Introduction

The lower crust was for a long time assumed to represent the weak layer of the continental lithosphere, sandwiched between a strong upper crust and mantle (the ‘jelly sandwich model’13). Yet, during continent collision, earthquakes, although more frequent in the shallow crust, occur at all crustal levels (Fig. 1A)14,15. Recently, Dunkel et al.16 reported textures indicative of seismic faulting in dry lower crustal rocks from the Lofoten Archipelago in the Northern Norwegian Caledonides, indicating very high (≥1 GPa) stress levels and therefore suggesting that the lower crust was strong, not weak17. Similar suggestions have been made also for other field areas where dry, lower-crustal lithologies occur18,19. For the Bergen Arcs of Western Norway, such high stress levels were recently demonstrated directly by the presence of highly overpressured frictional melts along lower crustal faults20.

Fig. 1: Geophysical and field constraints on orogenic lower crust.
figure 1

Characteristics of lower crust during continent collision. A Distribution of earthquakes during the India-Asia collision exemplified by a cross-section along 90°E. Lower crust denoted by yellow color (modified from Jackson et al.15). Lithostatic pressures are given along the right vertical axis. The red rectangle indicates the Indian lower crust that experiences a lithostatic pressure of ca. 1.5 GPa. B Spatial distribution of reacted and unreacted rock volumes on the island of Holsnøy, Norway. The reacted zones correspond to highly deformed regions where the mineral assemblages suggest metamorphic pressures in the range 1–2 GPa (image modified from Austrheim, 20131, with permission from Elsevier).

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When fluids are introduced into the lower crust along seismic faults, metamorphic reactions taking place in the damaged wall-rocks cause weakening and development of shear zones localized around the initial faults10,12. In the Bergen Arcs of Western Norway (Fig. 1B) and the Lofoten Archipelago in Northern Norway, some of these shear-zones develop eclogite-facies mineral assemblages and appear to have formed at higher pressure than the pressures prevailing during faulting and shear zone initiation21. These high-pressure assemblages were initially assumed to have formed at an early stage near the bottom of an exceptionally thick crust. However, recent tectonic reconstructions, petrologic studies and new geochronological data from the Bergen Arcs indicate that the eclogite-facies shear zones formed synchronously with the development of amphibolite-facies shear zones in neighbouring outcrops22,23. Based on these observations, a unifying mechanical model for lower crustal evolution during orogeny should explain both an early stage characterized by highly localized brittle deformation, often accompanied by fluid infiltration, and a later stage dominated by ductile deformation in hydrated shear zones with highly variable pressures at similar crustal levels. In particular, mechanical models that have been used to quantify pressure differences in viscously deforming rocks consider only idealized scenarios where the viscosity contrasts and the geometry are pre-defined8,21,24. The orientation of planar structures, such as shear zones in this case, plays a dominant role on the sign of the pressure variations24,25. Isolated shear zones having an acute angle to the far-field maximum compressive stress tend to develop negative pressure differences from the surrounding matrix24. In contrast, isolated shear zones at obtuse angles to the far-field maximum compressive stress develop positive overpressure values24,26. Clearly, a rotation of the shear-zone network during finite-strain deformation is expected to induce changes in the sign of the pressure differences8. However, the pressure variations caused by viscosity heterogeneities scale proportionally to the effective viscosity contrast24,25,27, which does not generally remain constant. Thus, models that predict the spontaneous formation, the finite-strain evolution, and the effective viscosity distribution in a shear zone network are needed in order to capture the temporal character of stress and pressure distribution.

The model presented below is based on previous works26,28, which have demonstrated that the localization of brittle faults in pressure-sensitive materials leads to negative pressure deviations (underpressure) within the fault zones when compared to the surrounding matrix. These pressure differences can be preserved even after the localization of the fault, for as long as the damaged fault zone material remains mechanically weaker than the surrounding rock24,27,29. The lower pressure experienced by brittle materials allows further localization of deformation and promotes fluid influx from the surroundings, if available. Fluid introduction to lower crustal rocks will invariably lead to metamorphic reactions and rheological weakening both due to a reduction in grain size and the formation of weaker hydrous minerals, such as micas2,8,30,31,32,33. Sustained far-field (tectonic-) loading will then lead to viscous deformation and the development of shear zones along the weakened and reacted rock volumes12. The shear zones effectively develop into volumes where the effective viscosity is lower than in its unreacted surrounding, i.e. weak zones (Fig. 1B).

Once a shear zone or a shear zone network has formed, the amount of finite strain can be very large and this can significantly reorient the original structure34. Weak zones are expected to experience significant mean-stress variations. In this work, negative mean stress is taken as synonymous with pressure, thus, pressure variations are expected depending on orientation of the weak zones in the shear zone network8,28,35. The maximum pressure values are expected when the elongated weak zones are oriented perpendicular to the direction of the maximum normal stress24,25. More recent visco-elasto-plastic thermo-mechanical models have confirmed that the re-orientation of lithospheric-scale shear zones during finite deformation leads to a dynamic pressure evolution, independently of burial depth36. Such pressure variations exert first-order control on the stable mineral assemblages37. Indeed, it has been suggested that the local occurrence of ‘over-pressured’ rocks (eclogite) in shear zones in the Bergen arcs is the result of pressure perturbations associated with the formation of weak reacted volumes in strong, highly stressed, host rocks21. Despite the physical feasibility of such models, a self-consistent model that would predict and resolve the development of a shear zone network, as well as the subsequent dynamic development of both overpressured and underpressured regions, is still unavailable.

Results and Discussion

To analyze the mechanical conditions prevailing during tectonic compression of a lower crustal volume when subject to localized fluid-induced weakening, we have performed 2D high-resolution visco-elasto-plastic thermomechanical simulations of a 4 × 1 km region in the lower crust under shear (see Methods section for technical details). As a case study we have considered lower-crustal granulites from the Bergen Arcs in Western Norway (e.g. Figure 1B). These rocks recrystallized to form dry, lower-crustal granulites at ca 930 Ma38 and experienced subsequent amphibolite to eclogite-facies (ca 1–2 GPa at 600–700 °C) conditions during the Caledonian orogeny at ca 425–430 Ma21,38. Since plagioclase is by far the dominant mineral in the dry granulites, the initial creep rheology is represented by dry plagioclase17. A single weak inclusion (wet plagioclase rheology17) is added at the bottom of the model domain to trigger localized deformation. This inclusion is assumed to be connected to an external fluid (water-) reservoir located immediately below the model, to simulate the field situation of the Lindås Nappe in the Bergen Arcs where dry granulites are thrust upon Paleozoic sedimentary rocks undergoing prograde, fluid-producing, metamorphism22.

With ongoing deformation, stresses build up until the yield stress is reached. Field observations demonstrate that this is followed by dynamic rupturing and highly localized seismic slip19,39. Associated wall rock damage allows fluid infiltration, metamorphic hydration reaction, and mechanical weakening of a 0.1–1 m wide zone of wall rocks8. The details of these processes cannot be described within the temporal and spatial resolution of our model. We therefore parameterize this by changing the rheology from dry to wet plagioclase once an accumulated plastic strain of 10% is reached in our model (see Methods for more details). Figure 2 shows the output of our simulations for a constant sinistral shear strain rate of 5 × 10−15 s−1 after 7 million years. We observe striking and dynamic variations in stress, deformation rate and pressure (= mean stress) in the deforming lower crust (see also Supplementary Notes 3). Maximum pressure variations within the model domain approach 1 GPa, with local and continuous pressure gradients that may exceed the lithostatic pressure gradient by a factor of ~30. Even within low-viscosity shear zones, significant along-shear zone variations in dynamic pressure occur, with intermittent high-pressure values frequently occurring at the intersection of shear zones. Pressure magnitudes depend on orientation with respect to the overall kinematic deformation and the local state of stress (which evolves depending on the presence of other shear zones). The resulting shear zone pattern is complex and consists of both small-scale and large-scale deformation zones, with the widest being internally heterogeneously deformed.

Fig. 2: Numerical simulation of the formation hydrated shear zones in the lower crust.
figure 2

The simulation, using a grid resolution of 4m2, started with an initially homogeneous, dry, lower crust (at 650 °C) with a single embedded wet-plagioclase-dominated inclusion (inset in A). When imposing a constant, sinistral shear strain rate of 5 × 10−15 s−1, brittle shear zones develop, followed by hydrated, weak, shear zones. Shown are snapshots that illustrate A effective viscosity, B second invariant of strain rate tensor, C second invariant of plastic strain, D second invariant of the deviatoric stress tensor, E dynamic pressure, and F detail of dynamic pressure within the shear zones. Complex shear zone patterns emerge that have significant variations in stresses and dynamic pressures and may explain the coexistence of high and lower pressure assemblages in the same rocks. See Supplementary Movies S1–4 (Supplementary Notes 3) for animation and (Fig. S1, Supplementary Notes 2; Fig. S7, Supplementary Notes 4) for the temporal evolution for a range of imposed strain rates.

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In order to investigate the sensitivity of our model to our model parameters, we have performed systematic simulations in which we varied the background strain rate, the temperature, the weakening parameters and the numerical resolution (Supplementary Notes 4). Results are generally consistent for all reasonable choices of input parameters. Second order variations occur due to strain weakening and the critical hydration strain, i.e. the strain value where the damaged rocks become effectively weaker and they are approximated by a “wet” flow law. The timing is to a large extent controlled by the applied background strain rate. A primary requirement, however, is that the background viscosity and deformation rate are such that the brittle yield stress is reached. Simulations under conditions where this is not the case, for example because the temperature is higher (e.g., 700 °C instead of 650 °C, for a strain rate of 5 × 10−15 s−1) are shown in the supplementary notes (Supplementary Notes 4, Fig. S3a). Field observations from a variety of localities, including the Norwegian Caledonides, the Alps, the Musgrave ranges and the Himalayan-Tibetan orogen, do however indicate that brittle deformation is common in lower crustal volumes during plate convergence12,40.

Our results are consistent with previous work emphasizing that lower crustal shear zones originate by brittle failure12,40. Importantly, this leads to a drop in pressure within the highly localized shear zone compared to the surrounding matrix26,28,41,42. Hydration weakening further enhances the viscosity variations, resulting in larger stress and pressure variations within the system. It is also interesting to note that the local sense of shear within many of these shear zones appears inconsistent with the overall applied background kinematic deformation rate. This is in agreement with previous studies of the formation of brittle and ductile shear zones43 and is caused by local changes in the principal stress direction.

To analyze the petrological consequences of the inferred pressure variations, we performed phase equilibrium calculations to identify the stable mineral assemblages for a typical granulite from Holsnøy as a function of the pressure and temperature (P-T) conditions (Fig. 3A). For the calculation we used the measured loss on ignition (LOI) as an upper bound of the H2O content of these rocks. Since it is expected that the presence of water will facilitate mineral reactions, our equilibrium phase equilibria calculations are relevant only for the reacted and the partly reacted zones characterized by the presence of hydrous minerals and/or recrystallized material1,8,44.

Fig. 3: Phase diagram section for a representative granulite from Holsnøy.
figure 3

The phase diagram section has been calculated via Gibbs-free energy minimization by assuming a fixed amount of H2O (see Methods for more details). A Equilibrium mineral assemblages for the granulite from Holsnøy (mineral abbreviations: Cpx: clinopyroxene, Grt: garnet, Ky: Kyanite, Zo: zoisite, cAmph: clinoamphibole, Pl: plagioclase feldspar, Qz: quartz, Pa: paragonite mica, H2O: pure H2O fluid). B The black solid line shows the amount of H2O needed for water-saturation, i.e. fluid-present conditions (the assumed temperature conditions (650 °C) are indicated by dashed line in (A). The red line indicates the amount of H2O (LOI) that was also used for the calculation of the pressure-temperature section (shown in A). The intersection and relative positions of the black and red lines in (B) shows that the H2O content is sufficient to saturate the system only in a pressure range below ~1.0 GPa. For the pressure range between 1–2 GPa, the rock is H2O-undersaturated and no free H2O phase is stable.

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It is expected that a limited amount of H2O in the rock may be insufficient to saturate the system with respect to a free H2O fluid phase. Figure 3B shows the amount of water required for saturation at 650 °C, a temperature relevant for the Holsnøy situation based on previous work21,45, as a function of pressure (see details on Methods). For pressures in the range 1–2 GPa, Fig. 3B shows that a pressure increase will tend to stabilize hydrous assemblages and absorb any free H2O that may have been available at lower pressures. Hence, high pressure reacting regions may, counterintuitively, act as fluid sinks rather than sources. This result is not limited to a particular composition, and it is relevant for similar systems that experience dehydration reactions exhibiting positive slopes in the P-T space.

Spatial and temporal variation in pressure may have first order effects both on the rheological and petrological evolution of the lower crust. The pressure drop associated with initial brittle failure would naturally draw in water from any external water reservoir. Hence, this effect would naturally couple retrograde fluid-consuming metamorphism of dry rocks to spatially associated volumes undergoing prograde, fluid-producing, metamorphism. Relevant geological scenarios from collisional orogens, exemplified by the Lindås Nappe in the Bergen Arcs, include thrusting of lower crustal units over a footwall containing lower grade metasedimentary rocks23. Continuous pressure gradients that may exceed the lithostatic gradient by over an order of magnitude would furthermore act as an effective local distribution system for fluids, with the additional complexity that reacting volumes that are about to run out of fluid would act as fluid sinks even if the rock pressure remains high46.

The presence of pressure variations imposed by mechanical processes, as described above, is highly relevant for the interpretation of the pressures recorded by metamorphic mineral assemblages in terms of underlying tectonic scenario25,47,48,49. In our modelling scenario, high-pressure (≈2 GPa) assemblages would locally form without the necessity of excessively deep burial of the relatively low density granulites. At the same time, abundant underpressurized (≈1 GPa) regions would form at more or less similar depths. Traditionally these rocks would be interpreted to have formed at some later stage following 20–40 km of crustal exhumation. Hence, our model has radical consequences for the interpretation of metamorphic mineral assemblages in terms of the underlying geodynamic processes.

High (≈1 GPa) differential stress levels in the dry lower crust have important consequences for its rheological and physico-chemical evolution. Under high stress, the deformation of the lower crust is dominated by plastic shear bands that will provide the available pathways for any external fluid phase. Following fluid-introduction at high temperatures, the shear bands will evolve into a shear-zone network where rocks behave in a visco-plastic manner. The model presented above naturally produces shear zone networks (Fig. 2, and movies in Supplementary Notes 3) at a similar scale and with similar geometry to what is observed at Holsnøy in the Bergen Arcs (Fig. 1B). As the lower crustal rheology changes from that of dry and strong granulites to that of weaker eclogites and amphibolites, a characteristic pattern develops where rounded blocks of strong granulites are displaced along growing hydrated shear zones that reflect a range of metamorphic pressure conditions. This large range of metamorphic pressure conditions may thus not always reflect metastability and can be explained by the particular mechanical configuration.

Methods

Thermo-mechanical simulations

We performed 2D simulations using LaMEM, which solves the conservation equations for mass, energy and momentum of slowly moving rocks using a staggered grid finite difference method combined with a marker-and-cell approach50,51. We employ a temperature-dependent visco-elasto-plastic rheology, where dislocation creep is combined with non-associated Drucker-Prager plasticity. We have implemented a regularized plasticity52. More details on all employed material parameters are given in the supplementary notes 1.

Properties are tracked on markers that are mapped to the computational grid in a conservative manner53. A constant value of 1000 MPa is added to the pressure value to take into account that our model domain is at around 35 km depth within the crust. A uniform constant density of 3000 kg/m3 is assumed in our model and therefore the effects of gravity are limited to the generation of a uniform lithostatic pressure gradient. For simplicity, we assume a constant temperature within the model domain with flux-free lateral thermal boundaries and isothermal upper and lower boundaries. In order to simulate the shear induced by a subducting slab moving underneath the crust (see Fig. 1), we apply kinematic velocity boundary conditions in which we move the lower boundary to the right and keep the upper boundary fixed, such that a constant background shear strain rate of 5 × 10−15 s−1 is achieved in our reference simulation. The side boundaries are kinematically prescribed, which induces stress heterogeneities at the lateral boundaries that initiate shear zones similar to what would happen if small heterogeneities in material strength were taken into account. Brittle localization results from non-associated plasticity, while the effect of damaging rocks is taken into account through frictional strain softening that linearly lowers both the friction angle and cohesion between an accumulated plastic strain of 0.01 and 0.1 until it is reduced by 90% of its initial value, while normalized for a fault thickness of 10 m (see Supplementary Notes 4 for variations of this; Fig. S5a,b).

Water migration through shear zones is a process that is fast compared to the typical time step of our model. Its main mechanical effect is to change the rheology of the rocks once the shear zones become hydrated. We parameterize this effect by changing the rheology from dry to wet plagioclase once an accumulated plastic strain (critical hydration strain) of 0.1 is reached. This value is based on the cumulative value of the second invariant of the plastic strain rate. The reason for this choice lies in the fact that, in the presence of fluids, metamorphic reactions can occur at laboratory timescales for temperatures of 600 °C and higher54. As a consequence, the weakening is expected to occur almost instantaneously when compared to the geological deformation rates that are modeled in this work. A critical value of plastic strain (e.g. 0.1) is chosen since pressure differences at nucleating plastic shear bands are proportional to strain42. Furthermore, with progressive strain, it is expected that isolated microcracks (below the limit of our resolution) will interconnect55. Both the underpressure development and the micro-fracture interconnection will enhance the fluid supply needed for the relatively instantaneous hydration reactions. A systematic investigation of the value of the critical plastic strain showed that different values produce very similar results (see Supplementary Notes 4 for variations in this parameter; Fig. S6a,b). To prevent material that flows in from the left boundary from being instantly weakened, we set the accumulated plastic strain of inflowing markers to zero. This feature has been chosen as a better approximation for deformation in subduction settings compared to periodic boundary conditions.

We apply the Flexible-GMRES Krylov method to solve the governing incompressible Stokes equations, preconditioned with a direct LU solver and a penalty term on the pressure block. We configure the models with 27 markers per control volume to set the material properties and temperature structure. LaMEM is written on top of PETSc56 and utilizes SNES nonlinear solver framework. The non-linear SNES solver has a convergence criterion that is either a relative tolerance (rtol) of 10−4 or absolute tolerance (atol) of 10−7 and we employ the Eisenstatt-Walker algorithm, combined with line search (l2). The inner linear KSP solver is terminated when a relative tolerance of 10−3, an absolute tolerance of 10−10, or 100 iterations are reached.

We have performed a total of over 50 simulations to better understand the dynamics of the system, and the sensitivity of the results to the model parameters (see Supplementary Notes 4). Whereas details of the simulations, such as the number of shear zones are a function of the material parameters, the overall conclusions with respect the dynamic stress and pressure variations are robust.

LaMEM is open-source software and available at https://bitbucket.org/bkaus/lamem. Detailed instructions and scripts to reproduce the results presented are uploaded to zenodo (https://zenodo.org/record/6538290)57.

Equilibrium Phase diagram sections

We performed phase equilibrium calculations by minimizing the Gibbs-free energy in the Na2O-CaO-FeO-MgO-Al2O3-SiO2-H2O model system. We used the Perple_X collection of programs58,59,60 and the hp02ver.dat thermodynamic database61 to construct isochemical pressure-temperature (P-T), phase-diagram sections. The bulk composition that was used is (in wt.%): Na2O: 4.53, CaO: 9.88, FeO: 2.74, MgO: 2.33, Al2O3: 25.96, SiO2: 53.34 and H2O:0.37 and the solid solutions that were considered are: “cAmph(DP)” for clinoamphibole, “Omph(GHP)”, for clinopyroxene, “feldspar” for plagioclase feldspar, “Opx(HP)” for orthopyroxene, “Gt(GCT)” for garnet and “Chl(W)” for chlorite (details for the solution models can be found in the solution_model.dat file in the following link http://www.perplex.ethz.ch/perplex/ibm_and_mac_archives/Perple_X_6.9.0_data_files.zip).

For the calculation of the amount of water needed for saturation, a P-T section was calculated for a sufficiently large amount of H2O (e.g. 20% wt.) by keeping the proportions of the other elements the same. The saturation amount was calculated as the amount of H2O that is bounded in the mineral phases (as OH). The CORK H2O equation of state was used in all the calculations61,62.