Zhang and Zhang (2024a, 2025) established an arch tectonic dynamics model for basin-mountain coupling in their study of basin-mountain coupling evolution. They argued that the basin-mountain-basin (e.g., Tarim-Tianshan-Junggar) composed of the basin-mountain system constitutes an arch, which creates differences in the stress distribution of the basin-mountain system. The mountain range is the arch, and the basins (or flatlands) on both sides of the mountain range are the foot of the arch ( Figure 1(A) ). The arch (mountain range) is able to convert its huge gravity into lateral compression force (i.e., circumferential stress) to be transmitted to the basins on both sides, so that the edge of the mountain range and the basins are subjected to much greater pressure than the hinterland of the mountain range. The stress difference generated by this arch tectonic effect provides a power mechanism for basin subsidence and mountain range uplift. The usual force characteristics of arch tectonics are: under the vertical load q of the arch tectonics, the bearing point produces not only the vertical reaction force V, but also the horizontal thrust force H ( Figure 1(B) ). As a result of this horizontal thrust, the bending moment of the arch is much smaller than that of a horizontal beam of the same span, so that the whole arch construction is mainly under compressive stress. If the arch construction material is hard enough, the full weight of the arch can be transferred to the foot of the arch on both sides through circumferential stresses, so that the pressure carried by the foot of the arch increases significantly, while the stress under the arch construction is greatly reduced, and can even be zero ( Mao et al., 2020 ).

In the basin-mountain-basin arch tectonic system, the vertical height of the arch is usually much smaller than the lateral span of the arch, and such a low curvature will weaken the effect of the arch tectonics; however, because the Earth itself is nearly spherical and has a certain curvature that amplifies the arch tectonics of the basin-mountain system, the effects of the stress transformations will be significant even if the curvature of the basin-mountain-basin arch tectonics is small ( Mao et al., 2020 ).

Arch structure is mainly composed of rocks with a certain degree of rigidity. The upper crust is the main body of the arch structure; the middle and lower crust and lithospheric mantle have a certain contribution to the arch structure. The asthenosphere beneath the lithosphere is easy to flow or creep and is difficult to resist the shear effect, so the thickness of the arch structure is basically generally not greater than the thickness of the lithosphere. The thickness of the Earth’s lithosphere is 0 - 80 km (local variations of 5 - 200 km), and the lithosphere’s own gravity-induced stress distribution is about 3 GPa on average. According to the elastic buckling load formula, the maximum critical elastic buckling load that the lithosphere of different compositions can withstand does not exceed 30 MPa.

( Li & He, 2022 ). Therefore, the lithosphere cannot withstand its own gravity. Fortunately, it is supported by the underlying mantle and the asthenosphere, so that the lithosphere is usually in a state of mechanical equilibrium. In regions with arch structures (e.g., basin-ranges-basin systems), the gravity of the lithosphere is partially shifted from directly below the arch structures to the sides, which causes the mantle and the asthenosphere below the basins to be subjected to higher stresses than those below the ranges, which results in the plastic mantle and the asthenosphere melts being extruded and flowing slowly from the basins on both sides to the bottom of the mountain ranges ( Zhang & Zhang, 2025 ).

Wolfenstein (1978) , Mikheyev and Smirnov (1989) showed that when neutrinos propagate in matter, when the energy of the neutrinos matches the density of the matter, the neutrinos can form an MSW (Mikheyev-Smirnov-Wolfenstein) resonance with the matter atoms, thus increasing the neutrino flavor transition probability. Zhang and Zhang (2024b; 2024c; 2025) further investigated that the MSW resonance is actually a typical physical resonance with energy excitation. While increasing the probability of neutrino flavor conversion, this resonance also has an effect on the propagation medium, exciting unstable radioactive nuclei in it and increasing the probability of their decay, thus releasing more heat and causing some of the material to melt (forming magma). Calculations based on MSW resonance conditions and the content of radioactive materials in various layers of the Earth show that magma can be formed only when atmospheric neutrinos resonate with upper mantle materials in MSW, and therefore magma generally originates in the upper mantle (including the asthenosphere). Once formed, the magma migrated upward under buoyancy. Initially, the magma produced is sporadic and dispersed, and as more molten material is produced, some of the magma converges with each other. In the plastic mantle, magma usually migrates by infiltration; after arriving at the rigid lithosphere, the permeability barrier at the lithospheric boundary blocks its ascent, so magma can hardly rise by infiltration and can only move upward along fissures or fractures, invade the crust and solidify to form plutonite, interact with sedimentary layers to form metamorphic rocks,, or move along fissures directly to the surface to form volcanic eruptions. Using this theory of magma formation, Zhang and Zhang (2024b; 2025) better explained the formation of inner and outer Earth tectonics such as the asthenosphere, the Lithosphere-Asthenosphere Boundary (LAB), the new oceanic crust of mid-oceanic ridges, and the striped magnetic anomalies and Oceanic Core Complexes (OCC).

In the orogenic belt, due to the arch tectonic effect, the rock layers at the edge of the mountain range and below the basins on both sides are subjected to higher stresses than those below the mountain range’s hinterland ( Zhang & Zhang, 2024a, 2025 ). Under the effect of this difference in stresses, magma migrates from the basins on both sides and the edge of the mountain range to the mountain range’s hinterland, and converges below the mountain range’s lithosphere. With the increase of magma convergence, there are two main effects: first, the magma heats and softens the overlying rocks, which increases their plasticity; second, the thermal pressure increases, which squeezes the overlying rocks, leading to uplift of the overlying rock layers and pushing the mountain range to grow taller. The uplift of the overlying rocks makes room for the magma that rises later. Thus, below the belly of the mountain range, more and more magma collects. Of course, the magma in the uppermost layers also solidifies as it dissipates heat, forming new plutonic rocks and undercutting the overlying rock layers, causing them to rise or fracture. In this way, the magma will rise along the cracks and squeeze the rock cracks, resulting in further enlargement of the cracks and opening up new space for the magma to rise. In short, the arching tectonic effect of the orogenic belt causes magma from the mantle and the asthenosphere to flow continuously into the belly of the mountain range, and to gradually encroach on the upper part of the belly. As a result, three distinct regions of temperature and pressure gradients are created in the orogenic belt. Below the belly of the mountain range, due to the convergence of magma, (red circled area in Figure 2 ).

Temperatures are higher, but, being directly below the arch tectonics of the mountain range, stresses are minimized, so a high-temperature, low-pressure environment results ( Figure 2 Pink portion of the magma perimeter). At the edge of the mountain range (blue ellipse in Figure 2 ), a high-pressure, low-temperature environment is created because it is far away from the magma area and is at the foot of the mountain range, where lateral stresses are the highest. The zone between the edge of the mountain range and the belly of the mountain range (yellow ellipse in Figure 2 ) is closer to the magma convergence area and is subject to lower lateral stresses than the foothills and higher lateral stresses than the belly of the mountain range, resulting in a medium-temperature, medium-pressure zone. For example, in the paired metamorphic belts exposed in the eastern section of the Dabie Mountains in China, high-pressure, low-temperature metamorphic rocks are mostly located at the margins of the mountain ranges, while low-pressure, high-temperature hornblende-phase rocks are mostly located in the central part of the mountain ranges and are associated with granites ( Ma & Zhang, 1988 ). Currently, metamorphism is categorized into three series based on P-T trajectories, i.e., the Alpine metamorphic series with a low thermal gradient (low T/P value), the Barrovian metamorphic series with a medium thermal gradient (medium T/P value), and the Buchan metamorphic series with a high thermal gradient (high T/P value) ( Figure 3 ) ( Zheng & Chen, 2017 ; He & Zheng, 2019 ). These three series correspond to the blue, yellow, and pink areas in Figure 2 , respectively.

A heat source is one of the most important conditions for metamorphism, especially for high-temperature and low-pressure metamorphic conditions, which require an additional heat source. Regarding the heat supply mechanism of metamorphism, it is usually believed by previous authors ( Dewey & Bird, 1970 ; England & Thompson, 1984 ; Wen et al., 2020 ) that the heat originates from the heat conduction of crustal thickening, including internal radiative heat as well as conductive heat from the bottom of the crust ( England & Thompson, 1984 ) or localized radiative anomalous heat gain ( Engi et al., 2001 ). Such heat supply is a gradual and cumulative process, so the metamorphic time of metamorphism is generally around 50 Ma or longer ( England & Thompson, 1984 ; Wen et al., 2020 ). However, short-term, multi-acting thermal events in the Grampian orogenic belt of the Barrovian metamorphic belt series are clearly incompatible with this model of heat supply. Multiple episodes of thermal activity in the Barrovian metamorphic belt ( Ague & Baxter, 2007 ; Viete et al., 2011 ) document localized thermal “disequilibrium” within the crust rather than crustal-scale thermal return to equilibrium, and therefore the source of heat must be the result of repetitive, rapid episodic thermal advection within the crust. In addition, for the source of heat for the formation of Buchan metamorphic series of high-temperature, low-pressure metamorphic belts, England and Thompson (1984) showed that normal thermal models do not lead directly to a field metamorphic gradient in low-pressure facies series in nature. An additional source of heat is necessary to form such a thermal gradient, and this source can only be magma. The conventional view is that the heat supply of magma in the crust may be related to mechanisms such as lower crustal dismantling and sinking, upwelling of the soft rheosphere, ocean ridge subduction, and mantle column activity ( Harley, 2008 ; Guo et al., 2012 ; Zheng & Chen, 2017 ). However, these mechanisms of magma formation are clearly inconsistent with the distribution of magmas or melts ( Zhang & Zhang, 2024b ). Based on field observations, gabbro intrusion in the Grampian orogenic belt is located within the mid-crust while providing a heat source for Barrovian and Buchan metamorphism ( Fettes, 1970 ; Ashworth, 1975 ). The output of gabbro is closely associated with the most advanced metamorphism (including mixed petrogenesis), and its output should have been a major heat source for metamorphism. In the Grampian orogeny, the close spatial and temporal relationship between bimodal magmatism and epithermal metamorphism suggests that the metamorphism was caused by heat flow from the lower crust or mantle to the mid-crust and was a large-scale contact metamorphism ( Ren et al., 2018 ), implying that the heat of metamorphism may have originated from magma and related fluids ( Baxter et al., 2002 ). This is fully consistent with the mechanism in this paper.

From the previous analysis, it can be seen that in the orogenic belt, due to the existence of the arch tectonic effect, the internal pressure of the lithosphere below the middle and lower crust is not equal to its lithostatic pressure, but rather, a low-pressure environment is formed in some areas while an overpressure environment is formed in other areas. The factors that contribute most to the formation of overpressure are: 1) circumferential stress formed by arch tectonics. In the orogenic belt, the crust is thicker, such as the thickness of the crust along the Himalayas is about 75 km. According to hydrodynamics, the lithostatic pressure is about P = ρgh, substituting ρ = 2670 kg/m³ (the average density of the mountain), g = 9.8 m/s² (the acceleration of gravity), and h = 75 km into this equation gives P = 2 GPa. Due to the effect of arch tectonics, the overlyinglithostatic pressure is not simply equal to the gravity of the overlying rock mass, and in some areas (e.g., near the roots of basins), the static rock pressure is much higher than the gravity of the overlying rocks ( Zhang & Zhang 2024a, 2025 ), up to several times. Thus, beneath the crust of the Himalayan margin, the pressure may be much greater than 2 GPa due to arch tectonics. 2) Thermal pressure. Chen (2005) concluded that under the lithospheric pressure and isotropic elasticity conditions of 15 - 20 km in the middle and upper part of the crust, the thermal stresses due to the change of temperature by 100˚C are about 100 MPa. Hu et al. (2003, 2008) showed that the pressure gradient in the lithosphere is generally a superposition of the thermopressure (thermal) gradient and the gravity gradient, which is related to the ground temperature, composition, phase, and nature of the system. Influenced by these factors, the pressure gradient in the lithosphere is significantly higher than the lithostatic pressure gradient, even up to 2 - 4 times the lithostatic pressure gradient. In particular, the thermal pressure coefficient in the lithosphere at the material phase transition point increases dramatically, thus causing a thermal pressure increase or even a localized explosion. 3) System phase change. In a nearly closed environment, the system temperature increase and metamorphism caused by changes in the phase state of substances and changes in the composition of substances, etc., can lead to pressure changes. For example, the volume of water-bearing serpentine increases by 7.78% - 15.56% after dehydration reaction in the temperature region above 500˚C, and the volume of talc can increase by 0.72% - 4.12% after dehydration. According to the Preliminary Reference Earth Model (PREM), the adiabatic bulk modulus varies from 127.0 to 131.5 GPa over a range of 24.4 to 220 km, and a 1% increment in volume causes a pressure increment of 1.27 to 1.315 GPa ( Anderson, 1993 ). Another experiment showed that at the melting point temperature of a solid, an 8% increase in the volume of a molten solid can result in a localized pressure increment of the solid of up to 10.16 - 10.52 GPa ( Hu et al., 2015 ). Even in an open environment, an ultrahigh-pressure environment can be formed as long as the rate of pressurization is greater than the rate of pressure release ( Wang, 1996 ). Magmatic activities in the orogenic belt will undoubtedly cause some minerals to undergo dehydration and phase changes, resulting in the formation of UHP metamorphism. In conclusion, the pressure source of UHP metamorphism is not only the static rock pressure, but also the superposition of various pressures. In the orogenic belt, it is easier to form an ultrahigh-pressure environment due to arch tectonics and magmatism. Therefore, ultrahigh-pressure metamorphic rocks can be formed entirely within the Earth’s crust.

It is common for previous authors to equate metamorphic pressure simply with lithostatic pressure, an approach that, except in the plastic mantle, may be at variance with reality in the hard lithosphere, especially the crust. Therefore, many researchers have questioned the direct conversion of pressures determined from metamorphic reactions and mineral phase transitions to lithospheric depth ( Wang, 1996 ; Wu & Chi, 2003 ; Moulas et al., 2014, 2022 ; Tang & Hou, 2016 ; Zhou & He, 2017 ; Chu et al., 2017 ; Lü et al., 2017 , 2024; Putnis et al., 2021 ). Hu et al. (2015) argued that the total pressure inside the rock system = overlying static rock load pressure + tectonic pressurization + internal phase change pressurization of the system, so the pressure of UHP metamorphism should be composed of 3 parts, such as the overlying static rock load pressure, the tectonic pressurization and the internal phase change pressurization of the system. According to Liu et al. (2017) , the UHP is synthesized by gravity, tectonic force and other forces, and thus the tectonic force and other combined forces should be subtracted from the total pressure when calculating the depth from the pressure determined by mineral phase change. Lü et al. (2017) established a “hydrostatic pressure model of gravity-tectonic force composite” based on this discussion, and used this model to project the depth of Dabie UHP metamorphic rock formation to be between 23 and 55 km, which is much shorter than the depth of more than 100 km in the traditional view ( Shen et al., 2018 ; Zhang et al., 2021a ). Obviously, these researchers all agree that tectonic stress has an important role in the formation of overpressure. The mechanism in this paper further clarifies the main source of tectonic stress in the orogenic belt.

Paired metamorphic belts refer to two metamorphic belts with different pressure types or metamorphic facies that are roughly parallel to each other, a concept first proposed by the Japanese geologist Miyashiro (1961) . He believed that the Pacific Rim region and many metamorphic areas in the world usually consist of a paired metamorphic belt composed of a low-pressure belt (or low P/T-type metamorphic belt) on the continental side and a high-pressure belt (or high-P/T-type metamorphic belt) on the oceanic side, and the formation periods of the two are the same or close to each other. The formation mechanism is as follows: in a plate subduction to the other plate below, along the subducting plate side, due to the higher pressure, the plate is colder, and a high-pressure, low-temperature metamorphic belt is usually formed; the symbol mineral is glaucophane, and on the ascending plate side, due to the magma produced by subducting plate erosion, low-pressure, high-temperature metamorphic belts are usually formed, and the symbol mineral is andalusite. As a result, paired metamorphic belts are usually exposed in pairs at convergent plate margins ( Zheng & Chen, 2017 ; He & Zheng, 2019 ; Zhang et al., 2021b ). However, based on the temperature-pressure gradient-to-depth relationship conversion, glaucophane forms at a depth of about several tens of kilometers, whereas andalusite forms at a depth of less than a few kilometers or even shallower. So, we have to ask, why are minerals with a difference of several tens of kilometers in formation depth always exposed at the same time? If it is caused by exhumation, what is the mechanism? This cannot be explained by the theory of subduction ( Zhou et al., 2020 ). In the mechanism of this paper, the formation of double metamorphism is not a difference in the depth at which the minerals are located, but rather a difference in location; the high-temperature, low-pressure metamorphic belt in the belly of the mountain range and the low-temperature, high-pressure metamorphic belt at the edge of the mountain range are at roughly the same depth, and so the paired metamorphic belts are usually capable of being exposed at the same time.

In fact, in many orogenic belts, not all are such double metamorphic pairs; multiple metamorphisms coexist. For example, a medium-temperature, medium-pressure Barrovian metamorphic belt and a high-temperature, low-pressure Buchan metamorphic belt ( Zheng et al., 2004 ; Kohn, 2014 ; Zhang et al., 2019 ), as well as a low-temperature, high-pressure Alpine metamorphic belt ( Wang et al., 2017 ; Li et al., 2018 ; Zhang et al., 2019 ), exist in the Himalayan orogenic belt, and the various metamorphisms are superimposed, intertwined, and even inverted. The Grampian Massif at the southern margin of the Scottish Highlands is a classic Barrovian metamorphic series outcrop area, with a typical “medium isothermal pressure gradient P/T” metamorphic series, while the Buchan metamorphic belt is located to the north of the Barrovian metamorphic belt ( Ren et al., 2018 ); the Barrovian metamorphic belt and the Buchan metamorphic belt can share the sillimanite belt. The Grampian orogeny in western Ireland produced high-pressure glaucophane schist-phase metamorphism (−1.0 GPa) ( Chew et al., 2003 ; Sawaki et al., 2010 ). For these intricate metamorphisms, subduction does not provide a good explanation. In the mechanism of this paper, the intrinsic connection of various types of metamorphism is very clear and readily apparent ( Figure 2 ). Of course, not all orogenic belts have three types of metamorphic facies, due to the fact that the migration of magma is affected not only by arch tectonic stress but also by crustal fractures or fissures, which leads to the migration route and intrusion of magma into an area far away from high-pressure or medium-pressure zones, resulting in the high-pressure or medium-pressure zones, due to the lower temperature, not undergoing metamorphism, and thus a type of metamorphic facies series is missing.