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The supercontinent cycle has been the focus of researchers for many years, but the parameters of its cyclicity remain a central debate; thus, prediction of the occurrence of the next supercontinent remains elusive. In this research, a mathematical point of view is adopted, based on the assumption that the supercontinent Columbia assembled at – 2000 Myr $$\left( {X\left( { - 2} \right)} \right)$$ X - 2 and the supercontinent Rodinia assembled at – 1000 Myr $$\left( {X\left( { - 1} \right)} \right)$$ X - 1 . The younger supercontinents are calculated following this mathematical equation: $$X\left( n \right) = 2*X\left( {n - 1} \right) - X\left( {n - 2} \right) - \left( {\frac{540}{{3^{n} }}} \right)$$ X n = 2 ∗ X n - 1 - X n - 2 - 540 3 n , where $$X\left( n \right)$$ X n represents the assembly and n is the position of the supercontinent in the sequence. Therefore, Gondwana $$\left( {X\left( 0 \right)} \right)$$ X 0 amalgamated at -540 Myr, Pangea $$\left( {X\left( 1 \right)} \right)$$ X 1 at – 260 Myr, Eurasia $$\left( {X\left( 2 \right)} \right)$$ X 2 at – 40 Myr and Pangea Proxima $$\left( {X\left( 3 \right)} \right)$$ X 3 might form at + 160 Myr. Moreover, two logarithmic regressions give fairly similar results, confirming that a constant acceleration of the supercontinent cycle is probable. The detrital zircon, metamorphic and hafnium isotope records support the assemblies’ hypotheses that produce the mathematical equation. However, a recent supercontinent or “megacontinent” called Eurasia lacks strong geological evidence in the three datasets. These findings might reconcile the paradox brought about by the closer ages in time for the Earth’s more recent supercontinental assemblies and the assumed constant cyclicity of the cycle.

The nature of the lower crust and tectonic setting of the Chinese Altai in the early to middle Paleozoic are still hotly debated. Decoupling between zircon Hf and whole-rock Nd isotopic systems for granites results in different interpretations for the above issues. In order to solve the problem, whole-rock Nd–Hf isotopic analyses were conducted on representative early to middle Paleozoic I-type granite and strongly peraluminous granites and rhyolites from the Chinese Altai. The I-type granites show metaluminous to weakly peraluminous feature and have eNd(t) values ranging from − 2.2 to + 0.8 and eHf(t) from + 3.9 to + 12.9, respectively. The strongly peraluminous granites and rhyolites have similar eNd(t) and eHf(t) values ranging from − 3.0 to + 1.7 and from + 2.1 to + 10.4, respectively. All samples plot above the Terrestrial Array on Nd–Hf isotopic diagram, indicating significant Nd–Hf isotopic decoupling in the magma sources. These samples show flatten HREE pattern and have Lu/Hf ratios similar to the average crust, suggesting that Nd–Hf isotopic decoupling was not originated from an ancient basement with elevated Lu/Hf ratios. The observed isotopic decoupling is similar to those modern island arcs, such as the Lesser Antilles and Sunda, where Nd selectively enriched over Hf due to metasomatism in the mantle wedge and consequently resulted in decoupling between the Sm–Nd and Lu–Hf isotopic systems. Our results, combined with the available data, show that prolonged subduction and crust–mantle interaction caused the Nd–Hf isotopic decoupling in the lithospheric mantle beneath the Chinese Altai. The crust of the Chinese Altai was extracted from the lithospheric mantle and inherited the Nd–Hf isotopic decoupling feature. Therefore, the Hf, rather than Nd, isotopic data more faithfully reflect the nature of the lower crust that was quite juvenile in the Paleozoic, and the Chinese Altai represents an early Paleozoic magmatic arc possibly built near western Mongolia.

The general structure of the Chinese Altai has been traditionally regarded as being formed by five tectono-stratigraphic ‘terranes’ bounded by large-scale faults. However, numerous detrital zircon studies of the Paleozoic volcano-sedimentary sequences shown that the variably metamorphosed Cambro-Ordovician sequence, known as the Habahe Group, is present at least in four ‘terranes’. It structurally represents deepest rocks unconformably covered by Devonian and Carboniferous sedimentary and volcanic rocks. Calc-alkaline, mostly Devonian, granitoids that intruded all the terranes revealed their syn-subduction related setting. Geochemistry and isotope features of the syn-subduction granitoids have shown that they originated mainly from the melting of youthful sediments derived from an eroded Ordovician arc further north. In contrast, Permian alkaline granitoids, mostly located in the southern part of the Chinese Altai, reflect a post-subduction intraplate setting. The metamorphic evolution of the metasedimentary sequences shows an early MP-MT Barrovian event, followed by two Buchan events: LP-HT mid-Devonian (ca. 400–380 Ma) and UHT-HT Permian (ca. 300–270 Ma) cycles. The Barrovian metamorphism is linked to the formation of a regional sub-horizontal possibly Early Devonian fabric and the burial of the Cambro-Ordovician sequence. The Middle Devonian Buchan type event is related to intrusions of the syn-subduction granitoids during an extensional setting and followed by Late Devonian-Early Carboniferous NE-SW trending upright folding and crustal scale doming during a general NW-SE shortening, responsible for the exhumation of the hot lower crust. The last Permian deformation formed NW-SE trending upright folds and vertical zones of deformation related to the extrusion of migmatites, anatectic granitoids and granulite rocks, and to the intrusions of gabbros and granites along the southern border of the Chinese Altai. Finally, the Permo-Triassic cooling and thrust systems affected the whole mountain range from ca. 265 to 230 Ma. In conclusion, the Chinese Altai represents different crustal levels of the lower, middle and upper orogenic crust of a single Cambro-Ordovician accretionary wedge, heterogeneously affected by the Devonian polyphase metamorphism and deformation followed by the Permian tectono-thermal reworking event related to the collision with the Junggar arc. It is the interference of Devonian and Permian upright folding events that formed vertical boundaries surrounding the variously exhumed and eroded crustal segments. Consequently, these crustal segments should not be regarded as individual suspect terranes.

A debate exists on whether the deep crust of the Altai Orogenic Belt contains ancient crustal components. To further address this issue, geochemical analyses and zircon hafnium isotopic measurements were conducted on five Devonian magmatic rocks from the Southern Chinese Altai. Three volcanic rocks have rhyolitic compositions and two other intrusions have granite and granodiorite compositions, respectively. These samples all have calc-alkaline, peraluminous compositions and “arc-related” trace element signatures, marked by enrichment in large-ion lithophile elements relative to many of the high field strength elements. Hf-in-zircon isotopic data for these rocks show variable eHf(t) values ranging from −25 to +5, with corresponding TDMc model ages varying from ca. 2.7 to ca. 0.9 Ga. These findings represent the first report describing negative zircon eHf(t) values for the Devonian magmatic rocks of the region, documenting magmatic reworking of ancient crustal components. The very similar trace elemental patterns and indistinguishable zircon Hf isotopic characteristics, between the studied magmatic rocks and the pre-existing Ordovician accretionary wedge sediments (the Habahe Group), supports the notion that the magmatic rocks are derived from magmatic reworking of the wedge that contains ancient crustal components. The studied magmatism is synchronous with Middle Devonian anatexis of the Ordovician wedge at low-pressure/high-temperature conditions and extrusion of bimodal volcanic rocks occurred in Devonian extensional basins. These events have been collectively taken as proxies of Devonian lithospheric extension in the Chinese Altai. Integrated mapping of Hf isotopic data for the bulk S-type Devonian magmatism of the Chinese Altai shows different domains with dissimilar Hf isotopic signatures. This further indicates that the magma source, i.e., the Ordovician wedge, is compositionally heterogeneous and contains ancient crustal components.

Structural analysis and U–Pb geochronological study on zircons from the southern Chinese Altai (the Kalasu area, SE of the Altai city) show that the Cambro-Ordovician accretionary wedge (ca. 520–492 Ma) underwent four major geological events: 1) emplacement of Early Devonian magmas (ca. 410–400) associated with formation of a volcano-sedimentary cover, 2) major Middle Devonian (ca. 390–374 Ma) tectono-metamorphic event, 3) Late Devonian-Early Carboniferous folding without apparent metamorphism, and 4) a regional folding with localized Early Permian high- to ultrahigh-temperature reworking (ca. 300–280 Ma). The Early Devonian magmatism is characterized by emplacement of mafic rocks and granitoids in the centre of the NE-SW profile, coevally with granitoid magmatism and rhyolite volcanism in the southwest and northeast, respectively. The whole volcano-sedimentary and magmatic edifice was transposed by sub-horizontal metamorphic fabric associated with variable metamorphic degrees in different areas ranging from greenschist facies in the northeast (mu + bi±g) to amphibolite facies in the southwest (st + g ± sill) and granulite facies in the centre (g + sill+kfs). This metamorphic architecture, distribution of magmatism and character of metamorphic zircon populations allow to correlate these areas with upper, middle and lower orogenic crust that developed during important vertical shortening and horizontal flow in Middle Devonian. Subsequently, the whole edifice was affected by regional NE-SW trending upright (possibly Late Devonian-Early Carboniferous) folding. Finally, Early Permian shortening produced NW-SE trending regional upright folds in the southwest and northeast and a crustal-scale vertical, tabular deformation zone in the centre. The Permian deformation is accompanied by granulite facies (kfs + cd + sill+g) metamorphism and anatexis reworking the Devonian lower orogenic crust, with extensive resetting and growth of new zircons and with intrusions of Permian granites and gabbros. This study suggests that the Early Permian event was related to massive perturbation of thermal structure of the mantle lithosphere due to the collision of the Junggar arc with the Chinese Altai terrane.

The Chandman massif, a typical structure of the Mongolian Altai, consists of a migmatite–magmatite core rimmed by a lower grade metamorphic envelope of andalusite and cordierite-bearing schists. The oldest structure in the migmatite–magmatite core is a subhorizontal migmatitic foliation S1 parallel to rare granitoid sills. This fabric is folded by upright folds F2 and transposed into a vertical migmatitic foliation S2 that is syn-tectonic, with up to several tens of metres thick granitoid sills. Sillimanite–ilmenite–magnetite S1 inclusion trails in garnet constrain the depth of equilibration during the S1 fabric to 6–7 kbar at 710–780 °C. Reorientation of sillimanite into the S2 fabric indicates that the S1–S2 fabric transition occurred in the sillimanite stability field. The presence of cordierite, and garnet rim chemistry point to decompression to 3–4 kbar and 680–750 °C during development of the S2 steep fabric, and post-tectonic andalusite indicates further decompression to 2–3 kbar and 600–650 °C. Widespread crystallization of post-tectonic muscovite is explained by the release of H2O from crystallizing partial melt. In the metamorphic envelope the subhorizontal metamorphic schistosity S1 is heterogeneously affected by upright F2 folds and axial planar subvertical cleavage S2. In the north, the inclusion trails in garnet are parallel to the S1 foliation, and the garnet zoning indicates nearly isobaric heating from 2.5 to 3 kbar and 500–530 °C. Cordierite contains crenulated S1 inclusion trails and has pressure shadows related to the formation of the S2 fabric. The switch from the S1 to the S2 foliation occurred near 2.5–3 kbar and 530–570 °C; replacement of cordierite by fine-grained muscovite and chlorite indicates further retrogression and cooling. In the south, andalusite containing crenulated inclusion trails of ilmenite and magnetite indicates heating during the D2 deformation at 3–4 kbar and 540–620 °C. Monazite from a migmatite analysed by LASS yielded elevated HREE concentrations. The grain with the best-developed oscillatory zoning is 356 ± 1.0 [±7] Ma (207Pb-corrected 238U/206Pb), considered to date the crystallization from melt in the cordierite stability ~680 °C and 3.5 kbar, whereas the patchy BSE-dark domains give a date of 347 ± 4.2 [±7] Ma interpreted as recrystallization at subsolidus conditions. The earliest sub-horizontal fabric is associated with the onset of magmatism and peak of P–T conditions in the deep crust, indicating important heat input associated with lower crustal horizontal flow. The paroxysmal metamorphic conditions are connected with collapse of the metamorphic structure, an extrusion of the hot lower crustal rocks associated with vertical magma transfer and a juxtaposition of the hot magmatite–migmatite core with supracrustal rocks. This study provides information about tectono-thermal history and time-scales of horizontal flow and vertical mass and heat transfer in the Altai orogen. It is shown that, similar to collisional orogens, doming of partially molten rocks assisted by syn-orogenic magmatism can be responsible for the exhumation of orogenic lower crust in accretionary orogenic systems.