Introduction

Knowing how and how much felsic crust was consumed during collision plays a critical role in addressing the key problem of continental dynamics. According to the plate tectonics theory, continental crust (CC), especially the felsic upper and middle continental crust (UCC and MCC), cannot subduct due to its buoyancy. Therefore, most, if not all, of the felsic crustal mass will be preserved in continental collision zones or eroded by the surface process. Consequently, the continent-continent convergence is generally slower and more short-lived than oceanic plate subduction. By considering crustal thickening, surface erosion and tectonic escape, previous studies revealed a loss of ~50% of the pre-collisional crustal mass between India and Asia in the archetype of active collisional systems, the Himalayas1. The Greater Indian Oceanic Basin hypothesis2 and the subduction of mafic Indian lower continental crust (LCC) after UCC scrapoff3 have been invoked to explain the loss of crust. However, it remains a contentious issue for the missing (felsic) crustal mass of the Greater Indian Continent. Another puzzling issue is the driving force for the unusually fast and long-lasting convergence (18–4 cm/yr) of the Indian-Asian continental collision. Many hypotheses have been proposed: (1) the negative buoyancy of the Greater Indian lithosphere without UCC3, (2) the push of the Indian Ocean ridge4, and (3) the drag from the neighboring oceanic slab pull beneath Burma5. However, these existing hypotheses and models have great difficulty in explaining multiple facts, including the imbalance of crustal mass, the rapid convergence rate, and the long collisional period. A key problem is that all the aforementioned explanations assumed that the felsic UCC and MCC are buoyant, but ignored the effect of metamorphic phase transformation on their density under ultrahigh pressure conditions.

Below, we will first evaluate the mass deficit of felsic crust in the Greater Indian continent, then explore the density evolution of CC and the effect of metamorphic densification on continental subduction evolution using both a petrological-thermo-mechanical model and a simplified analytical model. Our results show that the phase transition-induced densification of subducted continental crust provides a large slab pull force when it is dragged below a depth of about 170 km, which consequently drives the long-lasting fast convergence between India and Asia and accounts for the mass imbalance of felsic crust in Greater Indian continent.

Results and discussion

Mass imbalance in the felsic crust of Greater Indian continent (GIC)

Previous calculations of the crustal mass deficit have focused on the whole India-Asia collisional orogen1,6,7. In order to better understand the behavior of felsic crust during continental subduction, we focus on the GIC and reassess its mass balance of UCC/MCC. Greater India is the part of the Indian plate that has been consumed since the onset of Cenozoic continental subduction and collision. However, the extent of GIC from reconstructions varies greatly from ~900 km to ~2600 km (Supplementary Table 1). Using the relatively well-constrained pre-collisional data of Greater India1,6,7,8,9 and the global average UCC and MCC crustal thickness of 23 km10, we derive the volume of Greater Indian felsic crust, ranging from 7.13 ± 0.69 × 107 km3 to 10.81 ± 1.15 × 107 km3 (Supplementary Table 2). After collision, the Greater India-derived continental felsic crust is mainly preserved in the Himalaya fold-thrust belt11. Besides, the seismic reflection profiles indicate that the Indian-affinity UCC/MCC is rarely transported northwards beyond the Yarlung Zangbo suture or added into the Lhasa and Qiangtang terranes12, which means the modern Himalaya thrust belt conserves the major pre-collisional Greater Indian UCC/MCC except for the surface erosion and lateral extrusion. The Himalaya thrust belt occupies an area of ~0.83 × 106 km2 with an average crustal thickness of 57 km6. Even under an extreme assumption that the entire Himalayan crust is felsic, the volume of felsic crust in the Himalaya domain is only 4.73 × 107 km3. On the other hand, we use an average erosion rate of about 0.25 km/Ma since 50 Ma13 to obtain the erosional volume flux in GIC of 10.38 × 106 km3, which is consistent with the previous estimate of the erosional volume of ~10.4 × 106 km3 in Himalaya6. Another possible contribution in estimating the mass balance of GIC is the lateral extrusion of crustal blocks. However, the southeastward material extrusion generally occurred with the deformed Asia domain14, whereas the escaped felsic crust of GIC is negligible and thus ignored in our evaluation. Therefore, if there is no subduction of felsic crust, the UCC/MCC crustal volume of GIC must balance the net volume of UCC/MCC in the present Himalaya and that being eroded. However, the final results (Supplementary Table 2) reveal the missing GIC felsic crust of 1.36 × 107 km3 to 5.04 × 107 km3, or ~20–47% of the pre-collisional UCC/MCC, based on different reconstructions of GIC1,6,7,8,9. It is worth noting that the estimate is just the lower limit of mass deficit due to an overestimate of the UCC/MCC thickness in the present Himalaya. These results may imply that a significant amount of Greater Indian felsic crust is subducted and recycled into the mantle.

Phase transition-induced densification of subducting continental crust

The density of CC in the subduction channel plays an essential role in controlling the continental deep subduction or not15. Previous experimental studies have explored the phase transitions and density profiles of continental crust16,17,18. Here, we use Perple_X to compute the phase relations and densities for the average UCC, MCC, and LCC compositions10 (Supplementary Table 3) in the pressure (P)–temperature (T) range of 0–24 GPa and 0–1800 °C. The density of UCC lies in the range of ~2420-4380 kg/m3 (Fig. 1 and Supplementary Fig. 1a). Within the P–T range of interest (2–10 GPa, 400–1800 °C), the P–T–density (ρ) diagram of UCC (Fig. 1) reveals four major density jumps. The first jump, with an increase of density by up to 75–90 kg/m3 at ~2.7 GPa, is caused by the phase transition from quartz to coesite. The phase transitions of feldspars at 5.5–7 GPa, i.e. microcline –> K-wadeite or plagioclase-kalsilite –> K-wadeite, result in the second density jump (by 120 kg/m3), which brings the UCC density closer to that of the mantle at the same depth. The third dramatic density jump by 380–400 kg/m3 was induced by the phase transition from coesite to stishovite at 7–9 GPa, after which UCC becomes ~400 kg/m3 denser than the surrounding mantle and can provide a large driving force for continental subduction. Finally, the phase transition of K-wadeite –> K-hollandite (Liebermannite) occurs at 8–9 GPa, with the fourth major density jump of 80–90 kg/m3.

Fig. 1: The 3D density evolution of the chosen average UCC composition.
figure 1

The white lines denote the major metamorphic phase transitions controlling the density increase of UCC. The four major density jumps with characteristic values are shown in white. The stable mineral assemblages are shown. Mineral abbreviations are: cpx clinopyroxene, gt garnet, pl plagioclase, ky kyanite, mic microcline, kls kalsilite, wa K-wadeite, hol K-hollandite, coe coesite, stv stishovite.

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In order to verify the phase diagram with P–T-dependent density evolutions, we further extract the density profiles of UCC along three different P–T paths in the cold, normal and hot subduction channels, respectively. The results are comparable with previous experimental studies16,17,18 (Supplementary Fig. 2). On the other hand, the density evolution of MCC is comparable to that of UCC (Supplementary Fig. 1a, b) due to their similar bulk compositions. Similarly, the density of mafic LCC is comparable to that of MORB (Supplementary Fig. 1c, d).

The sensitivity tests with different crustal compositions10 (Supplementary Table 4) are further conducted and compared with the reference model (Supplementary Fig. 3 and 4). The density profiles of UCC along a typical subduction P–T path with different bulk-rock compositions indicate that the higher Si content reduces the density of UCC at P < ~8 GPa, but increases its density at P > ~8 GPa (Supplementary Fig. 3), with the density reversal mainly due to the phase transition of coesite –> stishovite. The density variation induced by different Si content is about −2.79%~3.53% (Supplementary Fig. 4). On the other hand, the effects of variable XMg [MgO/(MgO+FeO)], XAl [Al2O3/(Al2O3 + MgO+FeO)] and XCa [CaO/(CaO+MgO+FeO+Na2O)] on the density evolution are negligible, with even low-density variations of −0.63%~0.31%, −0.37%~0.54%, −0.32%~0.35%, respectively (Supplementary Fig. 4). The effect of hydration state of subducted UCC on their density evolution was further tested by conducting two end-member models: UCC_NAn (H2O = 1 mol.%)19 and UCC_MHy (H2O = 9.1 mol.%)20. The results (Supplementary Fig. 5) show that the subducted UCC in the fluid-absent system is ~100 kg/m3 denser than the hydrated felsic crust, especially at HP condition (P < 2.7 GPa). However, after the third density jump induced by the phase transition from coesite to stishovite, even UCC_Mhy with a high water content becomes ~300 kg/m3 denser than the surrounding mantle at ~8 GPa and thus can provide high enough driving force for continental subduction. Consequently, the possible composition variation and hydration state of UCC does not play a critical role in the density evolution and thus will not affect the general perspective of this study.

Integrated petrological-thermo-mechanical modeling of continental subduction

In order to better understand the role of phase transition-induced density evolution on the dynamics of continental subduction, the P–T-dependent density database (see Methods) is further integrated into a thermo-mechanical numerical model using 2-D finite difference code I2VIS21,22. The original model consists of Greater Indian and Asian continents on the left and right sides, respectively, with a section of Neo-Tethyan oceanic plate in between (Fig. 2a). The subducting plates are pushed internally by a prescribed velocity of 10 cm/yr for 7 Myrs, with a total convergence of 700 km (Fig. 2b). It leads to a snapshot with the beginning of continental collision, after which the prescribed constant convergent velocity is cancelled, leaving the continental subduction driven purely by the negative buoyancy of the slab.

Fig. 2: The model results of continental subduction with two different density evolutions.
figure 2

a Original model configuration with a subducting continental plate, an overlying continental plate on both sides and a subducting oceanic plate in between. The subducting plates are pushed internally by a constant velocity of 10 cm/yr for 7 Myrs. b The beginning of continental collision after 7 Myr. This snapshot is used as the initial model for the following study, which is pure density-driven free subduction without any pushing. Two different continental density structures are further applied in Model-I and Model-II. c, d Evolution of Model-I without phase transition. e, f Evolution of Model-II with phase transition and metamorphic densification. The inset figure in f shows the continuous subduction of a part of the felsic crust. g The density structure of continental subduction zone in f. h The convergence velocity evolutions of Model-I and Model-II (left axis) and the accumulated recycled volume of subducted felsic continental crust in Model-II (right axis).

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In the following study, the initial collision scenario (Fig. 2b) is employed as the initial model. Two different models with contrasting density evolutions are further applied and compared. In Model-I, the density is linearly dependent on pressure and temperature, but does not include any phase transition. In contrast, Model-II incorporates our calculated density database with multiple phase transitions and density jumps (Supplementary Fig. 1). The results of Model-I (Fig. 2c, d) show that the continental lithosphere subducts with a low convergence velocity of ~1 cm/yr for about 2 Myrs (Fig. 2h) dragging by the preceding oceanic slab. The accumulated buoyancy of subducted continental crust resists and finally terminates the subduction process, with the oceanic slab break-off occurring at the end. The results of Model-II (Fig. 2e, f) show that the continental plate is firstly dragged into mantle by the subducted oceanic slab, with a high velocity of ~8.5 cm/yr (Fig. 2h). The continuous subduction of low-density felsic crust decreases the convergence velocity gradually, to a low value of ~4 cm/yr (Fig. 2h). However, the deep continental subduction leads to phase transitions of silicates in the felsic crust and results in remarkable density increase (Fig. 2g). Consequently, the increasing negative buoyancy of continental plate contributes to faster subduction with a peak convergent velocity of ~12 cm/yr (Fig. 2h). During collision, a large portion of felsic crust is gradually scraped off and enters the orogenic system of Himalaya fold-thrust belt. Meanwhile, a certain amount of UCC/MCC subducts with the sinking slab and is recycled into the deep mantle (Fig. 2f). The cumulative recycled volume of felsic crust is calculated to be ~26% of the initial felsic crust in the left continent at the model time of 20 Ma when the entire subducting continental plate is consumed (Fig. 2h).

It is worth noting that the resultant convergent velocity in the simple numerical model (Fig. 2h) is not aimed to match the exact kinematic evolution of the natural Indian-Asian collision system, because the latter has a complex tectonic evolution history and differential subduction in eastern and western Himalayas11,23. However, the integrated petrological-thermo-mechanical model indicates that the phase transition-induced densification of deeply subducted felsic crust could be involved to explain not only the mass deficit of GIC, but also the driving force for long-lasting Indian-Asian convergence. In addition, the intermittent subduction with frequent slab break-off episodes may be a characteristic phenomenon on the Earth24, and the slab pull caused by phase transformation at ~9 GPa may change the intraplate stress and induce slab break-off. We speculate that the multi-stage reduction of India-Asia convergence velocity6,23 may be caused by the multiple break-offs of subducted continental lithosphere, although it is not reconciled in the current simple model.

The continental crust is generally considered to be relatively dry, compared to the hydrous oceanic crust. Thus, the time scale of reaction kinetics may not be ignored in the case of dry or low water-content systems, and the metastable phases of mineral assemblages would hamper the densification of the subducted continental crust25. Besides, the large-scale metastability of subducted UCC has been observed in some continental metamorphic terranes25. Here, we systematically evaluate the effect of metamorphic transformation degree (φ) on the subduction process of continental lithosphere (see Methods). The result (Supplementary Fig. 6) indicates that when the metamorphic transformation degree of subducted felsic crust is >70%, the continental slab can spontaneously subduct under its own negative buoyancy. In contrast with φ < 70%, the metastability of subducted UCC significantly decreases the density, hinders the on-going subduction, and eventually terminates continental collision. Therefore, the degree (φ) of metamorphic transformation in UCC plays a crucial role in the density evolution and subduction dynamics; however, it is difficult to quantify the φ in the progressive stages of subduction based on the natural metamorphic rocks after the retrograde exhumation25.

Analytical examinations of continental slab pull with metamorphic densification

The phase transition-induced density evolution is further coupled with a typical P–T structure of subduction zone26 (Fig. 3a and see Methods), which shows dramatic density changes of the subducted CC, especially UCC/MCC (Fig. 3b), due to the major phase transitions, e.g., quartz → coesite → stishovite (2633 kg/m3 → 2910 kg/m3 → 4290 kg/m3) and kalsilite/microcline → K-wadeite → K-hollandite (2600/2560 kg/m3 → 3110 kg/m3 → 3890 kg/m3). The UCC at the top of the slab experiences more intense conductive heating and reaches the great density jump of about +350 kg/m3 at 240–250 km; the MCC is slightly colder due to the less conductive heating which leads to a similar density jump at a relatively shallow depth due to the positive Clapeyron slope of coesite → stishovite. After the transformation from K-wadeite to K-hollandite in the depth range of 240–270 km, the whole CC, especially UCC and MCC, is about 450 kg/m3 denser than the surrounding mantle and can thus provide a great slab pull force.

Fig. 3: The density variation and slab pull of continental crust with metamorphic densification.
figure 3

a The thermal structure of the subducted continental lithosphere above 660D (see Methods). b The density variation of the subducted continental lithosphere above 660D.The dashed lines are the interfaces between MCC, LCC, and LM. Mineral abbreviations are: qtz quartz, coe coesite, stv stishovite, mic microcline, kls kalsilite, wa K-wadeite, hol K-hollandite, wad wadsleyite, ring ringwoodite. c The slab pull of subducted CC, OC, and the entire slab along the prescribed subduction channel above 660D during the transition from oceanic subduction to continental collision, where \({{{{{{\rm{L}}}}}}}_{{{{{{\rm{CC}}}}}}}\) is the length of the subducted CC increasing from 0 to \(\frac{660}{{{\sin }}{{\theta }}}\) km (θ = 30° is the prescribed subduction angle), \({{{{{{\rm{L}}}}}}}_{{{{{{\rm{OC}}}}}}}\) is the length of the residual subducted OC above 660D (\({{{{{{\rm{L}}}}}}}_{{{{{{\rm{OC}}}}}}}=\frac{660}{{{\sin }}{{\theta }}}-\,{{{{{{\rm{L}}}}}}}_{{{{{{\rm{CC}}}}}}}\)). d The slab pull of CC, UCC, MCC, and LCC during the continental subduction, indicating the contributions of \({{{{{{\rm{F}}}}}}}_{{{{{{\rm{UCC}}}}}}}\), \({{{{{{\rm{F}}}}}}}_{{{{{{\rm{MCC}}}}}}}\), and \({{{{{{\rm{F}}}}}}}_{{{{{{\rm{LCC}}}}}}}\) to\(\,{{{{{{\rm{F}}}}}}}_{{{{{{\rm{CC}}}}}}}\). For \({{{{{{\rm{D}}}}}}}_{1}\approx 170\,{{{{{\rm{km}}}}}},\) \({{{{{{\rm{F}}}}}}}_{{{{{{\rm{CC}}}}}}}=0{{{{{\rm{N}}}}}}/{{{{{\rm{m}}}}}}\), indicating the body force of the entire CC becomes >0 when the continental slab sinking deeper than ~170 km; and for \({{{{{{\rm{D}}}}}}}_{2}\approx 320\,{{{{{\rm{km}}}}}},\) \({{{{{{\rm{F}}}}}}}_{{{{{{\rm{UCC}}}}}}}=0{{{{{\rm{N}}}}}}/{{{{{\rm{m}}}}}}\), indicating the body force of the entire UCC become >0 when the UCC sinking deeper than ~320 km. The slab pull evolutions of CC with different subduction angles are shown in Supplementary Fig. 8.

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By analytical model of density evolution in continental subduction zone, we reevaluate the slab pull of OC, CC, and the entire slab (OC + CC) (\({{{{{{\rm{F}}}}}}}_{{{{{{\rm{OC}}}}}}}\), \({{{{{{\rm{F}}}}}}}_{{{{{{\rm{CC}}}}}}}\) and \({{{{{{\rm{F}}}}}}}_{{{{{{\rm{total}}}}}}}\), respectively) above 660-km discontinuity (660D), from oceanic subduction to continental collision (see Methods).The result (Fig. 3c) shows that \({{{{{{\rm{F}}}}}}}_{{{{{{\rm{OC}}}}}}}\) is largest at the beginning with a value of up to 1.0 × 1013 N/m when the OC is completely subducted and continental collision starts. Assuming there is no break-off between OC and CC, the total body force \({{{{{{\rm{F}}}}}}}_{{{{{{\rm{total}}}}}}}\) is always positive (\({{{{{{\rm{F}}}}}}}_{{{{{{\rm{total}}}}}}}\) > 0). This means that even if the UCC and MCC have not been scraped off, the entire CC can still be dragged by the preceding oceanic slab into the mantle, even to the bottom of the mantle transition zone (MTZ). With continuous subduction, the residual oceanic slab above 660D is shorter and shorter and finally \({{{{{{\rm{F}}}}}}}_{{{{{{\rm{OC}}}}}}}\) goes down to zero (Fig. 3c). In contrast, \({{{{{{\rm{F}}}}}}}_{{{{{{\rm{CC}}}}}}}\) firstly decreases to a minimum of \(-1.6\times {10}^{12}{{{{{\rm{N}}}}}}/{{{{{\rm{m}}}}}}\) at a depth of ~90 km and then gradually increases to a high value of \(4.0\times {10}^{13}{{{{{\rm{N}}}}}}/{{{{{\rm{m}}}}}}\) (Fig. 3c) due to the eclogitization of mafic LCC and the phase transformations of silicates in UCC and MCC. The high \({{{{{{\rm{F}}}}}}}_{{{{{{\rm{CC}}}}}}}\) is in the same order of magnitude as the downward gravitational body force of the descending oceanic lithosphere caused by thermal contraction and elevation of the olivine phase change (F = 3 ~ 5 × 1013 N/m), which was previously regarded as the dominant force driving plate tectonics27. Therefore, after considering the metamorphic phase transition and densification, the negative buoyancy of CC (without slab break-off) is sufficient to sustain the fast and continuous convergence between the Indian and Asian plates. Further on, the slab pull forces of UCC, MCC and LCC are calculated separately, in order to understand their relative contributions to the entire\(\,{{{{{{\rm{F}}}}}}}_{{{{{{\rm{CC}}}}}}}\) (Fig. 3d). The result shows the maximum driving forces of UCC, MCC, and LCC are 9.0 × 1012 N/m, 1.2 × 1013 N/m and 2.4 × 1013 N/m, respectively, and account for 20%, 26%, and 54% of\(\,{{{{{{\rm{F}}}}}}}_{{{{{{\rm{CC}}}}}}}\). Thus, with the metamorphic phase transition and induced densification, \({{{{{{\rm{F}}}}}}}_{{{{{{\rm{CC}}}}}}}\) is in the same order of magnitude with \({{{{{{\rm{F}}}}}}}_{{{{{{\rm{OC}}}}}}}\).

In the above calculations, the whole continental plate is presumed to subduct together, which is however not the case for the natural Earth, because a large portion of felsic crust could be scraped off when entering the subduction channel which, for example, contributes to the formation of Himalaya range in the Indian-Asian collision system. Thereby, we further calculate the slab pull of subducted CC after different thicknesses of UCC/MCC being scraped off (Supplementary Fig. 7a). The results show a clear positive correlation between the slab pull and the degree of scraping (Supplementary Fig. 7b). For example, if ~20–47% of the pre-collisional UCC/MCC is recycled into the mantle, i.e. the possible case for GIC, the slab pull of subducted GIC ranges from ~2.93 × 1013 N/m to ~3.38 × 1013 N/m which is high enough to drive continuous subduction.

The metamorphic phase transition and densification offer a key to re-exploring the fate of subducted CC. At the beginning of continental collision, the subduction of buoyant CC into the mantle levels must be assisted by the drag of the high-density oceanic slab. When the CC reaches a critical depth of ~170 km (D1 in Fig. 3d), it is negatively buoyant after the major phase transitions, i.e. \({{{{{{\rm{F}}}}}}}_{{{{{{\rm{CC}}}}}}} > 0\). Accordingly, if the break-off of the subducted slab occurs below 170 km, the negative buoyancy of the entire CC can still drive the continuous continental subduction. In contrast, a slab break-off at a shallower depth would impede further subduction of CC. On the other hand, if the continental plate subducts continuously to about 320 km (D2 in Fig. 3d), the UCC layer itself is negatively buoyant. This means that even if the UCC is decoupled from the subducting slab, it can still sink by itself to the bottom of MTZ.

Deep subduction and recycling of felsic crust in Greater India and globally

The deep subduction of the Greater Indian continent is revealed by many geological and geophysical observations. Metamorphic rocks of the India-Asia collision system provide crucial insights into deep subduction processes. In the Tso Morari and Kaghan massifs, the coesite-bearing eclogites indicate the Indian continent has subducted to a minimum depth of 90 km28,29. Moreover, according to conventional geothermobarometry, the ultrahigh-pressure (UHP) coesite-bearing eclogites in Tso Morari show a peak pressure of around 44–48 kbar at 560–760 °C and indicate a deep subduction depth of about 160 km30, which is approaching the critical depth (i.e. 170 km). However, the extremely high metamorphic pressure of up to 4.8 GPa is argued to be overestimated due to mineralogical disequilibrium25. The huge discrepant P–T estimates of Tso Morari and Kaghan terranes over a smally length scale are incomprehensible, and diamond has not been identified in Tso Morari under ~4.8 GPa25. In addition, the Oligocene-Miocene ultrapotassic rocks and the latest Eocene Quguosha gabbros in the Lhasa block (i.e. the overriding plate of Indian subduction) originated from relatively deep levels, with exceptional depletion in Nb-Ta-Ti, significant enrichment in LILE, LREE and Sr-Nd isotopic composition; these geochemical signatures are generally considered to result from the addition of a large amount of sediment derived from the subducted Indian UCC to the mantle31,32. The deep subduction of Indian UCC and MCC could have provided abundant potassium for the Eocene-Oligocene K-rich magmatism widespread in the Lhasa terrane from west to east. Additionally, many seismic tomographic images reveal that the Indian lithosphere is subducted to mantle depths6,33,34,35, although it is challenging in identifying subducted felsic crust from the Indian lithosphere due to the limit of tomographic resolution.

The combined thermodynamic phase transition, thermo-mechanical numerical modeling and slab pull force analyses imply that the deep subduction of CC in continental collision belts may play a crucial role in the global crustal recycling and the reconstruction of CC growth and preservation throughout geological history36. According to our results of mass reconstruction and numerical modeling, ~20–47% of the felsic crust in Greater India is subducted and recycled into the mantle. Assuming an average convergence of 5 cm/yr along a ~2500 km long suture zone, we estimate that the average recycling rate of Indian UCC and MCC is about 0.58-1.35 AU (km3/yr), which is comparable with previous estimates of recycling oceanic sediments flux36 (~1.4 AU). On the other hand, abundant input of felsic crust into deep mantle contributes significantly to the mantle properties and geochemical heterogeneities37. Some recognized mineralogical evidences in global, well-studied UHP terranes also demonstrate the subduction and exhumation of CC from deep levels of the upper mantle (Supplementary Table 5 and Fig. 9). It is noteworthy that the exhumed rocks from the deeper upper mantle, i.e. >8 GPa, is generally rare, which should be accompanied with and dragged by other buoyant materials; this problem requires further studies.

Methods

Phase equilibria modelling and density calculation

Here we use the version 6.8.5 of Perple_X software package38 to compute the phase relations and density evolution of continental crust, bulk oceanic crust (BOC) and pyrolite. Pseudosection calculations are based on the revised internally consistent thermodynamic data of Holland et al. (2013)39 for the continental crust, and Xu et al. (2008)40 for bulk oceanic crust and pyrolite. The global average rock compositions (Supplementary Table 3) are chosen for the calculations of pseudosections and densities. The compositions of UCC and MCC are normalized in the NCKFMAS (Na2O–CaO–K2O–FeO–MgO–Al2O3–SiO2) model system, and the composition of LCC, BOC and pyrolite are normalized in the NCFMAS (Na2O–CaO–FeO–MgO–Al2O3–SiO2) model system. The simplified compositions used in phase equilibrium modeling are shown in Supplementary Table 3. The solid solution models include garnet (gt)39,40, clinopyroxene (cpx)39,40, orthopyroxene (opx)39,40 and its high-P polymorph (C2/c)39, wadsleyite (wad)39,40, ringwoodite (ring)39,40, CaSi-perovskite (ca-pv)39,40, wuestite (wus)40, plagioclase (pl)39, kalsilite (kls)39, microcline (mic)39, K-wadeite (wa)39, K-hollandite (hol)39, corundum (cor)39,40, spinel (sp)39,40 and melt39. Quartz (qtz), coesite (coe), stishovite (stv), kyanite (ky) are treated as pure end-member phases. The software and thermodynamic data used to generate the phase diagrams can be downloaded from http://www.perplex.ethz.ch/.

Petrological-thermo-mechanical model configuration

The 2D large-scale numerical model is conducted in a Cartesian box of 5000 × 670 km and discretized using an Eulerian grid of 1397 × 267 nodes with variable spacing. The original model consists of a subducting continental plate of 2650 km, an overlying continental plate of 1650 km, and an oceanic plate of 700 km in between. The crustal thickness of pre-collisional GIC is difficult to constrain. Nabelek et al. (2009)41 suggested the Greater Indian crust of about 40 km in thickness, and Ingalls et al. (2016)X assigned a crustal thickness of 35 ± 5 km to the Indian coastal plain and 31 ± 5 km to Tethyan shelf. Therefore, the continental lithosphere is set up with a 23-km-thick felsic crust (12 km UCC and 11 km MCC), a 17-km-thick mafic LCC10 and a mantle layer in this paper. The oceanic lithosphere is composed of a 2-km-thick basaltic upper OC, a 5-km-thick gabbroic lower OC and a mantle layer with the thickness dependent on the age of lithosphere. A narrow weak zone with wet-olivine rheology is applied between the subducting oceanic and overlying continental plates to localize the initial convergence. A 10-km-thick ‘stick air’ layer with low density and viscosity is set above the crust to mimic a pseudo free surface condition42,43.

The velocity boundary conditions are free slip at the left, right, and top boundaries. The lower boundary is treated as a mass-conversation preamble boundary for the purpose of satisfying free slip at about 1000 km below the base of the model (external lower boundary)44. Details of the external lower boundary are provided elsewhere44. The original model (Fig. 2a) is pushed internally by a constant convergence velocity of 10 cm/yr for 7 Myrs after Guillot et al. (2003)45, with a total convergence of 700 km. It leads to a scenario with the beginning of continental collision (Fig. 2b), after which the convergence velocity is cancelled, leaving the collisional process driven purely by the internal buoyancy.

The initial temperature structure of oceanic lithosphere is defined by the half-space cooling model27. For the continental plate, a linear temperature gradient is applied with 0 °C at the surface and 1350 °C at the bottom of lithospheric mantle (Fig. 2a). An adiabatic temperature gradient of 0.5 °C/km is applied for the sub-lithospheric mantle. The temperature boundary conditions have a fixed value (0 °C) for the upper boundary and zero horizontal heat flux across the side boundaries. An infinity-like external constant temperature is imposed in the lower thermal boundary, which allows both temperatures and vertical heat fluxes to vary along the permeable lower boundary44.

Petrological-thermo-mechanical modelling approach

The calculated density database is further integrated into the 2-D thermo-mechanical numerical code I2VIS, which is based on the finite-difference method and marker-in-cell technique21,22. The fundamental equations of the numerical model include the conservation equations of mass, momentum, and energy (1)-(3).

$$\frac{\partial {{{{{{\rm{v}}}}}}}_{i}}{\partial {{{{{{\rm{x}}}}}}}_{i}}=0$$
(1)
$$\frac{\partial {{{\sigma }}}_{{ij}}^{{\prime} }}{\partial {{{{{{\rm{x}}}}}}}_{j}}-\frac{\partial P}{\partial {{{{{{\rm{x}}}}}}}_{i}}=-\rho {g}_{i}$$
(2)
$${{\rho }}{C}_{p}\left(\frac{{DT}}{{Dt}}\right)=\frac{\partial }{\partial {{{{{{\rm{x}}}}}}}_{i}}\left(k\frac{\partial T}{\partial {{{{{{\rm{x}}}}}}}_{i}}\right)+{H}_{r}+{H}_{a}+{H}_{S}+{H}_{L}$$
(3)

where \({{{{{\rm{v}}}}}}\) is velocity,\(\,{{{{{{\rm{x}}}}}}}_{{{{{{\rm{i}}}}}}}\) coordinate, \({{{\sigma }}}^{{\prime} }\) the deviatoric stress tensor, \({{{{{\rm{P}}}}}}\) dynamic pressure, \({{\rho }}\) effective density, \({{{{{\rm{g}}}}}}\) gravitational acceleration, \({{{{{{\rm{C}}}}}}}_{{{{{{\rm{p}}}}}}}\) heat capacity, \({{{{{\rm{T}}}}}}\) temperature, \({{{{{\rm{k}}}}}}\) thermal conductivity, \({{{{{{\rm{H}}}}}}}_{{{{{{\rm{r}}}}}}}\) radioactive heating, \({{{{{{\rm{H}}}}}}}_{{{{{{\rm{a}}}}}}}\) adiabatic heating, \({{{{{{\rm{H}}}}}}}_{{{{{{\rm{S}}}}}}}\) shear heating, and \({{{{{{\rm{H}}}}}}}_{{{{{{\rm{L}}}}}}}\) latent heating. Complete details of the numerical method are provided elsewhere21,22.

Two different density models are applied and compared in the numerical simulations. In the first model, the density is linearly dependent on pressure and temperature, but does not include any phase transition. Thus, the effective density for a specific rock type can be calculated according to the Eq. (4)

$$\rho (P,T)={\rho }_{0}\left[1-\alpha\left(T-{T}_{0}\right)\right]\left[1+\beta \left(P-{P}_{0}\right)\right]$$
(4)

where \({{{\rho }}}_{0}\) is the standard density under the reference condition with P0 = 0.1 MPa and T0 = 298 K; \({{\alpha}}\) the thermal expansion coefficient and \({{\beta }}\) the compressibility coefficient (Supplementary Table 6). Alternatively, the second model incorporates our calculated density database with multiple phase transitions and density jumps obtained from Perple_X (Supplementary Fig. 1), including the remarkable phase transition boundaries at 410 km and 660 km discontinuities. The effective density is thus a complex, non-linear function of temperature, pressure, and composition \(\left({{\rho }}={{{{{\rm{f}}}}}}\left({{{{{\rm{P}}}}}},{{{{{\rm{T}}}}}},{{{{{{\rm{C}}}}}}}_{{{{{{\rm{m}}}}}}}\right)\right)\). In order to evaluate the effect of metastability of subducted UCC on subduction dynamics, the metamorphic transformation degree-controlled density is further considered in the model sensitivity tests (Supplementary Fig. 6):

$$\rho ={\rho }_{0}+{{\varphi }}({\rho }_{m}-{\rho }_{0})$$
(5)

where \({{{\rho }}}_{0}\) is the standard density under the reference condition, \({{{\rho }}}_{{{{{{\rm{m}}}}}}}\) is obtained from Perple_X (Supplementary Fig. 1), and \({{\varphi }}\) is the metamorphic transformation degree.

The combined visco-plastic rheology is employed in the numerical model to describe the rock mechanical behavior21. The viscosity of rocks deforming by dislocation creep is defined as

$${\eta }_{{ductile}}={\left({\dot{\varepsilon }}_{{II}}\right)}^{\frac{1-n}{n}}{\left({A}_{D}\right)}^{-\frac{1}{n}}{{\exp }}\left(\frac{E+{PV}}{{nRT}}\right)$$
(6)

where \({\dot{{{\varepsilon }}}}_{{{{{{\rm{II}}}}}}}\) is the second invariant of the strain rate tensor, AD (preexponential factor), E (activation energy), V (activation volume), and n (creep exponent) are experimentally determined flow law parameters46,47,48,49,50 as listed in Supplementary Table 7. The parameter R is the gas constant.

We combine the viscous rheology with an extended Drucker-Prager yield criterion50 to simulate the visco-plastic behavior of the rocks:

$${\eta }_{{plastic}}=\frac{{\sigma }_{{yield}}}{2{\dot{\varepsilon }}_{{II}}}$$
(7)
$${\sigma }_{{yield}}={C}_{0}+P\;{\sin }\left({\varphi }_{{eff}}\right)$$
(8)

where \({{{\sigma }}}_{{{{{{\rm{yield}}}}}}}\) is the yield stress, P dynamic pressure, C0 the residual rock strength at P = 0; \({{{\varphi }}}_{{{{{{\rm{eff}}}}}}}\) the effective internal friction angle (Supplementary Table 6).

The integrated viscosity of ductile and plastic deformation is the minimum value of them50.

$${\eta }_{{eff}}={\min }\left({\eta }_{{ductile}},{\eta }_{{plastic}}\right)$$
(9)

Analytical model for subducting slab pull quantification

In the simplified subduction model, a continental lithosphere is subducting following the preceding oceanic slab to the maximum depth of 660 km. The continental slab includes a 12-km-thick UCC, an 11-km-thick MCC and a 17-km-thick LCC, according to the global average thickness of crust10, as well as a subjacent lithospheric mantle (LM). The oceanic slab consists of a 7-km-thick OC and the subjacent lithospheric mantle. The possible composition-induced density contrast between the continental/oceanic lithospheric mantle and the surrounding mantle is ignored for simplicity. The model geometry is shown in Fig. 3a, with a high resolution of 300 m × 300 m. The analytical model of the subduction zone thermal structure is calculated from Davies (1999)26 and shown below:

$$\,{T}_{\left(x,y\right)}\,= \; {T}_{1}+\left(\frac{{T}_{1}-{T}_{0}}{h}\right)\left\{\left(\frac{x-h}{2}\right)\left[{erf}\left(-\frac{x-h}{\sqrt{4\kappa y/v}}\right)-{erf}\left(-\frac{x}{\sqrt{4\kappa y/v}}\right)\right]\right.\\ \left.-\left(\sqrt{\frac{\kappa y}{v\pi }}\right)\left[{erf}\left(-{\left(\frac{x-h}{\sqrt{4\kappa y/v}}\right)}^{2}\right)-{erf}\left(-{\left(\frac{x}{\sqrt{4\kappa y/v}}\right)}^{2}\right)\right]\right\}\\ +\left(\frac{{T}_{1}-{T}_{0}}{d}\right)\left\{\left(\frac{x+d}{2}\right)\left[{erf}\left(-\frac{x+d}{\sqrt{4\kappa y/v}}\right)-{erf}\left(-\frac{x}{\sqrt{4\kappa y/v}}\right)\right]\right.\\ \left.-\left(\sqrt{\frac{\kappa y}{v\pi }}\right)\left[{erf}\big(-{\left(\frac{x+d}{\sqrt{4\kappa y/v}}\right)}^{2}-{erf}\left(-{\left(\frac{x}{\sqrt{4\kappa y/v}}\right)}^{2}\right)\right]\right\}$$
(10)

where the mantle potential temperature \({{{{{{\rm{T}}}}}}}_{1}=1325\,{\deg}\!{{{{{\rm{C}}}}}}\), the initial minimum temperature on the slab \({{{{{{\rm{T}}}}}}}_{0}=100\;{\deg}\!{{{{{\rm{C}}}}}}\), the lithosphere thickness \({{{{{\rm{h}}}}}}=100\;{{{{{\rm{km}}}}}}\), the thermal diffusivity \({{\kappa }}={10}^{-6}{{{{{{\rm{m}}}}}}}^{2}{{{{{{\rm{s}}}}}}}^{-1}\), the subduction angle \({{\theta }}=30^\circ\), the convergence velocity \({{{{{\rm{v}}}}}}=5{{{{{\rm{cm}}}}}}/{{{{{\rm{yr}}}}}}\), and the initial thickness of the boundary layer in the mantle wedge \({{{{{\rm{d}}}}}}=20\;{{{{{\rm{km}}}}}}\); The erf represents the error function.

For a specific position (x, y), the lithostatic pressure \({{{{{{\rm{P}}}}}}}_{\left({{{{{\rm{x}}}}}},{{{{{\rm{y}}}}}}\right)}\) is given by

$${P}_{\left(x,y\right)}\,=\rho g\left(x\;{\sin }\theta +y\;{\cos }\theta \right)$$
(11)

where \({{\theta }}\) is the subduction angle. The slab density, \({{{\rho }}}_{\left({{{{{\rm{x}}}}}},{{{{{\rm{y}}}}}}\right)}\), is a function of \({{{{{{\rm{T}}}}}}}_{\left({{{{{\rm{x}}}}}},{{{{{\rm{y}}}}}}\right)}\), \({{{{{{\rm{P}}}}}}}_{\left({{{{{\rm{x}}}}}},{{{{{\rm{y}}}}}}\right)}\) and the composition Cm:

$${\rho }_{\left(x,y\right)}=f\left({P}_{\left(x,y\right)},{T}_{\left(x,y\right)},{C}_{m}\right)$$
(12)

where Cm = UCC, MCC, LCC, MORB, or LM.

Based on the above density structure, the total negative buoyancy force of the descending CC (FCC) is obtained by integrating the density contrast \(\triangle {{{\rho }}}_{\left({{{{{\rm{x}}}}}},{{{{{\rm{y}}}}}},{{{{{{\rm{C}}}}}}}_{{{{{{\rm{m}}}}}}}\right)}\) in two dimensions on the vertical section of the subducted CC (Fig. 3b):

$${F}_{{CC}}= \int_{0}^{{L}_{C}}\int _{0}^{{T}_{{UCC}}}\left({\rho }_{\left(x,y,{C}_{{UCC}}\right)}-{\rho }_{m}\right)g\,{{\sin }}\theta \,{dxdy}\\ +\int_{0}^{{L}_{C}}\int_{{T}_{{UCC}}}^{{T}_{{MCC}}}\left({\rho }_{\left(x,y,{C}_{{MCC}}\right)}-{\rho }_{m}\right)g\,{{\sin }}\theta \,{dxdy}\\ +\int _{0}^{{L}_{C}}\int_{{T}_{{MCC}}}^{{T}_{{LCC}}}\left({\rho }_{\left(x,y,{C}_{{LCC}}\right)}-{\rho }_{m}\right)g\,{{\sin }}\theta {dxdy}$$
(13)

where \({{{{{{\rm{L}}}}}}}_{{{{{{\rm{C}}}}}}}\) is the length of the subducted CC after the transition from oceanic subduction to continental collision, and \({{{{{{\rm{L}}}}}}}_{{{{{{\rm{C}}}}}}}\) increases from 0 to \(\frac{660}{{{\sin }}{{\theta }}}\) km; \({{{{{{\rm{T}}}}}}}_{{{{{{\rm{UCC}}}}}}},\) \({{{{{{\rm{T}}}}}}}_{{{{{{\rm{MCC}}}}}}}\), and \({{{{{{\rm{T}}}}}}}_{{{{{{\rm{LCC}}}}}}}\) are the thicknesses of UCC, MCC and LCC, respectively, with \({{{{{{\rm{T}}}}}}}_{{{{{{\rm{UCC}}}}}}}=12\;{{{{{\rm{km}}}}}},\,{{{{{{\rm{T}}}}}}}_{{{{{{\rm{MCC}}}}}}}=23\;{{{{{\rm{km}}}}}},\,{{{{{{\rm{T}}}}}}}_{{{{{{\rm{LCC}}}}}}}=40\;{{{{{\rm{km}}}}}}\); \({{{\rho }}}_{{{{{{\rm{m}}}}}}}\) is the density of the surrounding rock derived from PREM51. These three terms on the right-hand side define the slab pull of UCC, MCC, LCC, respectively, which are further named as \({{{{{{\rm{F}}}}}}}_{{{{{{\rm{UCC}}}}}}}\), \({{{{{{\rm{F}}}}}}}_{{{{{{\rm{MCC}}}}}}}\), and \({{{{{{\rm{F}}}}}}}_{{{{{{\rm{LCC}}}}}}}\). Accordingly, the slab pull of the conjoint OC above 660D (\({{{{{{\rm{F}}}}}}}_{{{{{{\rm{OC}}}}}}}\)) is expressed as:

$${F}_{{OC}}={\int }_{{L}_{{CC}}}^{660}\left\{{\int }_{0}^{{T}_{{OC}}}\left({\rho }_{\left(x,y,{C}_{{OC}}\right)}-{\rho }_{m}\right)g\;{{\sin }}\theta \,{dx}\right\}\,{dy}$$
(14)

where \({{{{{{\rm{T}}}}}}}_{{{{{{\rm{OC}}}}}}}\) is the thickness of OC, with \({{{{{{\rm{T}}}}}}}_{{{{{{\rm{OC}}}}}}}=7\;{{{{{\rm{km}}}}}}\) in this study.

Calculation of the subducted felsic continental crust

The accumulated recycled volume of subducted felsic continental crust (ω) is defined as

$${{\omega }}=\frac{{Subducted}\,{felsic}\,{continental}\,{crust}\,{beneath}\,150\;{km}}{{Initial}\,{felsic}\,{continental}\,{crust}\,{in}\,{subducted}\,{continental}\,{plate}}$$
(15)

\({{\omega }}\) is calculated from the output results produced by I2VIS with a very high spatial resolution of 0.25 × 0.25 km. Thus, each grid is equivalent to an influence area of 0.0625 km2. At each time step, we counted the numbers of grids of subducted felsic crust that got recycled beneath 150 km and multiplied it by the influence area to determine the accumulated recycled volume within the 2D-model domain.