Introduction

Since the initial collision of India with Asia at about 60 Ma, the Tibetan plateau has experienced complex geologic evolution, including significant crustal shortening, large-scale tectonic deformation and intense crust-mantle interaction (Yin and Harrison 2000; DeCelles et al. 2014). It is generally accepted that the collision of India with Asia has led to large-scale uplifts of the Tibetan plateau and the rise of the Himalayas on the north edge of the Indian continent (Yin 2006; Kapp and DeCelles 2019). The collision can be generally clarified into three stages: syn-collision (65–41 Ma), late-collision (40–26 Ma), and post-collision (< 25 Ma) (Hou and Cook 2009). The post-collision stage is characterized by intense crustal extension and block horizontal movements, which developed a number of approximate N–S striking normal faults and strike-slip faults along northwest or northeast striking directions (Hou et al. 2021). With the east–west (E–W) extension of the crust, the approximate north–south (N–S) trending rifts are developed in the central and southern Tibetan plateau.

The mechanism of the crustal extension and deformation is of great significance for understanding the evolution of the Tibetan plateau, of which, the extension and the formation of N–S trending tectonic belts are closely related to the deep structure and the deep deformation. Several formation models have been proposed for the N–S trending tectonic belts of the Tibetan plateau. Some scholars have addressed the formation models controlled by regional stress fields and boundary conditions, such as lateral extrusion model, oroclinal bending model, radial spreading model, and oblique convergence model (Murphy et al. 2009; Styron et al. 2011). Alternatively, the proposed gravitational collapse model links the extension to the uplift of the plateau and the convective removal of lower lithosphere (Molnar et al. 1993). Later on, slab-tearing model has been proposed in previous studies based on the distribution and geologic characteristics of plateau rifts, potassic-ultrapotassic rocks and related deposits (Yin 2000; Hou et al. 2015). From thermodynamic point of view, thermomechanical modeling has indicated that the weak mid-lower crust is essential for the E–W extension of the plateau and the formation of N–S trending rifts (Pang et al. 2018).

Nevertheless, aforementioned models still lacked geophysical evidence to further reveal the mechanism of deep structures and processes, which can provide constraints for further understanding and evaluating various formation mechanisms of the crustal extension. The geophysical prospecting on the deep structures of the plateau revealed low-velocity and high-conductivity bodies in the upper mantle and lower crust, which might be closely related to fluid, partial melting and strength weakening. Under the guide of the magnetotelluric (MT) explorations, widely distributed high-conductivity bodies have been detected in the mid-lower lithosphere of the plateau, where the large-scale conductors should be dominantly caused by partial melting (Unsworth et al. 2005; Wei et al. 2010; Wang et al. 2017). Based on the analysis of high-conductivity bodies under the Yadong-Gulu rift, the formation of the rift is attributed to the possible tearing of Indian lithospheric slab (Wang et al. 2017; Sheng et al. 2021). Coincidentally, seismic tomography has shown that there exist low-velocity anomalies in the upper mantle under rift zones, which were interpreted to be mainly associated with the possible slab tearing and asthenospheric upwellings (Liang et al. 2016; Li and Song 2018).

However, the seismic research paid more attention on the general structures in the upper mantle beneath the central and southern Tibetan plateau. Meanwhile, it is worth noting that previous seismic studies were based on data acquired from sparse stations. Similarly, the referable MT data across the Yadong-Gulu rift, as one of the N–S tectonic belts, were recorded with sparse data stations. Therefore, these subsistent data might not be able to comprehensively reveal detailed crustal structures under N–S tectonic belts, which gives rise to the lack of systematic understanding on the crustal extension mechanism.

In this paper, another N–S trending tectonic belt in Tangra-Yumco region was chosen as the primary study area. The magnetotelluric method is effective in probing the crustal structure, especially for high-conductivity bodies. For the purpose of obtaining reliable constraints on crustal deformation and extension mechanism, a MT profile was deployed along the E–W direction with 41 dense stations and average spacing of 2.3 km across the Tangra-Yumco tectonic belt. The high-quality impedance tensor data at the periods of 0.01–2000s were obtained for the study of the crustal electrical structure. Two reliable resistivity models derived from two-dimensional (2-D) and three-dimensional (3-D) inversions can mutually provide geophysical constraints for the deformation and formation mechanism of the N–S tectonic belts, resulting in new insights on the E–W extension mechanism of the Tibetan plateau.

Geological setting

In the south of the study area located in the central Tibetan plateau (Fig. 1), the Lhasa terrane is mainly covered by Carboniferous-Permian sedimentary sequences and Jurassic-Tertiary volcano-sedimentary sequences, and Cretaceous intrusions are developed (Pan et al. 2013). The Qiangtang terrane in the north dominantly exposes Triassic-Cretaceous sedimentary sequences and Triassic-Jurassic intrusive rocks (Chen et al. 2020). Bangong-Nujiang suture zone (BNSZ) is a mélange zone containing ophiolitic rocks.

Fig. 1
figure 1

Map of topographic features, tectonic diagram, and MT stations in Tangra-Yumco region. QT: Qiangtang terrane; LS: Lhasa terrane; BNSZ: Bangong-Nujiang suture zone; BNF: Bangong-Nujiang fault

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The approximate north–south trending tectonic belts are mainly composed of rifts and normal faults on the edges of the rifts (Fig. 1). The normal faults on both sides of the Tangra-Yumco rift are inclined toward each other, and the Cenozoic thrust faults in the study area extends mainly along the E–W direction (Pan et al. 2013). The N–S striking normal faults extend intermittently northward through the BNSZ and into the Qiangtang terrane. The ages of the dikes along the N–S trending normal faults range from 18.3 ± 2.7 Ma to 13.3 ± 0.8 Ma (Williams et al. 2001). The eruption and distribution of the potassic-ultrapotassic rocks in central Tibet is closely associated with the N–S faults system, and the ages of the ultrapotassic rocks along the Tangra-Yumco rift range from 23 to 8 Ma (Zhao et al. 2006; Zheng et al. 2016). There are a series of lakes and extensional basins of varying sizes along the N–S trending tectonic belt, which are considered as the products of crustal extension (Kapp et al. 2008).

MT data acquisition, processing and analysis

Data acquisition and processing

The MT profile with dense stations has been carried out across the Tangra-Yumco tectonic belt along the E–W direction (Fig. 1). The profile with a total length of about 92 km includes 41 MT stations with an average spacing of about 2.3 km. MT data were acquired two horizontal electric field components (Ex and Ey) and two horizontal components of magnetic field (Hx and Hy), using MTU-5A instruments with recording time over 20 h. The MT data were processed using the SSMT2000 software of Phoenix Geophysics and the robust estimation algorithm proposed by Egbert (1997), converting the raw data to the high-quality impedance tensor data at periods of 0.01–2000s.

Dimensionality and strike direction

In order to determine which dimension of inversion might be suitable for this case, the phase tensor method (Caldwell et al. 2004), avoiding the influence of local electric field distortion, was conducted to assess the dimensionality of the MT dataset. The phase tensor is defined as three invariants: the maximum phase (Φmax), the minimum phase (Φmin) and the skew angle (β). The results are plotted as ellipses shown in Fig. 2 with the maximum phase as major axis and the minimum phase as minor axis, and the ellipses are colored by corresponding skew angle (β). Especially at the short period of 1 s, most of the skew angles are less than 3°, which denotes that two-dimensionality might be dominated (Booker 2014), indicating shallow quasi 2-D electrical structure of the study area. Nevertheless, a few large skew angles (> 5°) were identified at the long periods of 100 s and 1000 s, which may indicate the emergence of 3-D resistivity structures in the deep depth. Therefore, in this paper, 2-D and 3-D inversion scheme might be independently carried out for comprehensively interpretation on the shallow small-scale and deep complex structures.

Fig. 2
figure 2

Phase tensor ellipses and rose diagrams. The ellipses are colored by skew angle β at three periods (1 s, 10 s, 1000 s), and the rose diagrams represent strike angles with different period ranges of 0.01–1 s, 1–100 s and 100–2000s

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For the stage of the 2-D inversion, it is of importance to determine the strike direction to calibrate coordination system, where the MT data can be decomposed into two independent modes, i.e., transverse electric (TE) mode and the transverse magnetic (TM) mode. The strike analysis results of the phase tensor method were plotted as rose diagrams of different period range shown in the Fig. 2, indicating that the regional strike angle is approximately oriented along N–S or E–W direction. Combined with approximate N–S trending direction of the Tangra-Yumco tectonic belt, the N–S direction was chosen as the regional strike direction for the MT profile.

Data inversion

Two-dimensional inversion

After determining the strike direction, the decomposed electric field of TE mode and the magnetic field of TM mode were inverted to get a 2-D resistivity model with an initial model of 100 Ωm half space, using the nonlinear conjugate gradients (NLCG) algorithm (Rodi and Mackie 2001) in the WinGLink software package. On account of the effect of static shifts, downweighting the apparent resistivity was carried out in the 2-D inversion (Ye et al. 2019). Since the TE mode is more effective to the vertical electrical structure and the TM mode is more sensitive to the horizontal electrical variations (Becken et al. 2008), we comprehensively integrated both two modes into the inversion. The error floors of the TM mode were set as 10% and 5% for the apparent resistivity and phase, respectively. Considering the TE mode data are more easily affected by 3-D effects than the TM mode data, the error floors for the apparent resistivity and phase of the TE mode were set as 40% and 20%. After analyzing the L-curve shown in Fig. 3, the regularization factor τ was set to 5 (Farquharson and Oldenburg 2004). The ratio between the horizontal and vertical smoothing factors was set to 1. After 100 iterations, the root-mean-square (RMS) misfit decreased from 6.332 to 1.117 with the period of 0.01–2000s. Combined with the comparison of pseudosections in Fig. 4, global and site-by-site RMS misfits (Fig. 5a) show the high degree of fitting between calculated model response and measured data. The 2-D recovered resistivity model is shown in Fig. 5c, representing high resistivity of the upper crust and a significant high-conductivity body (C1) in the mid-lower crust.

Fig. 3
figure 3

Illustration of the relationship between RMS and roughness corresponding to different τ values. Regularization τ = 5 (red dot) was chosen at the inflection point in the L-curve

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Fig. 4
figure 4

Pseudosections of measured data and calculated model response. a TM mode, b TE mode

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Fig. 5
figure 5

Two-dimensional inversion resistivity model and tectonic interpretation. a Global and site-by-site RMS distribution. b Topography along the MT profile. c Resistivity model with tectonic interpretation and earthquakes. Black dashed lines are inferred faults, and green dots are the projection of the earthquakes (M > 3) from 1970 to 2022 within the latitude range of 0.5° on both sides of the MT profile. Black triangles above the resistivity model represent MT stations

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After obtaining the 2-D resistivity model, it is important to conduct sensitivity tests to confirm whether the model corresponds with the measured data. In this paper, the sensitivity was determined by editing the original 2-D resistivity model and comparing the discrepancy of fitting conditions before and after the modification. As shown Fig. 6, the changes in the low boundary of the original resistivity model led to obvious increases in the global and site-by-site RMS misfit values. The test results show that the measured data are sensitive to the changes of electrical structure.

Fig. 6
figure 6

Illustration of sensitivity tests for 2-D inversion model. a Comparison of RMS misfits between 2-D original resistivity model and edited models. b The edited model-1 filling with 1000 Ωm below the depth of 60 km. c The edited model-2 filling with 1000 Ωm below the depth of 75 km

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Three-dimensional inversion

Since the MT dataset showed the three-dimensionality features, 3-D inversions were subsequently conducted using the ModEM software (Egbert and Kelbert 2012; Kelbert et al. 2014). The full impedance elements (Zxx, Zxy, Zyy, Zyx) were inverted with 36 periods ranging from 0.01 to 2000s. The error floor for off-diagonal elements was set to 5% of |Zxy × Zyx|1/2 and 10% for diagonal elements. The model space was discretized with horizontal grid spacing of 1.4 km × 1.4 km in the core area and padded with 12 cells on all edges, where the grid spacing gradually increase with a factor of 1.5. The model area was designed from − 550 to 550 km along the x-axis and y-axis, respectively. In the vertical direction, the thickness of the first layer was set to 50 m and 63 layers were included. Similarity as the horizontal discretization, the thicknesses of the upper 55 vertical layers gradually increased with a factor of 1.1, and the thicknesses of the rest 8 layers below were padded with an increasing factor of 1.5. The total depth of the model was up to 668 km. The 3-D inversion started from an initial model of 100Ωm half space. After 100 iterations, the global RMS misfit decreased from 6.65 to 1.406. Figure 7 shows the fitting behaviors of apparent resistivity and phase at station 16 and 24, respectively, and the RMS misfits of most stations shown in Fig. 8a are less than 2, indicating that the measured data and model responses are well-matched. The 3-D resistivity model is shown in Fig. 8c, one can see that although there are some discrepancies in the shape of abnormal bodies as the 2-D result, the 3-D inversion remains the main features of the electrical structures in the subsurface.

Fig. 7
figure 7

Fitting behaviors of apparent resistivity and phase at station 15 and 24, respectively. Symbols of circles and squares represent measured Ex–Hy and Ey–Hx, respectively. Solid lines correspond to model responses of 3-D inversion model

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Fig. 8
figure 8

Three-dimensional inversion resistivity model and tectonic interpretation. a Global and site-by-site RMS distribution. b Topography along the profile. c Resistivity model with tectonic interpretation and earthquakes. Black dashed lines are inferred faults, and the green dots are the projection of the earthquakes (M > 3) from 1970 to 2022 within the latitude range of 0.5° on both sides of the MT profile. Black triangles above the resistivity model represent MT stations

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As shown in Fig. 9, changes in the low boundary of the original resistivity model of the 3-D inversion lead to significant increases in the global and site-by-site RMS misfit values. The test results show that the observed data are sensitive to the changes of electrical structure at the bottom as well.

Fig. 9
figure 9

Illustration of sensitivity tests for 3-D inversion model. a Comparison of RMS misfits between 3-D original resistivity model and edited models. b The edited model-3 filling with 1000 Ωm below the depth of 60 km. c The edited model-4 filling with 1000 Ωm below the depth of 75 km

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In summary, as shown in Fig. 5c and Fig. 8c, the inversion models provide detailed resistivity structures of the N–S trending tectonic belt in Tangra-Yumco region, revealing the obvious electrical discrepancy between the upper and the mid-lower crust. One can see that the upper crust is characterized by high resistivity, and the mid-lower crust shows the feature of high conductivity. There are two high-resistivity bodies (R1 and R2) identified in the upper crust and a large-scale high-conductivity body (C1) in the mid-lower crust under the N–S trending tectonic belt.

Interpretation and discussion

Origin and analysis of the conductor C1

It is worth noting that the remarkable and uniform feature of both 2-D and 3-D inversion results is the conductor (C1) with a trend of extending to the deep lithosphere in the mid-lower crust and against the bottom of the upper crust (Fig. 5c and Fig. 8c). Previous seismic studies have revealed lateral variations along the N–S trending tectonic belts in southern Tibet by the SKS-wave splitting measurements and the obvious differences in subduction angles of the Indian lithospheric slab by receiver function techniques (Chen et al. 2015; Zhao et al. 2010), which indicate the increases in the subduction angles from west to east and the possible slab tearing. Seismic tomography shows a series of low-velocity anomalies in the upper mantle under the N–S rifts (Liang et al. 2016; Li and Song 2018), which suggest the possible slab tearing and local asthenospheric upwellings. Furthermore, the distribution of the potassic-ultrapotassic rocks along the N–S trending tectonic belts might infer the upwelling of the asthenosphere and partially molten lithospheric mantle (Zhao et al. 2006; Zheng et al. 2016; Guo and Wilson 2019; Hou et al. 2021). Therefore, the conductor C1 recovered from the 2-D and 3-D inversions might be induced by the upward migration of hot mantle materials (Fig. 11).

Previous studies have suggested that partial melting or aqueous fluids are the most likely cause for the large-scale high-conductivity bodies in southern Tibet (Unsworth et al. 2005; Chen et al. 2018). The studies on granulite xenoliths in the north of our study area have inferred the high-temperature state of the lower crust (Hou et al. 2021). There exist high heat flow values around the Yarlung-Zangbo suture zone and N–S rift zones in southern Tibet (Francheteau, et al. 1984; Jiang et al. 2016). Under the high-temperature thermal state, aqueous fluids that can lower the melting point are unlikely to be preserved in the mid-lower crust for long term of geologic timescales. As discussed above, the high-conductivity body (C1) should be dominantly caused by partial melting.

For quantitatively estimating the melt fraction of the conductor C1, we used the modified Archie’s law that is suitable in southern Tibet (Rippe and Unsworth, 2010; Bai et al. 2010). The law can be expressed as:

$$\rho_{{{\text{eff}}}} = A^{ - 1}_{{{\text{eff}}}} \Phi^{ - n} \rho_{{\text{m}}},$$

where ρeff represents the bulk resistivity, Φ is the melt fraction, and ρm is defined as pure melt resistivity. It was suggested to set the coefficients Aeff and n as 1.47 and 1.3, respectively (Ten Grotenhuis et al. 2005). The ρm was assumed to be 0.1–0.3Ωm (Unsworth et al. 2005). For a given thickness, the bulk resistivity is determined by the ratio of conductance to thickness. The bulk resistivity of conductor C1 is about 6 Ωm.

Laboratory experiments showed that 5–7% melt fraction of aplite can reduce its effective viscosity by an order of magnitude (Unsworth et al. 2005; Rosenberg and Handy 2005). As shown in Fig. 10, the melt fraction is about 3.0–7.5%, which reaches the amount required for strain localization in geodynamic models (Beaumont et al 2001). Based on above analysis, the increase in melt fraction can significantly reduce the effective viscosity and strength of the crust, and the conductor C1 under the Tangra-Yumco tectonic belt meets the condition for deformation.

Fig. 10
figure 10

Relationship between bulk resistivity and melt fraction. The pure melt resistivity is assumed as 0.1–0.3 Ωm. The bulk resistivity of the high-conductivity body (C1) is about 6 Ωm, and the melt fraction range is shown as the shaded area

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Formation mechanism of the N–S tectonic belt

It shows that the apparent discrepancies between the upper and the mid-lower crust can be roughly differentiated at the depth of about 30 km. As shown in Fig. 5c and Fig. 8c, the distribution of the earthquakes collected adjacent to the profile are coincidentally around the edges of the two high-resistivity bodies (R1 and R2) above the differentiated depth. Given that earthquakes usually occur within brittle crust by strain accumulation and brittle deformation, we infer that the area around the differentiated depth might be considered as a transition zone connecting the ductile mid-lower crust with the brittle upper crust.

Under the guide of the aforementioned mechanism of the slab tearing and asthenosphere upwelling (Fig. 11a), the partial melting of the mid-lower crust (conductor C1) under the N–S tectonic belt can significantly reduce its viscosity and strength, which meets the condition for strain localization and deformation. The upward migration of the hot mantle materials could have driven the expansion and deformation of the partially molten crust (conductor C1) (Fig. 11b). In addition, referring with topography and the extending trend of N–S normal faults, we infer three concealed normal faults of the brittle crust throughout three apparent relative low resistivity zones and along the lateral electrical discontinuity boundaries (Fig. 5 and Fig. 8). Moreover, the thermomechanical modeling results have suggested that the weak mid-lower crust is essential for the E–W extension of the plateau and the formation of N–S rifts (Pang et al. 2018). Therefore, the expansion and deformation of the conductor C1 could have pulled the brittle upper crust and subsequently caused the significant E–W extension, leading to the formation of the approximate N–S trending rift and normal faults. With the upward migration of the hot mantle materials, the magmatism should develop, and the high-resistivity bodies (R1 and R2) are most likely to reflect the presence of intrusive rocks (Fig. 5c and Fig. 8c).

Fig. 11
figure 11

a Slab-tearing model; b The mechanism of E–W extension. Slab tearing might induce the upwelling of asthenosphere and partial melting of the Lithospheric mantle and mid-lower crust under the N–S tectonic belt. The upward migration of hot mantle materials could have driven the expansion and deformation of the partially molten crust with low viscosity and strength, which could have pulled the brittle upper crust and cause significant E–W extension, resulting in the formation of approximate N–S trending rift and normal faults

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Conclusions

The MT profile across the approximate N–S trending tectonic belt was carried out, and the results from the 2-D and 3-D inversions have provided the detailed resistivity models for the study on the deep structure and formation mechanism of the E–W extension in the Tibetan plateau. The conductor C1 should be caused by partial melting with the estimated melt fraction as 3.0–7.5%, which should lead to the low viscosity and weak strength of the mid-lower crust under the N–S trending tectonic belt. Comprehensively combined with the characteristics of seismic anomalies, tectonic activities and potassic-ultrapotassic magmatism, the conductor C1 is most likely induced by the asthenospheric upwelling through the slab-tearing window and the upward migration of the hot mantle materials, further providing partial evidence for the existing slab-tearing model for the E–W extension of the plateau. The inversion models revealed the brittle upper crust characterized by high resistivity and the ductile mid-lower crust with high conductivity. The upward migration of the hot mantle materials should have driven the expansion and deformation of the conductor C1, which, in subsequent, could have pulled the brittle upper crust, resulting in the E–W extension of the plateau and the formation of N–S trending rift and normal faults.