavolcanics and associated them with the 1984 ± 9 Ma Surumu Rhyodacite (SHRIMP U-Pb in zircons, [START_REF] Santos | Age, source, and regional stratigraphy of the Roraima Supergroup and Roraima-like outliers in northern South America based on U-Pb geochronology[END_REF].

The Colombian basement was first described as the "Basement Group" [START_REF] Gansser | The Guiana Shield (S. America) Geological Observations[END_REF] or as the "Guyanese Complex" [START_REF] Pinheiro | Geología -Projeto Radar na Amazônia. Folha NA.19-Pico da Neblina[END_REF], then as the Migmatitic Mitú Complex (Galvis Vergara et al., 1979b) and later as the Mitú Complex [START_REF] López Isaza | Unidades, petrografía y composición química del Complejo Migmatítico de Mitú en los alrededores de Mitú: Réplica[END_REF][START_REF] López Isaza | El Complejo Mitú: una nueva perspectiva[END_REF][START_REF] López Isaza | Ambiente geológico del complejo Mitú y perspectivas de ocurrencias minerales de niobio y tantalio en el territorio colombiano[END_REF]. Its extension has been initially inferred based on geophysical data. Most of this basement is constituted by Precambrian crystalline rocks. It is covered by Cenozoic sediments, as well as by a thick tropical forest covering peneplanes modeled by strong tropical weathering and meandering rivers in extensive alluvial plains, locally interrupted by inselbergs of the old basement.

The Mitú Complex is composed of high-grade metamorphic rocks and granitoids with various compositions and affinities, formed during different orogenic events [START_REF] Kroonenberg | The Proterozoic Basement of the Western Guiana Shield and the Northern Andes[END_REF][START_REF] López Isaza | El Complejo Mitú: una nueva perspectiva[END_REF]. The metamorphosed igneous and sedimentary protoliths appear mainly as quartz feldspathic gneisses with alaskite to monzonite composition, but also as amphibolite, quartzite, metagranitoids, calco-silicate (rich in epidote group minerals) and quartz gneisses, some of them with migmatitic structures.

Large parts of the Mitú Complex (Figure 2) are composed of monzogranites with calc-alkaline affinities, besides meta-to peraluminous granites (U-Pb in zircon LA-MC-ICP-MS Concordia age of 1574 ± 10 Ma for the Mitú granite; Ibáñez-Mejía et al., 2011), as well as of other granites. Among the clearly metamorphic rocks, quartz-feldspathic gneisses are the most abundant with U-Pb zircon ages between 1800-1760 Ma [START_REF] Bonilla | Petrografía, geoquímica y geocronología U/Pb en circones de rocas ígneas y metamórficas a lo largo del Río Cuiarí en el sur del Departamento de Guainía, Colombia[END_REF][START_REF] Cordani | U-Pb zircon ages of rocks from the Amazonas Territory of Colombia and their bearing on the tectonic history of the NW sector of the Amazonian Craton[END_REF][START_REF] Kroonenberg | The Proterozoic Basement of the Western Guiana Shield and the Northern Andes[END_REF][START_REF] López Isaza | El Complejo Mitú: una nueva perspectiva[END_REF]. Medium grade amphibolite facies metamorphic rocks within a series of essentially juvenile magmatic arcs in the Rio Negro Juruena province are interpreted by several workers as subduction-related [START_REF] Cordani | U-Pb zircon ages of rocks from the Amazonas Territory of Colombia and their bearing on the tectonic history of the NW sector of the Amazonian Craton[END_REF][START_REF] Tassinari | Geochronological provinces of the Amazonian Craton[END_REF].

Younger granitoids in the southeastern part (especially Guainía Department) exhibit variable compositions, porphyritic textures and may contain feldspar phenocrysts. They were emplaced ca. 1750 Ma ago during the Statherian [START_REF] Bonilla | Petrografía, geoquímica y geocronología U/Pb en circones de rocas ígneas y metamórficas a lo largo del Río Cuiarí en el sur del Departamento de Guainía, Colombia[END_REF] while some two-mica granite intrusions are 1600-1550 Ma old [START_REF] Bonilla | Petrografía, geoquímica y geocronología U/Pb en circones de rocas ígneas y metamórficas a lo largo del Río Cuiarí en el sur del Departamento de Guainía, Colombia[END_REF]. It must be noticed that other ~1600 -1500 Ma old granites have been described along the whole Colombian eastern territory [START_REF] Cordani | U-Pb zircon ages of rocks from the Amazonas Territory of Colombia and their bearing on the tectonic history of the NW sector of the Amazonian Craton[END_REF]Ibañez, 2010;[START_REF] Priem | Geochronology of the Precambrian in the Amazonas Region of Southeastern Colombia (Western Guiana Shield)[END_REF]Rodriguez et al., 2011).

The Parguaza batholith, emplaced 1550-1500 Ma ago, represents a primary source of Sn, Nb, Ta and REE mineralization [START_REF] Aarden | Minerales de estaño, niobio, tántalo y titanio en la zona del Cano Aguamena, Estado Bolívar, analizados con microsonda de electrones[END_REF][START_REF] Herrera-Bangerter | Die proterozoischen Rapakivigranite von El Parguaza (südliches Venezuela) -Dissertation[END_REF][START_REF] Mariño-Pardo | Potencial minero del Bajo Parguaza[END_REF][START_REF] Mariño | Coltán en Venezuela[END_REF] although it is largely covered by partially lateritic Cenozoic sediments in plains and valleys. In the Venezuelan localities of El Burro, La Fortuna and Aguamena, colluvial -alluvial deposits contain sub-to economic concentrations of minerals such as cassiterite, rutile-(Nb,Ta), columbite-tantalite and REE minerals.

An important feeder of rare element minerals in the Parguaza Batholith seem to be pegmatites, and similarly pegmatites associated to the Mitú Complex (e.g. López Isaza and Cramer, 2012) may also be the main primary source of the monazites and xenotimes discussed here.

Pegmatites

Due to their economic importance and variability, manifold pegmatite classification efforts (e.g. [START_REF] Ginsburg | Principles of geology of the granitic pegmatites[END_REF] were developed over time which are still controversial and object of research. Thus Černý (1991) proposed the existence of two main pegmatite families, the LCT (Li-Cs-Ta) and the NYF (Nb-Y-F), a concept however only applicable for highly fractionated pegmatites if exotic minerals such as spodumene, tantalite, pyrochlore, pollucite, etc. are present [START_REF] London | Ore-forming processes within granitic pegmatites[END_REF]. [START_REF] Černý | The classification of granitic pegmatites revisited[END_REF] and Černý et al. (2012) defined, based on metamorphic environment, mineralogy, elemental composition and texture, five pegmatite classes from which four may host Ta-Nb-Sn mineralization (especially the abyssal, muscovite-rare-element, rare-element and miarolitic classes) and 10 subclasses. The rare-element class is the most important for Nb-Ta mineralization, which are further subdivided depending on major and minor minerals carrying Li, Be, REE and Nb-Ta.

Most of the pegmatites with the LCT signature have compositional affinity with Stype granites (Chappell andWhite, 1974, 2001). Their protoliths are assumed to be pelitic marine sediments as source of Al -and trace elements enrichment like B, Be, P and Sn. From those after anatectic melting of metamorphic schists and gneisses, reduced granites and derived specialized pegmatites could form with high contents in Li, Cs, Ta where fluxing components like B, P, and F play an important role. Many of these trace elements with different grades of incompatibility are contained in micas and feldspars and liberated during the meltforming reactions and may concentrate furthermore in specialized pegmatites above the mineralization limit, i.e. forming abundant and large visible minerals characteristic of many famous and economic important pegmatite ore deposits worldwide.

On the other hand, most of the NYF-family pegmatites are thought to be derived from A-type granites, where "A" may mean "anorogenic" (e.g. [START_REF] Eby | The A-type granitoids: A review of their occurrence and chemical characteristics and speculations on their petrogenesis[END_REF] but also Al-rich or abnormal and their origins are debatable. For example, [START_REF] Frost | Essentials of igneous and metamorphic petrology[END_REF] emphasized their higher Fe-content and proposed to name them ferroan alkali-calcic to calc-alkalic granitic rocks. Their source may be gneissic granulites deep in the continental crust, with some mafic mantle contribution or low-density carbonic fluid. The NYF-family contains chemically complex oxides and silicates that carry heavy rare earth elements (HREE), Ti, U, Th, and Nb > Ta [START_REF] Cerný | Granitic Pegmatites as Reflections of Their Sources[END_REF]. Abundant fluorite or topaz reflects the enrichment in fluorine. The NYF pegmatites are depleted in phosphorus, and tourmaline is uncommon.

Subduction-related I-type granites may be a smaller source both of LCT and NYF pegmatites [START_REF] Černý | The classification of granitic pegmatites revisited[END_REF], but there are a lot of pegmatites worldwide, which may or may not fit clearly in any of these models [START_REF] Bonin | A-type granites and related rocks : Evolution of a concept[END_REF][START_REF] Cerný | Granitic Pegmatites as Reflections of Their Sources[END_REF][START_REF] Dall'agnol | Rapakivi granites from Brazil and adjacent areas[END_REF][START_REF] Dill | Pegmatites and aplites: Their genetic and applied ore geology[END_REF][START_REF] Dill | Accessory minerals in cassiterite: A tool for provenance and environmental analyses of colluvialfluvial placer deposits (NE Bavaria, Germany)[END_REF][START_REF] Gandhi | Essentials of Mineral Exploration and Evaluation[END_REF][START_REF] Kroonenberg | Paleoproterozoic evolution of the Guiana Shield in Suriname: A revised model[END_REF][START_REF] Laznicka | Giant Metallic Deposits -Future Sources of Industrial Metals[END_REF][START_REF] London | The Pegmatite Puzzle[END_REF][START_REF] Sial | Granite-related ore deposits[END_REF].

Selected mineral occurrences

The Guainía region is mostly covered by humid tropical forests and extensive alluvial plains with preferably west-east drainage of the main rivers Guaviare, Inírida, Guainía and Cuyarí to the Orinoco and Amazonas rivers, which constitute also the main ways of communication between local indigenous communities and non-local population. During several fieldtrips, sediments and basement rocks outcropping along the main rivers including inselbergs like Mavicure, Espina, Tortuga, Tabaquen, Matraca and Danta were sampled, and from Vichada to Guainía departments, four localities from north to south were defined for more detailed studies and are described elsewhere, especially the Cachicamo rutiles-(Nb), closely associated to the Parguaza Batholith [START_REF] Franco Victoria | Mineralogía y geocronología de rutilo-(Nb,Ta) relacionado a casiterita y columbita-tantalita provenientes de rocas Mesoproterozoicas del Cratón Amazónico cerca de Cachicamo, Colombia[END_REF]. For this study, we analyzed three of them in the Guainía Department (Figure 2): LOC (4) near to the Inírida River and the Espina hills, LOC (5) near to San Jose at the Guainía River, and LOC (6) near to Barranquilla at the Cuyari River. In the Espina foothills as main mineralization site of LOC (4) N 03° 12' 13.6'', W 068° 09' 19.6'' (Figure 2), monazite occurs in colluvial deposits with large blocks of quartz and muscovite pegmatites. Monazite crystals can reach up to 1 cm in length and are associated with rutile-(Nb,Ta), xenotime, REE-enriched zircon and U-Th bearing minerals and, in some cases, black tourmalines in the panning concentrates (Figure 3).

Monazite and Ta, Nb-minerals at the San Jose -Guainía River

LOC (5)

Near to the Indigenous community of San José labelled LOC ( 5) N 02° 41' 59.6'', W 068° 01' 38.4'' (Figure 2), monazite grains were found in the regoliths overlying pegmatitic dykes emplaced in gneiss and migmatites of the Mitú Complex. However, the most representative crystals occur in colluvium deposits together within blocks and gravels of quartz and muscovite dyke fragments along the Seje and Lombriz creeks. Monazite crystal can reach up to 3 cm in length and are found together with Fe-columbite, rutile-(Nb,Ta) and magnetite (Figure 4). Occasionally isolated xenotime and tourmaline crystals are found in the panning concentrates.

Monazite and Ta, Nb, Zr and REE-minerals from Barranquilla -Cuyari River LOC (6)

Monazite grains were found near Barranquilla labelled LOC (6) N 01° 48' 51.9'', W 068° 41' 12.5'' (Figure 2), in colluvium deposits cut by small drains along the Cuyari River basin, together with smoky quartz blocks, muscovite, beryl and Fecolumbite dikes as well as K-feldspar, quartz and garnet bearing dikes. They are related to plutonic rocks from syeno-granites to acidic granites, some of them with rapakivi texture. Monazite can reach up to 0,5 cm in length and are found together with Fe-columbite, Mn-Tantalite, rutile-(Nb,Ta), xenotime, zircon, and garnet (spessartine) (Figure 5). Isolated crystals of black tourmaline occasionally occur in panning concentrates.

Results

Monazite chemistry

The pXFR-measurements were in good qualitative agreement with the EPMA data (supplementary Table in Annex A) which reveal that all the monazite crystals are Ce and La dominated. As the BSE-images Figure 7 show very inclusion-poor monazites, the calculated mineral formulae should be very near to the real monazite compositions. The HREE Ho, Er, Tm, Yb and Lu were below EPMAdetection limit. In LOC (4), monazite grains are very homogeneous with Ce2O3 between 29 and 31% and ThO2 between 8 and 9 %. The standard deviation among the 7 measured monazite crystals of the main cations is below 0,1%. Their average formula including all elements could be expressed as Ce0.44La0.16Nd0.16Sm0.04Y0.03Gd0.02Dy0.01Pr0.05Th0.08Pb0.01Ca0.05Si0.05P0.91O3.94.

Monazite crystals from LOC [START_REF] Ludwig | User's Manual for Isoplot 3.00 -A Geochronological Toolkit for Microsoft Excel[END_REF] show a more heterogeneous composition with Ce2O3 between 27 and 34% and ThO2 between 4 and 13 % resulting in standard deviations (n=8) of 7% for Th, and around 1% for La, Ce, Sm and Ca.

Their average formula would be Ce0.44La0.16Nd0.14Pr0.04Sm0.04Y0.03Gd0.02 Dy0.01Th0.09Ca0.07Pb0.01Si0.05P,0.91O3.94.

In LOC (6), monazite grains are still less heterogeneous than in LOC (4) and LOC 5 with Ce2O3 between 26 and 29% and ThO2 between 9 and 12 %. The REE standard deviations (n=10) are around or below 0,1%. Their average formula would be: Ce0.42La0.13Nd0.19Pr0.05Sm0.05Y0.05Gd0.02Dy0.01Th0.10Ca0.04Pb0.01Si0.08P0.86O3,94.

In all 3 sites, the sum of cations including P is 2, assuming an idealized monazite formula LnPO4. Phosphor and oxygen deficits in all the formulas of the three sites are probably due to cation charge balance vacancies, especially of Ce( 3+ , 4+ ), and possible occupancy of elements like Si on the P-site. Also, the chondrite-normalized REE distribution patterns in Figure 6 for the monazite crystals from LOC (4, 5 and 6) are very similar among each another. Their REE pattern is much closer to granitic than pegmatitic monazites as defined by Zhu and O´Nions (1999), especially exhibiting higher La and Ce contents than the pegmatitic reference monazites. The Gd and Dy depletion is characteristic of the monazite structure, and HREE enter preferentially in minerals like xenotime, as garnet is nearly absent.

Figure 6 Chondrite-normalized [START_REF] Sun | Chemical and isotopic systematics of oceanic basalts: implications for mantle composition and processes[END_REF]) REE patterns of the investigated monazites (Ho, Er, Tm, Yb and Lu below EPMA-detection limit) and comparison with pegmatitic and granitic monazites after Zhu and O´Nions (1999). Observe the higher coincidence of E-Colombian monazites with those of granitc origin with higher La and Ce in comparision to Zhu and O´Nions (1999) pegmatitic monazites.

Geochronology

EPMA U-Th-Pb chemical ages

Th and Pb contents of all dated monazite grains are relatively high which helps to minimize background related errors [START_REF] Jercinovic | In-situ trace element analysis of monazite and other fine-grained accessory minerals by EPMA[END_REF]. Seven analyses of the monazite crystal from LOC (4) in Espina Hills yield an EPMA age of 1390 ± 17 Ma (2σ, MSWD = 0.59) (Figure 7A). Eight analyses from the San Jose monazite crystal LOC ( 5) return a chemical age of 1523 ± 20 Ma (2σ, MSWD = 1.3) (Figure 7B). Ten spots on a single monazite grain from Barranquilla LOC (6) yield a chemical age of 1527 ± 13 Ma (2σ, MSWD = 0.27) (Figure 7C).

LA-ICP-MS U-Th-Pb ages

The twenty-two analyses in 15 monazite grains from LOC (4) expressed as 208 Pb/ 232 Th versus 206 Pb/ 238 U concordia diagram (Figure 8A) plot all in a concordant position and yield a concordia age of 1346 ± 18 Ma (MSWD (conc+equiv) = 1).

The fourteen analyses in 10 monazite grains of sample LOC ( 5) plot all in a concordant position (Figure 8B). Although they spread along the concordia curve with apparent ages from 1606 down to 1468 Ma, they yield a relatively well constrained concordia age of 1525 ± 15 Ma (MSWD (conc+equiv) = 1.9). The fourteen analyses in 5 monazite grains of sample LOC (6) plot in a concordant position (Figure 8C). Two analyses (grey lines in Figure 8C) yield apparent ages of 1605 and 1650 Ma, respectively. However, the twelve remaining analyses yield a well-constrained concordia age of 1522 ± 16 Ma (MSWD (conc+equiv) = 1).

Discussion

Chemical data

The samples from this study were collected at the surface from colluvial deposits, weathered zones, and rock fragments, without the possibility of studying the magmatic to pegmatitic bodies present at depth. However, the geological, mineralogical, and geochemical data allow us to draw some preliminary, although contradictory conclusions about the three sites.

The chemical data suggest that the monazite crystals from all sites are very similar despite their distance of 70-150 km among each another. They are consistent with a granitic to pegmatitic origin, but without reaching highly specialized rare elements pegmatite characteristics. Parts of the mineral assemblage are indicative of a NYF-family affinity, with a geochemical signature Nb>Ta, Ti, Y, Sc, REE, Zr, U, Th, F [START_REF] Černý | The classification of granitic pegmatites revisited[END_REF]. [START_REF] Melcher | Mineralogical and chemical evolution of tantalum-(niobium-tin) mineralisation in pegmatites and granites. Part 2: Worldwide examples (excluding Africa) and an overview of global metallogenetic patterns[END_REF] proposed a possible NYF-family affinity for placer tapiolite, ixiolite, CGM (columbite group minerals) and rutile samples from not specified E-Colombian sites. One of their columbite, rutile and ixiolite samples however was collected near Barranco Minas at the Guaviare River (Figure 2). The presence of cassiterites and some personal information from the authors demonstrate that most of these samples were collected within the Vichada Department associated with the Parguaza Rapakivi Granite intrusion (see LOC (2) in Figure 2), which is also in agreement with the higher Sn-contents reported by [START_REF] Melcher | Mineralogical and chemical evolution of tantalum-(niobium-tin) mineralisation in pegmatites and granites. Part 2: Worldwide examples (excluding Africa) and an overview of global metallogenetic patterns[END_REF]. However, cassiterites were not found in panning concentrates in the Guainía Department study area. In the ixiolite and CGM-samples those authors also observed a CI-chondrite normalized HREE-enrichment trend and negative Eu and Y anomalies [START_REF] Melcher | Mineralogical and chemical evolution of tantalum-(niobium-tin) mineralisation in pegmatites and granites. Part 2: Worldwide examples (excluding Africa) and an overview of global metallogenetic patterns[END_REF]. [START_REF] Chappell | Two contrasting granite types: 25 years later[END_REF] recognized based on whole rock geochemistry an elevated phosphorus content as diagnostic of the S-type granites, and hence of LCT-pegmatites, whereas the NYF pegmatites are depleted in phosphorus, tourmaline is uncommon and abundant fluorite or topaz would reflect the enrichment in fluorine [START_REF] Cerný | Granitic Pegmatites as Reflections of Their Sources[END_REF]. If this is true, the abundant monazite, xenotime, and black tourmaline concentrations in the three sampling sites as well as the absence of fluor-bearing minerals advocate against a NYF affinity. The REE-monazite data of Zhu and O´Nions (1999) suggest a more granitic than pegmatitic origin of the mineralizations but are only one indication. Also, as the samples are from colluvial deposits, it may be that the two families of pegmatites (LCT and NYF) have been eroded and contributed to the overall chemical and mineralogical composition of the studied samples. We can therefore at this stage conclude that the mineralogical and geochemical data are not very conclusive to propose a clear affinity but support a more complex genesis that involve different primary sources related with S-and A-type granites from which mineralized pegmatites may have evolved.

Age and interpretations

We used EPMA and LA-ICP-MS as complementary technique, EPMA in this study was use for acquiring the chemical composition of the monazite as well as for calculating the chemical age while LA-ICP-MS was used to measure the isotopes U-Th-Pb for calculating directly the ages in a faster way which is better to do provenance analysis. LOC (5 and 6) yield an EPMA chemical and LA-ICP-MS ages of 1523 ± 20 Ma and 1525 ± 15 Ma and 1527 ± 13 Ma and 1522 ± 16 Ma respectively, all within the error, however LOC (4) yield an EPMA chemical and LA-ICP-MS ages of 1390 ± 17 Ma and 1346 ± 18 Ma respectively, a difference of ~45 Ma was found. This difference may be attributed to EPMA measurements due to imperfections in polishing. BSE Images (Figure 9) revealed a homogeneous non-zoned without inclusion monazite crystals for the three localities. For the other hand xenotime from the same pan concentrate used for LOC (4) yield an LA-ICP-MS U-Pb age of 1390 ± 8 Ma (unpublished data yet) that coud be related.

Age relation with the surrounding rocks

The oldest EPMA and LA-ICP-MS based ages at LOC (4) 1390 ± 17 Ma and 1346 ± 18 Ma, LOC [START_REF] Ludwig | User's Manual for Isoplot 3.00 -A Geochronological Toolkit for Microsoft Excel[END_REF] 1523 ± 20 Ma and 1525 ± 15 and LOC (6) 1523 ± 20 Ma and 1525 ± 15 Ma, respectively, indicate a crystallization age similar to Mesoproterozoic anorogenic intrusions recorded in homogeneous anorogenic Atype granites present in the study area (Table 1). This magmatic episodes represented by anorogenic granites in the surroundings of the Orinoco, Guainía, Inírida and Cuyari Rivers may be locally related with coeval granites from Vaupés River and regionally with rapakivi granites of the Pijiguaos range and Parguaza in Venezuela with reported ages of 1545-1500 Ma and in Brazil with granites from the intrusive suite of Serra da Provincia with U-Pb ages of 1600-1532 Ma (see Table 1), intruded at the end of the Rio Negro Juruena orogeny. Several of these intrusive rocks and their post magmatic phases are the primary source of Sn, Ta, Nb and Ti mineralizations.

The crystallization ages obtained from the monazite crystals from the three localities are comparable with those from exposed Mesoproterozoic rocks such as Parguaza in Venezuela and Vichada, Colombia from Orinoco River, Danta and Matraca granites from the Inírida River, Tabaquen and similar granites from the Guainía River and the rapakivi granites from the Cuyarí River reported in the Guainía Department (see Figure 2 and Table 1)). The oldest obtained age range of 1527-1525 Ma from the localities [START_REF] Ludwig | User's Manual for Isoplot 3.00 -A Geochronological Toolkit for Microsoft Excel[END_REF]6) may correspond to monazite mineralization from pegmatitic rocks related to granites near to Tabaquen and San José with U-Pb ages of 1606-1525 Ma and rapakivi granites at Cuyarí River with ages between 1550 -1600 Ma, and the younger ones in the locality (4) with an age range of 1346 to 1390 Ma could correspond to monazite mineralization from pegmatites of Espina, Danta and Matraca granitic rocks, the last one with an age of ~1343 Ma (Table 1). For other hand samples of LOC (2) and Venezuela were mineralogically compared and rutile-(Nb,Ta) U-Pb ages are 1512 ± 12 Ma (Franco et al., 2021).

Intraplate tectono-magmatic phenomena and paleogeographic implications

Intraplate tectono-magmatic phenomena are generally attributed to the ascent of deep mantle plumes, arising from the core-mantle boundary. Mantle plumes are consistent with experimental studies and mantle seismic tomography. In addition, the assembly of supercontinents and their subsequent breakup are inferred to relate to the arrival of mantle plumes [START_REF] Ernst | Large Igneous Provinces (1st edition)[END_REF]. The rising of mantle plumes and/or asthenospheric melts results in tectonic and magmatic manifestations that include crustal uplifts, continental rifting, the emplacement of anorogenic magmas, and LIPs (large igneous provinces) on continents. Some of the most significant global anorogenic magmatic rocks of Earth's history are recognized in the period between 1300 and 1800 Ma [START_REF] Ernst | Large Igneous Provinces (1st edition)[END_REF]. For comparison, in Laurentia, a distinctive A-type or "anorogenic" granites of ∼1.4 Ga age was emplaced heterogeneous Proterozoic crust see [START_REF] Goodge | Origin of Mesoproteroizoic A-type granites in Laurentia: Hf isotope evidence[END_REF], globally this magmatism according to conclusion in [START_REF] Vigneresse | The specific case of the Mid-Proterozoic rapakivi granites and associated suite within the context of the Columbia supercontinent[END_REF] appears to be unique because it requires a supercontinent with a zone of juvenile crust surrounded by older cratons.

Huge Fe-Ti-V deposits hosted by anorogenic gabbro-anorthosite complexes, and A-type granite related systems enriched in elements such as Sn, W, Cu, Zn, Bi, Mo, U, and F are related to intraplate processes and mantle plume associated magmatism [START_REF] Pirajno | Chapter 8.3 Ancient to Modern Earth: The Role of Mantle Plumes in the Making of Continental Crust[END_REF].

Based on the distribution of fragments of LIP of distinct ages, [START_REF] Chaves | Fragments of 1.79-1.75 Ga Large Igneous Provinces in reconstructing Columbia (Nuna): a Statherian supercontinentsuperplume coupling?[END_REF] have proposed a new reconstruction of Columbia (Nuna) supercontinent. This reconstruction is shown in Figure 10, where purple and green circles represent the thermal impact area promoted by 1.52 Ga and 1.38 Ga mantle plume activity, recorded by volcanic mafic dykes and sills (LIP fragments). The red circle in (Figure 10) corresponds to the studied area in the NW Amazon Craton, which probably suffered partial melting generating A-type granites and associated pegmatites with an age comparable to the one of mantle plumes.

Conclusions

The monazite ages obtained by EPMA and LA-ICP-MS dating are in the same range for LOC ( 5) and ( 6) confirm that EPMA may be a useful tool to establish the crystallization age of monazite crystals poor in initial Pb. The high U, Th and radiogenic Pb contents and lack of inclusions and zonations of the homogeneous monazite crystals may make them suitable as internal standard material, however it would be necessary to find their primary source rocks, since there are age variations between the samples and the monazite grains from various primary sources may be in the same colluvial deposit.

The two age ranges suggest at least two enrichment events related with felsic intrusions and possibly associated pegmatites. The oldest ca. 1527 Ma processes forming CGM and the youngest of ca. 1346-1390 Ma forming REE and U-Th bearing minerals and in low proportion rutile-(Nb,Ta) and CGM.

The several kinds of ore minerals found in the three localities suggest different enrichment cycles linked to Mesoproterozoic magmatism. The Nb, Ta, U, Th and REE mineralizations may be result of pegmatitic phases of 1.52 Ga and 1.38 Ga anorogenic granitic magmatism triggered by mantle plumes affecting the Columbia (Nuna) supercontinent.

Figure 1 .

 1 Figure 1. Regional map showing the geochronological provinces and some ages in Ma reported for rocks and minerals in and outside the study area: a. U-Pb in rutile (Nb,Ta) from Cachicamo hills; b. U-Pb in zircon from the basement zone (Bonilla et al., 2013); c. U/Pb in zircon from granitic rocks of Tabaquen in the Guainía River Bonilla (2019).

Figure 2 .

 2 Figure 2. Generalized geological map of Vichada and Guainía Department, eastern part of Colombia showing the localities (4, 5 and 6) (blue stars) and locality (2) (pink star) -

Figure 3 .

 3 Figure 3. Pictures of field and mineral found in panning concentrates from LOC (4) Espina Hills. A. view from the top of Espina Hills; B. colluvial deposits in the foothill of Espina Hills (yellow line shows the limit of the dissectect colluvium and red line basement rock); C and D. sample site and heavy mineral concentrate and pan concentrate, respectively; E. Monazite and xenotime crystals selected from the pan concentrates; F. U-Th bearing minerals; G. Rutile-(Nb) associated to monazite (brown color) and H. Polished epoxy resin puck of monazite for analysis.

Figure 4 .

 4 Figure 4. Pictures of field and mineral found in panning concentrates from LOC (5) San Jose. A. view of rocks of Mitú complex in the Guainía River at San Jose indigenous community; B. Pegmatite with an elevated radioactivity measures; C. Pegmatite with Fecolumbite crystal; D. Sample site of heavy mineral concentration E. Fe-columbite crystals from pan concentrates; F; Huge monazite crystals from pan concentrates; G. Monazite crystals selected from the pan concentrates and H. Polished epoxy resin puck of monazite for analysis.

Figure 5 .

 5 Figure 5. Pictures of field and mineral found in panning concentrates from LOC (6) Barranquilla. A. Colluvial deposits explored by local people from Barranquilla indigenous community; B. Block of two mica granite founded in the base of colluviums; C. Pegmatite with a retaining the shape of a beryl crystal y D Sample of K-feldspar -garnet pegmatite; E. Sample site of heavy mineral; F. Heavy mineral concentrate; G. Monazite crystals selected from the pan concentrates (1-5); H. Columbite-tantalite crystals; I. Garnet crystals and J. Polished epoxy resin puck of monazite for analysis.

Figure 7 .

 7 Figure 7. EPMA U-Th-Pb average ages calculated for each sample corresponding to Espina Hills (A), San José (B) and Barranquilla (C) localities. Data point errors are reported as 2σ. Below, BSE images of the corresponding monazite crystals showing the analyzed points (A', B' and C'). Data table in Annex B.

Figure 8 .

 8 Figure 8. LA-ICP-MS monazite concordia ages of localities 4-6: Espina Hills (A), San José (B) and Barranquilla (C). Data table in Annex C. Data errors are reported at 2σ.

Figure 9 .

 9 Figure 9. BSE images for some crystals use for LA-ICP-MS dating for the three localities showing a very homogeneous crystals of monazite. showing a rich thorium mineral were observed; (A1, 2 and 3) Monazite crystals from LOC (4); (B1, 2 and 3) Monazite crystals from LOC (5), small inclusion < 30 μm of Th mineral was observed; (C1, 2 and 3) Monazite crystals from LOC (6).

Figure 10 .

 10 Figure 10. Columbia (Nuna) supercontinent reconstructed after Chaves and Rezende (2019). Purple and green circles represent the thermal impact area promoted by 1.52 Ga and 1.38 Ga mantle plume activity, recorded by their associated LIP fragments (volcanic, mafic dykes and sills). The red dot corresponds to the study area in the NW-Amazon Craton.

Table 1 .

 1 Compiled ages of some Mesoproterozoic granites from Colombia, Venezuela, and Brazil including the isotopic method use to dating

	Locality	Country	Isotopic system	Age (Ma)	Reference
	Murciélago Hill (Rapakivi granite)	Colombia	Ar/Ar	1237 ± 13	SGC (2013)
	Murciélago Hill (Rapakivi granite)	Colombia	Ar/Ar	1292 ± 8	SGC (2013)
	Angelita Hill (Rapakivi granite)	Colombia	Ar/Ar	1359 ± 8	SGC (2013)
	Bita Hill (Rapakivi granite)	Colombia	Ar/Ar	1361 ± 9	SGC (2013)
	La Hormiga Hill (Rapakivi granite)	Colombia	Ar/Ar	1359 ± 8	SGC (2013)
	La Hormiga Hill (Rapakivi granite)	Colombia	Ar/Ar	1339 ± 8	SGC (2013)
	La Hormiga Hill (Rapakivi granite)	Colombia	Ar/Ar	1366 ± 9	SGC (2013)
	La Hormiga Hill (Rapakivi granite)	Colombia	Ar/Ar	1366 ± 9	SGC (2013)
	La Hormiga Hill (Rapakivi granite)	Colombia	Ar/Ar	1376 ± 14	SGC (2013)
	La Hormiga Hill (Rapakivi granite)	Colombia	Ar/Ar	1383 ± 8	SGC (2013)
	La Venturosa (Rapakivi granite)	Colombia	Ar/Ar	1368 ± 14	SGC (2013)
	La Venturosa (Rapakivi granite)	Colombia	Ar/Ar	1361 ± 8	SGC (2013)
	Tomo River (Rapakivi granite)	Colombia	U/Pb	1392 ± 5	Bonilla et al. (2013)
	Cachicamo Hills (Rapakivi granite)	Colombia	U/Pb	1402 ± 2	Bonilla et al. (2013)
	Inírida River, Matraca and Danta rapakivi granites	Colombia	U/Pb	1343 ± 8	Bonilla et al. (2016)

of ablation 208 Pb/ 232 Th PropErr2σAbs 206 Pb/ 238 U PropErr2σAbs Age 206 Pb/ 238 U PropErr2σAbs Age 208 Pb/ 232 Th PropErr2σAbs

  Annex B. EPMA mineral chemistry data of monazite crystals from the localities Espina Hills LOC (4); San José LOC[START_REF] Ludwig | User's Manual for Isoplot 3.00 -A Geochronological Toolkit for Microsoft Excel[END_REF] and Barranquilla LOC (6) and ages calculated using Th, U and Pb contents. All elements are expressed as main oxides measure in weighted percent (wt.%) independently of their real oxidation state.Annex C. LA-ICP-MS U/Th/Pb isotopic data of monazite crystals from Espina Hills LOC (4), San José LOC[START_REF] Ludwig | User's Manual for Isoplot 3.00 -A Geochronological Toolkit for Microsoft Excel[END_REF] and Barranquilla LOC (6).

	S
	Mass discrimination Common Pb correction e a m p l Analysis point/ oxide P2O5 SiO2 ThO2 UO2 Y2O3 La2O3 Ce2O3 Pr2O3 Nd2O3 Sm2O3 Gd2O3 Dy2O3 CaO PbO Total Standard-sample bracketing with 207 Pb/ 206 Pb, 206 / 238 U, 208 Pb/ 232 Th normalized to No common Pb correction reference material Moacir	U (ppm)	2σ %	Th (ppm)	2σ %	Pb (ppm)	2σ %	Age (Ma)	2σ (abs)
	Uncertainty level and 8 24.89 1.87 11.07 0.39 2.06 8.56 26.92 3.22 12.71 3.55 Ages are quoted at 2 sigma absolute, propagation is by quadratic addition 1.50 0.52 1.17 0.81 99.24 2819 3.5 97283	1	7519	1.3	1521	39
	propagation 9	according to Horstwood et al. (2016). Reproducibility and age uncertainty of 24.74 1.53 9.62 0.31 1.90 8.59 27.62 3.26 13.33 4.00 1.68 0.43 1.08 0.71 98.80 2195 4.6 84541	1	6591	1.5	1548	43
	10	reference material are propagated. 25.66 1.76 10.61 0.34 2.08 8.55 27.08 3.39 12.77 3.82	1.46	0.39 1.27 0.77 99.95 2404 4.2 93241	1	7148	1.4	1524	40
	Quality control / Validation	Manangoutry : 548 ± 6 Ma (MSWD=0.98 ; n=11)
	1
	S
	a m p l Mnz_Loc (4) p1 Analysis point/ oxide P2O5 SiO2 ThO2 UO2 Y2O3 La2O3 Ce2O3 Pr2O3 Nd2O3 Sm2O3 Gd2O3 Dy2O3 CaO PbO Total 0.0670 0.0051 0.230 0.016 1327 Mnz_Loc (4) p2 0.0660 0.0050 0.230 0.016 1327 e 1 27.99 1.05 8.65 0.27 1.38 10.83 30.00 3.04 10.75 2.90 1.18 0.64 1.49 0.57 100.73 1896 5.3 76016 U (ppm) 2σ % Th (ppm) 22 26 Mnz_Loc (4) p3 0.0716 0.0054 0.238 0.017 1377 22 2 26.28 1.07 8.56 0.26 1.51 10.54 29.74 3.02 11.02 2.97 1.28 0.61 1.46 0.56 98.86 1813 5.5 75225 Mnz_Loc (4) p4 0.0685 0.0052 0.239 0.017 1380 19 L 3 26.32 1.16 8.14 0.18 1.45 11.00 30.23 3.04 11.27 2.77 1.23 0.60 1.13 0.51 99.02 1131 8.8 71534 Mnz_Loc (4) p5 0.0673 0.0051 0.229 0.016 1322 22 O 4 27.30 1.14 8.33 0.20 1.40 11.10 30.48 3.16 11.31 2.83 1.28 0.47 1.22 0.53 100.73 1297 7.7 73204 Mnz_Loc (4) p6 0.0697 0.0052 0.233 0.016 1352 29 C 4 5 26.08 1.37 8.51 0.18 1.41 11.00 30.23 3.25 11.52 2.60 1.19 0.51 0.94 0.55 99.32 1111 9.0 74786 6 25.55 1.62 8.09 0.18 1.29 11.46 30.74 3.23 11.81 2.49 1.21 0.45 0.80 0.51 99.42 1134 8.8 71095 Mnz_Loc (4) p7 0.0690 0.0053 0.238 0.016 1371 22 7 26.15 1.04 8.65 0.28 1.48 10.71 29.31 2.96 10.86 2.89 1.21 0.68 1.45 0.58 98.23 1984 5.0 76016 Mnz_Loc (4) p8 0.0687 0.0053 0.239 0.017 1379 22	2σ % 1 1 1 1 1 1 1	Pb (ppm) 1311 1291 5291 1397 5198 1339 4734 1316 4920 1361 5106 4734 1350 5384 1343	2σ % 1.9 1.9 2.1 2.0 2.0 2.1 1.9	Age (Ma) 1393 1387 1366 1378 1412 1374 1412	2σ (abs)
	1 2 Mnz_Loc (4) p9 26.26 1.26 12.23 0.46 1.53 9.63 27.55 2.86 9.16 27.61 1.19 11.95 0.44 1.22 9.95 28.21 2.95 9.49 0.0636 0.0051 0.230 3 25.88 1.15 10.49 0.40 1.29 10.10 28.86 3.01 9.56 Mnz_Loc (4) p10 0.0676 0.0052 0.233	3.26 3.40 3.53	1.49 1.52 0.016 0.58 2.02 0.89 99.18 3371 3.0 107477 0.50 1.91 0.87 101.21 3210 3.1 105017 1325 55 1.53 0.53 1.65 0.79 98.75 2939 3.4 92186 0.016 1347 30	1 1 1	8262 8076 1245 7334 1321	1.2 1.2 1.4	1502 1506 1549
	L Mnz_Loc (4) p11 4 26.40 1.06 9.56 0.35 0.98 10.49 30.38 3.08 9.93 0.0637 0.0049 0.231 O C 5 5 25.10 1.23 11.04 0.44 1.14 10.42 29.41 2.87 9.38 6 25.39 1.20 11.14 0.44 1.20 9.83 27.86 2.88 9.66 Mnz_Loc (4) p12 0.0683 0.0052 0.233 7 27.96 0.77 4.10 0.21 1.44 13.58 33.57 3.15 10.08 1.79 3.48 3.09 3.34 Mnz_Loc (4) p13 0.0664 0.0051 0.232	1.46 0.016 0.32 1.52 0.69 99.69 2551 3.9 84013 1334 28 1.40 0.50 1.78 0.84 98.64 3261 3.1 97020 1.36 0.49 1.85 0.83 97.47 3255 3.1 97898 0.016 1345 27 0.77 0.39 0.59 0.32 98.71 1578 6.3 36004 1.00 2933 3.41 1 6405 1.6 1248 1 7798 1.3 1 7705 1.3 1334 0.016 1340 23 1298	1495 1556 1527 1529
	8 Mnz_Loc (4) p14 27.49 1.34 5.86 0.27 1.55 12.35 32.03 3.31 10.95 2.22 0.0696 0.0053 0.238	4 0.37 0.72 0.45 100.00 2026 4.9 0.016 1.10 1374 22	51506 1.00 4140 2.42 1360	1530
	1 2 Mnz_Loc (4) p15 23.43 2.27 10.89 0.37 2.11 8.36 27.95 3.43 12.98 3.34 L O 24.17 2.20 10.72 0.34 2.15 8.39 27.91 3.41 12.85 3.40 0.0686 0.0053 0.238 3 24.88 2.44 11.49 0.38 2.18 8.46 27.97 3.47 12.72 3.51 Mnz_Loc (4) p16 0.0683 0.0052 0.240 4 24.27 2.08 10.07 0.35 1.94 8.60 28.78 3.22 13.15 3.57 Mnz_Loc (4) p17 0.0711 0.0054 0.244	4 0.43 0.73 0.79 98.46 2652 3.8 95701 0.44 0.73 0.78 98.77 2397 4.2 94207 0.016 1.39 1.28 1373 23 1.31 0.37 0.72 0.85 100.73 2707 3.7 100974 0.017 1383 22 1.33 0.32 0.69 0.74 99.10 2522 4.0 88495 0.017 1406 21	1 1 1 1	7334 7241 1341 7891 1335 6869 1388	1.4 1.4 1.3 1.5	1514 1529 1547 1529
	C Mnz_Loc (4) p18 5 24.89 2.05 9.95 0.34 2.02 8.54 28.28 3.48 13.13 3.56 0.0662 0.0051 0.231 6 6 25.27 2.12 10.12 0.34 2.12 8.65 28.19 3.38 13.02 3.66 7 25.30 1.50 9.81 0.35 2.19 8.51 28.21 3.37 12.54 3.69 Mnz_Loc (4) p19 0.0672 0.0051 0.236	1.36 0.016 0.47 0.71 0.73 99.51 2441 4.1 87441 1331 26 1.31 0.52 0.68 0.74 100.11 2431 4.1 88935 1.59 0.41 1.10 0.71 99.29 2537 3.9 86210 0.017 1356 30	1 1 1	6777 1294 6869 6591 1314	1.5 1.5 1.5	1530 1527 1503

2

Points

Acknowledgment

We wish to thank to the indigenous communities of Chorro Bocón, San Jose y Barranquilla for facilitating access to the study area, recognition, and sampling. This work would not have been possible without the support of the other members of GEGEMA group, mainly to PhD. Amed Bonilla Perez and Zeze Amaya Perea. We are indebted to the Universidad Nacional de Colombia which also gave financial support through the grant Hermes 35441 and to the Federal University of Minas Gerais. The Funds CTeI of the Sistema General de Regalías financed the project "Investigación de minerales estratégicos, industriales y materiales de construcción, Región Llanos" prompted by Colciencias and supervised by the Vaupés Department Government which allowed to realize field trips and large parts of the analysis. Two anonymous reviewers helped to improve the manuscript considerably.

Annex A. Supplementary table of operating conditions for the LA-ICP-MS equipment (GeOHeLiS Platform).

Laboratory & Sample Preparation

Laboratory name

GeOHeLiS


Comment on "Discussion : Extracting thermal history from low temperature thermochronology/ A coment on the recent exchanges between Vermeesch and Tian and Gallagher and Ketcham", by Paul Green and Ian Duddy, Earth Science Reviews, https://doi.org/10.1016/j.earscirev.2020.103197 Kerry Gallagher, Ge osciences/OSUR, University of Rennes, Rennes, France

The discussion of Green and Duddy (which I will refer to as Geotrack, and use quote marks to indicate text from their discussion) aims to "highlight a key issue" concerning different approaches to thermal history modelling with thermochronological data. This key issue seems to be based around an assumption of continuous cooling in thermal histories modelling. While I and many others would agree with the statement of Geotrack that thermochronological data have limited thermal history information and the results are dependent on the nature of the assumed style of history, I would like to make one clear statement regarding the implementation of thermal history models in QTQt. This statement is : there is no assumption of continuous cooling history. Indeed, there is no default assumed style of thermal history. Perhaps then, the key issue highlighted by Geotrack represents a misunderstanding of how the QTQt software (and the algorithms implemented therein) work and how the output should be assessed. I welcome the chance to clarify these points further below.

As in most approaches, a thermal history in QTQt is parameterized in terms of discrete time-temperature points and linear interpolation between these points is used to construct a thermal history function. Note that this linear heating-cooling segment type of thermal history is not what we expect in reality. Given the nature of thermal diffusion, temperature histories should be relatively smooth, even when depth changes associated with burial or erosion are rapid and effectively linear. Parameterizations of the thermal history used with linear segments will then tend to over-estimate the maximum temperature and underestimate the duration spent at or near the maximum temperature.

Irrespective of this point, a specified thermal history function is used to make predictions which are then compared with observations through a quantitative measure known as the likelihood (or misfit). The algorithm in QTQt (reversible jump Markov J o u r n a l P r e -p r o o f chain Monte Carlo, RJMCMC) used to sample candidate thermal histories is formulated in a Bayesian framework and has the characteristic of parsimony. This is the preference for simpler thermal history solutions over more complex ones, provided the former can provide adequate predictions relative to the observations (i.e. the model can fit the data).

As shown by [START_REF] Gallagher | Transdimensional inverse thermal history modelling for quantitative thermochronology[END_REF], taking the single thermal history which provides the best fit to the observed data but has no constraints on complexity can lead to a which is grossly over-complex, particularly when using data from just one sample. This was demonstrated using near perfect synthetic data produced from a known and simple thermal history in which spurious rapid heating-cooling events are inferred from the much simpler true thermal history (see figure 2 of Gallagher 2012).

When a simple thermal history is inferred from thermochronological data alone this implies a lack of information in the data. If a sample is on the surface at the present day, then the simplest possible model will be one of cooling from an unknown timetemperature point in the past. In QTQt the first sampled model is based on a single timetemperature point drawn from the prior (the range of time-temperature specified for sampling), although it is also possible to specify a different starting model if desired. If the present day temperature is at the low end of the prior temperature range (as we anticipate for a surface sample), there is a higher probability that the first sampled temperature point in the past will be hotter than the present day temperature, producing a cooling thermal history. The sampling algorithm progresses, adding new time-temperature points and moving, or deleting, existing ones, to produce new proposed thermal histories. Apart from the prior distribution, there are no default constraints on where the time-temperature points can be selected. If the data really need more complexity in the thermal history, the models will adapt and we will see more structure in the solutions, according to the information in the data. Given, that, there is certainly no requirement or format underlying QTQt to produce continuous cooling or episodic heating-cooling events (the latter implied by Geotrack at the start of their 2nd last paragraph).

The predictions from each proposed thermal history model are compared to the observations (through the likelihood) and a probability-based decision is made to accept the proposed model or not. If the data require a more complex thermal history (e.g. heating/cooling events, changes in cooling rate, etc.), then new time-temperature points will tend to be accepted. A basic characteristic of any MCMC sampling algorithm is that J o u r n a l P r e -p r o o f the initial model is forgotten so the final results are independent of the starting model. Therefore, a simple starting model (e.g. linear cooling) has no effect on the final result. The final result is of course a distribution of thermal histories, referred to as the posterior, and this distribution is more informative than just (one) thermal history (as in the title of the comment of Geotrack).

An initial modelling exercise with no or minimal constraints on the samples is useful. Minimal constraints, which can also incorporate uncertainty, could represent present day temperatures and stratigraphic ages for samples. The rationale for modelling with no constraints is to assess explicitly what thermal history information the data alone can provide. Here I directly contradict the statement of Geotrack that the "much of VTGK debate appears to centre on methods to extract information that is not within the data". With a single sample or a single AFT analysis, the thermal history information is often limited and I think there Geotrack and most of us would agree again.

Given this, there is a clear motivation for modelling multiple samples together (joint modelling -see Gallagher et al. 2005, Stephenson et al. 2006). In doing that, valid thermal history information will tend to be reinforced, while data noise will tend to be cancelled out as it is random. This also reduces the tendency to over fit the data, in that we reduce the potential of unintentionally treating data noise as real signal. However, the relevant point here is that a thermal history inferred from the data alone, and that fits the data, can then be considered as an end member model. When using a sampling algorithm that prefers simpler models to complex ones, then if all else (e.g. the data fit) is equal, we can also think of this end member model as a lower limit on the complexity of the thermal history. Thus, the true thermal history may be more complex, but the data alone do not require nor justify more complexity.

In the context of QTQt, we need to remember that we have many models to choose from (which define the posterior distribution). In chossing one model, we typically consider the maximum likelihood (ML) model, maximum posterior (MP) model or the expected model. It seems to be this latter model that Geotrack focus on as the assumption of continuous cooling (and I thank Pieter Vermeesch for pointing that out to me). The expected model is not actually a sampled model and there are no asumptions about its form. It is the weighted average of the population of accepted sampled models, with the weighting being the posterior probability. In this case, the data fit for the expected model can be variable depending on the features of individual models captured J o u r n a l P r e -p r o o f in this average model. If a range of models, or different subgroups of models, are compatible with the data, then the expected model may effectively fall between these good models. This behaviour is captured in an old joke that a statistician can have her head in an oven and her feet in ice, but on average she feels comfortable.

In contrast to the expected model, the ML and MP models are both individual thermal histories that were directly sampled during the model run. The first is the sampled model that best fits the data, is often relatively complex and can have features that do not change how well we fit the data. The second is the sampled model that tries to balance fitting the data with keeping the model relatively simple. This model will then not fit the data as well as the first, but in general it will not be too different. Sometimes, these two models exhibit characteristics common to subgroups of the overall population of accepted models, demonstrating that there is a range, or even clusters, of possible thermal history solutions, with possibly quite different forms. This can only really be assessed by looking at the population of accepted models.

An example of the differences between the various models can be seen in figure 2 of [START_REF] Gallagher | Comment on the reply to the Comment on "Thermal history modelling: HeFTy vs. QTQt" by Vermeesch and Tian[END_REF], reproduced here as figure 1, based on synthetic data produced from a known thermal history with 2 heating/cooling events. In this case, the ML solution is close to the true solution, while the MP solution is simpler and notably does not imply any reheating, which would clearly require more complex models (i.e. more time-temperature points). The MP model does not imply the same maximum temperatures as the ML model at the time of reheating. However, the difference between the predictions for these two models is minor, especially given the noise anticipated in real data. Figure 1 also shows a selection of the accepted models colour coded by the likelihood and posterior values, demonstrating two different forms of models. While the models coded by the likelihood show the two reheating cooling events in the true model, the inferred rates of heating/cooling are quite variable. The models coded according to the posterior suggesting the earliest reheating event is not particularly evident in, or not really required by, the data. Some models do hint at limited resolution of the later event, but these are more complex models and their scarcity suggests this information, or the evidence of reheating, is not particularly strong. It is worth noting here that the credible intervals are informative about the resolution of the temperature at different times. In this example, the credible interval becomes relatively narrow around the time of the maximum temperature for the two heating events, but broader elsewhere, J o u r n a l P r e -p r o o f demonstrating less resolution on the heating/cooling rates and the thermal history between those times.

Returning to the expected model in figure 1, in this case it does not predicted the data nearly as well as the ML or MP models. As stated above, it is the average of the accepted sampled models, and averaging will tend to act as a smoothing process. It also reflects the fact that the posterior distribution is often not symmetrical, but skewed to lower temperatures. Thus, in this example, the expected model does not capture the maximum temperatures of the heating events, while it also has low temperatures relative to the MP model between the heating events. As a result, it, over-predicts the AFT age relative to the ML and MP models.. For a skewed posterior distribution, the expected model also does not always follow the mode (or maximum value) of the posterior distribution at each time (brighter colours in figure 1a). These points actually define the maximum mode model (MM in figure 1) and we can see this is similar to the MP model in this example. However, this is not always the case, for example if the posterior distribution is multi-modal.

So sometimes the expected model will not be able to make suitable predictions as it may not appropriately capture the particular features or temperatures in the sampled thermal histories that lead to better data fitting. In that case, this particular model should not be presented as representative of the good data fitting solutions. Then we might prefer to present the MP and/or ML models, although the discussion above demonstrates that each should be considered in the context of the population as a whole.

We also need to consider also how these models fit or explain the observations when considering model choice. Referring back to the original article of [START_REF] Vermeesch | Thermal history modelling: HeFTy vs[END_REF] an example of poor data fitting related to poor model choice is the linear regression example (their figure 6). As stated in the first comment of Gallagher and Ketcham (2017), the best fit straight line model presented just does not fit the data and the approach implemented could not adapt to the information in the data produced from a more complex (quadratic) function. The key point here is that we need to assess the quality of the data fit as part of the modelling-interpretation process, as I have gently suggested previously [START_REF] Gallagher | Comment on 'A reporting protocol for thermochronologic modeling illustrated with data from the Grand Canyon' by Flowers, Farley and Ketcham[END_REF]).

If we want to narrow the range of possible models, then adding constraints clearly becomes an important aspect of thermal history modelling. Any inferred thermal history model will be conditional on the constraints and the issue then is how robust any J o u r n a l P r e -p r o o f imposed constraint is. Constraints as I define them here may be parametric (e.g. rates of temperature change over time, number of time-temperature points defining the thermal history) or more geological in nature. In practice, if we understand the geological history of a region and have total confidence in a geological constraint, based on independent geological evidence, this should be specified in advance of any thermal history modelling. An example of a such a constraint was presented by [START_REF] Bernard | Evidence for Eocene-Oligocene glaciation in the landscape of the East Greenland margin[END_REF] when modelling a vertical profile from a fjord in East Greenland. The uppermost sample was collected a few tens of metres under a well dated basalt flow. It was reasonable to impose a constraint that that sample was near the surface at the time the basalt flow formed. When an imposed constraint is less sure, the scientific method would suggest we assess how data predictions change with and without such a constraint. Indeed, [START_REF] Bernard | Evidence for Eocene-Oligocene glaciation in the landscape of the East Greenland margin[END_REF] did that also and presented results demonstrating that a postbasalt heating event can be partially recovered for some samples without the near surface constraint.

Another way of using geological information is to consider it after modelling, justifying the relevance or significance a posteriori. For example, we can force heating/cooling events in the model set-up, and then argue that we can find geologically reasonable reasons to justify the resulting thermal history model. Again this may be that there is sediment or volcanic of a certain age found nearby, and then we assume that the sample was at or close to the surface at that time. In general, these arguments will have uncertainty and subjectivity and should presented in that context. For example, what is nearby, how well defined is the age of preserved sediment, can we be sure that extrapolating restricted outcrop over several tens km or more is valid ? The recent replies of [START_REF] Braun | Response to comment by Japsen et al. on "A review of numerical modeling studies of passive margin escarpments leading to a new analytical expression for the rate of escarpment migration velocity[END_REF] to the comment of [START_REF] Japsen | Elevated passive continental margins: Numerical modeling vs observations. A comment on Braun[END_REF] and [START_REF] Jess | Reply to: Thermal history solutions from thermochronology must be governed by geological relationships: A comment on Jess et al[END_REF] to the comment of [START_REF] Green | Thermal History Solutions From Thermochronology Must be Governed by Geological Relationships: A Comment on[END_REF] highlight some issues concerning geological constraints used in thermochronology. Indeed, we could rephrase the statement of [START_REF] Japsen | Elevated passive continental margins: Numerical modeling vs observations. A comment on Braun[END_REF] quoted in Braun (2019) -"...models can prove anything with the appropriate choice of parameters" to model results can be forced to prove anything with the appropriate choice of constraints,. The point here is that constraints are not necessarily facts bit results are strongly conditional on the constraints and their validity.

Consequently, resulting models do not provide apodictic evidence in support of a given hypothesis.

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

In their discussion, Geotrack refer more than once to episodic heating-cooling events, e.g. "episodic heating cooling events may be much more common that generally accepted", and that even without geological constraints, "thermal history constraints can still be obtained within a framework of episodic heating and cooling, using assumed heating and cooling rates". The latter is clearly true, but the former statement seems to be circular reasoning in that if we impose heating-cooling events, then that is what we will get. When geological constraints on the surface are imposed the effect is the same as we are effectively forcing cooling to the surface, then typically reheating. If modelling data does not produce heating-cooling events without imposing them and/or the data can be explained without such events, it is difficult to agree that "a signal is actually present in the data". Rather, we can say that the data are consistent with these events, but do not necessarily require them.

I do not know if Geotrack have ever used QTQt but I can state that I have never had access to the software used by Geotrack. This software is not obviously available (nor indeed the annealing model implemented in it) for independent assessment nor have the details been published. Therefore, based on the Geotrack discussion, their publications and available commercial reports, I can only speculate on how their modelling is implemented. A thermal history seems to be based on, or parameterized, in terms of heating/cooling events, defined within a specified rate of temperature change.

Geotrack state that "specific constraints can only be obtained by fixing heating and cooling rates (essential for comparing results between samples)". Here constraints implies inference on the nature of the thermal history, although clearly such inference depends on the imposed constraints (limits on the heating/cooling rates for example).

Presumably, some kind of starting thermal history is specified (perhaps continuous cooling), and, perhaps depending on how this initial model can explain the data, a first heating cooling event is searched for. The likelihood for that thermal history is calculated, then an additional, more recent, event is added, presumably under the constraint that the maximum temperature during heating is lower than that of the first event. More events are added until the fit to the observed data is deemed to not improve sufficiently to justify the last event. The thermal history that best fits the data (the maximum likelihood model) is then chosen and a form of resolution analysis is made. This step seems to be a form of the likelihood ratio test to estimate an uncertainty about J o u r n a l P r e -p r o o f given time-temperature point and the results are presented as range in time-and temperature about each point.

In general, the publications of Green, Duddy and their various collaborators do not seem to present the predictions from their preferred model, nor the predictions from alternative models (e.g. with less heating-cooling events). It is therefore not possible to assess the variations in the data fit for different models and make appropriately informed comparisons to thermal histories inferred from other approaches. Given the general availability of modelling software such as QTQt and HeFTy, perhaps this comment will encourage Geotrack to provide access to their software to allow the research community to make their own judgments concerning the validity and generality of the results it produces.

Figure Captions

Figure 1 This figure is taken from [START_REF] Gallagher | Comment on the reply to the Comment on "Thermal history modelling: HeFTy vs. QTQt" by Vermeesch and Tian[END_REF], which has a more detailed figure caption. (a) Output from QTQt showing the maximum likelihood (ML), maximum posterior (MP), maximum mode (MM) and expected (Exp) models, together with the marginal posterior distribution and the 95% credible interval (the region between thinner black lines). Note how the credible intervals narrow around the times of peak heating. . The values of the observed fission track age and mean track length and their predictions for each of the 4 individual models. SP represents sampled predicted, which summarises the mean and standard deviation of the predicted ages and mean track lengths for all accepted modelsLL is the log likelihood for each model .

(b) The predicted track length distributions for the 4 models highlighted in fig. 1a. (c) Representative thermal histories from the posterior distribution, colour coded by the relative likelihood, calibrated against the maximum likelihood with a value of 100%. The black line is the expected model with the 95% credible interval. The higher likelihood heating-cooling thermal histories are relatively complex and the timings of reheating events are dispersed, as are the pre-reheating temperatures. Simpler models similar to the maximum posterior model in 1a, also have relatively high likelihoods. Most of the accepted models fall into one of these two groups, effectively defining two local maxima in the likelihood. (d) Representative thermal histories from the posterior distribution, colour coded by the relative posterior, calibrated against the maximum posterior probability with a value of 100%. In comparison with figure 1c, we see the simpler models define the higher posterior probability, while the complex models have moderate to low posterior probability. This reflects limited information in the data on the form of the true thermal history.

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

There is no conflict of interest J o u r n a l P r e -p r o o f