Abstract
Marine Quaternary trench and slope sediments were sampled along the margin of the Southern Andes, Chile between 36° and 40°S. Major and trace element contents indicate only minor influence of weathering and transport fractionation. The whole rock composition of the sediments is similar to the average rock of the Cretaceous to Holocene magmatic arc of this section of the southern volcanic zone. Sr, Nd, and Pb isotope composition of the sediments also resembles closely the average composition of the magmatic arc. The contribution of compositionally distinct Palaeozoic crust, which makes up most of the volume of the forearc, is ~0–20% crustal Sr, Nd, and Pb according to the isotope record of the trench and slope sediments. Input of sediments from the continent into the subduction system was dominated by detritus from the magmatic arc at least for the last 20 My on the basis of the Oligocene to Holocene exhumation history of the margin.
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Introduction
The sedimentary infill of the deep sea trench from the continent affects the make-up of the interface between the oceanic and the continental plate in terms of sediment accretion versus erosion, and has a large effect on the subduction channel kinematics (e.g. Shreve and Cloos 1986; Lohrmann et al. 2006). It is also a major source for input of upper crustal material to the mantle source of arc magmas (e.g. Plank and Langmuir 1998; Sigmarsson et al. 2002). The deep sea trench of the Chilean subduction zone of the segment between the subducting Chile Triple Junction at ~45°S and Juan Fernández ridge at ~33°S (Fig. 1a), which both form morphological highs, deepens from ~3,800 m below sea level at 44°S to ~5,000 m at 36°S (e.g. Lindquist et al. 2004; Kukowski and Oncken 2006). The present average trench fill is ~2 km thick with high average sedimentation rates since the Pliocene linked to glaciation/deglaciation and fast denudation of the Andean Cordillera (e.g. Melnick and Echtler 2006; Glodny et al. 2008); south of 38°S the structural trench is filled by sediments (Thornburg and Kulm 1987; Völker et al. 2006). Accumulation of these sediments in an accretionary wedge appears to be minor and subduction of sediments is considered as important (e.g. Behrmann and Kopf 2001; Kukowski and Oncken 2006). The present sediment supply from the shelf (marine forearc basins) and upper slope into the trench is largely controlled by submarine cañon linked to the major E–W drainages (rivers) of the western flank of the Andes (e.g. Thornburg and Kulm 1987; Völker et al. 2006; Fig. 1). Erosion and sedimentation occur in a geographically well-defined system. The watershed of the Andean mountains limits the source area. The sediment transport follows the E–W morphological gradient to the final depositional area, the trench. The morphological barriers of the Chile Triple Junction and the Fernández ridge limit possible lateral sediment transfer within the trench and the depth gradient determines the general direction of sediment transport from South to North.
Geochemical studies including the isotope composition of the trench sediments are limited to the sample material of ODP Leg 141 (~45°S; Fig. 1a, Kilian and Behrmann 2003), whereas other studies address on sedimentological and petrographical aspects (Thornburg and Kulm 1987; Völker et al. 2006). This study focuses on the chemical and Nd, Sr, and Pb isotope compositions of 21 sediment samples from the trench and western slope (ts-sediments in the following) between 40° and 36°S from three sample sites related to the major sediment feeders CalleCalle, Tolten, and BioBio Cañón (Fig. 1). Our aim is to define the contribution of distinct continental sources to the ts-sediments and to characterize the composition of the influx from the continent into the subduction system.
Geology and composition of the source area
Considering the present morphology of the Chilean part of the Southern Andes, all continental sediments brought into marine forearc basins and the trench stem from the active arc and forearc (Fig. 1b). The oldest rocks west of the main Cordillera are of Devonian–Carboniferous to Triassic age and comprise the exposed accretionary complex of the Coastal Cordillera. Younger sequences of the accretionary complex are preserved in the offshore forearc, because the trench–arc geometry remained fairly stable throughout late Mesozoic and Cenozoic times (e.g. Duhart et al. 2001; Glodny et al. 2006 and references therein). Substantial erosion of the submarine forearc by subduction appears to be restricted to areas north of 36°S (e.g. Kay et al. 2005).
The accretionary complex is subdivided into an eastern and western series, which are separated by a NW–SE oriented fold (Fig. 1b). The W–E extension of the eastern series is ~100 km, that of the western series ~200 km. The latter comprises abundant siliciclastic (meta)sedimentary rocks from the high pressure–low temperature metamorphic regime of an accretionary wedge, which was accumulated between the latest Carboniferous to Triassic (Hervé 1988; Martin et al. 1999; Duhart et al. 2001; Willner et al. 2000; 2004; Glodny et al. 2005). The 200-km wide series includes some metabasites and (ultra)mafic rocks and forms the submarine part of the forearc. The eastern series comprises non-metamorphic to medium grade (meta)sedimentary rocks whereas high P metamorphism and metabasites are generally absent. The depositional age of these sediments is not well constrained, but they belong to Devonian–Carboniferous–Permian sedimentary basins along the western margin of Gondwana (González Bonorino 1991; França et al. 1995; López-Gamundi and Rossello 1998; Bandel and Quinzio-Sinn 1999). In contrast to the accretionary wedge of the Coastal Cordillera, Devonian metasedimentary rocks of the eastern foothills of the Main Cordillera are of the high-T, medium-P type (Lucassen et al. 2004).
Late Carboniferous to Permian granite batholiths intruded the Palaeozoic (meta)sedimentary sequence at shallow depth (e.g. Hervé et al. 1988; Martin et al. 1999; Lucassen et al. 2004) and scattered outcrops of granite are also found in the eastern part of the Main Cordillera (Fig. 1b, Caminos et al. 1988; Varela et al. 1994; Lucassen et al. 2004). The oldest Mesozoic magmatic rocks in the Coastal Cordillera are small late Triassic granites (Hervé et al. 1988; Lucassen et al. 2004). Subsequent abundant intrusive and volcanic rocks of the Jurassic to Holocene magmatic arc are mostly located in the Main Cordillera in Chile and Argentina (Fig. 1, e.g. López-Escobar 1984; Hickey et al. 1984; Hildreth and Moorbath 1988; Martin et al. 1999; south of 44°S see Pankhurst et al. 1999). Isolated Mesozoic and minor Mid-Tertiary magmatism also occurs west of the Main Cordillera (Martin et al. 1999; Muñoz et al. 2000). The intrusive rocks of the Main Cordillera form the northernmost part of the North Patagonian batholith, which extends to ca. 53°S (e.g. Pankhurst et al. 1999). The Plio-Pleistocene to Holocene arc volcanism in the Southern Volcanic Zone (SVZ) is mostly made up of basaltic andesite–andesite strato-volcanoes (e.g. López-Escobar 1984; Hickey et al. 1984; Hildreth and Moorbath 1988; Feeley et al. 1998). The Jurassic to present arcs remained at a near stationary position within the Main Cordillera and the trench-arc configuration shows no significant variation since approximately 200 Ma. This is in contrast to the evolutionary history of the Andean arcs north of 36°S.
The Palaeozoic (meta)sedimentary rocks and intrusions in the Coastal Cordillera are overlain by Triassic–Cretaceous sedimentary rocks (Ferraris 1981). The preservation of shallow-level late Palaeozoic intrusions and Triassic erosional unconformities indicate that denudation in the forearc was only in the range of a few km since the late Palaeozoic–early Mesozoic. Deeper sections of the crust are not exposed except in the accretionary complex of the Coastal Cordillera. Exhumation ceased in late Triassic times and low average rates of exhumation (0.03–0.04 mm/year) in the Coastal Cordillera between 200 Ma and Miocene were confirmed by fission track ages (Glodny et al. 2008).
A comprehensive study of the chemical and isotopic composition of the Palaeozoic to Tertiary metamorphic and magmatic basement between 41° and 36°S and a review of previous work was presented by Lucassen et al. (2004). The composition of the Pliocene to Holocene volcanic rocks from the Main Cordillera was studied by numerous authors (references see Fig. 2). Nd, Sr and Pb isotope compositions of (mid to late) Palaeozoic (meta)sedimentary and Palaeozoic granites are dominated by recycling of Proterozoic felsic continental crust. Nd–Sm model ages (Fig. 1b) vary between 1.3 and 2.1 Ga, in line with observations of similar rocks of comparable age between 50° and 21°S (e.g. Berg and Baumann 1985; Lucassen et al. 1999; Bock et al. 2000; Augustsson et al. 2006). In contrast to the recycled basement, isotope compositions of late Mesozoic to recent rocks of the arcs (in the following SVZ rocks; references see Fig. 2) indicate juvenile material from the relatively uniform sub-arc mantle and only small contributions of the ambient Palaeozoic basement.
Sampling, sample description and age of the ts-sediments
For this study we used bulk samples of unconsolidated sediment cores and dredge samples of hard rock outcrops. Cores were taken with a standard 1.5 to heavy gravity corer of 5–10 m length retrieving cores of 9 cm diameter. For hard rock outcrops we used a 1.0 × 0.4 m wide chain-bag dredge.
Samples were taken during RV SONNE cruise SO161-5 from 13 selected sites along the Chile trench and the neighboring lower to middle continental slope between latitudes 36° and 40°S (Fig. 1b; Table 1). Sampling locations concentrate near three submarine cañóns (CalleCalle: ~40–39°S; Tolten: ~39–38°S; BioBio: ~37–36°S) and provide material from two different geological units—(1) the present trench infill and (2) the lower slope sequence.
The present day trench fill was sampled using a gravity corer. Recovered cores are up to 8 m long. Sites were selected near the deformation front and in some distance to this structural lineament (Fig. 1b). To cover the slope sequence, several intraslope basins at the middle and lower slope were cored to define the composition of young and unconsolidated slope material. In addition, we dredged the steep escarpments of the deeply incised cañóns to recover consolidated and lithified (accreted?) sediments from somewhat older sequences, which form the lower slope.
From sediment cores commonly two separate bulk samples of 4–5 cm lengths and 60 g weight each were analyzed—one taken from an upper core meter and a second one near the core base. From dredged hard rock samples specimen of ~100–200 g weight were selected and processed for analyses.
Sedimentologically, samples comprise all variations of the clastic sequence—ranging from fine-grained silty mud to coarse graded sand beds and from mudstone to unsorted sandstones (details see Table 1). Commonly these lithologies stem from turbiditic sequences which are composed of an intercalation of mostly thin hemipelagic mud layers with silty to sandy, often graded turbidite beds. At slope locations we also sampled slumped clastic sequences which are mostly unsorted and also contain mud lenses. Occasionally lithified silt and sandstone slabs showed signs of tectonic strain. Additional information on sediments and their environmental interpretation can be found in the literature (Wiedicke et al. 2002; Völker et al. 2006, 2008; Raitzsch et al. 2007).
14C-age determinations (sample 50SL from ~2.2 kyr at 0.2 m to 23 kyr at 7 m core depth; ODP leg 1232 from ~12 kyr at 0.6 m to 138 kyr at 96 m) and oxygen isotope stratigraphy of some of the cores (Blumberg et al. 2008; Völker et al. 2008) and dredge samples indicate variable Quaternary ages. Sediments from the gravity cores represent the late Pleistocene glaciation in the southern Andes; some samples have been assigned to the post-glacial Holocene (Table 1).
Chemical and isotopic composition of the ts-sediments and their possible sources
For the analytical procedures and data quality see the Appendix. Results of XRF and ICP-MS analyses and determinations of Sr, Nd, and Pb isotope ratios are presented in Table 2.
Chemical composition
The major element compositions of the ts-sediments are similar for samples of the three distant feeder systems (CalleCalle, Tolten, and BioBio Cañón; Fig. 1). TiO2, Al2O3, FeO, MgO and K2O contents are correlated with the SiO2 contents (~56–64 wt%) following a gentle slope, whereas CaO and Na2O (and Sr) vary independently from SiO2.
In order to compare the major element composition of the ts-sediments with possible sources, we include published data of Palaeozoic granites and (meta)sedimentary rocks, and SVZ rocks (Fig. 2). The composition of the ts-sediments—except for the more variable CaO, Na2O and Sr contents—mainly plot into the field of the SVZ rocks close to the average of the latter. The variation of CaO, Na2O, and Sr contents is most likely caused by weathering of plagioclase (e.g. Nesbitt and Young 1984; McLennan et al. 1990), which also dominates the weathering index (Fig. 2i). The composition of the Palaeozoic basement especially of the Palaeozoic (meta)sedimentary rocks, is different. Significant contributions from these rocks to the major element compositions of the ts-sediments are unlikely (Fig. 2). In contrast, the composition of the ts-sediments and ODP Leg 141 sediments is fairly similar (Fig. 2). Both are—compared with the Palaeozoic (meta)sedimentary rocks—immature (Fig. 2i) and reflect largely the major element compositions of their sources.
Variation of trace element contents in the ts-sediments is moderate, which is indicated by the small compositional field (Fig. 3a). The average pattern of the ts-sediments resembles the pattern of a variety of rocks including the ODP Leg 141 sediments, SVZ rocks, average Global Subducted Sediment (GLOSS; Plank and Langmuir 1998) as a proxy for upper crust composition and even the most distinct pattern of the Palaeozoic (meta)sedimentary rocks is similar (Fig. 3a). The main difference between the REE patterns of the average ts-sediment (La/Ybnormalized ~5) and SVZ rocks (La/Ybnormalized ~4.5) is the slightly higher REE content of the latter (Fig. 3b). The average REE patterns (La/Ybnormalized ~9) of the Palaeozoic granite and Palaeozoic (meta)sedimentary rocks are broadly similar and the main difference between the ts-sediments and Palaeozoic basement is the slightly higher REE concentration of the latter (Fig. 3b).
Sr, Nd, and Pb isotope signatures
Isotope compositional ranges (Fig. 4a–c) of the ts-sediments are relatively small with 87Sr/86Sr ~0.7041–0.7061, 143Nd/144Nd ~0.51267–0.51278, 206Pb/204Pb ~18.57–18.71, 207Pb/204Pb ~15.61–15.63, and 208Pb/204Pb ~38.51–38.61. There are neither systematic differences between the three sample areas nor are they related to the water depth, i.e. slope or trench position of the sample locality, or to the presumed ages. Sr isotopes measured on the washing water of seven samples are different from the whole rock values and vary between ~0.7089 and 0.7092, i.e. the composition of the pore water is close to present Sr isotope composition of seawater (0.70907; Burke et al. 1982).
Isotope composition of the ts-sediments is distinct from those of the average Palaeozoic granite and (meta)sedimentary rocks, GLOSS, and ODP 141 sediments (Fig. 4). The differences between average SVZ rocks and ts-sediment compositions are small for all isotope systems (Fig. 4). The small compositional deviations of the ts-sediments appear to be systematic and can be described by binary mixing. Using the average isotope compositions and Sr, Nd, and Pb contents of average SVZ rocks and Palaeozoic (meta)sedimentary rocks as mixing endmembers, the Sr, Nd and Pb isotope compositions of the ts-sediments are explained by variable addition of ~0–20% of the respective elements from Palaeozoic (meta)sedimentary rocks to the average SVZ-rock (Fig. 4). The average composition of Palaeozoic granites plots on or close to the mixing lines and indicates a prominent contribution of Palaeozoic (meta)sedimentary crust in these rocks (Fig. 4; Lucassen et al. 2004). Therefore, contributions from the Palaeozoic granites would be difficult to trace in the isotope signature of the ts-sediments.
Discussion
Chemical and isotopic composition
The major element composition of the ts-sediments reflects mainly the averaged compositions of SVZ rocks, which is andesite in transition to basaltic andesite (Fig. 2). Systematic deviations of ts-sediment’s element composition from the compositional trends of the arc magmatic rocks restrict to the loss of Ca, Na, and Sr, which indicates weathering or transport-selection of plagioclase. The overall effect the latter is low to moderate (Fig. 2i) and the compositional range is small compared with the highly evolved rocks, e.g. the Palaeozoic (meta)sedimentary rocks (Fig. 2). Erosion of the material and transport was likely a fast process along the steep gradient from the mountain range to the trench. The high TiO2 (~1.5–2.0 wt%) and P2O5 (~0.3–0.8 wt%) contents, which were reported for vitric clasts in various ts-sediment samples of similar SiO2 and Na2O + K2O composition (Völker et al. 2006 including samples KD 32, SL 33, and SL 50 of this study) are not reproduced by the whole rock analyses. The vitric clasts are not dominant in the ts-sediments investigated here. Trace element patterns of the ts-sediments and their potential sources show minor differences and there is little chance to quantify the contributions of the various sources to individual samples by their trace element signatures (Fig. 3).
The isotope composition of ts-sediments is dominated by the composition of the SVZ rocks and the contribution of Palaeozoic basement is less than 20% (Fig. 4). Alteration by seawater cannot be discerned in the Sr isotope composition of the washed ts-sediments (Fig. 4a). Systematic incorporation of Sr derived from the seawater into silicate minerals obviously does not occur at least in the uppermost section of the sedimentary pile, which is represented by the piston cores. Influence of seawater Sr isotope signatures is also not evident in the solidified samples. Oceanic sediments from pelagic sedimentation on the oceanic plate should be different in isotopic composition and have been shown to reflect upper crust compositions in average (GLOSS; Plank and Langmuir 1998). In absence of data on the geochemical composition of the incoming oceanic sediments, we assume a composition similar to GLOSS for the sedimentary cover of the Nazca plate (Fig. 1a). The addition of oceanic sediments to the subduction system has been inferred from the interpretation of multichannel seismic data in the sediment pile (Reichert and Schreckenberger 2002; Völker et al. 2006). The near-surface sediments, however, appear to be dominated by turbidite deposits from the slope, which cover the trench–plane and parts of the seaward trench–slope (Völker et al. 2006). Small contributions of GLOSS would be difficult to distinguish from small contributions of Palaeozoic basement in the Sr–Nd isotope system of our samples (Fig. 4a). The Pb isotope compositions of the ODP 141 sediments (and their Sr–Nd isotope) and of two of our samples indicate the possible influence of a source different from the Palaeozoic basement, but the mixing patterns of uranogenic Pb (Fig. 4c, d) and thorogenic Pb (Fig. 4e, f) do not consistently indicate a GLOSS component. Possible contributions from an oceanic sedimentary source remain speculative.
The small compositional variations of the ts-sediments are not related to the variable W–E outcrop widths of the Palaeozoic series, which is 200 km south of 38°S and 100 km towards the North. Possible sediment transport from South to North along the Chile trench (Fig. 1a; Völker et al. 2006) is not evident in the composition of the samples.
Long-term evolution
Recent work on the exhumation history of the arc and forearc area of the studied section and its southern continuation reveals a strong geographic segmentation based on zircon and apatite fission track ages. The Palaeozoic basement of the forearc was already exhumed to depths <2 km in late Cretaceous, according to apatite fission track ages, which record the latest stage of the thermal history. Averaged exhumation rates were low in the western and eastern series (0.04 mm/a; Glodny et al. 2008). The only exception to this scheme is the young Pliocene to Holocene uplift of a Palaeozoic granite massif in the Coastal Cordillera ~37–38°S (Fig. 1b; Nahuelbuta Range; Melnick and Echtler 2006; Glodny et al. 2008) and the rare occurrences of Palaeozoic basement rocks within the Main Cordillera (Fig. 1b). Apatite fission track ages in the magmatic arc of the Main Cordillera indicate rapid exhumation from Pliocene to Recent south of 39°S (up to 2 mm/a), whereas the exhumation rates decreased towards the North and are up to one order of magnitude lower at 36°S (Thomson 2002; Glodny et al. 2008). The gradient is mainly related to latitudinally variable glaciation/deglaciation effects, which occur episodically since ca 6 My in the Main Cordillera and variable precipitation, which are both more intense towards the South and promote the high sedimentation rates in the trench (e.g. Lamy et al. 2001; Kilian and Behrmann 2003; Melnick and Echtler 2006; Thomson 2002; Glodny et al. 2006). The chemical and isotope composition of the ts-sediments is not affected by this exhumation pattern and the mixing ratios of Palaeozoic basement and SVZ rocks are indistinguishable at 40° and 36°S. Site 1232 of ODP leg 202 comprises ~362 m of lithological uniform turbidite deposits shed from the continental slope with a basal age of 780 kyr (Mix et al. 2003). The lithology of the gravity cores used in this study and the extended profile of site 1232 are similar and indicate similar deposition–source relationships on an extended time scale.
The dominance of detritus from the SVZ rocks in the continental sedimentary input is likely a stable feature at a time scale longer than that calculated for the subduction of sediment from the trench down to the depth of fluid–melt generation and eclogite formation. Subduction velocity similar to the averaged rates (80 mm/year; Somoza 1998) and the present convergence rates (66 mm/year; Angermann et al. 1999) respectively transport continental sediments from the trench to depth of ~100 km in ~3.4–4 My. Subducted sediments presently in the zone of fluid–melt and eclogite generation are of early Pliocene to late Miocene age. The low average long-term exhumation of the Palaeozoic western and eastern series combined with the evidence for pre-Pliocene exhumation of the Main Cordillera (Glodny et al. 2006, 2008 and references therein) after the late Oligocene/early Miocene reorganization of the oceanic plate (e.g. Tebbens and Cande 1997) opens a long-term perspective for the continental sedimentary contribution to the subduction system from early Miocene onwards. SVZ magmatic rocks older than the late Miocene to Holocene volcanic rocks comprise abundant late Cretaceous to Miocene intrusions. Holocene to Cretaceous magmatic rocks show all similar primitive arc signature (e.g. Lucassen et al. 2004). Most likely, since ~20 Ma arc material was the prevailing component of continental contributions to slope and trench sediments.
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Acknowledgments
We thank Maren Lewerenz for performing XRF analyses at the Technische Universität Berlin, Peter Dulski and Birgit Zander for ICP-MS analyses at GFZ-Potsdam, Cathrin Schulz for support in the GFZ radiogenic isotope laboratory, Rosemarie Geffe at TU-Berlin for polishing the Figures. We thank Rolf L. Romer for reading a previous draft of the manuscript and Christoph Breitkreuz and Diego Morata for their journal reviews, which all improved the manuscript. This study was funded by DFG (Deutsche Forschungsgemeinschaft) in the frame of Sonderforschungsbereich 267 ‘Deformation processes in the Andes’.
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Appendix
Appendix
Analytical methods
The initial sample size was ca. 50 g, which is representative even for the sand fraction. Semi-solidified rocks from the dredge samples were carefully disaggregated in a PE-bag using a hammer. All samples where transferred into Teflon beakers, washed several times in the ultrasonic in ultra clean water and dried. The water was preserved (with few drops HCl added). The dried samples were ground in an agate mill. Major elements were determined by XRF at TU-Berlin. Trace elements were determined by ICP-MS at GFZ-Potsdam (for the procedure and reproducibility of international standards see Dulski 2001).
For Nd, Pb, and Sr isotope analyses by TIMS at GFZ Potsdam, ~200 mg of sample were weighted into Savillex beakers. Prior to dissolution in HF–HNO3 mixture, the samples were treated with warm 1 N HCl followed by washing in ultra clean water in order to remove possible organic carbonates. All isotope ratios were determined using TIMS. Nd and Sr isotope ratios were measured using dynamic multi-collection on a MAT 262 mass spectrometer and on a VG 54 Sector mass spectrometer at the GFZ-Potsdam, respectively. Nd isotopic ratios were normalized to 146Nd/144Nd = 0.7219, Sr isotopic ratios to 86Sr/88Sr = 0.1194. During the analytical work at GFZ-Potsdam the NBS 987 Sr standard yielded 87Sr/86Sr = 0.710265 ± 28 (2σ; n = 47) and the La Jolla Nd standard yielded 143Nd/144Nd = 0.511850 ± 8 (2σ, n = 46). Pb isotope ratios were measured at GFZ-Potsdam using static multi-collection on a MAT 262 mass spectrometer at controlled temperatures between 1,220 and 1,250°C. The 2σ reproducibility of all Pb isotope ratios of the NBS SRM 981 standard (measured ratios, uncorrected for fractionation; 206Pb/204Pb = 16.906 ± 10, 207Pb/204Pb = 14.454 ± 10, 208Pb/204Pb = 36.583 ± 20, n = 28) is better than 0.1% and a 2σ error of 0.1% is assumed for the measured samples considering the uncertainty of correction for mass fractionation. Instrumental mass-fractionation has been corrected using 0.1% per amu (atomic mass unit) on the base of the NBS SRM 981 values. Procedural blanks were <30 pg for Pb, <50 pg Nd and <100 pg for Sr. No blank corrections have been applied to the measured ratios because blank contribution was insignificant in comparison to the amount of the respective elements in the sample.
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Lucassen, F., Wiedicke, M. & Franz, G. Complete recycling of a magmatic arc: evidence from chemical and isotopic composition of Quaternary trench sediments in Chile (36°–40°S). Int J Earth Sci (Geol Rundsch) 99, 687–701 (2010). https://doi.org/10.1007/s00531-008-0410-4
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DOI: https://doi.org/10.1007/s00531-008-0410-4