Mathilde Bablon
email: mathilde.bablon@u-psud.fr

Xavier Quidelleur

Pablo Samaniego

Jean-Luc Le Pennec

Pierre Lahitte

Céline Liorzou

Jorge Eduardo Bustillos

Silvana Hidalgo

Eruptive chronology of Tungurahua volcano (Ecuador) revisited based on new K-Ar ages and geomorphological reconstructions

Keywords:

This study focuses on the evolution through time of Tungurahua volcano (Ecuador), and provides new information regarding its history. Eighteen new K-Ar ages constrain its construction and the activity of its three successive edifices. We show that the volcano is much younger than expected. Indeed, the older edifice activity only began around 293 ± 10 ka, and ended at 79 ± 3 ka. After ~50 ka of quiescence, the second edifice started growing at 29 ± 2 ka after a major sector collapse, and itself collapsed at ~3 ka. Since then, the third edifice filled the amphitheatre and is still active. Together with numerical reconstructions of the morphology of the three edifices flanks before erosion, these new ages allow us to quantify the magmatic productivity rates during their construction, from 0.6 ± 0.3 and 0.9 ± 0.2 km 3 /ka for the two older edifices to 2.5 ± 1.0 km 3 /ka for the youngest, as well as an erosion rate of 0.2 ± 0.1 km 3 /ka, occurring since the end of Tungurahua I construction. Major and trace element contents of lavas from the three edifices display rather similar trends.

Combined with our new ages, the magmatic signature through time does not seem to have been significantly affected either by the sector collapses experienced by the volcano, or by changes of the deep magmatic source. Finally, our results show that the K-Ar dating method by the unspiked Cassignol-Gillot technique performed on groundmass can be successfully applied to lava flows older than the Holocene, while the uncertainties related to younger units can prevent an accurate age determination. Particularly, this method can be applied to Quaternary volcanoes from the Ecuadorian arc, with many of them remaining without knowledge of the timing of their past activity.

Introduction

The Ecuadorian arc presents a remarkably dense volcanism, composed of about 85 Quaternary volcanic edifices [START_REF] Hall | Ecuadorian Andes volcanism: A review of Late Pliocene to present activity[END_REF][START_REF] Bernard | Volcanes Cuaternarios del Ecuador Continental[END_REF]. Twenty-five of them are potentially active or presently erupting, such as Sangay, Cotopaxi, Reventador and Tungurahua volcanoes (Fig. 1; [START_REF] Bernard | Volcanes Cuaternarios del Ecuador Continental[END_REF]. Tungurahua volcano (5023 m a.s.l.; Lat. 01°28'S; Long. 78°27'W) is one of the most active volcanoes in the Andean Northern Volcanic Zone with at least one eruption per century since the 13 th century [START_REF] Le Pennec | The AD 1300-1700 eruptive periods at Tungurahua volcano, Ecuador, revealed by historical narratives, stratigraphy and radiocarbon dating[END_REF][START_REF] Le Pennec | Combining historical and 14C data to assess pyroclastic density current hazards in Baños city near Tungurahua volcano (Ecuador)[END_REF]. It is characterized by a strombolian to subplinian activity, and experienced at least two major sector collapses during the last 30 ka [START_REF] Hall | Tungurahua Volcano, Ecuador: structure, eruptive history and hazards[END_REF][START_REF] Le Pennec | A Devastating Plinian Eruption at Tungurahua Volcano Reveals Formative Occupation at ∼1100 cal BC in Central Ecuador[END_REF]. Since 1999, the ongoing eruption has seriously threatened surrounding villages and infrastructures [START_REF] Samaniego | Mapa de los peligros potenciales del volcán Tungurahua[END_REF][START_REF] Le Pennec | Impact of tephra falls on Andean communities: The influences of eruption size and weather conditions during the 1999-2001 activity of Tungurahua volcano, Ecuador[END_REF]. The recent activity is well studied and carefully monitored (e.g., [START_REF] Molina | Three-dimensional P-wave velocity structure of Tungurahua Volcano, Ecuador[END_REF][START_REF] Arellano | Degassing patterns of Tungurahua volcano (Ecuador) during the 1999-2006 eruptive period, inferred from remote spectroscopic measurements of SO2 emissions[END_REF][START_REF] Kumagai | Ascending seismic source during an explosive eruption at Tungurahua volcano, Ecuador[END_REF][START_REF] Hall | Pyroclastic density currents (PDC) of the 16-17 August 2006 eruptions of Tungurahua volcano, Ecuador: Geophysical registry and characteristics[END_REF][START_REF] Bernard | Pyroclastic flow erosion and bulking processes: comparing field-based vs. modeling results at Tungurahua volcano, Ecuador[END_REF][START_REF] Hidalgo | SO2 degassing at Tungurahua volcano (Ecuador) between 2007 and 2013: Transition from continuous to episodic activity[END_REF], but the timing of its pre-Holocene history remains poorly documented. Reconstructing the past eruptive history of Tungurahua volcano is essential to better understand its growth and evolution. This study combines stratigraphic analyses, new K-Ar ages and geomorphometric reconstructions to better constrain the construction and destruction stages of Tungurahua volcano through time, and to quantify its magmatic output rates, as well as the erosion rate occurring during quiescence periods. In addition, geochemical analyses allow us to study the long-term evolution of the lavas composition. We show in particular that the initial activity of Tungurahua volcano is much younger than previously thought, and that its construction is characterized by an increase of the eruptive rate since the last 3 ka BP.

Geological context

The Andean volcanic arc originates from the subduction of the oceanic Nazca plate beneath the continental South American plate. The arc comprises four distinct zones, including the Northern Volcanic Zone (NVZ), which lies in Ecuador and Colombia. To the west of the NVZ, an oceanic plateau, the Carnegie ridge, subducts below Ecuador (Fig. 1a). It has been proposed that the subduction of this ridge may impact the thermal gradient at depth and the deep magmatic sources (e.g., [START_REF] Samaniego | Transition from calc-alkalic to adakitic magmatism at Cayambe volcano, Ecuador: insights into slab melts and mantle wedge interactions[END_REF][START_REF] Bourdon | Magmatic response to early aseismic ridge subduction: the Ecuadorian margin case (South America)[END_REF][START_REF] Hidalgo | Role of crustal and slab components in the Northern Volcanic Zone of the Andes (Ecuador) constrained by Sr-Nd-O isotopes[END_REF][START_REF] Ancellin | Across-arc versus along-arc Sr-Nd-Pb isotope variations in the Ecuadorian volcanic arc[END_REF], which could explain the high density of volcanoes observed in Ecuador [START_REF] Martin | Why Archaean TTG cannot be generated by MORB melting in subduction zones[END_REF]. Tungurahua volcano is located in the southern part of the Ecuadorian volcanic arc, on the Eastern Cordillera (Fig. 1b). Constructed upon the Palaeozoic-Mesozoic metamorphic basement [START_REF] Aspden | The geology and Mesozoic collisional history of the Cordillera Real, Ecuador[END_REF], this andesitic stratovolcano is surrounded by the Puela (S), Chambo (W) and Pastaza (N) rivers (Fig. 2).

The upper part of the edifice presents steep flanks with 40° slopes, while ~20-25° slope plateaux incised by deep valleys constitute its lower part, with a progressive change in steepness. The morphology of the eastern flank shows features of glacial erosion (u-shaped valleys; [START_REF] Clapperton | Glacial and volcanic geomorphology of the Chimborazo-Carihuairazo Massif, Ecuadorian Andes[END_REF][START_REF] Heine | Tropical South America during the last glacial maximum: evidence from glacial, periglacial and fluvial records[END_REF], as well as deep fluvial incisions due to the tropical precipitation regime. It contrasts with the western flank which is smoothed by the recent volcanic deposits. The internal structure and plumbing system of Tungurahua volcano are not well known. Nevertheless, petrological, melt inclusions, seismic tomography and interferometric studies suggest the presence of a subvertical upper conduit located above a shallow magmatic reservoir, supplied by mafic magmas from a deeper reservoir, located around 5 and 8.5 km below the summit, respectively [START_REF] Molina | Three-dimensional P-wave velocity structure of Tungurahua Volcano, Ecuador[END_REF][START_REF] Samaniego | Petrological analysis of the pre-eruptive magmatic process prior to the 2006 explosive eruptions at Tungurahua volcano (Ecuador)[END_REF][START_REF] Kumagai | Ascending seismic source during an explosive eruption at Tungurahua volcano, Ecuador[END_REF][START_REF] Champenois | Large-scale inflation of Tungurahua volcano (Ecuador) revealed by Persistent Scatterers SAR interferometry[END_REF][START_REF] Myers | Replenishment of volatile-rich mafic magma into a degassed chamber drives mixing and eruption of Tungurahua volcano[END_REF].

Previous works showed that Tungurahua volcano was built in three construction stages, namely Tungurahua I, II and III, and experienced two major sector collapse events [START_REF] Hall | Tungurahua Volcano, Ecuador: structure, eruptive history and hazards[END_REF][START_REF] Le Pennec | A Devastating Plinian Eruption at Tungurahua Volcano Reveals Formative Occupation at ∼1100 cal BC in Central Ecuador[END_REF][START_REF] Le Pennec | Combining historical and 14C data to assess pyroclastic density current hazards in Baños city near Tungurahua volcano (Ecuador)[END_REF]. Inclined plateaux of the northern, eastern and southern flanks essentially belong to Tungurahua I activity, which started during the Pleistocene, based on two available whole-rock K-Ar ages of 770 ± 5 and 350 ± 4 ka [START_REF] Barberi | Plio-Quaternary Volcanism in Ecuador[END_REF]. The western part of Tungurahua I was destroyed by a first sector collapse, 14 C dated at 33.1 ± 0.2 ka BP [START_REF] Le Pennec | A Devastating Plinian Eruption at Tungurahua Volcano Reveals Formative Occupation at ∼1100 cal BC in Central Ecuador[END_REF], which might have been triggered by a silicic cryptodome intrusion [START_REF] Le Pennec | The AD 1300-1700 eruptive periods at Tungurahua volcano, Ecuador, revealed by historical narratives, stratigraphy and radiocarbon dating[END_REF]. The resulting amphitheatre volume was estimated at 10 km 3 [START_REF] Bustillos | Las avalanchas de escombros en el sector del volcán Tungurahua (MSC)[END_REF], but the collapse scar location is not accurately identified in the present-day edifice morphology. Tungurahua II lavas and deposits then filled the amphitheatre, before being destroyed in turn by a new western sector collapse 14 C dated at 2955 ± 90 BP [START_REF] Hall | Tungurahua Volcano, Ecuador: structure, eruptive history and hazards[END_REF] and 2960 ± 30 BP [START_REF] Le Pennec | A Devastating Plinian Eruption at Tungurahua Volcano Reveals Formative Occupation at ∼1100 cal BC in Central Ecuador[END_REF]. It was triggered by a new viscous intrusion or magma mixing occurring in the chamber [START_REF] Hall | Tungurahua Volcano, Ecuador: structure, eruptive history and hazards[END_REF][START_REF] Le Pennec | The AD 1300-1700 eruptive periods at Tungurahua volcano, Ecuador, revealed by historical narratives, stratigraphy and radiocarbon dating[END_REF], 2013). The avalanche deposits associated with this second event cover between 23 and 80 km², for a collapse volume estimated between 2.8 and 6 km 3 [START_REF] Bustillos | Las avalanchas de escombros en el sector del volcán Tungurahua (MSC)[END_REF]Hall et al., 1999 respectively). However, the area and the volume obtained by [START_REF] Hall | Tungurahua Volcano, Ecuador: structure, eruptive history and hazards[END_REF] are necessarily higher because they mapped as a single sector collapse the deposits of the two sector collapses of Tungurahua, and the one experienced by Huisla volcano (Fig. 2; [START_REF] Bustillos | Las avalanchas de escombros en el sector del volcán Tungurahua (MSC)[END_REF]. The southern location of the scar boundary is well delimited in the morphology, whereas the northern part was first proposed along the Pondoa plateau [START_REF] Hall | Tungurahua Volcano, Ecuador: structure, eruptive history and hazards[END_REF], and recently shifted to the west based on geomorphological and seismological studies [START_REF] Molina | Three-dimensional P-wave velocity structure of Tungurahua Volcano, Ecuador[END_REF][START_REF] Le Pennec | The AD 1300-1700 eruptive periods at Tungurahua volcano, Ecuador, revealed by historical narratives, stratigraphy and radiocarbon dating[END_REF]Fig. 2). Due to this collapse and continuous erosion, remnants of Tungurahua II mainly crop out on the eastern summit area and in the southwestern valleys (i.e. the Tiacos lava sequences of [START_REF] Hall | Tungurahua Volcano, Ecuador: structure, eruptive history and hazards[END_REF].

Products from the younger and still active Tungurahua III cone have then filled the amphitheatre left by the second sector collapse [START_REF] Hall | Tungurahua Volcano, Ecuador: structure, eruptive history and hazards[END_REF][START_REF] Le Pennec | The AD 1300-1700 eruptive periods at Tungurahua volcano, Ecuador, revealed by historical narratives, stratigraphy and radiocarbon dating[END_REF], 2013). Lavas and pyroclastic flow deposits, as well as tephra fall and epiclastic layers displaying basaltic andesite to dacitic composition make up the present western flank. Eight pre-Columbian eruptive periods were identified, and five major eruptions occurred during historical times: AD 1640-1641, 1773-1776, 1886-1888, 1916-1918 and 1999-present, with therefore a recurrence rate of about one pyroclastic flow-forming event per century (Hall et al., 1999;[START_REF] Le Pennec | The AD 1300-1700 eruptive periods at Tungurahua volcano, Ecuador, revealed by historical narratives, stratigraphy and radiocarbon dating[END_REF][START_REF] Le Pennec | Combining historical and 14C data to assess pyroclastic density current hazards in Baños city near Tungurahua volcano (Ecuador)[END_REF].

Given that Tungurahua III activity has already been well described and 14 C dated [START_REF] Hall | Tungurahua Volcano, Ecuador: structure, eruptive history and hazards[END_REF][START_REF] Le Pennec | The AD 1300-1700 eruptive periods at Tungurahua volcano, Ecuador, revealed by historical narratives, stratigraphy and radiocarbon dating[END_REF][START_REF] Bustillos | Las avalanchas de escombros en el sector del volcán Tungurahua (MSC)[END_REF], 2013[START_REF] Le Pennec | Combining historical and 14C data to assess pyroclastic density current hazards in Baños city near Tungurahua volcano (Ecuador)[END_REF], in this study we focus on the two older edifices, Tungurahua I and II.

Materials and methods

Sampling

Twenty-four fresh hand-size samples of lava flows were collected during several field trips from 2013 to 2016 (Fig. 3a). Geographical coordinates of the samples are provided in Table 1 and the associated KMZ file is available in Appendix C. In order to constrain the onset of the volcano activity, seven samples were taken from the basal flows, close to the contact with the metamorphic basement (PS-102, PS-106, PS-110, 16EQ15, 16EQ12, PS-118 and 16EQ26). Sample 16EQ12 was collected from a breccia containing monogenic blocks.

Seven lavas were sampled in the uppermost part of Pondoa, Runtún, Ulba and Patacocha plateaux (Fig. 2). Because of their position in the stratigraphic sequence of these plateaux, we infer that they were emplaced late in Tungurahua I history 16EQ16,16EQ17,16EQ25,TUNG 3,TUNG4). Seven lavas of Tungurahua II were sampled along Ulba valley (PS-111, 16EQ19), in Las Juntas and Juive Grande areas (PS-107, PS-109), and near Palitahua waterfalls (Fig. 2; 16EQ13). Two recent lavas were also sampled to compare our dating method with published 14 C ages: a dacitic flow near Cusúa (16EQ36), which belongs to the beginning of Tungurahua III activity [START_REF] Hall | Tungurahua Volcano, Ecuador: structure, eruptive history and hazards[END_REF], and the Baños lava flow (16EQ37). In addition, a massive lava flow erupted from an unknown source and exposed between the Pastaza valley and Vizcaya village was also sampled (16EQ20). The aim was to determine whether it could be contemporaneous with Tungurahua volcano activity.

K-Ar dating

The potassium-argon (K-Ar) dating method was applied here by using the unspiked Cassignol-Gillot technique [START_REF] Cassignol | Range and effectiveness of unspiked potassium-argon dating: experimental groundwork and application[END_REF], which was developed for Quaternary volcanics with low radiogenic argon ( 40 Ar * ) contents [START_REF] Gillot | The K/Ar dating method : principle, analytical techniques, and application to Holocene volcanic eruptions in Southern Italy[END_REF]. It has been shown to be especially suitable for dating young subduction lavas with low K and high Ca contents, as is the case for instance in South America and in the Lesser Antilles (e.g., [START_REF] Samper | Effusive history of the Grande Découverte Volcanic Complex, southern Basse-Terre (Guadeloupe, French West Indies) from new K-Ar Cassignol-Gillot ages[END_REF][START_REF] Germa | The K-Ar Cassignol-Gillot technique applied to western Martinique lavas: A record of Lesser Antilles arc activity from 2 Ma to Mount Pelée volcanism[END_REF]. The technique relies on the detection of a very small difference between the isotopic 40 Ar/ 36 Ar ratio extracted from the sample and the atmospheric ratio. The radiogenic argon content, which derived from the radioactive decay of 40 K, together with the potassium content of the sample and the 40 K decay constant [START_REF] Steiger | Subcommission on geochronology: convention on the use of decay constants in geo-and cosmochronology[END_REF], allow determining the age of the lava sample.

Sample preparation

The groundmass is the last phase to crystallize when lavas cool. It is thus enriched in incompatible elements, including potassium, and in equilibrium with the atmosphere. Hence the initial argon isotopic ratios in the groundmass are atmospheric, and it is devoid of radiogenic argon ( 40 Ar * ). On the other hand, phenocrysts can carry inherited 40 Ar * , that might bias ages significantly (e.g., [START_REF] Harford | The volcanic evolution of Montserrat using 40Ar/39Ar geochronology[END_REF][START_REF] Samper | Radiometric dating of three large volume flank collapses in the Lesser Antilles Arc[END_REF]. We therefore carried out our measurements on the groundmass following a careful mineralogical separation.

Observation of thin sections (available on Appendix A) helped us to attest of the samples freshness, and to determine the size fraction. The selected samples were crushed and sieved at 80-125 µm, 80-160 µm, or 125-250 µm, then ultrasonically washed with a 10% nitric acid solution and deionized water. Heavy liquids, mainly bromoform, were used to isolate the groundmass by removing heavy mafic minerals, and light weathered fractions, if present.

Finally, the separation was refined with a magnetic separator, which removed non-magnetic plagioclases remaining within the magnetic groundmass, as their respective ranges of density overlap. The obtained fractions of groundmass, which amount to only a few percent of the initial sample, have a narrow density range, with a typical value of 2.71. Their homogeneity was checked under a binocular magnifier, and both potassium and argon measurements were carried out at the Laboratoire GEOPS of Université Paris-Sud (Orsay, France).

Potassium and argon measurements

Potassium was measured with an Agilent 240 Series AA flame absorption spectrometer, after dissolving samples with an acid attack. Results were corrected with reference values of MDO-G (K = 3.510%; [START_REF] Gillot | Two reference materials, trachytes MDO-G and ISH-G, for argon dating (K-Ar and 40Ar/39Ar) of Pleistocene and Holocene rocks[END_REF] and BCR-2 (K = 1.481%; [START_REF] Raczek | High-Precision Trace Element Data for the USGS Reference Materials BCR-1, BCR-2, BHVO-1, BHVO-2, AGV-1, AGV-2, DTS-1, DTS-2, GSP-1 and GSP-2 by ID[END_REF] standards.

Argon was measured using a mass spectrometer similar to the one described by [START_REF] Gillot | The Cassignol technique for Potassium-Argon dating, precision and accuracy: exemples from the late Pleistocene to recent volcanics from southern Italy[END_REF]. Very stable conditions reached during the measurements rendered the use of the 38 Ar spike, needed for the conventional K-Ar technique, unnecessary. Gases extracted by fusing the sample were purified with high temperature Ti foam and SAES getters. An air pipette containing a known amount of 40 Ar atoms was used to calibrate the mass spectrometer. Another air pipette, with the same 40 Ar signal as the sample to be dated, allows an accurate atmospheric correction to be performed. The accuracy of this correction and of the 40 Ar calibration are routinely checked by analyses of international standards samples measurements, such as ISH-G (1301-1302 AD; [START_REF] Gillot | Two reference materials, trachytes MDO-G and ISH-G, for argon dating (K-Ar and 40Ar/39Ar) of Pleistocene and Holocene rocks[END_REF] and HD-B1 (24.21 ± 0.32 Ma; [START_REF] Hess | Compilation of K-Ar measurements on HD-B1 standard biotite, 1994 status report[END_REF].

The total relative age uncertainty (σ tot ) is calculated using the following formula:

The relative uncertainties of the potassium content ( ) and the 40 Ar calibration ( ) are both evaluated at 1%. The uncertainty of radiogenic argon ( ) depends on the radiogenic content of the sample. For young samples, this uncertainty is larger because of their high atmospheric and low radiogenic argon contents. The 40 Ar* detection limit of our measurements is presently at 0.1% [START_REF] Quidelleur | K/Ar dating extended into the last millennium: application to the youngest effusive episode of the Teide volcano (Spain)[END_REF].

All potassium and argon measurements were performed at least twice in order to check their reproducibility within uncertainty. Final ages and uncertainties were calculated by averaging each analysis, weighted by their 40 Ar* content. However, for the youngest samples where 40 Ar* content is lower than 0.1%, ages were calculated using an unweighted average.

Ages obtained here are given at the 1 σ confidence level (Table 1).

Geochemical analyses

Major and trace element whole-rock contents of all samples were measured at the Laboratoire Géosciences Océan of the Université de Bretagne Occidentale (Brest, France).

Agate-crushed powders of the twenty-four samples were analysed by ICP-AES (Inductively Coupled Plasma -Atomic Emission Spectrometry), following the analytical procedure detailed in [START_REF] Cotten | Origin of anomalous rare-earth element and yttrium enrichments in subaerially exposed basalts: Evidence from French Polynesia[END_REF]. Relative uncertainties are ≤ 2% for major elements and ≤ 5% for trace elements. Major elements data were recalculated to a total of 100% on a water freebasis and together with trace elements are provided in Table 2. Our geochemical database was completed by seventy-two unpublished major and trace elements analyses of samples from the three edifices and blocks from the sector collapse deposits [START_REF] Hall | Tungurahua Volcano, Ecuador: structure, eruptive history and hazards[END_REF][START_REF] Bustillos | Las avalanchas de escombros en el sector del volcán Tungurahua (MSC)[END_REF], which are presented in Appendix B.

Numerical reconstructions of past morphology

Numerical reconstructions of palaeotopographies were used to model the morphology of the volcano during its main phases of construction, erosion and collapse. They provided information regarding evolution of the magmatic productivity through time, and the erosion rates, which are influenced by precipitation and glacial-interglacial alternating periods. The present topographic data are extracted from a 30-m SRTM Digital Elevation Model (DEM).

The reconstruction method used here was developed in [START_REF] Lahitte | DEM-based reconstruction of southern Basse-Terre volcanoes (Guadeloupe archipelago, FWI): Contribution to the Lesser Antilles Arc construction rates and magma production[END_REF] and improved in [START_REF] Germa | Construction and destruction of Mont Pelée volcano: Volumes and rates constrained from a geomorphological model of evolution: Construction and Destruction of Mont Pelée[END_REF]. It is summarized below.

Past Tungurahua topographic models are constrained from points selected from the present-day topography, as belonging to non-eroded surfaces. In general, they are from crests, upper parts of plateaux, planeze surfaces or recent deposits (Fig. 4a andb). ShapeVolc, a specifically developed method, is used for modelling the different palaeotopographies based on these points [START_REF] Lahitte | DEM-based reconstruction of southern Basse-Terre volcanoes (Guadeloupe archipelago, FWI): Contribution to the Lesser Antilles Arc construction rates and magma production[END_REF]. This method first finds a global model, by defining the best summit location and the parameters of the function that define a revolution surface, which best fit the selected points following a least-squares method adjustment. Thereby, Tungurahua I reconstruction displays a conical shape with linear flank profiles and an elliptical base, while Tungurahua II and III have an exponential shape with a concave profile (Fig. 4c). The software then adjusts the first-order modelling by modifying locally the parameters of the global function, in order to take into account local elevation variations, i.e.

the irregularity of the surface of each stage of construction [START_REF] Lavigne | Source of the great A.D. 1257 mystery eruption unveiled, Samalas volcano, Rinjani Volcanic Complex, Indonesia[END_REF][START_REF] Germa | Construction and destruction of Mont Pelée volcano: Volumes and rates constrained from a geomorphological model of evolution: Construction and Destruction of Mont Pelée[END_REF]. These second-order surfaces correspond to our final construction models. The evolution of Tungurahua I altitude after its erosion is calculated by lowering each elevation of the model as a linear function of time, between the model elevation and the present topography. Moreover, as the geometry of the depressions of the collapses is not precisely known, we modelled them by an interpolation between points currently located on the edge of the scars and two profiles forming the possible bottom surface represented by the discontinuous curves in Fig. 4a, located so as to respect the collapse volumes estimates, respectively of ~10 and ~2.8 km 3 , based on the deposits located in the Río Chambo valley [START_REF] Hall | Tungurahua Volcano, Ecuador: structure, eruptive history and hazards[END_REF][START_REF] Bustillos | Las avalanchas de escombros en el sector del volcán Tungurahua (MSC)[END_REF].

Finally, the reconstruction of pre-Tungurahua topography is obtained by selecting DEM points which belong to the metamorphic basement outcropping around the volcano, in order to extrapolate them under the present volcano surface. This palaeosurface is modelled applying a Local Polynomial Interpolation method with a resolution of 100 m, using ArcGis software. The model is therefore smooth, since we cannot constrain the exact morphology of the basement 300 ka ago, which is currently overlaid by Tungurahua products.

Magmatic productivity and erosion rates

The volume , either constructed or eroded , corresponds to the integration of the difference between the upper and the lower surface, over the area of the edifice considered. In this fashion, the eroded volume is the difference between the modelled surface and the present topography ( . The deposits volume for each edifice corresponds to the difference between the surface elevation modelled at the end of their constructions and the one which preceded the edifice construction. Erosion that occurred during the Tungurahua I and II construction lowered the apparent volume of emitted magma. To take into account this erosion, we added to the raw volume the eroded volume estimated by considering that the erosion rate calculated for the last 80 ka was rather constant though time. The volume uncertainty ( ) is calculated using the following formula:

where the uncertainty of the elevation ( ) is defined as , where the uncertainties of the initial ( ) and the final ( ) surface elevation are estimated to 200 m for the interpolated surface before Tungurahua construction, 50 m for our surface models, and null for the present elevation. These uncertainties are obtained from the standard deviation of the elevation dispersion of the points selected to construct the palaeotopographies around the surface model, and calculated from the error map of the kriging interpolation method for the pre-Tungurahua surface (Ricci et al., 2015a).

Together with our new K-Ar ages, these volumes, divided by the period of activity or quiescence ( allow us to calculate the apparent magmatic productivity ( ) and erosion ( ) rates of Tungurahua volcano, with , and . As the parameters involved in these ratios are independent, the uncertainty of the ratio is then defined as the square root of the quadratic sum of the relative uncertainties of both stage duration ( ) and volume ( . Consequently, the uncertainty of the magmatic productivity or erosion rate ( ) is calculated using the following formula:

where is the considered rate.

The uncertainty on the duration is estimated from K-Ar ages uncertainty, which constrains the timing of each edifices construction and erosion. Consequently, because of the relatively good age precision, is mainly dominated by the volume uncertainty Moreover, this technique of calculation based on numerical reconstructions is more accurate than traditional methods, which generally use approximate volumes. We also present the minimum and maximum values of emission rates, considering the upper and lower values of both volume and time period. However, we chose to only use the previous calculation method for discussion and comparisons, since it provides a more realistic result and takes into account the Gaussian distribution of the data. Results of the volumes, magmatic productivity and erosion rates calculations are provided in Table 3.

Results

Petrography of the samples

There is no clear mineralogy difference between the lava flows from the three edifices.

Most of the Tungurahua lava flow samples have porphyric textures with a variable amount of plagioclase, orthopyroxene, clinopyroxene and olivine phenocrysts, except samples of Vizcaya lava flow (16EQ20) and the lower Runtún plateau (PS-110 and PS-106), which present a vitreous texture with scarce crystals (Appendix A). Sample PS-119, from the southern flank, also present some amphibole crystals, but none of our lava flow sample contains biotite crystals. The groundmass contains plagioclase, pyroxene and Fe-Ti oxide microcrysts separated by volcanic glass, and mainly represents about 50-70% of the rock volume. Moreover, some samples present color variations of their groundmass, such as 16EQ15 and 16EQ17 from the Ulba plateau, 16EQ19 and PS-111 from the bottom of Ulba

Valley, PS-99 from the Runtún upper part, as well as PS-117 and PS-118 from the southern flank (Fig. 3). These variations correspond to more or less differentiated magmas and display that magma mixing processes occurred.

K-Ar dating

K-Ar ages obtained in this study are presented in Table 1 andFig

Whole-rock geochemical analyses

The major and trace element contents for all samples are presented in Table 2. Loss on ignition (L.O.I) measurements are low, with a maximum value of 1.15%, which attests for samples freshness and their low content in volatiles.

Major elements

Tungurahua lava flows show typical trends of subduction-related volcanic rocks, and are similar to the previous analyses from its different units and the published data from the Eastern Cordillera (Fig. 6). Indeed, most samples fall within basaltic andesite and andesite fields in the K 2 O vs. SiO 2 diagram [START_REF] Peccerillo | Geochemistry of Eocene calc-alkaline volcanic rocks from the Kastamonu area, northern Turkey[END_REF]; Fig. 6), and two samples are dacites (16EQ17 and 16EQ20). Silica content ranges between 53.3 and 67.0 wt.%, and K 2 O content between 1.3 and 3.6 wt.%. Consequently, rocks from Tungurahua belong to the medium-K calc-alkaline series, except for some samples from Tungurahua I, which are more alkaline-rich and belong to the high-K calc-alkaline series.

Variation diagrams, shown as a function of Th (as a differentiation index), also show typical trends of subduction zone volcanism (Fig. 7). Th is a highly incompatible element, which is not fractionated during partial melting or fractional crystallization process. The

Trace elements

Spider diagrams of trace elements, normalized to the primitive mantle [START_REF] Sun | Chemical and isotopic systematics of oceanic basalts: implications for mantle composition and processes[END_REF]; Fig. 8a), shows enrichment of Large-Ion Lithophile Elements (LILE; Rb, Ba, and K) and depletion of High-Field Strength Elements (HFSE; Nb, Ti and Y), also typical of subduction magmas. These signatures are also found on the Rare Earth Elements (REE)

diagram normalized to chondrites values [START_REF] Sun | Chemical and isotopic systematics of oceanic basalts: implications for mantle composition and processes[END_REF]; Fig. 8b), with an enrichment in Light REE (LREE; to the left) compared to Heavy REE (HREE, to the right), without a negative Eu anomaly.

Overall, lavas from Tungurahua I have higher REE contents, which can be linked with its high-K signature (Fig. 6). In the Sr/Y versus Y diagram (Fig. 9e), most of the rocks plot in the classical calc-alkaline arc lavas field, but some lavas are more depleted in Y and tend toward an "adakitic" signature. However, all samples are too enriched in Yb and too depleted in La to reach the "adakitic" domain in the La/Yb versus Yb diagram (Fig. 9f). Moreover, the Sr/Y ratio decreases as the fractional crystallization proceeds, whereas La/Yb and Th are positively correlated (Fig. 9c andd, respectively). Tungurahua I lavas are rather scattered, particularly for Pondoa basal unit and younger plateau lavas, which differ significantly from the general trend (Fig. 7). Indeed, old lavas of Pondoa, including PS-102, show a high enrichment in all incompatible elements and REE, notably Y and Yb (Fig. 8; Fig. 9e andf).

Overall, all samples are porphyritic except one from the upper part of Ulba plateau (16EQ17), which is almost entirely crystallized and presents a trachytic texture (Appendix A). It is the most evolved sample of plateau lavas, and presents high enrichment in the most incompatible elements and REE (Fig. 7; Fig. 8; Fig. 9).

Tungurahua II and III lavas compositions are rather homogeneous, and major and trace element contents do not allow us to clearly discriminate between these two different edifices.

However, it can be noticed that sample PS-117, which corresponds to the beginning of Tungurahua II activity shortly after the first sector collapse event, is the most depleted in HFSE and HREE, notably in Nb, Y and Yb (Fig. 8; Fig. 9e andf). Moreover, the composition of the "Cusúa dacite" sample (16EQ36) is slightly less differentiated than the one of Hall et al. (1999), with 62.2 wt.% of SiO 2 . Finally, the Vizcaya lava flow (16EQ20) differs significantly from Tungurahua lavas for most major elements (Fig. 6; Fig. 7) and for some trace elements (Fig. 9b).

Geomorphological reconstructions

Palaeotopographical reconstructions were used to propose a temporal evolution of Tungurahua volcano morphology (Fig. 10; Table 3).

The morphology of the metamorphic basement suggests that a north-south crest was present under the present edifice before its construction (Fig. 10a), extending the one currently found south of the volcano. As the volcano grew, Río Chambo and Pastaza palaeovalleys (Fig. 2), which were present initially, were shifted westward and northward.

Overall, the present Tungurahua edifice presents a conic morphology, with a rather circular base and a concave profile. According to our extrapolation of the basement and the present topography, the present volume of this volcano is 108 ± 30 km 3 (Table 3), with a basal surface of about 150 km². Given our maximum age of 293 ± 10 ka, the apparent production rate is 0.4 ± 0.1 km 3 /ka.

In detail, Tungurahua I was a volcano with a rather flat summit, which peaked at a minimum elevation of 4500 m (Fig. 10b), 2 km southeast to the present summit. Based on our numerical reconstructions, the volume of Tungurahua I at the end of its construction was 56 ± 33 km 3 . Considering that the erosion rate affecting its flanks during its growth was similar to the erosion rate calculated since the end of its construction, we obtain an eroded volume of 68 ± 41 km 3 between ~293 and 81 ka. This volume is added to the first volume of 56 ± 33 km 3 , which provides a total volume of 124 ± 74 km 3 of products emitted during the ~212 ka of Tungurahua I construction (Table 3). As a result, the magmatic productivity rate of this first edifice was 0.6 ± 0.3 km 3 /ka. A quiescence period favoured the erosion of Tungurahua I flanks between 80 and 33 ka (Fig. 10c). Then, the sudden loss of ~10 km 3 of deposits [START_REF] Bustillos | Las avalanchas de escombros en el sector del volcán Tungurahua (MSC)[END_REF] during the first western sector collapse at ~ 33 ka (Fig. 10d; Table 3) may have favoured the rise of magma (e.g., [START_REF] Hildenbrand | Volcano-tectonic and geochemical evolution of an oceanic intra-plate volcano: Tahiti-Nui (French Polynesia)[END_REF] and the rapid construction of Tungurahua II within the resulting amphitheatre (Fig. 10e). This second edifice culminated at about 5070 m, with a concave upward profile similar to the present volcano. Although the volume of the emitted products (24 ± 4 km 3 ) is significantly lower than the one calculated for the first edifice, its eruptive rate was similar (0.9 ± 0.2 km 3 /ka) given the shorter duration of this stage, between 29 ± 2 ka (Table 1) and 2.96 ± 0.03 ka [START_REF] Le Pennec | A Devastating Plinian Eruption at Tungurahua Volcano Reveals Formative Occupation at ∼1100 cal BC in Central Ecuador[END_REF]. A new flank failure occurred at ~3 ka (Fig. 10f), mobilizing around 3 km 3 of deposits [START_REF] Bustillos | Las avalanchas de escombros en el sector del volcán Tungurahua (MSC)[END_REF] from the western summit part. Finally, the third and still active edifice was rapidly constructed in the depression left by this collapse (Fig. 10g). Tungurahua III is characterized by the lowest volume of deposits (7 ± 3 km 3 ), but displays a relatively high eruptive rate of 2.5 ± 1.0 km 3 /ka. In addition, an erosion rate of 0.2 ± 0.1 km 3 /ka for the eastern part of Tungurahua I not affected by the collapses is obtained, considering the eroded volume of ~16 km 3 during ~80 ka, i.e. since the end of the first edifice construction (Table 3).

As Tungurahua II collapsed rapidly after its construction without significant periods of quiescence, and as Tungurahua III is still active, we cannot calculate erosion rates for these edifices.

Based on these new results and field observations, we propose in Fig. 3 an update of the Tungurahua geological map [START_REF] Hall | Tungurahua Volcano, Ecuador: structure, eruptive history and hazards[END_REF][START_REF] Bustillos | Las avalanchas de escombros en el sector del volcán Tungurahua (MSC)[END_REF]. Tungurahua II not only consists of the lava flow sequence of the Tiacos unit (Fig. 2), but also crops out in the northern and southwestern flanks. We also propose that the Tungurahua I collapse scar is located to the west of the Tungurahua II scar, as suggested by the location of the upper parts of the Pondoa, Runtún and Ulba plateaux.

Discussion

New groundmass K-Ar ages

Comparison with previously published ages

The new K-Ar ages of Tungurahua I (Table 1 and Fig. 3b, c andd) are strikingly younger than previously published whole-rock K-Ar ages of 770 ± 5 and 350 ± 4 ka [START_REF] Barberi | Plio-Quaternary Volcanism in Ecuador[END_REF], for samples from Tungurahua, but whose location is unknown. Such difference can be explained by the analysis of whole-rock samples that include phenocrysts, which can carry inherited radiogenic argon and/or weathering areas that have experienced loss of potassium. Both phenomena will induce older K-Ar ages. Our results highlight the importance of analysing the groundmass alone, after a thorough mineralogical separation, as previously reported in different contexts, including arc volcanism (e.g., [START_REF] Samper | Timing of effusive volcanism and collapse events within an oceanic arc island: Basse-Terre, Guadeloupe archipelago (Lesser Antilles Arc)[END_REF][START_REF] Germa | The K-Ar Cassignol-Gillot technique applied to western Martinique lavas: A record of Lesser Antilles arc activity from 2 Ma to Mount Pelée volcanism[END_REF][START_REF] Zami | Initial sub-aerial volcanic activity along the central Lesser Antilles inner arc: New K-Ar ages from Les Saintes volcanoes[END_REF]. Although unpublished, four 40 Ar/ 39 Ar ages obtained at the Laboratoire Geoazur (Côte d'Azur University, Nice, France) support our K-Ar ages. Indeed, inverse isochron ages of 27 ± 4 and 104 ± 44 ka (M. Fornari, pers. com.) agree with our ages of 29 ± 2 and 153 ± 14 ka obtained for the same lava flows (PS-117 and PS-110 respectively;

Table 1). In addition, two distinct lava flows sampled in the same eruptive phase than PS-99 and PS-118 have 40 Ar/ 39 Ar ages of 99 ± 2 and 252 ± 6 ka (M. Fornari, pers. com.), which are in the range of our K-Ar ages of 79 ± 3 and 293 ± 10 ka, respectively (Table 1). Moreover, most samples from Tungurahua II and III are younger than 15 ka (Table 1), in agreement with their emplacement after the Last Glacial Maximum [START_REF] Hall | Tungurahua Volcano, Ecuador: structure, eruptive history and hazards[END_REF][START_REF] Clapperton | Glacial and volcanic geomorphology of the Chimborazo-Carihuairazo Massif, Ecuadorian Andes[END_REF].

Although they display a large relative uncertainty, our ages are also consistent with previously published 14 C ages of less than ~3 ka for Tungurahua III deposits [START_REF] Hall | Tungurahua Volcano, Ecuador: structure, eruptive history and hazards[END_REF][START_REF] Le Pennec | The AD 1300-1700 eruptive periods at Tungurahua volcano, Ecuador, revealed by historical narratives, stratigraphy and radiocarbon dating[END_REF], 2013[START_REF] Le Pennec | Combining historical and 14C data to assess pyroclastic density current hazards in Baños city near Tungurahua volcano (Ecuador)[END_REF].

In this southern part of the Ecuadorian arc, within the Inter-andean valley, radiometric ages are available only for Chimborazo and Carihuairazo volcanoes (Fig. 1b). Both were built up since 230 ka, and until Holocene for Chimborazo volcano [START_REF] Samaniego | Eruptive history of Chimborazo volcano (Ecuador): A large, ice-capped and hazardous compound volcano in the Northern Andes[END_REF][START_REF] Barba | Holocene recurrent explosive activity at Chimborazo volcano (Ecuador)[END_REF]. Further south, the construction of the Sangay volcano, the last active edifice of the Eastern Cordillera, started around 500 ka [START_REF] Monzier | Sanguay volcano, Ecuador: structural development, present activity and petrology[END_REF]Fig. 1b). Hence, it appears that the construction of Chimborazo, Carihuairazo, Sangay and Tungurahua volcanoes are rather coeval, which suggests a recent development of this part of the arc.

Association between ages and volcanic phases

The distribution of our new ages is fairly homogeneous on the scale of the volcano activity, apart from the end of the first edifice construction (Fig. 5). Indeed, the oldest basal lava flows of Tungurahua I have an age of 300 ka, and the edifice remained active until the emplacement of lava flows forming the upper parts of plateaux, at around 80 ka. The edifice collapsed around 33 ka [START_REF] Le Pennec | A Devastating Plinian Eruption at Tungurahua Volcano Reveals Formative Occupation at ∼1100 cal BC in Central Ecuador[END_REF]), but we do not have any sample with an age between 80 ka and the 33 ka destabilization. Tungurahua I activity might have continued between 80 and 33 ka if the lava flows were only emplaced in the summit area or in the western flank that have been destroyed by latter flank collapses, since the plateaus do not seem covered by any younger deposits. Similarly, we did not observe any activity between 246 ± 17 and 188 ± 7 ka (Fig. 5). Although it could be due to a sampling bias, these ~50 ka quiescence periods would be the longest experienced by the volcano. Moreover, owing to the relatively high age-uncertainty of lavas younger than 15 ka (Table 1), and the similar geochemistry observed for the two younger edifices, we cannot determine whether these lavas belong to Tungurahua II or III. Therefore, we rely on stratigraphic relationships observed in the field to associate young samples with a given eruptive phase. Sample PS-109 (7 ± 4 ka) is older than 3 ka and corresponds to Tungurahua II activity (Fig. 3), probably as well as sample PS-107 (5 ± 8 ka), which belongs to a nearby lava flow. [START_REF] Hall | Tungurahua Volcano, Ecuador: structure, eruptive history and hazards[END_REF] associated the young lava flow at the bottom of the Ulba valley (sampled here as PS-111 and 16EQ19) to

Tungurahua III activity based on petrological similarities. However, there are very few mineralogical differences between the two younger edifices (Appendix A). We associate PS-111 and 16EQ19, as well as PS-119 and 16EQ13 (southwestern flank lavas), to

Tungurahua II activity (Fig. 3), because Tungurahua III deposits in the sector collapse depression are not thick enough to have overflown into the eastern and southern valleys.

Regarding the Baños lava flow (16EQ37; 6 ± 9 ka), there is no place where a clear stratigraphic relationship could be observed between the lava and the ~3 ka collapse deposits (namely the blast deposits associated with the sector collapse). Indeed, these Tungurahua II blast deposits are dated between 2640 ± 45 and 3195 ± 45 BP ( 14 C on charcoal and carbonized twigs), crop out along the Chambo and Puela valleys (Fig. 2) and cover the northern flank of the volcano [START_REF] Le Pennec | A Devastating Plinian Eruption at Tungurahua Volcano Reveals Formative Occupation at ∼1100 cal BC in Central Ecuador[END_REF], especially Pondoa and Runtún plateaux around Baños city (Fig. 2), but do not crop out above the Baños lava flow. The lava flow originated from a lateral vent (Fig. 3b), and was later covered by an ash deposit dated at 1470 ± 85 BP ( 14 C on charcoal; [START_REF] Hall | Tungurahua Volcano, Ecuador: structure, eruptive history and hazards[END_REF]. Assuming that the Baños lava flow is younger than the blast deposits, we associate the Baños lava flow with the beginning of Tungurahua III activity, in agreement with [START_REF] Hall | Tungurahua Volcano, Ecuador: structure, eruptive history and hazards[END_REF][START_REF] Le Pennec | Combining historical and 14C data to assess pyroclastic density current hazards in Baños city near Tungurahua volcano (Ecuador)[END_REF].

The Vizcaya lava flow is coeval with Tungurahua I activity (253 ± 5 ka), but its major and trace contents clearly differ from Tungurahua rocks (Fig. 7; Fig. 9). Hence, this flow cannot be associated with Tungurahua volcano and was rather erupted from an unknown volcanic centre, probably located to the north.

Unfortunately, the southeastern flank could not be sampled and dated in this study.

Indeed, access to the Minsas plateau (Fig. 2) was not possible during the erupting period, when our last field trip took place. However, previous major and trace element analyses [START_REF] Hall | Tungurahua Volcano, Ecuador: structure, eruptive history and hazards[END_REF]Appendix B) indicate a composition close to those of Ulba upper part (16EQ17;

Table 2). Minsas plateau lava geochemistry, morphology and erosion state therefore suggest that the flow is coeval with other Tungurahua I plateau lavas, and was erupted around 80 ka (Fig. 3).

Location of the ~33 ka sector collapse scar

The succession of construction stages of the volcano and the erosion prevent to accurately determine the location of the Tungurahua I collapse scar. However, morphology analysis of the DEM, and observations made during field campaigns allow us to propose that the northern part of the scar follows the western escarpment of the Pondoa plateau (Fig. 3).

Indeed, a "diamond-shaped" plateau, located west of Pondoa, is made of Tungurahua I collapse deposits overlain by Tungurahua II lava flows (Fig. 11). This part of the volcano was therefore destroyed by the first collapse, but was not affected by the second one. Note that such observations are in agreement with the geological map of [START_REF] Hall | Tungurahua Volcano, Ecuador: structure, eruptive history and hazards[END_REF]. The morphology of the southwestern flank, from Patacocha plateau to the second collapse scar, seems to constitute a single unit filling a wide valley (Fig. 3d and Fig. 11d). Indeed, lava flows cover a Tungurahua I breccia deposit, where sample 16EQ12 comes from (Fig. 3a), and no dated lava is there older than 30 ka (Fig. 3d). We therefore propose that the top of the first (~33 ka) collapse scar is located on the eastern flank at around 3900 m a.s.l., where plateaux slopes change (Fig. 4) forming the lower boundary of the Tiacos unit, and located along the summit part of the Patacocha plateau (Fig. 3).

Geochemical evolution of the volcanic products

Overall, the lavas of the three successive edifices of Tungurahua volcano show quite similar compositions. Indeed, their silica content varies between 52 and 62 wt.%, and their Mg# between 40 and 60 (Fig. 12a), except for 16EQ17 sample, which is more differentiated than the other lavas, and presents higher content of incompatible elements (Fig. 7; Fig. 9).

The La/Yb ratio varies depending on the depth, composition and nature of the magmas source, fractional crystallization and/or interaction with the mantle [START_REF] Moyen | High Sr/Y and La/Yb ratios: The meaning of the "adakitic signature[END_REF]. Temporal evolution of the La/Yb ratio for Tungurahua samples (Fig. 12b) shows an overall decrease between 300 and 100 ka, and a significant increase toward the end of Tungurahua I activity,

shown by samples younger than 100 ka. During Tungurahua II and III construction, La/Yb contents are relatively scattered, and vary within the range observed for Tungurahua I lavas.

Moreover, the La/Sm ratio provides information about the degree of partial melting, and the Sm/Yb ratio is affected by the depth or nature of the magmatic source (e.g., [START_REF] Wilson | Igneous petrogenesis. A global tectonic approach[END_REF][START_REF] Rollinson | Using geochemical data: evaluation, presentation, interpretation[END_REF]. Fig. 12b shows that these ratios are relatively constant through time for Tungurahua lavas, except a high Sm/Yb content after the ~33 ka collapse (PS-117) and a relatively high La/Sm content towards the end of Tungurahua I construction (16EQ17).

Overall, these geochemical evolutions seem to be mainly due to the nature of the magmas.

The La/Sm and La/Yb ratios have the same trend than the SiO 2 content as a function of time, except for sample PS-117. The higher ratios correspond to the most differentiated lava flows, such as sample 16EQ17, which is a dacite significantly enriched in the most incompatible elements (LILE, HFSE and LREE; Table 2) compared to other andesite samples. Concerning sample PS-117, the high La/Yb ratio is correlated with its high Sm/Yb ratio, due to its depletion in Dy, Er, Y and Yb (Table 2) that could be related to the heterogeneity of the mantle wedge composition. Large scale sector collapses occurring in volcanic islands may cause an increase of the partial melting rate due to the pressure reduction affecting the magma chamber (e.g., [START_REF] Hildenbrand | Volcano-tectonic and geochemical evolution of an oceanic intra-plate volcano: Tahiti-Nui (French Polynesia)[END_REF]. On the other hand, the thick crust may prevent sector collapses to affect the deep magmatic source in continental environments. In Ecuador, Robin et al. ( 2010) observed large geochemical variations just after two major sector collapses in Pichincha volcano lavas (Fig. 1b). The authors infer that new magma batches, associated with new magmatic cycles, may have triggered these sector collapses. We have fewer analyses for Tungurahua volcano, and they are spread over a shorter time scale. However, the geochemistry of Tungurahua lava flows is rather homogeneous for the three edifices and does not seem to be affected by the two observed collapses.

Several studies have focused on the evolution through time of Ecuadorian lavas geochemistry, notably for Atacazo [START_REF] Hidalgo | Les interactions entre magmas calco-alcalins "classiques" et adakitiques : exemple du complexe volcanique Atacazo-Ninahuilca (Equateur)[END_REF], Cayambe [START_REF] Samaniego | Temporal Evolution of Magmatism in the Northern Volcanic Zone of the Andes: The Geology and Petrology of Cayambe Volcanic Complex (Ecuador)[END_REF], Iliniza [START_REF] Hidalgo | Adakitic magmas in the Ecuadorian Volcanic Front: Petrogenesis of the Iliniza Volcanic Complex (Ecuador)[END_REF], Mojanda-Fuya Fuya [START_REF] Robin | Evolution of the late Pleistocene Mojanda-Fuya Fuya volcanic complex (Ecuador), by progressive adakitic involvement in mantle magma sources[END_REF], and Pichincha [START_REF] Samaniego | Evolving metasomatic agent in the Northern Andean subduction zone, deduced from magma composition of the long-lived Pichincha volcanic complex (Ecuador)[END_REF] volcanoes (Fig. 1b). These edifices are located in the northern part of the Ecuadorian arc, in front of the Carnegie ridge (Fig. 1a). They were constructed since 1.3-1.0 Ma until the Holocene, except for Mojanda-Fuya Fuya and Iliniza, which are not precisely dated yet. These edifices present a long-term evolution, between typical calc-alkaline compositions for the oldest lavas, to adakitic compositions for the most recent deposits, which is interpreted as a modification of the sources of the magmas induced by the subduction of the Carnegie ridge, and the subsequent increase of the geothermal gradient. The relatively short duration of Tungurahua activity (about 300 ka), and its location in the southern part of the arc (farther away from the Carnegie ridge than the northern volcanoes), prevent us to identify these long term deep processes, if present. This latter conclusion has been corroborated by the recent work of [START_REF] Ancellin | Across-arc versus along-arc Sr-Nd-Pb isotope variations in the Ecuadorian volcanic arc[END_REF], who analysed the Sr-Nd-Pb isotopic signature of the Ecuadorian magmas and conclude that magmas from the southern part of the arc (as those of Tungurahua and Sangay volcanoes) do not display a clear subduction slab partial melting component.

Magmatic productivity and erosion rates

Tungurahua eruptive and erosion rates

The overall volume obtained for the present edifice of Tungurahua (108 ± 30 km3/ka; Table 3 and4) is similar to the one obtained for Viejo Cayambe [START_REF] Samaniego | Temporal Evolution of Magmatism in the Northern Volcanic Zone of the Andes: The Geology and Petrology of Cayambe Volcanic Complex (Ecuador)[END_REF], and seems to correspond to a medium size compared to arc volcanoes in general (Table 4; [START_REF] Grosse | Morphometry and evolution of arc volcanoes[END_REF]. However his volume is higher than Ecuadorian Antisana [START_REF] Hall | Antisana volcano: A representative andesitic volcano of the eastern cordillera of Ecuador: Petrography, chemistry, tephra and glacial stratigraphy[END_REF]; Table 4), Imbabura (Le Pennec et al., 2011) and Chimborazo [START_REF] Samaniego | Eruptive history of Chimborazo volcano (Ecuador): A large, ice-capped and hazardous compound volcano in the Northern Andes[END_REF] volcanoes, which are more eroded or younger, and is lower than Rucu Pichincha [START_REF] Robin | New radiometric and petrological constraints on the evolution of the Pichincha volcanic complex (Ecuador)[END_REF] and Mojanda (> 140 km3; [START_REF] Robin | Mojanda volcanic complex (Ecuador): Development of two adjacent contemporaneous volcanoes with contrasting eruptive styles and magmatic suites[END_REF] volcanoes, located more to the north (Fig. 1b), and significantly older. Our palaeotopographical reconstructions suggest that Tungurahua I was a volcano with lower sloping upper flanks, while Tungurahua II and III have an exponential shape with a concave profile and steeper slopes (Fig. 4; Fig. 10). The nature of lavas composing these three edifices is very similar and cannot explain this morphological difference. Tungurahua I has been subjected to erosion longer than Tungurahua II and III, and the erosion mainly affected steep slopes of areas near the summit. Less eroded parts, in particularly flanks with low slopes, constitute the present planezes. Our model of Tungurahua I morphology is based on the surface of these planezes, and it does not exclude the possibility that Tungurahua I could have had a similar concave profile as the present edifice at the end of its construction. Assuming that the activity of Tungurahua I ended ~80 ka, we determined the erosion rate by calculating the volume loss between our topographic model at 80 ka and the present-day topography. This was performed only considering the eastern flank, where the remnants of Tungurahua I not affected by sector collapses crop out, and yielded a volume of 16 ± 4 km 3 , corresponding to an erosion rate of 0.2 ± 0.1 km 3 /ka (Table 3). Assuming the long term erosion rate is constant over time, we obtain a total eroded volume of 68 ± 41 km 3 during the construction of Tungurahua I, between 293 and 81 ka (PS-118 and PS-116 respectively; Table 1 and3). Based on our models, the volume of Tungurahua I corresponds to 56 ± 33 km 3 of deposits. In order to take into account the erosion that affected the edifice during its construction phase, we have added the 68 ± 41 km 3 eroded volume to calculate the volume of emitted products and the magmatic productivity rate. Our result of 0.6 ± 0.2 km 3 /ka (Table 3) thus corresponds to a magmatic production volume of 124 ± 74 km 3 during a period of 212 ka. However, these values should be considered with caution, as the basement elevation under Tungurahua volcano is not well constrained, and the constant erosion rate applied over the whole construction period was most probably variable through time, as a function of the climatic conditions and the nature of outcropping volcanic products. Moreover, we consider that the deep valleys have been dug by erosion, which may have occurred mainly before 30 ka since Tungurahua II lavas outcrop at the bottom of these valleys (Fig. 3). However, these lavas are younger than 15 ka (e.g. sample PS-111), and we cannot quantify the volume of deposits eroded by the Last Glacial Maximum, which occurred between 25 and 15 ka in this region [START_REF] Clapperton | Glacial and volcanic geomorphology of the Chimborazo-Carihuairazo Massif, Ecuadorian Andes[END_REF][START_REF] Heine | Tropical South America during the last glacial maximum: evidence from glacial, periglacial and fluvial records[END_REF]. Furthermore, tephra deposits can easily erode when they are not covered with lava flows. It is possible that such deposits existed, but it is difficult to estimate and take into account this volume in our calculations of erosion rates. Similarly, from a calculated volume of 21 ± 4 km 3 obtained for Tungurahua II, added with a volume of 4 ± 2 km 3 for erosion, we obtain a volume of 24 ± 4 km 3 of emitted products, giving an eruptive rate of 0.9 ± 0.2 km 3 /ka, similar to Tungurahua I. Finally, the magmatic productivity rate calculated for Tungurahua III the whole field constructed during the last million years and the youngest cone, respectively; [START_REF] Lewis-Kenedi | The eruptive history of the Tequila volcanic field, western Mexico: ages, volumes, and relative proportions of lava types[END_REF]. These data show that eruptive rates may vary significantly in the same geodynamic context. Moreover, volcanoes which experienced a long period of activity (in the order of one million years) seem to have lower eruptive rates than younger edifices, averaged over shorter times (e.g., [START_REF] Klemetti | Volcanic evolution of Volcán Aucanquilcha: a longlived dacite volcano in the Central Andes of northern Chile[END_REF]. The magmatic productivity rates also vary during construction stages of a single edifice, where a few thousand years period of high activity will display a higher eruptive rate than the one averaged on the whole eruptive history of the volcano. Indeed, stratovolcanoes grow in spurts (e.g., [START_REF] Hildreth | Potassium-argon geochronology of a basalt-andesitedacite arc system: The Mount Adams volcanic field, Cascade Range of southern Washington[END_REF][START_REF] Lewis-Kenedi | The eruptive history of the Tequila volcanic field, western Mexico: ages, volumes, and relative proportions of lava types[END_REF], with sporadic eruptive pulses, separated by longtime periods of quiescence, producing most of the volcano volume. The magmatic productivity rates averaged over the whole period of construction are therefore systematically lower, such observed for Tungurahua with ~0.4 km 3 /ka for the whole volcano (Table 3), while the eruptive rate of the three individual edifices is higher than 0.6 km 3 /ka. Magmatic productivity rates of Tungurahua I, II and the whole edifice arelong-term averaged eruptive rates, which include quiescence periods, whereas Tungurahua III, younger than 3 ka, represents a « peak » of activity with a significantly higher eruptive rate (Table 3). A similar picture seems to occur in Peru at Ampato-Sabancaya volcanic complex. Ampato, the older edifice, has an eruptive rate of 0.08-0.09 km 3 /ka, whereas it is of 0.6-1.7 km 3 /ka for the younger edifice Sabancaya, constructed since 6-10 ka (Samaniego et al., 2016).

As expected, Tungurahua magmatic productivity rates are lower than in a subduction context where the velocity of the plate is faster (5 km 3 /ka for Mount Fuji in Japan; [START_REF] Crisp | Rates of magma emplacement and volcanic output[END_REF], and higher than in a subduction context where the convergence rate is slower, as for instance in the Lesser Antilles. Indeed, eruptive rates there vary between 0.13 km 3 /ka in Martinique (Mount Pelée; [START_REF] Germa | Construction and destruction of Mont Pelée volcano: Volumes and rates constrained from a geomorphological model of evolution: Construction and Destruction of Mont Pelée[END_REF], 0.15 km 3 /ka at Montserrat [START_REF] Harford | The volcanic evolution of Montserrat using 40Ar/39Ar geochronology[END_REF], and 0.04 to 0.7 km 3 /ka in Guadeloupe [START_REF] Lahitte | DEM-based reconstruction of southern Basse-Terre volcanoes (Guadeloupe archipelago, FWI): Contribution to the Lesser Antilles Arc construction rates and magma production[END_REF]Ricci et al., 2015a;2015b; Table 4). Finally, Tungurahua eruptive rates are lower than those obtained in Argentina for Payún Matrú volcano (4 km 3 /ka, averaged over the last 300 ka; [START_REF] Germa | Volcanic evolution of the back-arc Pleistocene Payun Matru volcanic field (Argentina)[END_REF], where back-arc extension may have favoured the magma ascent.

Comparison between erosion rates of Tungurahua volcano and other studies

Since only a few studies have investigated erosion rates, their relationship with the geodynamic context or the climate variability is still poorly understood. Our erosion rate for Tungurahua I volcano of 0.2 ± 0.1 km 3 /ka, equivalent to 6.5 ± 1.7 t/km 2 /ka and 2.4 ± 0.6 mm/a, calculated for the last 80 ka, is significantly higher than rates obtained in the arid central Andes and in Peru (between 0.01 and 0.11 mm/a; [START_REF] Karátson | Erosion rates and erosion patterns of Neogene to Quaternary stratovolcanoes in the Western Cordillera of the Central Andes: An SRTM DEM based analysis[END_REF] or in tropical environments, such as in the Lesser Antilles with0.05 ± 0.02 km 3 /ka in Martinique [START_REF] Germa | Construction and destruction of Mont Pelée volcano: Volumes and rates constrained from a geomorphological model of evolution: Construction and Destruction of Mont Pelée[END_REF], and between 0.2 ± 0.2 and 1.4 ± 0.6 t/km 2 /ka in Guadeloupe (Ricci et al., 2015a;2015b) islands. This difference could be explained by the succession of glacial and interglacial periods experienced by Tungurahua volcano, whereas the Antilles islands were only subject to rainfalls. However, morphology and extreme rainfalls experienced by La Réunion island, as well as the faster weathering of basaltic than andesitic lavas (e.g., [START_REF] Gislason | Chemical weathering of basalt in Southwest Iceland; effects of runoff, age of rocks and vegetative/glacial cover[END_REF][START_REF] Louvat | Present denudation rates on the island of Reunion determined by river geochemistry: basalt weathering and mass budget between chemical and mechanical erosions[END_REF], may explain its high erosion rate of 1.2 ± 0.4 km 3 /ka [START_REF] Salvany | Geomorphic evolution of the Piton des Neiges volcano (Réunion Island, Indian Ocean): Competition between volcanic construction and erosion since 1.4 Ma[END_REF], compared to the one of Tungurahua volcano.

Conclusions

This study allows us to refine the eruptive history of Tungurahua volcano, which was built in three stages since the last 300 ka. The overall volume calculated for the remaining edifice is ~110 km 3 , which corresponds to a mean eruptive rate of ~0.4 km 3 /ka. Tungurahua I was a ~125 km 3 andesitic to dacitic stratovolcano, built between 293 ± 10 and 79 ± 3 ka with a magmatic productivity rate of 0.6 ± 0.2 km 3 /ka. Pondoa, Runtún, Ulba, Minsas and Patacocha plateaux are present-day remnants of this first edifice. After a ~50 ka long period of quiescence, the first western sector collapse occurred at ~33 ka [START_REF] Le Pennec | A Devastating Plinian Eruption at Tungurahua Volcano Reveals Formative Occupation at ∼1100 cal BC in Central Ecuador[END_REF].

Tungurahua II was built between 29 ± 2 and ~3 ka [START_REF] Hall | Tungurahua Volcano, Ecuador: structure, eruptive history and hazards[END_REF][START_REF] Le Pennec | A Devastating Plinian Eruption at Tungurahua Volcano Reveals Formative Occupation at ∼1100 cal BC in Central Ecuador[END_REF].

Around 25 km 3 of volcanic products filled the collapse amphitheatre, with an eruptive rate of 0.9 ± 0.2 km 3 /ka, similar to those of Tungurahua I. They mainly crop out in the southwestern flank and around Juive Grande area, in the northwestern flank (Fig. 2). Collapse of Tungurahua II western flank was followed by rapid construction of Tungurahua III during the last 3 ka. This third and still active edifice constitutes the western flank of the present-day volcano, and is being built with a relatively high productivity rate of 2.5 ± 1.0 km 3 /ka. We also estimated that around 16 km 3 of Tungurahua I volcanic material was eroded since the end of its construction, corresponding to an erosion rate of 0.2 ± 0.1 km 3 /ka. The composition of Tungurahua lavas is rather homogeneous, and the magmatic signature of the three edifices do not seem to have been affected by the two sector collapses experienced by the volcano.

Moreover, the geochemistry do not show changes in the deep magmatic source as observed for northern Ecuador volcanoes. [START_REF] Sun | Chemical and isotopic systematics of oceanic basalts: implications for mantle composition and processes[END_REF]. Symbols are the same used in Fig. 8a.

Figure captions

  . 3 and 5. Six samples were not considered because they were either altered (16EQ12) or too contaminated by atmospheric argon (16EQ13, 16EQ19, 16EQ36, TUNG3) to yield a meaningful age.Moreover, as the base and the top of Ulba sequence are well constrained by samples 16EQ15 and 16EQ17 respectively, dating sample 16EQ16 was not necessary, since it is an intermediate lava located between the other two samples. Eighteen samples were successfully dated, with the K content of the groundmass ranging between 1.122% and 3.253%, and the maximum radiogenic argon content reaching 13.78%. These new data allow us to refine the timing of activity of Tungurahua volcano. The oldest edifice is well constrained by eleven ages, and was built between 293 ± 10 and 79 ± 3 ka. Our ages obtained for the lavas from Ulba, Pondoa and Runtún plateaux range between 92 ± 1 and 79 ± 3 ka, and suggest a gap of activity between 76 ka and the ~33 ka first sector collapse event (Fig.5; Le[START_REF] Le Pennec | A Devastating Plinian Eruption at Tungurahua Volcano Reveals Formative Occupation at ∼1100 cal BC in Central Ecuador[END_REF]. The construction of Tungurahua II started at least 29 ± 2 ka (PS-117), therefore quickly after the first sector collapse. Similarly than for Tungurahua I, we have no evidence of activity between 27 and 15 ka. The five youngest ages are below 15 ka, but their relatively large uncertainties prevent us to determine whether they belong to Tungurahua II, or are younger than 3 ka and are part of Tungurahua III. Only lava from the sample PS-109 clearly belongs to Tungurahua II. We propose that samples PS-107, PS-111 and PS-119 are related to Tungurahua II activity, while the sample of Baños lava flow (17EQ37) was emitted in the early stage of Tungurahua III construction, based on their stratigraphic relationships, further described in the discussion. Finally, the Vizcaya lava flow (16EQ20) dated at 253 ± 5 ka, is coeval with the early construction of Tungurahua I.

  decrease of MgO, Fe 2 O 3 , Al 2 O 3 , CaO and TiO 2 (Fig.7a, b, c and d) suggests fractional crystallization of plagioclase and Fe-Ti oxide phenocrysts present in the samples, sometimes along with pyroxene and olivine crystals (Appendix A). Magmas are not evolved enough to loose K 2 O and Na 2 O through incorporation into crystals, and hence the alkali content increases as the fractional crystallization proceeds (Fig.7e and f).

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Acknowledgments

We are particularly grateful to Pablo Grosse for his detailed review and constructive comments, which greatly helped us to improve the clarity of this paper, as well as Joan Marti for his editorial handling. We wish to thank members of Instituto Geofísico, Escuela Politécnica Nacional of Quito for their support, assistance and warm welcome. We also thank J. Bernard and M. Almeida for sampling rocks from upper parts of the volcano, as well as J.

Cotten for carrying out the geochemical analyses of the samples presented in Appendix B, and C. Pallares for discussion regarding geochemistry data. This work is part of an Ecuadorian-French cooperation program carried out between the Instituto Geofísico, Escuela Politécnica

(2.5 ± 1.0 km 3 /ka; Table 3) is consistent with the eruptive rate of ~1.5 km 3 /ka estimated by [START_REF] Hall | Tungurahua Volcano, Ecuador: structure, eruptive history and hazards[END_REF] over the last 2300 years, for a similar volume to ours. The relatively high production rate calculated for Tungurahua III may be explained by its recent construction and rather continuous activity, compared to the two older edifices, which are averaged over a larger time scale, certainly including periods of quiescence.

Comparison between eruptive rates of Tungurahua volcano and other studies

Many phenomena may impact on the magmatic productivity, such as the geodynamic context, the nature and thickness of the crust, or the period of time considered. In a compilation of the magmatic productivity calculated over the world, [START_REF] White | Long-term volumetric eruption rates and magma budgets[END_REF] obtained an average rate of 4.4 ± 0.8 km 3 /ka for continental crust volcanoes and 2.3 ± 0.8 km 3 /ka for andesitic edifices. Our eruptive rate of 2.5 km 3 /ka, corresponding to Tungurahua III activity (Table 3 and4), falls within this latter range. Note that the rates of 0.6 and 0.9 km 3 /ka, obtained here for Tungurahua I and II, respectively (Table 3 and4), are comparable to the ones obtained on Chimborazo (0.1 to 1 km 3 /ka; [START_REF] Samaniego | Eruptive history of Chimborazo volcano (Ecuador): A large, ice-capped and hazardous compound volcano in the Northern Andes[END_REF] and Pichincha (~0.6 km 3 /ka for both Rucu and Guagua Pichincha; [START_REF] Robin | New radiometric and petrological constraints on the evolution of the Pichincha volcanic complex (Ecuador)[END_REF] volcanoes, both also from Ecuador (Fig. 1). Tungurahua eruptive rates are also similar to those from other arc volcanoes, for instance in Chile at Parinacota (~0.3 and 1 km 3 /ka for the whole edifice and the young cone, respectively; [START_REF] Hora | Volcano evolution and eruptive flux on the thick crust of the Andean Central Volcanic Zone: 40Ar/39Ar constraints from Volcan Parinacota, Chile[END_REF], Puyehue-Cordón Caulle (0.42 km 3 /ka; [START_REF] Singer | Eruptive history, geochronology, and magmatic evolution of the Puyehue-Cordon Caulle volcanic complex, Chile[END_REF] and El Misti (0.63 and 2.1 km 3 /ka for the whole edifice and peak eruptive rates, respectively; [START_REF] Thouret | Geology of El Misti volcano near the city of Arequipa, Peru[END_REF] volcanoes, which were active since less than 320 ka, or with Ceboruco volcano in Mexico (~0.5 km 3 /ka; [START_REF] Frey | Magma eruption rates constrained by 40Ar/39Ar chronology and GIS for the Ceboruco-San Pedro volcanic field, western Mexico[END_REF]. However, Tungurahua eruptive rates are significantly higher than at Aucanquilcha volcano in Chile (0.04 and 0.16 km 3 /ka for the whole edifice and the highest eruptive rate stage, respectively; [START_REF] Klemetti | Volcanic evolution of Volcán Aucanquilcha: a longlived dacite volcano in the Central Andes of northern Chile[END_REF] and at Tequila volcano in Mexico (0.13 and > 0.24 km 3 /ka for

Table captions Table 1:

New K-Ar ages obtained on groundmass in this study. Results are listed from the oldest to the youngest. Column headings indicate sample name, detail of the outcrop location, sample coordinates projected using the Universal Transverse Mercator (UTM) coordinate system (Zone 17), potassium concentration in percent, radiogenic argon content in percent and 10 11 atoms per gram, ages and weighted mean age in ka, with 1-sigma accuracy. Ages marked with an asterisk (*) were calculated using unweighted average.

Table 2:

Major and trace element composition of whole-rock samples. All major data were brought down to a total of 100%. Samples marked with an asterisk (*) have not been dated.

Table 3:

Results of volumes, magmatic productivity and erosion rates calculations, given at 1-sigma accuracy, obtained from the palaeosurfaces modelling. Raw volume corresponds to the volume calculated from the surface model without taking into account erosion that occurred during the construction. Total volume corresponds to the sum of the raw volume and the volume eroded during the construction, based on the erosion rate. Min-max values were calculated by dividing the minimum volume by the maximum time period, and the maximum volume by the maximum time period, respectively. Erosion rate in T/km2/ka was calculated considering a rock mean density of 2.7. Ages marked with an asterisk (*) are previous 14C published ages [START_REF] Le Pennec | A Devastating Plinian Eruption at Tungurahua Volcano Reveals Formative Occupation at ∼1100 cal BC in Central Ecuador[END_REF].

Table 4:

Summary of Tungurahua eruptive and erosion rates, compared to rates from other published studies.

Appendix captions Appendix A:

Thin sections of all samples (in alphabetical order), observed under an optical microscope. Photographs in left-hand column were taken with a polarized light, and in right-hand column with a natural light.

Appendix B:

Major and trace element composition of Tungurahua whole-rock samples, presented in [START_REF] Hall | Tungurahua Volcano, Ecuador: structure, eruptive history and hazards[END_REF] and in [START_REF] Bustillos | Las avalanchas de escombros en el sector del volcán Tungurahua (MSC)[END_REF]. All major data were brought down to a total of 100%. Column headings indicate edifice, sample name, outcrop coordinates projected using the Universal Transverse Mercator (UTM) coordinate system (Zone 17) and given within 100 meters, and volcanic unit. Results are listed in two parts: lavas, from potentially oldest to youngest, then blocks belonging to sector collapse deposits. pl : plateau.

Appendix C:

KMZ file containing the location of the samples described in this article.