Journal of Earth Science  2019, Vol. 30 Issue (3): 535-548   PDF    
Timing of Displacement along the Yardoi Detachment Fault, Southern Tibet: Insights from Zircon U-Pb and Mica 40Ar-39Ar Geochronology
Hanwen Dong 1,2, Yuanku Meng 2, Zhiqin Xu 3, Hui Cao 1, Zhiyu Yi 1, Zeliang Ma 1     
1. Key Laboratory of Deep-Earth Dynamics of Ministry of Natural Resources, Institute of Geology, Chinese Academy of Geological Sciences, Beijing 100037, China;
2. College of Earth Science and Engineering, Shandong University of Science and Technology, Qingdao 266590, China;
3. School of Earth Sciences and Engineering, Nanjing University, Nanjing 210023, China
ABSTRACT: The Yardoi dome is located in the eastern end of the northwest-southeast extending North Himalayan domes (NHD). The dome exposes a granite pluton in the core and three lithologictectonic units separated by the upper detachment fault and the lower detachment fault. The Yardoi detachment fault (YDF), corresponding to the lower detachment fault, is a 800 m strongly deformed top-NW shear zone. LA-ICP-MS zircon U-Pb dating yielded a crystallization ages of 19.57±0.23 to 15.5±0.11 Ma for the leucogranite dyke swarm, which indicates that the ductile motion along the YDF began at ca. 20 Ma. The 40Ar/39Ar muscovite ages of 14.05±0.2 to 13.2±0.2 Ma and the 40Ar/39Ar biotite age of 13.15±0.2 Ma, suggest that the exhumation led to cooling through the 370℃ Ar closure temperature in muscovite at~14 Ma to the 335℃ Ar closure temperature in biotite at~13 Ma. Our new geochronological data from the Yardoi dome and other domes in the Tethyan Himalayan Sequences suggest that the ductile deformation in the region began at or before~36 Ma in a deep tectonic level, resulting in southward ductile flow at the mid-crustal tectonic level that continued from 20 to 13 Ma. Comparing the Yardoi dome to other domes in the NHD, the cooling ages show a clear diachronism and they are progressively younger from the West Himalayan to the East Himalayan.
KEY WORDS: leucogranite    geochronology    Yardoi dome    southern Tibet    Himalayan Orogen    

The collision between the India and Eurasia continents is the most spectacular major geological event during the Cenozoic (55–65 Ma, Meng et al., 2018a, b; Xiong et al., 2018; Zhang L et al., 2018; Hu et al., 2016; Xu et al., 2011; Ding et al., 2005; Beck et al., 1995). Since the collision, the Tibetan Plateau has experienced deformation, landform, environmental and deep structural changes in a broad region. The collision directly leads to the Himalayan orogenesis, strong tectonic deformation, magmatism, and metamorphism in Tibetan Plateau (Zhang Z M et al., 2018; Xu et al., 2011; Zeng et al., 2009; Tapponnier et al., 1986). Thus, the Himalayan Orogen is the most ideal natural laboratory for studying plate collision and continental dynamics (Ding et al., 2016; Xu et al., 2012; Yin and Harrison, 2000). In the Himalayan region, the tectonic feature of post-collision is manifested as contemporary thrust and extensional structures along south-north direction, which form two parallel granite belts, the Greater Himalayan leucogranites zone and the North Himalayan Domes (NHD) zone (Gao et al., 2017; Zeng and Gao, 2017; Zeng et al., 2009; Harrison et al., 1997; Burg and Chen, 1984).

The NHD is consisted of a chain of isolated domes exposed as structural windows within the Tethyan Himalaya (THM), which between the Indus-Tsangpo suture zone (ITSZ) to the north and the South Tibetan detachment system to the south (Fig. 1a). The domes are commonly cored by variable amounts of two-mica granite, leucogranite, migmatite, orthogneiss and high-grade metasedimentary rocks with a surrounding carapace of unmetamorphosed Tethyan Himalayan sedimentary sequence (Wang et al., 2018; Smit et al., 2014; Langille et al., 2010; Guo et al., 2008; Kawakami et al., 2007; Aoya et al., 2006, 2005; Lee et al., 2006, 2004, 2000; Quigley et al., 2006; Chen et al., 1990; Burg and Chen, 1984).

Figure 1. (a) Simplified geologic map of the Himalayan Orogen (modified after Xu et al., 2013; Yin and Harrison, 2000), showing locations and leucogranite ages of the North Himalayan domes (NHD) in the southern Himalaya. Data sources: Purang (Xu et al., 2013), Niuku (Ding et al., 2005), Malashan (Gao et al., 2013), Mabja (King et al., 2011; Lee et al., 2006), Kuday (King et al., 2007; Zhang et al., 2004), Yadong (Xu et al., 2013) and Yardoi dome (Zeng et al., 2011, 2009; Aikman et al., 2008 and this study). (b) Simplified geological map of the Yardoi dome, modified after 1 : 250 000 Geological Map of the Longzi County (China) (Geological Survey of Yunnan Province, 2004) and 1 : 200 000 Geological Map of the Zedong County (China) (Geological Survey of Shannxi Province, 1994). ITSZ. Indus-Yarlung Tsangpo River suture zone (ITSZ); GCT. great counter thrust; STDS. South Tibetan detachment system; MCT. main central thrust; MBT. main boundary thrust; MFT. main front thrust; ZGT. Zhongba-Gyantse thrust.

Three different mechanisms have been proposed to explain the structural development of the NHD, i.e., contractional mechanism, extensional mechanism, combination of these processes. The contractional model suggested that the domes in fault-bend folds developed above either a simple thrust ramp or a thrust duplex system (Makovsky et al., 1999; Hauck et al., 1998; Burg and Chen, 1984). However, the extentional model argued that the dome developed the same as metamorphic core complexes (Chen et al., 1990). The third model suggested that the domes resulted from both contractional and extensional deformations (Lee et al., 2006, 2000). The model is consistent with the large thermochronological data and structural constraints of the domes (Wang et al., 2018; Zhang et al., 2012; Lee et al., 2006, 2004).

In this work, we focused on the Yardoi dome, the easternmost dome in the NHD (Aikman et al., 2008). The structural kinematics context is based on the detailed mapping of Zhang et al. (2012), and we demonstrate some additional structural observations from areas which were not visited by these authors, notably from critical localities at the Yardoi detachment fault (YDF). This paper presents new geochronological data on structural and intrusive events of the YDF. Our new data brackets the formation and exhumation of Yardoi dome and provides new and critical indications on the tectonic evolution of middle crust rocks in southern Tibet.


The Himalayan Orogen forms a convex southward, east-west trending 2 500 km long arc (Fig. 1a). The structure and boundary fault assemblage of the Himalayan Orogen identified through studies is a classic model of global orogens (Sun et al., 2018; Xu et al., 2011; Yin, 2006). The Indian Plate rocks involved in the Himalayan collision zone occupy the areas between the ITSZ in the north and the Himalayan main frontal thrust (MFT) in the south. It can be divided into four geologic zones from north to south, which are generally continuous along the entire length of the orogen: (1) the Tethyan Himalaya (THM), (2) the Greater Himalayan Complex (GHC), (3) the Lesser Himalaya (LHM), and 4) the Sub-Himalaya (SHM) (Yin, 2006; Gansser, 1964; Heim and Gansser, 1939). These zones are separated by the STDS, the main central thrust (MCT), and the main boundary thrust (MBT) (Yin and Harrison, 2000; Burg and Chen, 1984; Heim and Gansser, 1939) (Fig. 1a).

The NHD is in the THM between the STDS and ITSZ with a series of discontinuously distributed dome structures (Fig. 1a). Except for the cores of a few domes that outcrop Cambrian granites, such as the Kangmar dome (Lee et al., 2000) and Kampa dome (Quigley et al., 2008), others primarily consist of Cenozoic leucogranites, two-mica granites, gneisses, and schists. The rims are overlain with low-grade metamorphism THM which largely consists of the Late Triassic flysch sequence interbedded by diabase and gabbro sills and dikes. The cores and rims interact through extensional detachment faults (Zhang et al., 2012).


The Yardoi dome is located in the eastern end of the NHD (Fig. 1b), distributed in NW-SE direction. To better decipher the nature of the Yardoi dome, we conducted field mapping of one (northwest-southeast) transect across the northern edge of the dome along S202 (Figs. 1 and 3). Zhang et al. (2012) established the distribution of three lithologic-tectonic units, positions of the upper detachment fault (UDF) and the lower detachment fault (LDF), which are the lower unit (Ptyd), middle unit (Pzqd) and upper unit (T3), respectively (Fig. 2). The lower unit is the core of the Yardoi dome. It chiefly consists of sillimanite-kyanite paragneiss, orthogneiss and amphibolite with sillimanite-bearing garnet-mica schist on the top. The core of the dome consists of three granitic intrusions, which are the Yardoi granite, Biri granite, and Dala granite, from the northwest to the southeast (Fig. 1b). A decrease in metamorphic grade outward from the dome is observed in the middle unit overlying the lower unit. These rocks pass outward from garnet mica schist, locally containing staurolite, to mica-bearing quartzite to phyllite (Yan et al., 2012; Zhang et al., 2012). The upper unit localized by the great counter thrust (GCT) to the north and the Eocene Zhongba-Gyantse thrust (ZGT) to the south is about 10–50 km wide, an extensive Late Triassic flysch thrust-fold belt (Li et al., 2015; Ding et al., 2005). Detailed structure and kinematics investigations by Zhang et al. (2012) and Yan et al. (2012) revealed that the Yardoi dome experienced three stages of major ductile deformation: N-S compressional top-to-south phase (D1); N-S extensional top-to-north phase (D2); and deformational phase (D3) related to rapid uplift and collapse of the dome. This paper mainly studies the macroscopic structures and microstructures related to D2.

Figure 2. Stratigraphic section of the Yardoi Dome showing major stratigraphic units (modified from BGMRXAR, 1993; 1 : 250 000 Geological Map of the Longzi County (China) (Geological Survey of Yunnan Province, 2004) and 1 : 200 000 Geological Map of the Zedong County (China) (Geological Survey of Shannxi Province, 1994). YDF. Yardoi detachment fault.
Figure 3. Geological map of the Yardoi detachment fault (YDF) transect, with equal area stereo plots of structural data.

The lower detachment fault separates the lower unit from the middle unit. The mylonite section is approximately 800 m thick, consisting of garnet/graphite bearing schist and gneiss with a large number of leucogranitic lenses, which is strongly deformed into a detachment fault termed as the Yardoi detachment fault (YDF) (Fig. 3). The YDF is the equivalent to the LDF by Zhang et al. (2012) (Fig. 1b).

Within the main foliation, the mineral stretching lineations are defined by quartz, biotite, garnet, and tourmaline, plunging moderately to the north-northwest (Figs. 3, 4a, 4b). The metamorphic mineral assemblages consist of Mus+Pl+Bi+Grt+Qtz (Fig. 5), indicating lower amphibolite-facies conditions that produced along the lower detachment fault. Leucogranitic veins are deformed by asymmetric boudinages. S/C fabric (Fig. 5a), sigma- type plagioclase porphyroclasts (Fig. 5b), delta-type garnet porphyroclasts (Figs. 5c, 5d), and meter-scale asymmetric boudinages (Figs. 4c, 4d) occur across the YDF and are in accordance with the stretching lineations. All fabrics across the YDF are consistent with top-to-north-northwest shear sense. The leucogranites within the schist are mainly sub-parallel to the foliation. Locally, they also cut the foliation of the schist (Fig. 4e).

Figure 4. Field photographs showing the deformation fabrics of the rocks in the Yardoi detachment fault (YDF). (a) View from the YDF to the west-southwest, Gama-Lakang Temple for scale. (b) Garnet schist with typical mylonitic fabrics, such as stretching lineation and pressure shadows of garnets. (c)–(e) Meter-scale leucogranitic lenses are foliated and deformed by asymmetric boudinage. These leucogranites intruded into the schist sub-parallel (c) and (d). Locally, they also cut the foliation of the schist (e).
Figure 5. Microphotographs showing the deformation fabrics of the rocks in the Yardoi detachment fault (YDF). (a) Mylonitic schist with top-north S-C fabric; (b) sigma-type plagioclase porphyroclasts in mylonitic gneiss; (c) delta-type garnet porphyroclasts in garnet-bearing mica schist; and (d) garnet-beating biotite granitic gneiss.

Most samples in this study were all collected from the YDF, except samples XQ15-7-6 and XQ15-7-13. We selected four leucogranite samples (XYL1-1-5, XYL1-1-11, XYL1-1-14, and XQ16-2-9) for LA-ICP-MS zircon U-Pb dating, and one leucogranite sample (XQ16-2-9) and two garnet-bearing two-mica gneiss samples (XQ15-7-6 and XQ15-7-13) for mica 40Ar/39Ar dating to constrain the evolution process of the Yardoi dome.

3.2 U-Pb Geochronology

LA-ICP-MS zircon U-Pb geochronology was carried out at the Key Laboratory of Mineral Resources Evaluation in Northeast Asia, Ministry of Land and Resources of China, Jilin University, Changchun. The descriptions of zircon U-Pb analytical method is provided as an electronic supplement (ESM). The LA-ICP-MS zircon U-Pb dating results are shown in Table 1.

Table 1 LA-MC-ICP-MS U-Pb zircon data of the samples from the Yardoi dome, southern Tibet
3.3 40Ar/39Ar Geochronology

Muscovite and biotite grains from three crushed samples were carefully handpicked and checked under a binocular microscope. After that, they were purified by a magnetic separator and cleaned in an ultrasonic ethanol bath. Each sample was irradiated for 1 440 min in the nuclear reactor (1 000 kW) at the Chinese Institute of Atomic Energy (CIAE) and subsequently cooled for about three months. The descriptions of 40Ar/39Ar analytical method is provided as an electronic supplement (ESM). All data are given in Table 2.

Table 2 The results of 40Ar/39Ar step heating analysis of muscovite and biotite of samples from the Yardoi dome, southern Tibet

We obtained zircon U-Pb ages from leucogranitic lenses in the YDF (samples XYL1-1-5, XYL1-1-11, XYL1-1-14 and XQ16-2-9) to constrain the timing of top-northwest motion. The leucogranites consist of similar mineral compositions, such as quartz, plagioclase, K-feldspar, muscovite, tourmaline and garnet, suggesting that they should be derived from a homogeneous magma. The cathodoluminescence (CL) images of representative zircon grains from the samples are shown in Fig. 6. Analyzed zircon grains are euhedral crystals with grain lengths of 100–200 μm and length-width ratios of 1 : 1–4 : 1. On cathodoluminescence (CL) images, zircon grains show clearly sponge-like texture (Fig. 6). Details of each sample are as follows.

Figure 6. Representative cathodoluminescence (CL) images of analyzed zircon grains. Circles indicate the analytical spots with a diameter of ~32 μm.

For sample XQ16-2-9, 15 spots were analyzed. The results show that they contain a broad range of U (5 653 ppm–45 429 ppm) and Th (26 ppm to 647 ppm) concentrations and a broad range of Th/U ratios between 0.003 and 0.017 (Table 1). A comparatively high concordance and a smaller scattering in 206Pb/238U ages from 15.0 to 16.1 Ma can be obtained and a weighted mean age of 15.5 Ma with mean square weighted deviation (MSWD) equal to 2.1 (Fig. 7a) can be defined.

Figure 7. U-Pb concordia diagrams of zircons of samples from the Yardoi dome, southern Tibet.

For sample XYL1-1-14, 15 spots were analyzed. The results show that they contain a broad range of U (15 937 ppm–22 987 ppm) concentrations and Th (370 ppm to 1 076 ppm) concentrations and the Th/U ratio between 0.02 and 0.05 (Table 1). A comparatively high concordance and a smaller scattering in 206Pb/238U ages between 15.8 and 17.8 Ma can be obtained and a weighted mean age of 17.12 Ma (MSWD=2.7, Fig. 7b) can be defined.

For sample XYL1-1-11, 6 spots were analyzed. The results indicate that they contain a broad range of U concentrations (12 623 ppm–35 739 ppm), Th concentrations (158 ppm– 3 170 ppm) and Th/U ratios (0.01–0.09) (Table 1). The 206Pb/238U ages are from 17.5 to 18.4 Ma and a weighted mean age is 18.15 Ma (MSWD=2.3, Fig. 7c).

For sample XYL1-1-5, 16 spots were analyzed. The analyses data of 15 spots show a broad range of U concentrations (2 624 ppm–24 479 ppm), Th concentrations (612 ppm–4 849 ppm), and Th/U ratios (0.03–0.83) (Table 1). A comparatively high concordance and a smaller scattering in 206Pb/238U ages from 18.7 to 20.5 Ma can be obtained and a weighted mean age of 19.57 Ma (MSWD=1.5, Fig. 7d) can be defined. Only one spot was performed on the zircon grain that is colorless and transparent. This zircon has (1) relatively lower U (227 ppm) and Th (1 214 ppm) concentrations, (2) generally higher Th/U ratio (5.35), and (3) older 206Pb/238U age (458 Ma) (Table 1).

4.2 40Ar-39Ar Dating

The results of four muscovite 40Ar/39Ar dating samples are shown in Fig. 8. Samples XQ15-7-6 and XQ15-7-13 are garnet- bearing two-mica gneisses collected from the southern flake of the Yardoi dome, but sample XQ16-2-9 was collected from the northern flake of the Yardoi dome (Fig. 1b). The three samples XQ15-7-6, XQ16-2-9 and XQ15-7-13 reveal approaching concordant apparent age spectra and record similar plateau ages. They are 14.05±0.2 Ma (Fig. 8a), 13.2±0.2 Ma (Fig. 8b) and 13.51±1.06 Ma (Fig. 8d), respectively. The other one biotite from sample XQ15-7-13 yielded a plateau age of 13.15±0.2 Ma (Fig. 8c) (Table 2).

Figure 8. Age and 40Ar/39Ar spectra for muscovite and biotite from the Yardoi dome. (a) XQ15-7-6 muscovite, (b) XQ16-2-9 muscovite, (c) XQ15-7-13 biotite, and (d) XQ15-7-13 muscovite.

The 40Ar/36Ar initial ratios of three samples are almost equal to 295.5. This result demonstrates that a little argon have possibly been lost. However, the accuracy of data has not been affected. Because these data yield generally accordant 40Ar/39Ar age spectra with very small error bars. Thus, the results of the four samples are reliable and reasonable.

5 DISCUSSION 5.1 Timing of Shearing along the YDF

Zircon contains a high 206Pb/238U isotope closure temperature (800±50 ℃, Mezger, 1990; Pidgeon and Aftalion, 1978) and is hard to be influenced by thermal disturbance (Harrison et al., 1987). Therefore, the dating of different type of zircons can be used to constrain the ages of magmatism, metamorphism or deformation (Xu et al., 2012). The 40Ar/39Ar isotope dating method indicates the mineral plateau age recorded using the 40Ar/39Ar isotope system when each individual mineral cooled to the closure temperature of the mineral (McDougall and Harrison, 1999; Dodson, 1973). For example, the closure temperature of amphibole is 535±50 ℃ (Harrison, 1982), the closure temperature of muscovite is 370±50 ℃ (Lister and Baldwin, 1996), and the closure temperature of biotite is 335±50 ℃ (Grove and Harrison, 1996).

Our mapping displays the presence of an ~800 m thick top-northwest shear zone, termed as Yardoi detachment FAULT (YDF), along the northern margin of the Yardoi dome. Timing of shearing along the YDF is constrained by zircon U-Pb isotope dating from leucogranites. Ages measured on zircons separated from the leucogranite are 19.57±0.23 to 15.5±0.11 Ma. The new 40Ar/39Ar data are in excellent agreement with the previous data by Zhang et al. (2012), who measured 14.40±1.31 Ma for mylonitized paragneiss near the bottom wall of the YDF. Therefore, the ages of plateau are the cooling ages of the tectonic thermal events. Three samples we studied all generally exhibit age spectrum features without disturbance, indicating that the plateau ages should be the age of a tectonic event.

Ductile deformation (D2) produced main foliation and mineral stretching lineation, asymmetric boudinage, S-C fabrics, plagioclase and garnet porphyroclasts (Figs. 3 and 5), indicating top-to-north shear sense in the middle ductile crustal layer and shallower tectonic levels. D2 was coeval with peak metamorphism (Wang et al., 2018). Petrology and phase equilibria modeling show that the P-T conditions of peak metamorphism was 7–8 kbar and 630–660 ℃ (Ding et al., 2016). Previous studies in Mabja dome show that extension, synchronous with peak metamorphism, began at 35 Ma, was ongoing at 23 Ma and then ceased at 16 Ma (Lee and Whitehouse, 2007; Lee et al., 2006, 2004, 2000). In addition, the earliest emplacement of syn- deformational leucogranite along the STDS was at ~36–32 Ma (Zhang et al., 2012). Thus, our new structural and geochronological data from the Yardoi dome and other domes in the Tethyan Himalayan Sequences (THS) suggest that the ductile deformation in the region began at or before ~36 Ma in a deep tectonic level, resulting in southward ductile flow at the mid-crustal tectonic level that continued from 20 to 13 Ma (Yan et al., 2012; Zhang et al., 2012; this study).

5.2 Tectonic Implications

Our study, combined with previous work of Ding et al. (2016), Zhang et al.(2012, 2007), Hou et al. (2012), Yan et al. (2012) and Zeng et al.(2011, 2009) show that metasedimentary rocks and orthogneisses occur across the YDF, leucogranites occur within the YDF, and granites occur structurally below the YDF. The metamorphism rocks of the YDF witnessed medium- pressure amphibolite-facies metamorphism with P-T conditions of ca. 7–8 kbar and 630–660 ℃ (Ding et al. 2016). In addition, the STDS has a dominant structural fabrics of top-to-north sliding, separating the overlying the THS from the GHC (Yin, 2006; Searle and Godin, 2003; Burchfiel et al., 1992; Burchfiel and Royden, 1985; Burg and Chen, 1984).

The structural events preserved in Yardoi and other domes (e.g., Lhagoi Kangri, Diedesch et al., 2016; Mabjia, Langille et al., 2010; Malashan, Aoya et al., 2006; and Kangmar, Lee et al., 2000) are similar and consist of three primary events: (1) D1 deformation: folding and thickening formed by NS-contraction, (2) D2 vertical thinning and horizontal extension, and (3) D3 deformation characterized by a top-down-to-outside of the dome resulted from collapse. The remarkable similarities suggest that the physical processes that produced these domes may have been responsible to each other. However, thermochronologic studies show that the cooling ages in these domes are progressively younger from the West Himalayan to the East Himalayan (Fig. 9). The maximum muscovite 40Ar/39Ar cooling age of the Tso Morari gneiss dome in the West Himalayan is 31.1±0.3 Ma, which decreased into the Mabja in the Central Himalayan upto 16.8 Ma and decreased further in the east (Yardoi dome, Yan et al., 2012; Zhang et al., 2012; and this study) upto 14 Ma. Previous studies showed that the NHD exposed midcrustal rocks and granite that correlated to the midcrustal GHS exposed in the south of the STDS (Diedesch et al., 2016; Langille et al., 2014, 2010; Yan et al., 2012; Zhang et al., 2012; Lee and Whitehouse, 2007; Aoya et al., 2006, 2005; Lee et al., 2004, 2000; Chen et al., 1990; Burg and Chen, 1984). The cessation timing of the STDS (Webb et al., 2017) is similar to the cooling age of the NHD, which indicates the same tectonic setting. Our results, in combination with previous work, indicate that the cooling age of the NHD, the southward extrusion of the Greater Himalayan crystalline complex, and even the initial timing of India-Asia collision show a clear diachronism (Yu et al., 2010; Jain and Manickavasagam, 1993; Harrison et al., 1992; Treloar and Coward, 1991).

Figure 9. Longitudinal variations in compiled age constraints on cooling of the North Himalayan gneiss domes (NHD).

(1) The Yardoi detachment fault (YDF) is a ~800 m thick, strongly deformed, and top-to-northwest shear zone.

(2) The ductile deformation in the region began at or before ~36 Ma in a deep tectonic level, resulting in southward ductile flow at the mid-crustal tectonic level that continued from 20 to 13 Ma

(3) Thermochronologic studies show that the cooling ages in NHD are progressively younger from the West Himalayan to the East Himalayan.


This research was supported by the Chinese Academy of Geological Sciences (CAGS) Research Fund (Nos. J1623, YYWF201708), the National Natural Science Foundation of China (Nos. 41502196, 41472198, 41872224, 41430212), the State Scholarship Fund (No. 201809110029), and the China Geological Survey (No. DD20160022). It's an honor to be invited by Prof. Jingsui Yang to contribute our research into this special issue. Comments on an earlier version of this study from Dr. Kyle Larson improved the clarity of the manuscript. Constructive reviews by two anonymous reviewers and the editors are appreciated. The final publication is available at Springer via

Electronic Supplementary Materials: Supplementary materials are available in the online version of this article at

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