2. Geological setting

The Jiaodong Peninsula, located at the southeastern margin of NCC, consists of the Sulu terrane in the southeast and the Jiaobei terrane in the northwest (Fig. 1a). The two terranes are separated by the lithospheric-scale ENE- to NE-trending Wulian–Qingdao–Yantai Fault (WQYF; Fig. 1a, b). The Jiaodong Peninsula is bounded by the Pacific Plate to the east and separated from the Luxi Block of the NCC by the 2400 km long NNE–SSW- (between 010° and 025°) trending and steeply dipping Tan-Lu Fault (TLF) to the west (Yan et al. Reference Yan, Zhu, Lin and Zhao2014). The striking feature of the peninsula is the regional-scale NNE–SSW- to NE–SW-striking faults, which were developed either in the cratonic interior or along pre-existing suture zones like the TLF, Zhaoyuan–Pingdu Fault (ZPF) and WQYF, respectively, from west to east (Fig. 1b; Liu et al. Reference Liu, Ji, Ni, Shen, Zheng, Chen and Craddock2021).

The basement in the Sulu terrane, to the southeast of the WQYF, is composed of Palaeoproterozoic and Neoproterozoic crystalline rocks of YC (Li et al. Reference Li, Xiao, Liu, Chen, Ge, Zhang, Sun, Cong, Zhang, Hart and Wang1993) and was subjected to an ultrahigh-pressure (UHP) metamorphic event at c. 244−220 Ma (Cong, Reference Cong1996). The Jiaobei terrane to the northwest of the WQYF (Faure et al. Reference Faure, Lin and Breton2001) includes the Jiaobei Uplift and the Jiaolai Basin (Fig. 1b; Wang et al. Reference Wang, Yang, Deng, Santosh, Zhang, Liu, Li, Huang, Zheng and Zhao2014). The Jiaobei Uplift is mainly composed of the Precambrian high-grade metamorphic rocks of NCC (Fig. 1b; Tang et al. Reference Tang, Zheng, Wu, Gong and Liu2007). The latter rocks were intruded by the Linglong granite between 163 and 149 Ma (Yang et al. Reference Yang, Fan, Santosh, Hu, Wilde, Lan, Lu and Liu2012), which subsequently uplifted between c. 143 and 128 Ma during the exhumation of the Linglong metamorphic core complex (Charles et al. Reference Charles, Augier, Gumiaux, Monie, Chen, Faure and Zhu2013) and the contemporaneous formation of the Jiaolai Basin (Liu et al. Reference Liu, Ji, Ni, Shen, Zheng, Chen and Craddock2021). The Jiaolai Basin consists of the clastic and volcanic rocks that span the period from 135 Ma (Ni et al. Reference Ni, Liu, Tang, Yang, Xia and Zhang2016) to 55 Ma and is grouped into the Laiyang, Qingshan, Dasheng, Wangshi and Wutu Groups from bottom to top (B Zhang et al. Reference Zhang, Weinberg, Yang, Groves, Sai, Matchan, Phillips, Kohn, Miggins, Liu and Deng2020). Except for the limited occurrence of 215−200 Ma Shidao alkaline complex occurring in the southeastern boundary of the Sulu terrane (Yang et al. Reference Yang, Chung, Wilde, Wu, Chu, Lo and Fan2005), the widely developed magmatism both in the Jiaobei Uplift and the Sulu terrane occurred during the Late Jurassic – Early Cretaceous (Fig. 1b; Wang et al. Reference Wang, Yang, Deng, Santosh, Zhang, Liu, Li, Huang, Zheng and Zhao2014). The Late Jurassic Linglong-type granitoids usually exhibit a NNE–SSW-trending mylonitic foliation associated with the WNW–ESE-trending stretching lineations (LQ Yang et al. Reference Yang, Dilek, Wang, Weinberg and Liu2018). In contrast, the Early Cretaceous granitic plutons are undeformed (QY Yang et al. Reference Yang, Deng, Goldfarb, Zhang, Gao and Wang2014).

The emplacement of the Late Jurassic Linglong-type granitoids, with the magmas produced by the partial melting of the juvenile crust with the alkaline rocks of the Sulu terrane and the lower crust containing the garnet–amphibolite of the Jiaobei terrane (Hou et al. Reference Hou, Jiang, Jiang, Ling and Zhao2007), was induced by the rapid and steepening rollback of the Palaeo-Pacific plate during 165−160 Ma (LQ Yang et al. Reference Yang, Dilek, Wang, Weinberg and Liu2018). The latter symbolized the initiation of a lithospheric tectonic extension and the associated magmatism in the Jiaodong Peninsula, which continued into the Early Cretaceous time (Liu et al. Reference Liu, Rudnick, Walker, Xu, Gao and Wu2015). Accordingly, in the Early Cretaceous time (135−110 Ma), the crustal deformation in the Jiaodong Peninsula was dominated by various extensional structures, such as extensional basins, normal faults, low-angle detachment faults and metamorphic core complexes (MCCs) (Fig. 1; Liu et al. Reference Liu, Ji, Ni, Shen, Zheng, Chen and Craddock2021), accompanied by extensive gold mineralization (Fig. 1; Goldfarb et al. Reference Goldfarb, Taylor, Collins, Goryachev and Orlandini2014).

The Precambrian basement rocks in the Jiaobei terrane display a gross E–W-trending tectonic fabric at a regional scale prior to the emplacement of the Late Jurassic Linglong-type granitoids, which is associated with the broadly E–W-trending reverse faults and ENE–WSW- to E–W-trending shear zones in the Archaean and Palaeoproterozoic rocks (Lu et al. Reference Lu, Archambault, Li and Wei2007). By contrast, the Mesozoic magmatic rocks, the MCCs, the Jiaolai Basin and the crustal- to lithospheric-scale oblique-slip faults showing both transpressional and transtensional kinematics, i.e. TLF and WQYF (Meng, Reference Meng2003; Wang et al. Reference Wang, Zheng, Zhang, Zeng, Donskaya, Guo and Li2011), collectively exhibit strong NE–SW- to NNE–SSW-aligned tectonic fabric (Fig. 1b; LQ Yang et al. Reference Yang, Dilek, Wang, Weinberg and Liu2018).

The TLF developed as a Late Jurassic left-lateral strike-slip fault and then reactivated as a normal fault in the Early Cretaceous, controlling the development of the Jiaolai Basin (Fig. 1; Zhu et al. Reference Zhu, Niu, Xie and Wang2010). However, more recently, B Zhang et al. (Reference Zhang, Weinberg, Yang, Groves, Sai, Matchan, Phillips, Kohn, Miggins, Liu and Deng2020) argued that the TLF initially occurred as a normal fault under a NW–SE extension from c. 120 to 93 Ma, postdating the deposition of the Laiyang Group under the E–W extension between c. 135 and 122 Ma. The E–W extension led to the activity of the WQYF along the suture zone connecting the Jiaobei and Sulu terranes (B Zhang et al. Reference Zhang, Weinberg, Yang, Groves, Sai, Matchan, Phillips, Kohn, Miggins, Liu and Deng2020). The WQYF, striking ENE–WSW to NE–SW and dipping at gentle to medium angles to the NNW to NW (B Zhang et al. Reference Zhang, Weinberg, Yang, Groves, Sai, Matchan, Phillips, Kohn, Miggins, Liu and Deng2020), is considered to occur in the upper-middle crust from c. 135 to 122 Ma, causing the initial expansion of the Jiaolai Basin, then progressing into the lithospheric mantle from c. 122 to 110 Ma (Liu et al. Reference Liu, Ji, Ni, Shen, Zheng, Chen and Craddock2021). Many lower-order faults, striking NNE–SSW to NE–SW, were developed within the Jiaobei Uplift and the Sulu terrane. On the other hand, only a few nearly E–W normal faults occurred within the Jiaolai Basin (Fig. 1b). The NNE- to NE-trending faults with dips either to the NW or SE are distributed across the Jiaobei Uplift and the Sulu terrane, with an interval of c. 15–35 km, on both sides of the ZPF and WQYF (Fig. 1b), which are named as the Sanshandao, Jiaojia, Fengyidian, Qixia, Taocun–Dongdoushan, Muping–Jimo, Qingdao–Haiyang and Muping–Rushan faults from west to east (Fig. 1b), respectively.

The Jiaojia Fault, striking NNE–SSW (between 010° and 030°) and dipping WNW with angles of 20– 40°, controls the Sizhuang gold deposit (Fig. 2a). The mine is established on the Linglong granite (Fig. 2b), which was replete with many irregular and discontinuous lamprophyre dikes, and a great number of quartz veins (Wei et al. Reference Wei, Yang, Feng, Wang, Lv, Li and Liu2019; Fig. 2c). The host granite is dominated by a gneissic foliation better seen in the fresh exposures (Fig. 2d) that generally trends NNE–SSW to NE–SW (Wang et al. Reference Wang, Yang, Guo, Marsh, Wang, Liu, Zhang, Li, Zhang, Zheng and Zhao2015), and the faults and fractures better seen in the altered parts of the granite (Fig. 2e). Three alteration zones are identified in the footwall of the Jiaojia Fault, going from the unaltered granite to the Jiaojia Fault plane (Fig. 2b): (a) the potassic, (b) the sericite–quartz and (c) the pyrite–sericite–quartz alteration zone. The pyrite–sericite–quartz alteration zone was characterized by a network of multi-directional quartz–sulphide veinlets, typically 0.2 to 1 cm thick (Fig. 2b). In the sericite–quartz and potassic alteration zones, the veins are mainly single quartz–sulphide veins varying from 1 to 500 cm in thickness, controlled by the brittle fracture networks (Fig. 2b).

3. Lamprophyre dikes and quartz veins of the Sizhuang gold deposit: occurrence, sampling and acquisition

Lamprophyre dikes are abundant and cut across the Linglong granite in the Sizhuang mine with lengths of several tens of metres to more than 100 m. Most dikes occur within the altered granites, are sub-vertical and, as a rule, have variable strike orientations such as WNW–ESE (Fig. 3a), NNW–SSE (Fig. 3b, e), NNE–SSW (Fig. 3c, d, f, g) and NW–SE (Fig. 3h), although only a few dikes are inclined (Fig. 3c, d). Their thicknesses vary from 8 to 90 cm. As observed in the underground Sizhuang gold mine, the lamprophyre dikes show sharp contacts, with some chilled, against the host Linglong granite (Fig. 3a–h). Few dikes are straight with parallel edges in sub-vertical sections (Fig. 3a) because most dikes are displaced, forming continuous (Fig. 3b–e) or discontinuous dike bodies (Fig. 3f–h) and zigzag (Fig. 3b) or sinuous shapes along their long dimensions (Fig. 3c–h). In some cases, displacements cause much more complicated dike patterns (Fig. 3b, c). Nevertheless, it seems that the dike bodies are aligned parallel to the pre-existing joints trending ∼N0°–N042° (Fig. 3d) and ∼N130°–N175° (Fig. 3b, e), showing that the magma propagation took place along the pre-existing joint sets (Fig. 3d, e).

Fig. 3. Field photographs of the lamprophyre dikes in the Sizhuang gold deposit. (a) WNW-striking steep-dipping lamprophyre dike, with sharp straight contacts and (b) NNW–SSE-striking continuous dike segments, with non-overlapping and zigzag morphologies, in the K-feldspar altered granites. (c) NNE–SSW-striking dike segments with non-overlapping morphologies and horns beyond the offset step. (d) NNE–SSW-striking dike with small stepping continuous offsets in the K-feldspar altered granites. Note the localized dike-normal quartz veins near the stepovers in (c) and (d). (e) NNW-striking continuous dike segments with small stepping offset and horn beyond the offset step in the sericite–quartz altered granites. Note the quartz vein cutting through the step segment sharply. (f) NNE–SSW-striking discontinuous dike segments with lower-stepping overlapping offsets in the K-feldspar altered granites. Note the dike-normal quartz veins restricted to rock-bridge zone. (g) NNE-striking discontinuous dike segments with upper-stepping non-overlapping offsets in the sericite–quartz altered granites. Note the slight curvatures around dike tips. (h) NW–SE-striking discontinuous dike segments with lower-stepping non-overlapping offsets in the sericite–quartz altered granites. Note the slight curvature in the internal part and the thin apophyse in the outer part around dike tips.

The fact that slickenlines have hardly been observed along the dike margins implies more dilational than shear intrusion origin. Discontinuous dikes are characterized by an en echelon array of long tabular bodies striking NNE–SSW (∼0–042°; Fig. 3f, g) and NW–SE to NNW–SSE (∼130–175°; Fig. 3h), respectively. They form upwards-, left- or right-stepping geometries (Fig. 3f) with or without overlapping (Fig. 3g, h). Dike tips are frequently bent, appearing as horn structures (Fig. 3f–h), whereas apophyses between two opposite-directed dike tips often occur (Fig. 3h). In addition, some quartz veins oriented at high angles or perpendicular to the dikes occur within the bridge zones formed by the ∼N0°–N042° dikes (Fig. 3f) but not along the ∼N130°–N175° dikes (Fig. 3h).

Based on the detailed field and structural observations, two representative fresh and non-deformed lamprophyre dike samples of SZ16D004B1 (Fig. 4a) and SZ16D002B2 (Fig. 4b) were picked from the underground adits in the Sizhuang gold deposit. The sample SZ16D004B1 (Fig. 4a) was collected from a lamprophyre dike cutting the K-feldspar altered granite with a dip to the NW at 60° (300−60°) (Fig. 3d). The sample SZ16D002B2 (Fig. 4b) was collected from a lamprophyre dike dipping WNW at 70° (290–70°), which cut the sericite–quartz altered granite (Fig. 3g). They are porphyritic to equigranular and consist of pyroxene, biotite, phlogopite and hornblende phenocrysts in a microcrystalline matrix of pyroxene, biotite, phlogopite, hornblende and plagioclase accompanied by accessory minerals including sphene, magnetite and zircon (Fig. 4c, d). These samples are used for dating the lamprophyre dikes with the ⁴⁰Ar–³⁹Ar analysis of the phlogopite.

Fig. 4. Hand sample and micro-scale photographs of the lamprophyre dikes in the Sizhuang gold deposit. (a, b) Lamprophyre dike samples SZ16D004B1 and SZ16D002B2 for ⁴⁰Ar–³⁹Ar dating. (c) Pyroxene and hornblende phenocrysts in an undeformed matrix of pyroxene, biotite, hornblende and plagioclase. (d) Biotite, hornblende and plagioclase, with accessory minerals of zircon, sphene and magnetite. Mineral abbreviations: Hb = hornblende, Px = pyroxene, Bt = biotite, Mt = magnetite, Pl = plagioclase, Sph = sphene, Ser = sericite.

In general, the quartz veins show rough surfaces without slickenlines and tapering geometries (Fig. 5a) and have quartz crystals (sub)perpendicular to the fracture wall (Fig. 5b), indicating the dilational origin. Their lengths are usually more than 1 m and can be up to 200 m, whereas their thicknesses vary between 2 mm and 5 m. The smaller veins with lengths up to 20 m usually form a mesh-like structure with mutually cross-cutting relationships (Fig. 5c). In contrast, the bigger veins usually occur, in (sub)parallel bands (Fig. 5d, e), although in a few cases one band intersects another (Fig. 5f). In addition, while most of them have planar shapes (Fig. 5a–f), some zigzag or curved alignments can be observed (Fig. 6a, b). The rough surfaces of the veins and the zigzag or curved alignments suggest the mode I or mixed-mode formation of the filled cracks. In addition, many veins are accompanied by offshoots, which depart either clockwise or anticlockwise from them (Fig. 6c, d).

Fig. 5. Field photographs showing the occurrence of the quartz veins in the Sizhuang gold deposit. (a) Quartz vein with tapering geometry; (b) quartz veins with the quartz grains growing perpendicular to the fracture walls; (c) quartz veins showing a mesh-like structure with mutually cross-cutting relationships; (d) sub-parallel banded quartz veins; (e) banded quartz veins; (f) banded quartz veins including a few bands of different orientations.

Fig. 6. Field photographs showing the geometry of the quartz veins in the Sizhuang gold deposit. (a) Quartz veins consisting of the curved segments longer than 1 m; (b) quartz veins consisting of curved segments with sharp bends and shorter than 1 m; (c, d) main veins accompanied by offshoots oriented either clockwise or anticlockwise from main veins.

The attitudes of the lamprophyre dikes and quartz veins in the underground shaft of the Sizhuang mine were collected in two perpendicular directions from drive to drive in the study area, i.e. parallel and perpendicular to the mean strike (015°) of the main ore body. Based on the data acquisition technique and principle of Yamaji et al. (Reference Yamaji, Sato and Tonai2010) and Lahiri and Mamtani (Reference Lahiri and Mamtani2016), the threshold values of 0.5 cm and 1 m for the thickness and length, respectively, of a mining face are used in the present study. For the dikes and quartz veins, if they are planar and single, the orientations were measured when they fitted the above criteria; if they are planar and banded, each band meeting the criteria was measured. In the case of curved dikes and quartz veins, the attitude of each planar segment of those fitting the criteria was collected, whereas if they were longer than the threshold but had short-wavelength curves, we measured the average attitude.

Orientation data of 79 lamprophyre dikes and 320 quartz veins were collected in the underground shaft of the Sizhuang gold deposit. The lamprophyre dikes strike mainly NNW–SSE and NNE–SSW, whereas WNW–ESE is a subordinate direction (Fig. 7a, b). The NNW–SSE-striking set is the most populated, including the strikes from azimuths 310° to 355°, with an average azimuth at 338° (Fig. 7a). The NNE–SSW-striking set includes the strikes from azimuths 0 to 042°, with an average azimuth at 023° (Fig. 7a). The WNW–ESE-striking set only accounts for a small percentage of the very steep to almost vertical dikes striking from 275° to 295° (Fig. 7a, b). These dikes are shorter than those grouped into the two main sets (Fig. 3c–f). Moreover, the dikes dipping in general to the W are well separated into two sets, but not the dikes dipping to the E (Fig. 7b).

Fig. 7. (a) Rose diagram of 79 dike segments from the Sizhuang gold deposit; dashed lines represent the mean strikes of the two main sets formed by NNW–SSE- and NNE–SSW-trending lamprophyre dikes. (b) lower-hemisphere, equal-area stereogram of poles to 79 dike segments from the Sizhuang gold deposit; dashed great circles represent the mean orientations of dikes trending NNW and NNE. (c) Rose diagram of 320 quartz veins from the Sizhuang gold deposit; the dashed line represents the mean strike of 320 quartz veins. (d) Lower-hemisphere, equal-area stereograms of poles to 320 quartz veins from the Sizhuang gold deposit; dashed great circles represent the mean orientation of 320 quartz veins.

Since a cross-cutting relationship between the two dike sets can hardly be concluded, we imagine the differently oriented dikes have intruded into the pre-existing fractures with geometries induced by the left-lateral strike-slip tectonics mentioned for the TLF during Late Jurassic times (Zhu et al. Reference Zhu, Niu, Xie and Wang2010). In particular, these fractures are (a) NNE–SSW-striking fractures dipping to the WNW parallel to the Jiaojia Fault, (b) NNW–SSE-striking Riedel shears dipping to the WSW, and (c) WNW–ESE-striking R′ Riedel shears dipping to the SSW.

The quartz veins strike mainly NNE–SSW with azimuths from 0° to 45° and a mean azimuth at 017° dipping towards the WNW in their majority (>70%) (Fig. 7c, d). As a rule, they seem to have followed fractures parallel to the Jiaojia Fault.

It has been observed that the quartz veins cut sharply across the NNW–SSE- (∼310°–355°) trending continuous dikes (Fig. 3e), showing that the NNW–SSE-trending lamprophyre dikes formed earlier than the quartz veins. Furthermore, some quartz veins with high angles or perpendicular to the dikes occur within the bridge zones formed by the NNE–SSW- (∼0–042°) trending dikes (Fig. 3f) but not the dikes trending NNW–SSE (∼310–355°) (Fig. 3c, e).

5. Palaeostress analysis and age of the lamprophyre dikes and quartz veins

5.a. The stresses for lamprophyre dikes

The poles to the lamprophyre dikes, as projected in a contoured stereogram (1 % contour per 1 % area) (Fig. 9a), show an overall clustered distribution with two distinct maximum concentration orientations. These concentrations correspond to two sets of symmetry axes (Fig. 9a) that imply the existence of two main sets for the lamprophyre dikes in the Sizhuang gold deposit, i.e. those trending NNW–SSE and NNE–SSW. We applied the fuzzy clustering technique not only for K = 2, i.e. two clusters, but for testing K values from 1 to 5 with the aid of software GArcmB (Yamaji, Reference Yamaji2016). As a result, we can test which K value provides the minimum BIC value, i.e. the optimum value. Among the obtained BIC values in the XY plot, the minimum value is when K = 2 (Fig. 10a), thus indicating that two homogeneous clusters, A and B, better describe the recorded data. Accordingly, these clusters define two stress states, LDA and LDB, with the $\omega $ values equal to 0.76 and 0.24, respectively, explaining the emplacement of 76 % and 24 % of the lamprophyre dikes under stresses LDA and LDB, respectively.

Fig. 9. (a) Contoured lower-hemisphere equal-area projection of poles to 79 dike segments from the Sizhuang gold deposit, showing two distinct clusters indicated by the solid black circles and the solid black triangles, respectively. (b) Contoured lower-hemisphere equal-area projection of poles to 320 quartz veins from the Sizhuang gold deposit, showing the overall distribution of a girdle type except that there is a significant cluster of poles indicated by the solid black circles in the northeast.

Fig. 10. Palaeostress analysis based on the lamprophyre dike orientation data with the fuzzy clustering technique. (a) The lamprophyre dike orientation data show the minimum BIC at K = 2, meaning that the dike orientations should be partitioned into two clusters. The stresses corresponding to the clusters are called stresses LDA and LDB. (b) Equal-area projection of the poles to the lamprophyre dikes. The colour of a datum point indicates the membership of the orientation. The stress axes are indicated by the circles with crosses for stress LDA and the diamonds with crosses for stress LDB, which centre their 95 % error ellipses. The optimal stresses have a stress ratio of 0.50 for stress LDA and 0.16 for stress LDB. (c, d) Mohr circles of the stresses and the normalized normal and shear stresses on the vein walls exerted by the stresses. The colour of each datum point indicates the membership of the datum. The dark line defines P _f.

However, whether a dike was deposited under stress LDA or LDB depends on its memberships, which are denoted by the probability of belonging to clusters A and B. The memberships are indicated by gradation between black and white circles on the equal-area projection (Fig. 10b), each of which has a value between 0 and 1. Dikes deposited under stress LDA are shown with solid black circles in Figure 10b, the membership of which to cluster A is 1; whereas the dikes formed under stress LDB are shown with solid coloured to open white circles in Fig. 10b, the membership of which to cluster A is <1. Stress LDA was an extensional stress regime with the attitudes of ${\sigma _1}$ , ${\sigma _2}$ and ${\sigma _3}$ axes at 151–168°, 338–322° and 247–203°, respectively, and ${\rm{\Phi }}$ = 0.50 (Fig. 10b). Stress LDB was a strike-slip regime with the attitudes of ${\sigma _1}$ , ${\sigma _2}$ and ${\sigma _3}$ axes at 215–217°, 334–359° and 117–126°, respectively, and ${\rm{\Phi }}$ = 0.16 (Fig. 10b). The two groups showed the driving pressure R′’ values at 0.47 and 0.06, respectively (Fig. 10c, d).

5.b. The stresses for quartz veins

For the 320 quartz vein orientation data, the BIC is minimum at K = 1 (Fig. 11a). Therefore, a single stress regime, called QVA (Fig. 11b), can explain all the orientations. QVA defines an inclined stress state with the attitudes of σ₁, σ₂ and σ₃ axes at 212–21°, 326––47° and 106–36°, respectively, and ${\rm{\Phi }}$ = 0.40 (Fig. 11b, c). The driving pressure R′ value is high at 0.75. The stress QVA is consistent with the fact that the poles to the quartz veins, lying inside the 0.5 % contour per 1 % area in the contoured diagram, show the overall distribution of a girdle type with ${P_{\rm{f}}}$  >  ${\sigma _2}$ (Fig. 9b).

Fig. 11. Palaeostress analysis based on the quartz vein orientation data with the fuzzy clustering technique. (a) The quartz vein orientation data show the minimum BIC at K = 1, meaning that a single stress state QVA-FC explains all the vein orientations. (b) Equal-area projection of the poles to the quartz veins. The stress axes are indicated by the circles with crosses, which centre their 95 % error ellipses. The optimal stress has a stress ratio of 0.40. (c) Mohr circles of the stress and non-dimensional normal and shear stresses on the vein walls. The dark line defines P _f. (d) For the clustered distribution in Figure 9b, the BIC is minimum at K = 1. (e) Equal-area projection of the poles to the quartz veins belonging to the clustered distribution. The stress axes are indicated by the diamonds with crosses, which centre their 95 % error ellipses. The optimal stress has a stress ratio of 0.20. (f) Mohr circles of the stress and non-dimensional normal and shear stresses on the vein walls. The dark line defines P _f.

However, it should be noted that there is a significant cluster of poles in the northeast (Fig. 9b), suggesting that a great number of quartz veins strike NNE–SSW with dips towards NW (mean orientation of 287–55°; Fig. 7d). These veins are the largest, with no slickenlines, forming bands (Fig. 5d–f) (sub)parallel to the NNE–SSW lamprophyre dikes, indicating that the dilation of NNE–SSW fractures was not only at high P _f but also at low P _f. More interestingly, the distribution of the poles lying within the 3 % contour includes 81 orientation data (solid black circles), accounting for 25 % of the quartz veins, and has different symmetry axes from those of the overall girdle-type distribution (Fig. 9b), indicating changes in the state of stress during the vein emplacement (Tran & Ravoof, Reference Tran and Ravoof2007; Mondal & Mamtani, Reference Mondal and Mamtani2013). The clustered distribution indicates low ${P_{\rm{f}}}$ ( ${P_{\rm{f}}}$  <  ${\sigma _2}$ ).

For the clustered distribution, the BIC is minimum at K = 1 (Fig. 11d). The obtained stress regime, called QVB (Fig. 11e), has the attitudes of ${\sigma _1}$ , ${\sigma _2}$ and ${\sigma _3}$ axes at 238–46°, 004–29°, and 112–29°, respectively, and ${\rm{\Phi }}$ = 0.16 (Fig. 11e, f). The driving pressure R′ value is low at 0.09, suggesting that whenever ${P_{\rm{f}}}$ is of magnitude almost equal to ${\sigma _3}$ stress, the formed veins are perpendicular to the ${\sigma _3}$ axis, which is consistent with the fact that only a very limited number of vein poles lie to the left of the ${P_{\rm{f}}}$ line (Fig.11f).

5.c. Comparison of stresses (for lamprophyre dikes and quartz veins)

Two stress states have been defined by the lamprophyre dikes, and two stress states by the quartz veins, using the fuzzy clustering technique of Yamaji & Sato (Reference Yamaji and Sato2011). These four stress states indicate similarities and differences, and because of this, herein, we attempt to clarify better and unify these results. In total, three different stress regimes are defined (Table 1):

1. (1) Stress regime A (i.e. LDA). Only the lamprophyre dikes define it. It has a sub-vertical ${\sigma _1}$ axis, and sub-horizontal ENE–WSW-trending ${\sigma _3}$ axis (Fig. 10b, c), indicating an extensional stress regime with obtained stress ratio values defining Radial-Pure extension to Pure Extension stress regimes (stress types based on Tranos et al. Reference Tranos, Kachev and Mountrakis2008), under which ${P_{\rm{f}}}$ was lower unless almost equal to ${\sigma _2}$ .

2. (2) Stress regime B (i.e. LDB and QVB). This is the main stress state defined by the clustered distribution of the lamprophyre dikes and quartz veins (Figs 10b, d, 11e, f). This stress regime is characterized by the more stable position of the ${\sigma _3}$ axis, which plunges towards the ESE at low angles, i.e. between the trends of the least principal stress axes of the ST1 and ST2 stress regimes (see Section 5.d for details). Although ${\sigma _1}$ and ${\sigma _2}$ axes vary in position along the principal stress ${\sigma _1}$ – ${\sigma _2}{\rm{\;plane}}$ (see LDB in Fig. 10b and QVB in Fig. 11e), the defined stress ratio Φ and driving pressure R′ are similar. Because of this, it is better described as an inclined (or oblique) strike-slip stress regime fitting with a transtension stress regime, under which, ${P_{\rm{f}}}$ magnitude was very low, much smaller in magnitude than ${\sigma _2}$ .

3. (3) Stress regime C (i.e. QVA). Only the quartz veins define it. Although the calculated ${\sigma _3}$ axis, plunging towards the ESE at low angles, is the same as that in stress regime B, stress regime C has higher ${\rm{\Phi }}$ and R′, and ${P_{\rm{f}}}$ was also high, i.e. higher than ${\sigma _2}$ . Furthermore, the ${\sigma _1}$ and ${\sigma _2}$ axes are both inclined, defining an inclined (or oblique) stress regime fitting with a transtension stress regime.

Table 1. Palaeostress analysis results from the lamprophyre dike and quartz vein orientation data in the Sizhuang gold deposit, Jiaodong Peninsula

5.d. Fault-slip data inversion and stress inversion

In order to accomplish a complete analysis concerning the palaeostresses in the Sizhuang gold deposit, we tried to define them from the fault-slip data in addition to using the dikes and veins. For this purpose, we applied a stress inversion to the available fault-slip data from stations in Jiaolai Basin located closest to the mine area (Fig. 1b), as these fault-slip data have recently been published by B Zhang et al. (Reference Zhang, Weinberg, Yang, Groves, Sai, Matchan, Phillips, Kohn, Miggins, Liu and Deng2020). Those authors, based on their palaeostress analysis and reconstruction, conclude that the Jiaolai Basin has been subjected to six stress regimes since the Cretaceous. Among them, four extensional regimes are defined: (a) an E–W extension during 135−121 Ma, controlling the formation of the Laiyang Group, (b) a NW–SE extension between 120 and 93 Ma, controlling the formation of the Qiangshan Group, (c) a N–S extension from 85 to 60 Ma, controlling the formation of the Wangshi Group, and (d) a NE–SW extension later than 55 Ma. In the catalogue of B Zhang et al. (Reference Zhang, Weinberg, Yang, Groves, Sai, Matchan, Phillips, Kohn, Miggins, Liu and Deng2020), the fault-slip data stations located closest to the Sizhuang gold deposit are K1Ly-05, K1ly-06, K1Ly-07, K1ly-10, K1Ly-25 and K1ly-27 within the Laiyang Group (Fig. 1b). They include 97 fault-slip data, which are heterogeneous since the area experienced multiple deformation events (B Zhang et al. Reference Zhang, Weinberg, Yang, Groves, Sai, Matchan, Phillips, Kohn, Miggins, Liu and Deng2020). Because the fault-slip data are heterogeneous, we applied the TR method (TRM) (Tranos, Reference Tranos2015), which was deployed to separate heterogeneous fault slip data into homogeneous groups and define either in situ or bulk Andersonian stress tensors for each of these groups.

The TRM is a simple graphical and semi-automatic method plotting the heterogeneous fault-slip data on TR diagrams and defining the slips on the faults, which are simultaneously compatible with a specific orientation of the Andersonian stress axes and a specific stress ratio $R$ ( $R = \left( {{\sigma _2} - {\sigma _3}} \right)/\left( {{\sigma _1} - {\sigma _3}} \right)$ with $0{\rm{\;}} \le R{\rm{\;}} \le 1$ ) (for details, see Tranos, Reference Tranos2015). Stress ratio ( $R$ ) equals ${\rm{\Phi }}$ . These faults are called Tensor Ratio Compatible Faults (TRCF), and the optimal TRM stress tensor is the one that explains the largest number of the TRCF with MA ≤ 20° and secondly provides the smallest Mean Misfit Angle (MMA).

Applying the TRM on the 97 fault-slip data, two extensional bulk stress tensors, ST1 (Fig. 12a) and ST2 (Fig. 12b), are defined. The former has attitudes for σ₁: 102−90°, σ₂: 012−00°, σ₃: 102−00° and $R$ = 0.85 from 35 TRCF with ≤30°, 30 with MA ≤ 20° and MMA = 12.9°; and the second has attitudes for σ₁: 143−90°, σ₂: 053−00°, σ₃: 143−00° and $R$ = 0.9 from 25 TRCF with ≤30°, 20 with MA ≤ 20° and MMA = 11.8°. Although their stress ratios are very similar, based on the percentages of the Stress Tensor Discriminator Faults (STDF), i.e. the faults activated by either A or B stress tensor, but not from both (Tranos, Reference Tranos2015, Reference Tranos2017), they are different stress tensors since these percentages are more than 70 % (Tranos, Reference Tranos2015, Reference Tranos2017). In particular, three STDF percentages were calculated: 92.9 % for the unified ST1 and ST2, 88.6 % for the ST1, and 84.0 % for the ST2 fault-slip datasets, respectively.

Fig. 12. Results of the TRM application (Tranos, Reference Tranos2015) on the recently published fault-slip data by B Zhang et al. (Reference Zhang, Weinberg, Yang, Groves, Sai, Matchan, Phillips, Kohn, Miggins, Liu and Deng2020). The optimal resolved stress tensors (a) ST1 and (b) ST2. Explanation: 1. Equal-area, lower-hemisphere projection of the TR-compatible fault slip data. ${\sigma _1}$ , ${\sigma _2}$ and ${\sigma _3}$ axes are shown with solid red rhomb, circle and square, respectively; 2. TR diagram showing the TR-compatible faults (blue balls), the ‘real’ (blue line) and ‘theoretical’ (red dashed line) Final Tensor Ratio Lines (for details, see Tranos, Reference Tranos2015); R is the stress ratio; 3. Misfit angle distribution of the TR-compatible faults.

ST1 and ST2 stress tensors define an ∼E–W pure extension – transtension (PE-TRN) and a NW–SE transtension (TRN) stress regime, respectively (stress type classification according to Tranos et al. Reference Tranos, Kachev and Mountrakis2008).

5.e. Phlogopite ⁴⁰Ar–³⁹Ar ages

Two phlogopite aliquots from each sample of the lamprophyre dikes were carried out to examine the reproducibility of the ⁴⁰Ar–³⁹Ar ages. Table 2 shows all the isotopic analytical data for each increment. All samples’ apparent age spectra and ages, including the plateau ages, total fusion ages and isochron ages, are presented in Figure 13a, b, c, d, f, g, h. If no plateau ages are defined, pseudo-plateau ages are shown (Fig. 13e). All the age errors, derived from the uncertainties in the J value and the irradiation correction factor without including the potassium decay constant, are given with a 95 % confidence level (2 $\sigma )$ . Plateau ages are the weighted mean of a sequence of consecutive, concordant step ages, indistinguishable at the 95 % confidence level and encompassing over 50 % of the total ³⁹Ar gas released (Dallmeyer & Lecorche, Reference Dallmeyer and Lecorche1990).

Table 2. Phlogopite ⁴⁰Ar–³⁹Ar step-heating isotopic analytical results for the lamprophyre dike from the Sizhuang gold deposit, Jiaodong Peninsula

Fig. 13. Phlogopite ⁴⁰Ar–³⁹Ar plateau (a, c, e, g) and isochron ages (b, d, f, h) for the lamprophyre dike from the Sizhuang gold deposit. (a, b) Aliquot WZL1-1 from sample SZ16D004B1; (c, d) aliquot WZL1-2 from sample SZ16D004B1; (e, f) Aliquot WZL2-1 from sample SZ16D002B2; (g, h) aliquot WZL2-2 from the sample.

In contrast, pseudo-plateau ages are the weighted mean of contiguous step ages consistent within 2σ, which account for at least 30 % of the total ³⁹Ar gas released (Bi & Zhao, Reference Bi and Zhao2017). Total fusion ages and isochron ages are obtained by adding all step ages to derive a single total gas age and from the slope of the line best fitted to plateau-forming step compositions using a least-squares regression (York, Reference York1969), respectively. All the isochron plots (Fig. 13b, d, f, h) commonly show the initial ⁴⁰Ar/³⁶Ar ratios identical or close within error to the value of 298.56 ± 0.31 for the present-day atmospheric argon (Lee et al. Reference Lee, Marti, Severinghaus, Kawamura, Yoo, Lee and Kim2006), meaning that the non-atmospheric initial argon (excess argon) has no significant effect on our samples.

Three of four phlogopite aliquots, comprising WZL1-1 and WZL1-2 from sample SZ16D004B1, and WZL2-2 from sample SZ16D002B2, show the ideal flat spectra encompassing 60.6 %, 76 %, and 61.3 % of the released total ³⁹Ar, yielding the well-defined high precision plateau ages of 119.18 ± 0.08 Ma, 119.16 ± 0.07 Ma, and 119.14 ± 0.23 Ma, respectively (Fig. 13a, c, e). These well-defined plateau ages of individual phlogopite aliquots are reproducible with respective total fusion ages (Fig. 13a, c, e). In addition, the three phlogopite aliquots produce the isochron ages consistent with their respective plateau ages (Fig. 13b, d, h). Therefore, the well-defined high-precision plateau ages, as well as the reproducibility of the plateau, total fusion and isochron ages, imply that the effect of minor argon loss, indicated by the relatively younger ages in the initial steps (Fig. 13a, c, e), is not significant.

The other phlogopite aliquot, WZL2-1 from sample SZ16D002B2, has somewhat perturbed age spectra (Fig. 13e). However, a pseudo-plateau age of 118.9 ± 0.3 Ma is given by 8 to 11 steps with c. 42.7 % of the released total ³⁹Ar. It is also reproducible with both the total fusion age at 118.8 ± 0.7 Ma (Fig. 13e) and the isochron age of 119.65 ± 0.43 Ma (Fig. 13f). Furthermore, the pseudo-plateau age is indistinguishable from the plateau age of aliquot WZL2-2 from the same sample SZ16D002B2 (Fig. 13e, g) and thus is considered to be geologically meaningful.

Different samples collected from the fresh and non-deformed NNE–SSW-trending lamprophyre dikes, which are moderately and steeply dipping, respectively, have plateau ages that are reproducible within uncertainties, meaning that these lamprophyre dikes formed in a single, short-lived magmatic event.

6. Discussion

The lamprophyre dikes and quartz veins in the Sizhuang gold deposit have various geometric properties regarding their orientations and sizes, revealing a complex deformational history. The lamprophyre dikes and quartz veins are dilational with mineral crystals normal to their generally rough wall surfaces in their majority. As we already mentioned, dikes are strongly affected by the mechanical properties of their host rocks and, more precisely, the host-rock lithology, stress field and pre-existing fractures (Pollard et al. Reference Pollard, Muller and Dockstader1975; Baer, Reference Baer1991). Previous studies have revealed that c. 90 % of the lamprophyre dikes trend from azimuths 0° to 040° (Li et al. Reference Li, Li, Santosh, Li, Gu, Lü, Zhang, Shen and Zhao2016), i.e. parallel to the Jiaojia Fault and the dominant Mesozoic tectonic fabric in the Jiaodong Peninsula, and only a small proportion of them trend NNW–SSE (Li et al. Reference Li, Li, Santosh, Li, Gu, Lü, Zhang, Shen and Zhao2016).

In contrast, the lamprophyre dikes in the Sizhuang gold mine are grouped into two major sets and a subsidiary one. The two main sets trend NNW–SSE and NNE–SSW, respectively, whereas a subsidiary set trends WNW–ESE. Although with various dips, the quartz veins mainly trend similarly to the NNE–SSW-trending lamprophyre dikes, suggesting their formations were penecontemporaneous. However, the quartz veins cut across the NNW–SSE-trending lamprophyre dikes sharply, indicating that the latter were formed relatively earlier than the quartz veins and the NNE–SSW-trending lamprophyre dikes. Therefore, the well-defined and high-precision plateau ages of 119.18 ± 0.08 Ma, 119.16 ± 0.07 Ma and 119.14 ± 0.23 Ma, obtained herein by the phlogopite ⁴⁰Ar–³⁹Ar dating on the NNE–SSW-trending lamprophyre dikes, indicate that the quartz veins and the NNE–SSW-trending lamprophyre dikes were formed at c. 119 Ma.

Furthermore, L Zhang et al. (Reference Zhang, Weinberg, Yang, Groves, Sai, Matchan, Phillips, Kohn, Miggins, Liu and Deng2020) performed the ⁴⁰Ar–³⁹Ar dating of muscovite from the quartz–sericite–pyrite altered granite in the Sizhuang deposit, which was cut by the lamprophyre dikes and the quartz veins. It has been well accepted that sericite and muscovite are both susceptible to isotopic resetting during thermal events and deformation (Chesley et al. Reference Chesley, Rudnick and Lee1999), as was verified by the widely divergent isotopic ages between 133 and 108 Ma by the ⁴⁰Ar–³⁹Ar dating of the sericite or muscovite in the gold deposits in the Jiaodong Peninsula (Li et al. Reference Li, Vasconcelos, Zhou, Zhao and Ma2006; Zhang et al. Reference Zhang, Dong and Shi2003; LQ Yang et al. Reference Yang, Deng, Goldfarb, Zhang, Gao and Wang2014; L Zhang et al. Reference Zhang, Weinberg, Yang, Groves, Sai, Matchan, Phillips, Kohn, Miggins, Liu and Deng2020). Therefore, it is unclear if the sericite or muscovite may have suffered later modifications. Accordingly, given the cutting relations between the lamprophyre dikes and quartz–sericite–pyrite altered granite in the Sizhuang deposit, the age of 120.5 ± 0.9 Ma by the ⁴⁰Ar–³⁹Ar dating of muscovite from the quartz–sericite–pyrite altered granite (L Zhang et al. Reference Zhang, Weinberg, Yang, Groves, Sai, Matchan, Phillips, Kohn, Miggins, Liu and Deng2020) probably reflects the emplacement age of the NNW–SSE-trending lamprophyre dikes; whereas the 120.1 ± 0.9 Ma (L Zhang et al. Reference Zhang, Weinberg, Yang, Groves, Sai, Matchan, Phillips, Kohn, Miggins, Liu and Deng2020) overlaps with, within analytical uncertainties (±2σ), the emplacement age of the NNE–SSW-trending lamprophyre dikes in the Sizhuang deposit.

The analysis and stress inversion of the available fault-slip data recorded close to the area of the Sizhuang gold deposit with the TRM defines two stress regimes, ST1 and ST2, which fit, respectively, in orientation with stress A (E–W extension during 135−121 Ma) and stress B (NW–SE extension between 120 and 93 Ma), as the latter were defined by B Zhang et al. (Reference Zhang, Weinberg, Yang, Groves, Sai, Matchan, Phillips, Kohn, Miggins, Liu and Deng2020). Based on the dating provided by those authors, ST1 is relatively older than ST2, indicating that the least principal stress axis rotated from E–W to NW–SE and the PE-TRN changed progressively to the TRN, under which the strike-slip tectonics is more prevalent. In addition, under the ST1, the trend of the activated fault is NNW–SSE, whereas under the ST2 the activated faults are those with the trends parallel to the Jiaojia Fault, i.e. NNE–SSW.

Considering the above ages for the ST1 and ST2 and the age of the lamprophyre dikes, we can conclude that the formation of the dikes and veins in the Sizhuang gold deposit occurred while a change from the stress regime ST1 to ST2 was in progress. Moreover, the geometric properties of the lamprophyre dikes and quartz veins provide details about the change from ST1 to ST2 and verify the transtension tectonics during this change.

The fuzzy clustering technique of Yamaji & Sato (Reference Yamaji and Sato2011) suggests two stress states for describing the formation of the lamprophyre dikes and two stress states for describing the formation of the quartz veins. These stress states have been grouped into three regimes A, B and C (Table 1).

As mentioned above, the strike distribution of the lamprophyre dikes peaks at NNW-trending and, to a lesser degree, along the NNE trend, suggesting abrupt changes in the trend of ${\sigma _3}$ (c. 50° flip). Furthermore, all the dikes have narrow thicknesses, with none wider than 1 m, and no multiple dyke injections were observed. Therefore, it is logical to state that the resulting stress regimes A and B imply unstable stress conditions for the formation of the lamprophyre dikes (Table 1). In contrast, the distribution of the poles to the quartz veins shows the dominance of NNE trending (Figs 7d and 9b), and the banded veins with sub-parallel bands of large thicknesses (up to 5 m) were commonly observed, reflecting rather stable stress conditions. Although the stress regimes B and C for the quartz veins indicate changes in the local stresses with time, the direction of extension ( ${\sigma _3}$ ) is always constant during quartz vein emplacement (Table 1).

Extension and strike-slip tectonics, i.e. transtension and associated pre-existing structures, affect the emplacement of the lamprophyre dikes and quartz veins. In particular, the NNW–SSE-trending and the subsidiary WNW–ESE-trending lamprophyre dikes intruded into the pre-existing fractures interpreted herein as subsidiary R and R′ Riedel shears related to a left-lateral strike-slip deformation along the main faults like the TLF during Late Jurassic times under a NW–SE or N–S compression (or transpression) (Zhu et al. Reference Zhu, Niu, Xie and Wang2010). Under this strike-slip deformation, the Jiaojia Fault, which dips with intermediate dip angles, can be seen as a flower structure, off-strike and to the east of the TLF. In particular, stress regime A, i.e. LDA, is interpreted to represent the stress conditions in the initial stages when the NNW–SSE-trending lamprophyre dikes intruded into a large number of inherited structures (Fig. 14a). Dikes’ intrusion, at least at the initial stages, was characterized by ${P_{\rm{f}}}$ relatively high in magnitude values, almost equal to ${\sigma _2}$ (Fig. 10b, c). The formation of the main bodies of the NNE–SSW-trending lamprophyre dikes and quartz veins has been dominated by WNW–ESE extension, i.e. stress regime B (i.e. LDB and QVB) (Fig. 14b). Under this stress regime, ${P_{\rm{f}}}$ was very low and smaller in magnitude than ${\sigma _2}$ , giving rise to the emplacement of the dikes and veins into the structures oriented mainly normal to the ${\sigma _3}$ axis since the fractures’ permeability was poor, with only the structures that trend as the Jiaojia Fault facilitating it. Because of this, the quartz veins cross-cut the NNW–SSE-trending dikes driven by the stress regime A. However, the girdle-type distribution of the quartz vein poles implies that their formation should include the stage dominated by the increase in fluid pressure, i.e. stress regime C (QVA). Under such conditions, the smaller pre-existing structures with a wide range of orientations can dilate, giving rise to the local geometric complexities mainly in the tips of the NNE–SSW-trending dikes and veins (Fig. 14c).

Fig. 14. Schematic cartoons (not to scale) showing the stress regime corresponding to lamprophyre dikes and quartz veins in the Sizhuang gold deposit. (a) E–W extension led to the development of the NNW–SSE-trending and subsidiary WNW–ESE-trending lamprophyre dikes. (b) WNW–ESE extension led to the development of the NNE–SSW-trending lamprophyre dikes and quartz veins at low P _f. (c) WNW–ESE extension led to the formation of quartz veins with a wide range of orientations in the tips of the NNE–SSW-trending dikes and the NNE–SSW quartz veins at high P _f.

Thus, the cross-cutting network of quartz veins and fractures and the dominance of NNE–SSW-oriented quartz veins in the Sizhuang gold deposit are attributed to ${P_{\rm{f}}}$ fluctuations between ${P_{\rm{f}}}$  >  ${\sigma _2}$ and ${P_{\rm{f}}}$  <  ${\sigma _2}$ leading to the local stress perturbations from the regional far stress field, which remains transtension with the ${\sigma _3}$ axis changing from E–W through WNW–ESE to NW–SE trend, as shown by the fault-slip analysis and their stress inversion with the TRM.

Conclusively, the lamprophyre dikes and quartz veins show ae change in extension from an E–W through WNW–ESE to NW–SE trend (Fig. 14). This change reflects a significant clockwise rotation in the palaeo-Pacific plate subduction direction, and the switching time was precisely dated by the lamprophyre dating at c. 119 Ma.