Post-collisional tectonic evolution of the north branch of the Proto-Tethys Ocean: evidence from Early Devonian I- and A-type granite at the eastern end of the North Qilian Orogenic Belt Open Access

The Baoji–Tianshui (Xinyang–Yuanlong) fault currently marks the boundary between the eastern end of the the North Qinling Orogenic Belt (NQLOB) in the north and the western section of the NQOB in the south. The NQLOB is located between the Alxa Terrane (AT) and the Central Qilian Terrane (CQLT). It generally extends northwestward and is bounded by the Longshoushan Fault to the north, the northern margin of the CQLT to the south, the Tongxin–Guyuan right-lateral slip rift to the east and the left-lateal Altyn Fault to the west (Fig. 1a).

The NQLOB represents the site of the final closure of the ancient Qilian Ocean (QLO) and is recognized as a typical Early Paleozoic suture zone. It is characterized by subducted accretionary complexes, ophiolite remnants, high-pressure–low-temperature metamorphic rocks, island-arc volcanic rocks and granites. Additionally, it contains Silurian foreland basin flysch and Devonian molasse (Xu et al. 1994; Xiao et al. 2009; Song et al. 2013, 2019). Initial subduction of the QLO occurred around 520 Ma, with fore-arc ophiolites and island-arc magmatic rocks developing from 520 to 490 Ma (Zhang et al. 2007; Song et al. 2013; Chen et al. 2014). Continuous northward subduction led to the formation of a back-arc basin in the subsidence zone of the Hexi Corridor depression belt along the southern margin of the AT. The Jiugequan–Laohushan back-arc basin ophiolite developed between 490 and 445 Ma (Qian et al. 2001; Song et al. 2013; Fu et al. 2022). Additionally, subduction-related granite at c. 460–430 Ma (Liu et al. 2016) and adakitic granite at c. 460–440 Ma (Tseng et al. 2009; Zhang et al. 2017) along the southern margin of the AT were formed during the Proto-Tethys Ocean subduction stage of the NQLOB. Numerous syn-collision magmatic rocks from c. 430 to 410 Ma indicate the process of collisional orogeny in the NQLOB (Song et al. 2013; Zhang et al. 2017; Fu et al. 2019).

At the eastern end of the NQLOB in the study area, the sequence from south to north includes the Ordovician Huluhe Group continental marginal clastic rocks, the Ordovician Hongtubao Formation metabasic volcanic rocks, the Paleoproterozoic Longshan Group complex and the Middle–Late Ordovician Chenjiahe Group intermediate–acid volcanic and continental clastic rocks (Fig. 1b). The Chenjiahe Group consists of a series of low-grade greenschist-facies metamorphic rocks that originally belonged to ‘Huluhe Group’, with the protolith being a combination of intermediate–acid volcanic rocks and continental clastic rocks. Zircon U–Pb geochronological data indicate that the volcanic rocks formed in a continental margin arc environment between 448 and 447 Ma (Hu 2005; He et al. 2006; Li 2008; Wei 2013). The Hongtupu Formation metabasic volcanic rocks comprise a suite of low-grade greenschist-facies metamorphic basalt and diabase dykes, along with some siliceous rocks. The laser ablation inductively coupled plasma mass spectrometry (LA-ICP-MS) zircon U–Pb age of the metabasic volcanic rock is 443 Ma (He et al. 2007a), indicating that they formed in a small oceanic basin or intra-oceanic arc–basin system with both mid-ocean ridge margin and island-arc volcanism (He et al. 2007b). The Huluhe Group comprises Silurian low amphibolite-facies–greenschist-facies metamorphic clastic rocks with flysch sedimentation characteristics, derived from the eastern end of the NQLOB, the western section of the NQOB and the North China Block (NCB) (Pei et al. 2012). The Longshan Complex exhibits a general NW–SE orientation and comprises a suite of amphibolite-facies medium- to high-grade metamorphic rocks. The rock assemblage includes felsic gneiss, amphibolite, Al-rich gneiss and silicomagnesian marble. LA-ICP-MS zircon U–Pb dating indicates that the felsic gneiss formed during the Neoarchean–Paleoproterozoic, representing a Precambrian crystalline basement (He et al. 2005, 2006; Jia et al. 2021).

The PP, NP and GP are located north of the Baoji–Tianshui (Xinyang–Yuanlong) fault and are part of the eastern end of the NQLOB in terms of their regional tectonic settings. All samples were fresh and free of corrosion, with the U–Pb sampling locations shown in Figure 2.

The PP is located in the SE of the NP and intrudes various formations, including the Proterozoic complex (e.g. the Proterozoic Longshan Group), Early Paleozoic metasediment (e.g. the Chenjiahe Group), Early Paleozoic continental marginal clastic rock (e.g. the Huluhe Group), Early Paleozoic metabasic volcanic (e.g. the Hongtubao Formation) and collision-related granite (e.g. the Caochuanpu pluton) (Fig. 2). One zircon U–Pb dating sample (syenogranite TS19107-2) was collected from the PP, located in the Pandaoshi area. The sample is located at 34°35′29.92″N, 106°26′39.05″E. We also collected and later analysed 15 whole-rock geochemical samples. The pluton primarily consists of syenogranite, exhibiting a fine- to medium-grained, massive structure. The syenogranites comprise K-feldspar (40–55 vol%), plagioclase (15–30 vol%), quartz (25–35 vol%), biotite (2–5 vol%) and minor accessory minerals such as zircon, apatite and epidote (Fig. 3a and b).

The NP is located south of Qingshui County. The pluton intruded the Proterozoic complex (e.g. the Proterozoic Longshan Group) in the eastern section and sequentially intruded the Early Paleozoic meta-basic volcanic (e.g. the Hongtubao Formation) and Early Paleozoic continental marginal clastic rock (e.g. the Huluhe Group) in the southern section. It consists of syenogranite and monzogranite. Samples were collected from the Nantouhe–Saozhougou area (Fig. 2). The zircon U–Pb dating sample (TS19064-4) is located at 34°41′26.75″N, 106°09′29.48″E. We also collected and later analysed six whole-rock geochemical samples. The syenogranites exhibit medium- to coarse-grained, massive structure, with some displaying pseudoporphyritic characteristics. They contain K-feldspar (40–55 vol%), plagioclase (15–30 vol%), quartz (20–30 vol%) and biotite (c. 5 vol%), and the accessory minerals include zircon, apatite, titanite, ilmenite, monazite and hornblende (Fig. 3c and d).

The GP is located in the SE of Qingshui County and intrudes the Proterozoic granitic gneiss (e.g. the Proterozoic Longshan Group), Early Paleozoic meta-sediment (e.g. the Chenjiahe Group) and Early Paleozoic intermediate–basic rock (e.g. the Baiji complex). It is covered by Cretaceous and Quaternary loess to the north (Fig. 2). The pluton consists of syenogranite. Two zircon U–Pb dating samples (TS19076-2 and TS19076-4) and seven whole-rock geochemical samples were collected from the GP in the Guanshanhe–Shanmenzhen area and later analysed. The zircon U–Pb dating samples are located at 34°42′38.87″N, 106°18′44.54″E and 34°42′38.83″N, 106°18′44.57″E, respectively. The red syenogranite exhibits a medium- to coarse-grained, massive structure, with some samples displaying pseudoporphyritic characteristics. The syenogranite samples are composed of K-feldspar (40–55 vol%), plagioclase (15–30 vol%), quartz (20–30 vol%) and biotite (c. 5 vol%). The accessory minerals include zircon, apatite, titanite, ilmenite, monazite and hornblende (Fig. 3e and f).

The samples used for geochronological research were crushed, and zircon was separated by Xi'an Ruishi Geological Technology Co., Ltd. Zirconium target preparation and cathodoluminescence (CL) imaging were performed by Beijing Gaonianlinghang Geo Analysis Co. Ltd., Beijing, China. Zircon U–Pb isotope testing was conducted using a German Jena PQMS ICP-MS instrument with an NWR193 laser ablation system. Concentrations of U, Th, Pb and trace elements were calibrated by using ⁹¹Zr as an internal standard and NIST SRM 610 as an external standard. The two standard zircons 91500 and GJ-1 yielded weighted mean ²⁰⁶Pb/²³⁸U ages of 1061.5 ± 3.2 Ma (2$σ$⁠) and 604 ± 6 Ma (2$σ$⁠), respectively, which are in good agreement with the recommended LA-ICP-MS ages (Paton et al. 2010; Thompson et al. 2018). Data processing was performed using the ICPMSDataCal 10.9 program (Liu et al. 2010). Weighted mean age calculations and concordia diagrams were generated using the Isoplot (ver. 3.75) program (Ludwig 2012). A detailed description of the analytical methods and instrument parameters has been given by Li et al. (2009).

Testing of major, rare earth and trace elements in whole-rock samples was conducted at the Key Laboratory of Western China's Mineral Resources and Geological Engineering, Ministry of Education, Chang'an University. Major element analysis was performed by X-ray fluorescence spectroscopy (XRF). The XRF fusion method was conducted in accordance with the national standard GB/T 14506.28-1993, achieving an analysis precision better than 2–3%. The samples were weighed after heating at 1000°C for 90 min in an oven to determine the loss on ignition (LOI). Rare earth and trace elements were analysed by ICP-MS using a Thermo-X7 system.

The zircon Lu–Hf isotope dating was conducted at Langfang Fengzeyuan Rock Mine Detection Technology Co., Ltd. The selected zircon Lu–Hf isotope analysis point was located in the in situ region of the zircon U–Pb dating site. The zircon was ablated using the Resolution SE 193 nm excimer laser ablation system of ASI (American Applied Inc., Berkeley, CA, USA), with a spot beam diameter for laser ablation generally being 38 $μ$m, an energy density of 7–8 J cm^–2 and a frequency of 10 Hz, using a multicollector (MC)-ICP-MS analytical system (Neptune Plus, Thermofisher company, Waltham, MA, USA). The ablated zircon was transported to the Neptune Plus with high-purity helium as the carrier gas. The temperature requirement for the detection environment was maintained at 18–22°C, with a relative humidity of less than 65%. For instrumental mass bias correction Yb isotope ratios were normalized to ¹⁷³Yb/¹⁷²Yb = 1.35274 and Hf isotope ratios to ¹⁷⁹Hf/¹⁷⁷Hf = 0.7325 using an exponential law (Chu et al. 2002). During in situ zircon and baddeleyite Hf analyses, isobaric interference corrections of ¹⁷⁶Lu and ¹⁷⁶Yb on ¹⁷⁶Hf have to be precisely processed. Owing to the extremely low ¹⁷⁶Lu/¹⁷⁷Hf in zircon (normally <0.002), the isobaric interference of ¹⁷⁶Lu on ¹⁷⁶Hf is negligible (Iizuka and Hirata 2005). The mean $β$_Yb value obtained during Hf analysis on the same spot was applied for the interference correction of ¹⁷⁶Yb on ¹⁷⁶Hf (Iizuka and Hirata 2005; Hou et al. 2007). Zircon international standard GJ-1 was used as the reference standard, with a weighted mean ¹⁷⁶Hf/¹⁷⁷Hf ratio of 0.282008 ± 25 (n = 26, 2$σ$⁠) (Hou et al. 2007). The notations of $ε$_Hf(t) value, f_Lu/Hf, single-stage model age (T_DM1) and two-stage model age (T_DM2) are as defined by Yuan et al. (2008). Detailed experimental principles, analytical techniques and procedures have been given by Wu et al. (2007) and Geng et al. (2011).

Four representative samples from the three plutons were selected for zircon LA-ICP-MS dating and trace element analysis. The analytical results are listed in Tables 1 and 2. In CL images (Fig. 4), the majority of zircon grains display distinct oscillatory zoning, indicating an igneous origin (Hoskin and Black 2000). Numerous studies have shown that magmatic zircons have high Th and U contents, characterized by Th/U ratios that are commonly greater than 0.4 (Rubatto and Gebauer 2000).

Zircons (TS19107-2) from the Pandaoshi syenogranite range in length from 50 to 180 $μ$m, with aspect ratios of 2:1 to 4:1 (Fig. 4a). Thirteen out of 25 spots have U concentrations ranging from 262 to 2567 ppm and Th concentrations ranging from 56 to 841 ppm, with Th/U ratios between 0.18 and 1.09 (averaging 0.63). These 13 spots have ²⁰⁶Pb/²³⁸U ages ranging from 402 to 427 Ma (Fig. 4d) and yield a weighted mean age of 415.2 ± 4.5 Ma (MSWD = 1.6, n = 13).

Zircons (TS19064-4) from the Nantouhe syenogranite range in length from 50 to 200 $μ$m, with aspect ratios of 2:1 to 3:1 (Fig. 4b). Of the 25 analysis spots, 23 spots display concordant U–Pb ages. These spots exhibit high U and Th contents (U ranging from 819 to 1805 ppm, Th ranging from 241 to 2372 ppm, with variable Th/U ratios between 0.14 and 1.51, averaging 0.77). These 23 spots have ²⁰⁶Pb/²³⁸U ages ranging from 406 to 421 Ma (Fig. 4b) and yield a weighted mean age of 414.4 ± 2.1 Ma (MSWD = 0.70, n = 23).

Zircons (TS19076-2 and TS19076-4) from the GP range in length from 50 to 220 $μ$m, with aspect ratios of 1:1 to 4:1 (Fig. 4c and d). Excluding seven discordant spots, the remaining 43 concordant spots have U concentrations ranging from 1890 to 6286 ppm and Th concentrations ranging from 972 to 4409 ppm, with variable Th/U ratios between 0.34 and 0.75 (averaging 0.51). The 21 spots from sample TS19076-2 have ²⁰⁶Pb/²³⁸U ages ranging from 405 to 423 Ma (Fig. 4c) and yield a weighted mean age of 412.5 ± 2.1 Ma (MSWD = 0.69, n = 21). The 22 spots from sample TS19076-4 have ²⁰⁶Pb/²³⁸U ages ranging from 404 to 424 Ma (Fig. 4d) and yield a weighted mean age of 411.8 ± 2.1 Ma (MSWD = 0.92, n = 22).

The whole-rock major and trace element analysis results are listed in Table 3.

Fifteen samples from the PP plot within the syenogranite field on the Q–A–P diagram (Fig. 5a). The samples exhibit SiO₂ contents ranging from 71.65 to 74.21 wt%, Al₂O₃ from 13.89 to 14.39 wt%, TiO₂ from 0.15 to 0.32 wt%, Fe₂O₃^T from 1.11 to 2.29 wt%, MgO from 0.33 to 0.69 wt%, CaO from 0.95 to 1.80 wt% and P₂O₅ from 0.05 to 0.11 wt%. The Rittmann index (⁠$σ$⁠) values range from 1.77 to 2.49, indicating that PP belongs to the calc-alkaline series. In the total alkalis–silica (TAS) diagram (Fig. 5b), all samples plot within the subalkaline granite field. All samples have high total alkali contents (K₂O + Na₂O ranging from 7.40 to 8.63 wt%) and exhibit high-K calc-alkaline affinity (Fig. 5c). The syenogranites are classified as weakly peraluminous, with A/CNK ratios ranging from 1.00 to 1.12 (Fig. 5d). All samples exhibit high total rare earth element (⁠$Σ$REE) contents, ranging from 169 to 377 ppm. The samples show variable enrichments in light rare earth elements (LREE), with (La/Yb)_N ratios ranging from 24.87 to 65.77, and exhibit negative Eu anomalies, with Eu/Eu* ratios ranging from 0.54 to 0.71 (Fig. 6a). All samples show enrichments in Rb, K, Pb and U, along with significantly negative anomalies for Nb, Ta, Ti, P, Zr and Ce (Fig. 6b).

The Nantouhe syenogranite is characterized by high SiO₂ (73.09–74.24 wt%) and Al₂O₃ (13.61–14.21 wt%) contents, low MgO (0.3–0.67 wt%) and Fe₂O₃^T (0.92–1.53 wt%) contents, medium Na₂O + K₂O (6.78–8.88 wt%) contents, low Na₂O/K₂O ratios (0.52–0.86), low A/CNK values (1.03–1.18) and $σ$ values ranging from 1.48 to 2.53. All rocks plot within the syenogranite area in the Q–A–P diagram (Fig. 5a). Most samples fall within the subalkaline granite field (Fig. 5b) and calc-alkaline series in the SiO₂ v. K₂O diagram (Fig. 5c). These rocks also plot within the peraluminous series field in the A/CNK v. A/NK diagram (Fig. 5d). The syenogranite samples exhibit high $Σ$REE contents, ranging from 279 to 319 ppm, with enrichment in LREE with (La/Yb)_N values ranging from 12.8 to 53.3, and weak negative Eu anomalies with Eu/Eu* ranging from 0.55 to 0.71 (Fig. 6c). These rocks show relative enriched large ion lithophile elements (LILE) and high field strength elements (HFSE) (Fig. 6d).

Guanshanhe syenogranites show high SiO₂ (72.33–75.22 wt%) contents and Al₂O₃ = 13.24–13.95 wt%; as shown in the Q–A–P diagram (Fig. 5a), these samples plot in the syenogranite field. They have low Fe₂O₃^T (0.80–2.21 wt%) and MgO (0.24–0.65 wt%) contents and Mg^# (33.8–45.6) values, high K₂O (4.93–5.93 wt%) and high total alkali (K₂O + Na₂O = 8.40–8.96 wt%) contents, and low Na₂O/K₂O (0.50–0.73) ratios. In the TAS diagram (Fig. 5b) they plot in the subalkaline granite field. They have low Rittmann index (⁠$σ$⁠) values of 2.34–2.63. As shown in the SiO₂ v. K₂O diagram (Fig. 5c), most samples are in the high-K calc-alkaline and mugearite series. Most samples have moderate A/CNK values of 0.95–1.09 (Fig. 5d). They exhibit higher $Σ$REE contents, ranging from 184 to 548 ppm, extremely high (La/Yb)_N values, ranging from 6.53 to 61.49, and significant negative Eu*/Eu anomalies, ranging from 0.27 to 0.64 (Fig. 6e). They show enrichment in Rb, K and Pb, along with significantly negative anomalies for Nb, Ta, P, Zr, Ce and Ti (Fig. 6f).

Twelve Lu–Hf spots from the Pandaoshi syenogranite (TS19107-2, 415 Ma, Table 4) display variable Lu–Hf isotopic compositions. Seven of these spots exhibit negative $ε$_Hf(t) values ranging from −6.8 to −0.4, with corresponding two-stage model ages between 1426 and 1823 Ma. The remaining five spots have positive $ε$_Hf(t) values ranging from +0.1 to +8.9, with corresponding two-stage model ages between 848 and 1389 Ma. Fifteen Lu–Hf spots from the Nantouhe syenogranite (TS19064-4, 414 Ma, Table 4) exhibit positive $ε$_Hf(t) values ranging from +4.9 to +8.9, with corresponding two-stage model ages between 843 and 1092 Ma. Ten Lu–Hf spots from the Guanshanhe syenogranite (TS19076-2, 412 Ma, Table 4) show negative $ε$_Hf(t) values ranging from −25.6 to −20.6, with corresponding two-stage model ages between 2677 and 2983 Ma. Additionally, 10 Lu–Hf spots from the Guanshanhe syenogranite (TS19076-4, 411 Ma, Table 4) have negative $ε$_Hf(t) values ranging from −25.1 to −20.2, with corresponding two-stage model ages between 2654 and 2959 Ma.

Currently, the most widely used classification scheme for granite types is the MISA classification, where M-type granite, derived from mantle magmas, is rare, and I-type, S-type and A-type granite are predominant (Chappell and White 1974, 2001; Coleman and Peterman 1975; Loiselle and Wones 1979; Whalen et al. 1987; Amri et al. 1996; Wu et al. 2007). The Pandaoshi, Nantouhe and Guanshanhe syenogranite all exhibit relatively low Rb contents (115–205 ppm, 116–165 ppm and 177–300 ppm, respectively), which are significantly lower than those of highly fractionated granites (>270 ppm, King et al. 1997). In the Rb v. Ba v. Sr diagram (Fig. 7a), all samples from the three plutons plot within the granite field. In the (Zr + Nb + Ce + Y) v. FeO^T/MgO and (Zr + Nb + Ce + Y) v. (K₂O + Na₂O)/CaO diagrams (Fig. 7b and c), most samples from the three plutons plot within the unfractionated I- and S-type granite fields and A-type granite field.

Typical A-type granite is characterized by high 10 000 Ga/Al ratios (>2.60) and Zr + Nb + Ce + Y contents (>350 ppm), as well as elevated concentrations of Zr (>250 ppm), Nb (>20 ppm), Ce (>100 ppm), Y (>80 ppm) and Zn (>100 ppm) (Whalen et al. 1987). The Pandaoshi syenogranite exhibits low 10 000 Ga/Al ratios (2.23–2.63, averaging 2.46) and high Zr + Nb + Ce + Y contents (248–471 ppm, averaging 319 ppm), with Nb at 7.78–19.00 ppm, averaging 12.00 ppm, Zr at 150–278 ppm, averaging 193 ppm, Y at 8.69–18.65 ppm, averaging 12.36 ppm and Zn at 23.8–63.5 ppm, averaging 37.9 ppm. In comparison, the Nantouhe syenogranite shares similar characteristics with Pandaoshi syenogranite: it has 10 000 Ga/Al ratios ranging from 1.64 to 2.45 with an average of 2.08, Zr + Nb + Ce + Y contents ranging from 342 to 403 ppm, with an average of 377 ppm, Nb concentrations ranging from 5.04 to 10.71 ppm, with an average of 7.31 ppm, Ce concentrations ranging from 131 to 145 ppm with an average of 136 ppm, Zr concentrations ranging from 185 to 233 ppm, with an average of 209 ppm, Y concentrations ranging from 13.8 to 38.4 ppm, with an average of 23.3 ppm, and Zn concentrations ranging from 5.8 to 18.9 ppm, with an average of 14.8 ppm, showing clear distinctions from typical A-type granite (Whalen et al. 1987). Moreover, the samples from both plutons plot within the I- and S-type granite fields in the granite classification diagrams (Fig. 7d and e). Therefore, the Pandaoshi and Nantouhe syenogranites should be classified as I- or S-type granites, rather than A-type granites. The A/CNK ratio is effective in distinguishing between I- and S-type granites; typically, I-type granites have an A/CNK ratio of less than 1.1, whereas S-type granites have a ratio greater than 1.1 (Chappell and White 1974). Most samples of the Pandaoshi and Nantouhe syenogranite have A/CNK values below 1.1 (ranging from 1.00 to 1.12 for PP and 1.03 to 1.18 for NP), characteristic of I-type granites. Research has shown that phosphorus has high solubility in strongly peraluminous melts, and its content increases with the degree of differentiation; however, in metaluminous or weakly peraluminous melts, it has very low solubility, and its content decreases with increasing differentiation (Pichavant et al. 1992). The P₂O₅ contents of both plutons are low (0.05–0.11 wt% for PP and 0.06–0.07 wt% for NP), and these values decrease with increasing SiO₂ content (Fig. 7f), consistent with the evolutionary trend of I-type granites (Harrison and Watson 1984). Therefore, the Pandaoshi and Nantouhe syenogranites should be classified as I-type granites.

The Guanshanhe syenogranite exhibits high 10 000 Ga/Al ratios ranging from 2.22 to 2.98, with an average of 2.68, and Zr + Nb + Ce + Y contents ranging from 259 to 780 ppm, averaging 459 ppm. The Nb content varies between 17.3 and 36.0 ppm, averaging 25.5 ppm, Ce content ranges from 76 to 268 ppm, averaging 156 ppm, and Zr content varies between 127 and 479 ppm, averaging 245 ppm, which are characteristics similar to A-type granite (Whalen et al. 1987). Furthermore, the Guanshanhe syenogranite exhibits a high Fe₂O₃^T/MgO ratio ranging from 2.78 to 4.56. In the granite classification diagrams (Fig. 7), most samples plot within the A-type granite field. Zircon saturation temperatures can be used to infer the melting temperatures of granitic rocks (Watson and Harrison 1983; Siégel et al. 2018). With the exception of one sample, which has a lower zircon saturation temperature (762°C), the samples of Guanshanhe syenogranite exhibit zircon saturation temperatures ranging from 781 to 890°C, averaging 824°C, similar to A-type granites (Watson and Harrison 1983; Eby 1990, 1992; Siégel et al. 2018). Eu is more readily incorporated into plagioclase crystal compared with other rare elements. The fractional crystallization of plagioclase can lead to a depletion of Eu in the residual melts. Moreover, water-rich melts tend to inhibit the crystallization of plagioclase. Therefore, the Eu anomalies observed in zircons crystallized from the melt can also reflect, to some extent, the water-richness of the melt (Dilles et al. 2015). The zircons from two samples of the GP exhibit Eu/Eu* ratios ranging from 0.09 to 0.28, with an average of 0.13, indicating a pronounced negative Eu anomaly. This indicates that the magma from which the GP formed was a water-poor melt. According to Ballard et al. (2002), the positive Ce anomaly in zircons can also reflect the oxygen fugacity of the magma. In the case of zircons from the GP, one point exhibits a markedly high Ce/Ce* ratio of 72.27, whereas the remaining data points range from 1.18 to 17.85, with an average of 5.09, indicating a pronounced positive Ce anomaly. This suggests that the magma had high oxygen fugacity, implying that the granite predominantly formed under an oxidizing environment. The characteristics of the zircons from the GP are consistent with A-type granite. Furthermore, the GP is enriched in high field strength elements Nb and Ta, but depleted in CaO and Sr, and exhibits a pronounced negative Eu anomaly (Eu/Eu* ratios ranging from 0.27 to 0.64, with an average of 0.37). These characteristics are similar to those of A-type granites (Whalen et al. 1987). Collectively, these features indicate that the GP is classified as an A-type granite.

Generally, a positive $ε$_Hf(t) value suggests that the source rock originates from juvenile crust or depleted mantle, whereas a negative $ε$_Hf(t) value indicates that the source rock comprises ancient crustal components (Taylor and McLennan 1985; Wu et al. 2007). Zircon Hf isotope ratios are unaffected by processes such as partial melting or fractional crystallization. Consequently, these ratios indicate open-system dynamics involving end-members with varying degrees of radiogenicity, including those that are more radiogenic (i.e. mantle-derived) and those that are less radiogenic (i.e. crustal) components (Bolhar et al. 2008). Based on the aforementioned studies, we have found that the zircon U–Pb ages of the PP, NP and GP are similar (Fig. 4), and they exhibit comparable geochemical characteristics (Figs 5 and 6). However, these granites show differences in their $ε$_Hf(t) values, and their two-stage model ages also differ significantly. Therefore, we infer that despite forming within the same tectonic setting, these three plutons have distinct magma sources. The following section discusses the sources and genesis of the three plutons.

The petrogenesis of I-type granite can be interpreted in two main ways: they may form through the fractional crystallization of mantle-derived magmas (Chappell et al. 2012) or through the partial melting of metamorphic basic to intermediate igneous rocks in the crust (Chappell and Stephens 1988; Li et al. 2007b). The PP and NP have similar Cr contents (3.27–7.18 ppm for PP and 4.09–11.02 ppm for NP), which are significantly lower than the Cr contents of primitive tholeiitic magma formed by partial melting of the mantle peridotite source region (500–600 ppm, Wilson 1989). Their Rb/Nb ratios (8.79–20.78 for PP and 12.70–32.73 for NP) and Nb/La ratios (0.14–0.37 for PP and 0.07–0.10 for NP) differ considerably from those of mantle-derived magmas (Sun and McDonough 1989). In contrast, their Nb/U ratios (1.09–4.42 for PP and 1.12–3.73 for NP) and Ce/Pb ratios (1.87–4.80 for PP and 2.70–5.58 for NP) are smaller than those of primitive mantle and closer to those of the continental crust (Hofmann 1988). This suggests that PP and NP were not formed by fractional crystallization of mantle-derived magma.

The depletion of Sr and Ba and the negative Eu anomalies (Eu/Eu* = 0.54–0.71 for PP and 0.55–0.71 for NP) suggest the presence of a small amount of plagioclase residue or mild fractional crystallization in the source area (Rudnick 1995). Their $δ$Ce values range from 0.91 to 0.94 for PP and from 0.93 to 0.95 for NP. The depletions of Ti and Nb may result from the fractional crystallization of Ti–Fe oxides, whereas the depletions of P may result from the fractional crystallization of apatite (Qiu et al. 2005; Wang et al. 2022). The samples exhibit a strong fractionation between LREE and heavy REE (HREE) (LREE/HREE = 16.45–27.51 for PP and 11.22–21.32 for NP), with (La/Yb)_N values ranging from 24.87 to 65.77 for PP and from 12.80 to 53.26 for NP. The Sr/Y ratios are relatively high, averaging 20.52 for PP and 12.12 for NP, indicating the presence of garnet in the residual phase of the source region (Defant and Drummond 1990). The PP and NP are believed to have originated from the lower–middle crust (Fig. 8 and b) and primarily experienced partial melting (Fig. 8c). They have similar Zr/Hf ratios, averaging 38.19 for PP and 34.79 for NP, compared with the continental crust (Zr/Hf = 36.7, Rudnick and Gao 2003). The low Ti/Zr ratios (6.21 for PP and 5.57 for NP) and high K₂O contents (4.79 wt% for PP and 4.83 wt% for NP) indicate a crustal origin (Wilson 1989).

The PP displays evolved zircon Hf isotopic compositions (⁠$ε$_Hf(t) = −6.8 to +8.9) with corresponding two-stage model ages ranging from 1823 to 848 Ma (Fig. 9a). These features clearly suggest that the magma formation processes operate as an open system (Shaw and Flood 2009). It is possible that the magma originated from a combination of crust–mantle sources or, alternatively, that it was derived from a mixture of ancient and juvenile crustal material. Most zircons exhibit negative $ε$_Hf(t) values with corresponding two-stage model ages primarily between 1654 and 1426 Ma (Fig. 9a), and this, combined with their high SiO₂ contents (>71 wt%), elevated K₂O/Na₂O ratios (ranging from 1.15 to 1.66) and A/CNK ratios between 1.00 and 1.12, suggests that they originated from the melting of mature crustal material in the Mesoproterozoic (Patiño-Douce and Beard 1995). The positive $ε$_Hf(t) values of the PP, with corresponding two-stage model ages primarily ranging from 973 to 848 Ma broadly correlate with the timing of early Neoproterozoic tectono-magmatic events in the Central Qilian region and the northern margin of the West Qinling; these ages are associated with convergent processes and island-arc magmatism related to Rodinia (Pei et al. 2012). Furthermore, no mafic microgranular enclaves were found within the PP during the field investigations, and combined with geochemistry characteristics, it is impossible to attribute the origin to the mixing of crust–mantle magma. Therefore, we infer that the primary source of the PP originated from partial melting of ancient crustal materials, with a few samples having negative $ε$_Hf(t) values, indicating the addition of juvenile crustal material. Compared with PP, the NP has a relatively homogeneous Lu–Hf isotopic composition, with $ε$_Hf(t) values ranging from +4.9 to +8.9 (Fig. 9a). The corresponding two-stage model ages for NP fall between 1092 and 843 Ma, predominantly clustering around 997–843 Ma. The NP and the PP exhibit similar two-stage model ages corresponding to their positive $ε$_Hf(t) values, and they share comparable geochemical characteristics. Therefore, it is inferred that the juvenile crustal material in their source regions probably originated from a common magmatic source. Also, no mafic microgranular enclaves were found within the NP, which indicates that the source magma of NP probably derives from juvenile crust. As shown in the SiO₂ v. Mg^# diagram (Fig. 8d), both PP and NP plot within the meta-andesite field.

In summary, the partial melting of ancient crustal meta-andesite formed the parent magma, accompanied by the addition of juvenile crustal material, and underwent some degree of fractional crystallization, ultimately resulting in the formation of the Pandaoshan I-type granite. In contrast, the Nantouhe I-type granite primarily formed though the partial melting of juvenile crustal material.

A-type granites can originate from various magmatic sources, primarily including the following: (1) partial melting of F- and/or Cl-enriched dry granulitic residues in the lower crust (Collins et al. 1982; Whalen et al. 1987; King et al. 1997; J. S. Yang et al. 2006b); (2) low-degree partial melting or fractional crystallization of mantle-derived basaltic magma (Turner et al. 1992; Lee and Bachmann 2014); (3) mixing of crust-derived acidic magma with mantle-derived basic magma (Griffin et al. 2002; J. H. Yang et al. 2006b); (4) partial melting of crustal materials (Whalen et al. 1987; King et al. 1997; Chappell and White 2001).

Experimental petrology indicates that melts derived from residual F-rich sources typically have higher MgO contents than TiO₂ and exhibit strong peraluminous characteristics (Dooley and Patiño Douce 1996). The GP has low TiO₂/MgO ratios (0.42–0.53, with an average of 0.49) and exhibits metaluminous to weakly peraluminous characteristics (A/CNK = 0.95–1.09). Therefore, the Guanheshan A-type granite did not originate from the partial melting of F- and/or Cl-enriched dry granulitic residues. Generally, granites derived from mantle-derived magmas involve fractional crystallization of nine times the volume of mantle-derived mafic magmatic rocks (Turner et al. 1992). However, no evidence of such large-scale mafic magmatic activity during the same period has been found near the GP, making it unlikely that the GP formed through the partial melting or fractional crystallization of mantle-derived magma. The GP exhibits low Nb/La ratios (0.13–0.63) and high Rb/Nb ratios (5.32–15.42), which differ significantly from those of mantle-sourced magma (Nb/La = 0.93–1.32, Rb/Nb = 0.24–0.89) (Sun and McDonough 1989). Additionally, it has lower Nb/U ratios (2.88–13.50, averaging 5.34) and Ce/Pb ratios (1.41–7.43, averaging 3.55) than those of the primitive mantle (Nb/U = 30, Ce/Pb = 9), and is similar to the continental crust (Nb/U = 6.2, Ce/Pb = 4, Hofmann 1988). Furthermore, the Cr content of GP ranges from 2.03 to 17.33 ppm, which is significantly lower than that of the primitive basaltic magma (Cr = 500–600 ppm, Wilson 1989). Based on the above analysis, we conclude that the GP is unlikely to have formed from mantle-derived magmas.

The Zr/Hf values of the GP range from 27.51 to 38.76 (averaging 34.46), which is similar to the average value for continental crust (c. 36.7, Rudnick and Gao 2003). The Rb/Sr ratio of crustal source magmas is typically above 0.5, whereas the Ti/Zr ratio is usually below 20 (Wilson 1989). The GP has Rb/Sr ratio ranging from 0.59 to 4.85 (averaging 2.04), Ti/Zr ratios ranging from 4.12 to 6.26 (averaging 5.42), and higher K₂O contents averaging from 4.93 to 5.93 wt% (averaging 5.27 wt%). Furthermore, in the CaO v. Sr diagram (Fig. 8a), most samples plot within the continental crust region; in the Nb/Y v. Th/Y diagram (Fig. 8b), the samples are mainly located in the lower to middle continental crust region. The positive correlations of La and La/Sm suggest that the GP exhibits a partial melting trend (Fig. 8c). They may form from meta-greywackes, as shown in the SiO₂ v. Mg^# diagram (Fig. 8d). Additionally, mixing of crustal and mantle magmas often results in the presence of mafic microgranular enclaves and can produce a wide range of zircon $ε$_Hf(t) values (Wang et al. 2018). Zircons from the GP have negative $ε$_Hf(t) values (−25.6 to −20.2) with a relatively narrow range (Fig. 9a), and the two-stage model ages range from 2983 to 2654 Ma, reflecting a homogeneous source and indicating that the magma originated from ancient crustal material during the Neoarchean tectono-magmatic period. The zircon U–Pb age v. $ε$_Hf(t) and zircon U–Pb age v. ¹⁷⁶Hf/¹⁷⁷Hf diagrams (Fig. 9) indicate that the magma of the GP originates from partial melting of the lower ancient crustal materials (Zhu et al. 2009). However, the absence of mafic enclaves in this syenogranite indicates that the magma mixing model is unlikely. The samples exhibit negative Eu anomaly (⁠$δ$Eu ranges from 0.27 to 0.64, averaging 0.37), and the depletion of Sr and Ba suggests plagioclase and K-feldspar fractionation (Rudnick 1995). In summary, we propose that the GP was derived from the partial melting of meta-greywackes within the ancient crust and experienced some degree of fractional crystallization, ultimately resulting in the formation of A-type granite.

The Northern Qilian Orogenic Belt is a typical accretionary–collisional orogen, with numerous reports on ophiolites, high-pressure–low-temperature metamorphic rocks and magmatic rocks related to subduction–collision processes within the belt (Wang 2013; S. Z. Li et al. 2018a, 2022; X. Y. Li et al. 2018b; Yang et al. 2018; Fu et al. 2019, 2020, 2022; Song et al. 2019; Allen et al. 2023; Lu et al. 2023). However, the long-term tectonic evolution of the Northern Qilian Orogenic Belt remains a subject of considerable debate. Previous studies have proposed primarily three models for its tectonic evolution. Model 1: the oceanic crust of the Northern Qilian underwent northward subduction, followed by back-arc extension and the expansion of the back-arc basin (Xia et al. 2003, 2016; Song et al. 2006, 2013, 2014). Model 2: the oceanic crust continuously subducted southward beneath the Kunlun–Qaidam terrane (Wu et al. 2017; Zuza et al. 2018). Model 3: multiple island-arc subduction–accretion complexes were present (Xiao et al. 2009). The Qinling–Qilian conjunction zone is primarily divided into three tectonic units: the Liziyuan Subduction Complex (Shangdan Suture Zone), the Qinling Arc Metamorphic–Igneous Complex and the Qingshui–Zhangjiachuan Back-Arc Complex (Mao et al. 2017). The Qingshui–Zhangjiachuan area, located at the eastern end of the NQLOB, is in the southeastern part of the Laohushan area, which shares a similar tectonic evolution with LHSO (Fu 2020). Early Paleozoic volcanic–sedimentary facies developed to the south of the Longshan Complex in the study area. This includes the Middle–Late Ordovician Chenjiahe Group and the fore-arc basin sedimentary rock system immediately adjacent to the Longshan mafic rocks, as well as the oceanic crustal meta-basalt of the Early–Middle Ordovician Hongtubao Formation, situated to the south of the Chenjiahe Group. The metamorphic flysch of the Silurian Huluhe Group is also located to the south of the Chenjiahe Group (Pei et al. 2007a).

Recent studies indicate that the Hongtubao metabasaltic volcanic rocks (500–438 Ma) exhibit characteristics of both enriched mid-ocean ridge basalt (E-MORB) and island arc basalt (IAB), belonging to the back-arc basin system, and basalts with transitional geochemical characteristics between IAB and MORB have also been discovered in the Yangjiasi and Huluhe area (He et al. 2007a, b; S. Z. Li et al. 2018a; X. Y. Li et al. 2018b; Fu et al. 2019; Xin and Huang 2023). The metabasaltic volcanic rocks exhibit features of E-MORB, indicating that the Hongtubao back-arc basin evolved into a mature one (Klein and Langmuir 1987). Together with the ophiolite suite identified in the Huluhe area (Zhang et al. 2004), this suggests that the Hongtubao back-arc basin evolved into an oceanic basin, referred to here as the HTBO. This was parallel to the roughly NW–SE-striking LHSO, and the duration aligns well with that of the LHSO. Given their spatial and temporal relationship, we infer that the HTBO and the LHSO underwent similar tectonic evolution, closely associated with the subduction of the WSO and QLO, respectively (Fu 2020; Xin and Huang 2023). Zircon U–Pb geochronological data for the Chenjiahe Group volcanic rocks indicate that they formed in a continental margin arc environment from 448 to 443 Ma (Hu 2005; He et al. 2007a, b; Li 2008; Wei 2013; S. Z. Li et al. 2018a). The oldest age of the Chenjiahe arc is 462 Ma in the Houchuanxia area, characterized by meta-intermediate–acid volcanic rock, suggesting that the HTBO formed before 462 Ma (Wei 2013). Because the continental arc was coeval with and parallel to the Hongtubao back-arc oceanic basin, and given the presence of subduction-related magmatic sequences, we infer that the Chenjiahe arc was generated by the subduction of the HTBO to the southern margin of the NCB from 462 to 440 Ma (Zhang et al. 2006; Chen et al. 2007; Pei et al. 2007a–c; Wei 2013; S. Z. Li et al. 2018a; Xin and Huang 2023). The Silurian Huluhe Group consists of a series of low amphibolite-facies–greenschist-facies metamorphic clastic rocks with characteristics of flysch sedimentation, primarily sourced from the eastern end of the NQLOB, the western section of the NQOB and the NCB (Pei et al. 2012). The intrusion of island-arc magmatic mafic rocks, such as the Yanjiadian diorite (441–440 Ma), Changgouhe diorite (443 Ma) and Xinjie granodiorite (448 Ma), along with subduction-related granite (He et al. 2005; Zhang et al. 2006, 2019; Pei et al. 2007a), including the Huangmenchuan granodiorite at 440 Ma and the Wangjiacha diorite at 455 Ma (Chen et al. 2007; Wei et al. 2012), provides further evidence for the northward subduction of the HTBO. These results indicate that the subduction of the HTBO occurred between 462 and 438 Ma, comparable with the subduction period of the Laohushan back-arc basin, which is constrained to between 450 and 430 Ma (Xia et al. 2003, 2012, 2016; Shi et al. 2004; Tseng et al. 2009; Song et al. 2013; Chen et al. 2014; Liu et al. 2016; Zhang et al. 2017; Fu et al. 2019; Fu 2020). Furthermore, the closure of the Proto-Tethys Ocean is considered to have occurred during the Early Silurian (Song et al. 2014, 2018, 2019; Yan et al. 2019; Ye et al. 2020). Simultaneously, the HP (high-pressure) sedimentary rocks within the Qilian–Sunan suture zone are considered to have originated from a trench prior to continental collision, with the youngest detrital zircon recorded at 441 Ma (Lu et al. 2023). These sedimentary rocks, along with magmatic rock evidence, collectively indicate that the closure of the Paleo-Tethys Ocean in the study area occurred around 438 Ma.

The NQOB and the NCB were ultimately unified owing to the closure of the HTBO, resulting in a transformation of the tectonic setting into continent–continent or arc–continent collision. The Caochuanpu granite (434–431 Ma) formed in a syn-collision setting (Zhang et al. 2006; Zhang 2019; Qin et al. 2022), whereas the Shanmenzhen A-type granite (414 Ma, Zhang 2019; Qin et al. 2022) formed in a post-collision phase. The Xiangquan A-type granite (410 Ma, Xu et al. 2017) formed in a post-orogenic environment, suggesting that the eastern end of the NQLOB has completed post-collision adjustments and entered the post-orogenic phase. These collision-related granites provide information on the orogenic processes between the NQOB and the NCB. The Early Devonian molasse (c. 400 Ma) unconformably covers the accretionary complex, high-pressure and low-temperature metamorphic rocks and Silurian foreland basin flysch, marking the end of the accretionary–collision orogeny (Xu et al. 2010a, b). Similarly, this is comparable with the timing of the collisional process in the Laohushan region, which is constrained between 430 and 410 Ma (Song et al. 2013; Zhang et al. 2017; Chen et al. 2018; Fu et al. 2019; Fu 2020).

Earlier studies have defined A-type granite as alkaline, anhydrous and anorogenic granites (Loiselle and Wones 1979). The formation of A-type granite is typically associated with tectonic settings such as active continental arcs, back-arc extension, post-collisional extension and intraplate rifts (Collins et al. 1982; Chen et al. 2015). Consequently, the notion that A-type granites are produced in extensional tectonic settings has been widely accepted (Whalen et al. 1987; Eby 1990, 1992). Recent studies have further demonstrated that A-type granites can be subdivided into anorogenic (A1) and post-orogenic (A2) categories, which have distinct sources and correspond to different tectonic environments (Collins et al. 1982; Whalen et al. 1987; Eby 1992). Specifically, A1-type granites exhibit enrichment in Nb and Ta with Y/Nb ratios less than 1.2, and their magmas are primarily derived from the mantle, typically forming in environments associated with mantle plumes or rifts. In contrast, A2-type granites display negative anomalies in Nb and Ta with Y/Nb ratios greater than 1.2, and their magmas are mainly sourced from the crust, predominantly forming in extensional settings following back-arc, post-collision or late orogenic events. The GP exhibits pronounced negative anomalies in Nb and Ta (Fig. 6b), with Y/Nb ratios ranging from 0.57 to 1.83 and an average value of 1.21, which is greater than 1.2. These characteristics are indicative of A2-type granites. Furthermore, the closure of the Proto-Tethys Ocean is considered to have occurred during the Early Silurian (Song et al. 2014, 2018, 2019; Yan et al. 2019; Ye et al. 2020). Previous studies have suggested that the youngest island-arc volcanic rocks in the NQLOB formed c. 440 Ma, such as rhyolite (441 Ma) from the Baiyin area (Wang et al. 2005), andesitic–dacitic volcanic rocks (443 Ma) from the Chenjiahe Group and the basaltic rocks or basaltic andesites (438 Ma) from the Hongtubao Formation (X. Y. Li et al. 2018b). Simultaneously, the HP (high-pressure) sedimentary rocks within the Qilian–Sunan suture zone are considered to have originated from a trench prior to continental collision, with the youngest detrital zircon recorded at 441 Ma (Lu et al. 2023). These sedimentary rocks, along with magmatic rock evidence, collectively indicate that the closure of the Proto-Tethys Ocean in the study area occurred before 438 Ma. The PP (415 Ma), NP (414 Ma) and GP (412–411 Ma) exhibit geochemical characteristics similar to those of post-collision magma (Fig. 6; Xu et al. 2017; Qin et al. 2022). The zircon U–Pb ages of these rocks are consistent with the period of post-collisional extensional setting at the QQCZ, as indicated by previous researchers (420–409 Ma, Ren et al. 2021; Qin et al. 2022). The diagram in Figure 10a shows that the GP, NP and PP display characteristics typical of post-orogenic granites. Additionally, the GP, NP and PP also exhibit characteristics of post-collision extensional environments, showing a clear linear evolution from post-collision to intraplate granite (Fig. 10b; Zhang et al. 2006; Xu et al. 2017; Zhang 2019; Qin et al. 2022). We propose that the GP, NP and PP are probably products of the post-collisional extensional setting following the closure of the HTBO and during the post-collision stages of the North Qinling terrane and North Qilian terrane, similar to tectonic evolution model 1 of the NQLOB. The extension and thinning of the lithosphere caused decompression, leading to the upwelling of the asthenosphere or lithospheric mantle. This process provided additional material and heat, inducing partial melting of ancient or juvenile crustal material. The melting was accompanied by the incorporation of mantle material and there was some degree of fractional crystallization, resulting in the production of I-type and A-type granite (Fig. 11). These findings provide further insights into the late Early Paleozoic orogenic processes at the eastern end of the NQOBL.

In the global context, the WSO and HTBO were both segments of the Proto-Tethys Ocean (Song et al. 2017; Dong et al. 2021), which separated the NQOB, the NCB and eastern Gondwana (Zhang et al. 2015; S. Z. Li et al. 2018a; Yang et al. 2018). Their closure in the Silurian caused the collision between the NQOB and the NCB, ultimately attaching them to eastern Gondwana (X. Y. Li et al. 2018b; Zhao et al. 2018). The Early Paleozoic orogenic event recorded at the conjunction area between the NQOB and NQLOB was attributed to the closure of the Proto-Tethys Ocean, which resulted in the assemblage of eastern Gondwana.

1. The Pandaoshi I-type granite was formed at 415 Ma, with high SiO₂ contents, and with K-rich, calc-alkaline and weakly peraluminous characteristics. It was formed by the partial melting of Mesoproterozoic ancient crustal material with the addition of Neoproterozoic juvenile crustal material.

2. In contrast to the Pandaoshi pluton, the zircon U–Pb age of the Nantouhe I-type granite is 414 Ma. Similarly, it has the characteristics of high SiO₂ contents, low MgO and Fe₂O₃^T contents, and is K-rich; it was formed by the partial melting of Neoproterozoic juvenile crustal material.

3. The Guanshanhe pluton is a K-rich, calc-alkaline, weakly peraluminous A2-type granite, with zircon U–Pb ages ranging from 412 to 411 Ma, which was derived from the partial melting of the Neoarchean ancient crust and experienced some degree of fractional crystallization.

4. The Early Paleozoic orogenic event at the eastern end of the NQLOB is thought to have been caused by the northward subduction of the Hongtubao Ocean (associated with the subduction of the Wushan–Shangdan Ocean). The closure of this subduction zone led to collision between the North Qinling terrane and North Qilian terrane, resulting in the formation of the ‘trench–arc’ system represented by the Chenjiahe continental marginal arc. This event also resulted in the formation of the post-collision Pandaoshi I-type granite, Nantouhe I-type granite and Guanshanhe A-type granite at 415–411 Ma. These formations were ultimately attached to eastern Gondwana and are closely related to the evolution of the Proto-Tethys Ocean.

We thank the chief editor and the two anonymous reviewers for their constructive reviews, which have greatly improved our paper. We wish to acknowledge Y. C. Wang, X. Wang, Y. F. Wang, S. Q. Li and others for their help during the fieldwork.

HL: conceptualization (lead), formal analysis (lead), investigation (equal), methodology (equal), visualization (lead), writing – original draft (lead); ZL: conceptualization (equal), formal analysis (equal), funding acquisition (lead), investigation (equal), methodology (lead), visualization (equal); XP: funding acquisition (equal), investigation (lead), methodology (equal); MW: investigation (equal), methodology (equal), writing – review & editing (equal); HZ: formal analysis (equal), methodology (equal); SZ: formal analysis (equal), methodology (equal); LQ: investigation (equal), methodology (equal); MW: investigation (equal), methodology (equal), writing – review & editing (equal); FG: methodology (equal).

This work was supported by the National Natural Sciences Foundation of China under grant numbers 41872235, 42172236 and 41872233, the Fundamental Research Funds for the Central Universities under grant numbers 300102270202, 300103183081, 300104282717 and 300102274808, Double First-Class University Construction Special Project of Shaanxi under grant number 300111240014 and the Youth Innovation Team of Shaanxi Universities.

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

All data generated or analysed during this study are included in this article.