Below the seismogenic zone, faults are expressed as zones of distributed ductile strain in which minerals deform chiefly by crystal plastic and diffusional processes. We present a case study from the Caledonian frontal thrust system in northwest Scotland to better constrain the geometry, internal structure, and rheology of a major zone of reverse-sense shear below the brittle-to-ductile transition (BDT). Rocks now exposed at the surface preserve a range of shear zone conditions reflecting progressive exhumation of the shear zone during deformation. Field-based measurements of structural distance normal to the Moine Thrust Zone, which marks the approximate base of the shear zone, together with microstructural observations of active slip systems and the mechanisms of deformation and recrystallization in quartz, are paired with quantitative estimates of differential stress, deformation temperature, and pressure. These are used to reconstruct the internal structure and geometry of the Scandian shear zone from ~10 to 20 km depth. We document a shear zone that localizes upwards from a thickness of >2.5 km to <200 m with temperature ranging from ~450–350°C and differential stress from 15–225 MPa. We use estimates of deformation conditions in conjunction with independently calculated strain rates to compare between experimentally derived constitutive relationships and conditions observed in naturally-deformed rocks. Lastly, pressure and converted shear stress are used to construct a crustal strength profile through this contractional orogen. We calculate a peak shear stress of ~130 MPa in the shallowest rocks which were deformed at the BDT, decreasing to <10 MPa at depths of ~20 km. Our results are broadly consistent with previous studies which find that the BDT is the strongest region of the crust.Contractional fault systems that cut the crust and upper mantle are necessary consequences of plate convergence and continental collision [1]. At any one time, much of the relative plate motion is localized onto relatively narrow zones of high strain [2]. In the upper crust, these zones are manifested as discrete brittle faults or systems of faults that exhibit a frictional rheology. Below the brittle-to-ductile transition (BDT), which delineates the shift from dominantly brittle and frictional behavior to deformation dominated by crystal-plastic and diffusional processes, they are thought to widen into broad zones of distributed strain commonly referred to as ductile shear zones. In plate boundary-scale settings, these shear zones may be upwards of 20 km wide (depending on fault regime and geothermal gradient) for the quartz-rich crystalline continental crust [3–8] and even wider in the upper mantle [9].Studies on the San Andreas system in California suggest that some strike-slip faults continue as discrete, narrow fault zones down to the Moho [10–12], whereas SKS-splitting and xenolith data suggest that the San Andreas transform system may form a ~100 km wide shear zone in the upper mantle [13]. A 1-2 km thick zone of mylonites, derived from mid-crustal depths, has been described along the Alpine Fault in New Zealand, suggesting a mid-crustal shear zone of at least these dimensions [14]. These two systems exemplify the significant uncertainty concerning the deep structure and geometry of plate boundary-scale fault systems.Despite these and other studies that have made significant progress in understanding the deep roots of fault systems below the BDT, key information is still missing. This includes (1) the variation of stress as a function of depth in contractional and strike-slip fault systems, although considerable progress has been made on normal fault systems (e.g., [15]); (2) the geometry, thickness, and internal structure of shear zones as they transect the lithosphere; and (3) the mechanical properties (i.e., rheology) of these zones, including variability in space and time.Developing a naturally-constrained model for ductile shear zone geometry and rheology has broad implications for a better understanding of the processes that control plate interaction and faulting. Lithosphere-scale faults likely behave as systems with decoupling or complex feedbacks between regions where behavior is dominated by transient, stick-slip, frictional events in the upper crust and steady-state-dominated, ductile behavior in the mid and lower crust. Rocks around the BDT probably retain the majority of crustal strength and therefore play a significant role in the loading and activation of faults near the surface [16, 17]. As such, it is critical to characterize what happens at depth, within and below the BDT, to better understand how the crust behaves within the brittle realm. Ultimately, field-based observations on natural systems are required to construct models and provide validation for experimental research on the rheology of crustal rocks.Large displacements on plate boundary shear zones, and the complexities of the processes by which they are exhumed, can make it difficult to reconstruct the structure of such shear zones with depth. In the examples outlined above, both are strike-slip systems, meaning that barring oblique slip or postfaulting uplift and erosion, rocks deformed at mid- to lower-crustal levels are unlikely to become exposed. In a normal-sense fault system, footwall rocks are cooled and exhumed with motion along the fault system, often preserving a zonation in dynamic microstructures that records strain localization and the spatial and temporal evolution of the shear zone. Unlike normal-sense systems, reverse-sense systems generally bury rocks, advecting cold rocks downwards in the footwall, and thickening the crust. For rock microstructures that record a reverse-sense evolution to be preserved, hanging wall rocks must undergo syn-deformational exhumation to prevent static overprinting of dynamic microstructures.Here, we present an integrated field, microstructural, and analytical study from the Caledonian frontal thrust system in northwestern Scotland to better understand the geometry, structure, and rheology of a lithosphere-scale contractional shear zone from the BDT to the lower crust. To do this, we present estimates of differential stress (σd), pressure (P), and temperature (T) of deformation, along with field and microstructural observations from a continuous shear zone profile to reconstruct shear zone rheology, internal structure, and geometry.The Caledonian orogen extends from western Ireland north to Svalbard and records a collisional event that was likely of Alpine or Himalayan dimensions [18, 19], spanning a period of nearly 200 Ma from the late Cambrian to latest Devonian [20]. Broadly speaking, the Caledonian orogeny is the result of the closure of the Lower Paleozoic Iapetus Ocean accommodated along several intraoceanic subduction zones, and subsequent collision of Laurentia, Baltica, Avalonia, as well as oceanic arcs and other minor terranes [18, 21–23].In northwestern Scotland, two main phases of the Caledonian orogeny are expressed: the Grampian (475–460 Ma) and the Scandian (445–425 Ma) ([24] and references therein). The Grampian phase, attributed to the collision of an oceanic arc, marked the end of the eastern Laurentian passive margin and deposition of Cambrian to Ordovician shelf facies rocks, culminating in the emplacement of ophiolites and Barrovian-style metamorphism [21]. The Scandian phase, during which many of the ductile thrusts of the orogenic prowedge were formed, was a result of the collision of Baltica with Laurentia (c. 435-420 Ma), followed closely by Avalonia (c. 425 Ma) [18, 22–24].The foreland to the Caledonian orogenic belt comprises an Archean to Mesoproterozoic basement gneiss complex unconformably overlain by Proterozoic and Cambro-Ordovician sedimentary rocks. The basement Lewisian complex includes multiply-deformed gneisses comprising 3000–2700 Ma meta-granitoids, basites, and sediments that were affected by the Badcallian (c. 2450 Ma) and later Laxfordian (c. 1800 Ma) orogenic events [25]. Rocks of the Lewisian complex are unconformably overlain by Proterozoic (c. 1200–1050 Ma) continental red beds of the Torridonian Group and Cambro-Ordovician Laurentian shelf sequence rocks including the Eriboll Formation (quartzites), An t-Sron Formation (fine to medium-grained clastic rocks), and carbonate rocks of the Durness Group. Lewisian gneisses and Eriboll Formation quartzites are the only foreland rocks that crop out within the study area. Lewisian gneisses comprise an assemblage of feldspar (orthoclase + minor albite) + quartz + white mica + epidote group minerals + chlorite + opaques. Eriboll Formation quartzites that are unaffected by ductile strain have equant quartz grains with grain sizes up to >1 mm. Minor components of feldspar + white mica are also present.The retrowedge metamorphic hinterland of the Caledonian orogenic belt is dominated by rocks of the Moine Supergroup, tectonically interleaved with basement gneisses correlative with the Lewisian, and intruded by Caledonian granitoids (Figure 1). In northwestern Scotland, hinterland rocks make up four major ductile thrust sheets; from structurally lowest to structurally highest these are the Moine, Ben Hope, Naver, and Skinsdale Nappes. These ductile thrust sheets preserve internal gradients in metamorphic grade that increase structurally up from lower greenschist facies in the structurally lowest parts of the Moine Nappe to migmatitic upper amphibolite facies in the upper Ben Hope, Naver, and Skinsdale Nappes [26–28]; this field gradient is interpreted to be related to west-directed (present orientation) Scandian thrusting [29].The Moine Supergroup comprises strongly deformed Proterozoic metasediments consisting chiefly of psammites and pelites with minor marble and metaconglomerate [30, 31]. Rocks of the Moine Supergroup are likely more distal, time-equivalents of Torridonian Group rocks that crop out in the Moine Thrust Zone and Caledonian foreland [32]. The broad metasedimentary Moine Supergroup (herein referred to as Moine schist) is traditionally subdivided into three distinct groups: the Morar, Glenfinnan, and Loch Eil, although in the present study area, all Moine schist is included within the Morar group. Rocks of the Morar group are dominantly psammitic in composition with a metamorphic assemblage of quartz + white mica + feldspar (albite + orthoclase) + epidote group minerals ± biotite ± garnet ± opaques with accessory phases including titanite, zircon, apatite, and monazite. Pelitic layers, richer in micas, feldspar, garnet, epidote, and rare staurolite crop out in lenses, although none are exposed in the study area. Chlorite occurs throughout the sequence, generally as a retrograde breakdown product from biotite and/or garnet. Plagioclase is present as relict sedimentary porphyroclasts and smaller grains incorporated into the matrix, whereas potassium feldspar is chiefly incorporated into the matrix but occurs as porphyroclasts at lower structural levels. Garnets, where present, display varying morphologies from the euhedral to anhedral [33] and skeletal. Meter-scale thick lenses of amphibolite (hornblende + quartz + feldspar ± garnet ± white mica ± biotite ± titanite ± epidote group minerals) crop out at the base of the Ben Hope Nappe and as rare inliers within the Moine schist.Scandian deformation in NW Scotland can be traced from the Moine Thrust Zone (MTZ), an imbricated zone delineating the transition from the foreland to the hinterland of the Caledonian orogenic belt, eastwards for up to 40 km into the hinterland where deeper, mid- to lower-crustal structural levels are exposed. Exposure of the MTZ and overlying hinterland rocks extends approximately N-S for at least 200 km (Figure 1) and possibly greater than 450 km when considering suggested offshore continuations to the north and south [34]. The MTZ forms a belt of imbricated foreland rocks bound by the structurally lowest Sole Thrust below and Moine Thrust above.Timing of thrusting is based on dating of intrusive rocks and deformational fabrics; K-Ar and Rb-Sr dating of syn-kinematic micas in mylonites [35] and U-Pb dating of zircons in syn-kinematic intrusions [29, 36] constrains activity to between ~435–425 Ma. This timing is consistent with reported Rb-Sr ages on muscovite and 40Ar/39Ar cooling ages from hornblende and muscovite [37]. Thrusting was roughly WNW-directed, recorded by the pervasive stretching and mineral lineation and tight to isoclinal folds rotated into parallelism with the lineation [38–40].This study examines rocks exposed along a transect that extends from the southern head of Loch Eriboll at the settlement of Strabeg, in the footwall of the Moine Thrust (MT), SSE across the southern continuation of the Eriboll Peninsula, and the Ben Hope Thrust to the summit of Ben Hope (hereon referred to as the Strabeg transect; Figures 2(a) and 2(b)). This area was chosen based on the clear lithologic expression of the MT (Figure 3), the relatively simple tectonic stratigraphy (Figure 4), and extensive, continuous exposure along much of the transect. The transect is taken along a line trending 110°-290°, parallel to the average trend of the stretching lineation and inferred direction of transport [38–40]. In total, the transect spans 9 km on the ground, corresponding to a structural thickness of over 3 km. The lower structural levels of the transect record greenschist grade metamorphism, while the structurally higher levels record metamorphism at lower- to mid-amphibolite facies [43–45].Three primary ductile thrusts crop out along this transect (Figures 1, 2, and 4(a)). The structurally lowest Lochan Riabhach Thrust (LRT) emplaces Lewisian gneiss over the foreland Eriboll Formation quartzite. Structurally above, the Moine Thrust (MT) emplaces Moine schist of the Moine Nappe onto variably mylonitized Lewisian gneiss and Eriboll Formation quartzite. Exposed along the west flank of Ben Hope, the Ben Hope Thrust (BHT) emplaces Moine schist, along with thin layers of basement gneiss (likely Lewisian) and amphibolite, which make up the Ben Hope Nappe, over Moine schist of the Moine Nappe (Figure 2).Normal faults have been previously mapped striking N-S from the head of Loch Hope (Figures 1 and 2 and references therein). Due to a lack of exposure in this section of the transect, these cryptic structures have an unknown orientation and displacement. Because there is no distinct gap or repetition of lithology or microstructure across these structures, we conclude that the offset along these faults and any resulting discrepancy in structural distance across them is minimal.The sequence of thrusting generally propagated towards the foreland with earlier, hinterland thrust sheets transported “piggy-back” on younger thrusts [34, 38, 46]. In detail, and especially at the orogen-scale, the system likely had a more complex evolution with out-of-sequence thrusting and reactivation of older thrusts [47, 48]. Within the study area, however, fold geometries and interactions are consistent with a locally simple foreland-propagating model [49]. Additionally, the MT is the primary tectonic boundary between the Moine schist and foreland Cambro-Ordovician and Lewisian rocks, and it is therefore interpreted to be the approximate basal detachment of this broader crustal-scale shear zone system at depth, although foot wall rocks are involved in deformation [26]. Lastly, geochronological evidence indicates that the Scottish Caledonides were undergoing active erosion and cooling throughout much of the Scandian phase (syn-deformational cooling and erosion is suggested ca. post-425 Ma; [50] and references therein). We support these ideas and proceed with the interpretation that faults exposed along the Strabeg transect are part of the same shear zone at depth, which, within the study area, repeatedly propagated towards the foreland. We therefore treat the BHT, MT, and LRT as representing different structural levels of the Scandian shear zone (Figure 5). The hinterland thrust sheets that were uplifted piggy-back on these thrusts were simultaneously exhumed, preserving the rock microstructure and exposing deep levels of the same shear zone (Figures 5 and 6).Structural distance is taken as the foliation-perpendicular distance from the projected MT plane to the point of interest. Present-day structural distances along the Strabeg transect are calculated in order to place our samples in the context of the shear zone as a whole, and to provide a basis for reconstructing the geometry of the shear zone when it was active. Distances are calculated using the lithologic expression of the MT (i.e., the contact between Moine schist and underlying Lewisian gneiss) as the reference plane (Figure 4(a)). Although the lithologic contact likely does not coincide with the most localized, highest strain rocks, it provides an appropriate passive boundary within the shear zone.For distance measurements, the MT is assumed to extend as a planar feature at a constant dip beneath the area of interest. This is supported by the DRUM, MOIST, and LISPB seismic studies, which image reflectors interpreted to be thrust planes cutting through the upper and middle crust at a constant angle [51–53]. We assume that the thrust plane dips at 15°ESE, based on measurements in the field and published British Geological Survey mapping (Loch Eriboll sheet 114 W). We also include a correction for the change in elevation between the point of interest and the trace of the MT.For structural distance measurements to be valid, we assume that the foliation is parallel or subparallel to the shear plane. This is based on the fact that the foliation in a shear zone rotates towards the shear plane with progressive strain. We measured strain intensities on two outcrops of basal Moine metaconglomerate (Figure 1) which resulted in values of D=2.5 and D=2.3⁠, where D is a dimensionless measure of strain magnitude defined on a logarithmic Flinn diagram (Figure S3). Additional attempts to quantify strain using the nearest neighbor technique on feldspar porphyroclasts within the Moine schist were unsuccessful, likely due to the invalid initial condition assumption of a random distribution of clasts. Despite the lack of widespread quantitative finite strain estimates within the Moine schist, we posit that finite shear strains are generally large enough to approximate the foliation as being parallel to the shear plane, thus validating our calculations of structural distance (see [26, 54] for further discussion).Based on the examination of >50 thin sections from the Strabeg transect, we have identified four distinct yet gradational microstructural domains (Figures 4(a) and 4(c)–4(g)). These domains record progressive shear zone evolution and strain localization and are subdivided based on quartz recrystallization mechanism, rheological behavior (e.g., phases accommodating strain) and to a lesser extent, lithology. In the following section, we describe microstructures and defining characteristics for each of these domains, with emphasis on quartz microstructure and recrystallization mechanism.Across the transect, quartz recrystallizes by bulge nucleation (BLG), subgrain rotation (SGR), and high-temperature grain boundary migration (high-T GBM). BLG, SGR, and GBM, as outlined in Stipp et al. [55], broadly correspond to the experimental regimes 1, 2, and 3 of Hirth and Tullis [56], respectively. The reader should take note however that regime 3 of Hirth and Tullis [56] is better related to a transitional SGR/GBM zone of Stipp et al. [55]. For the remainder of this manuscript, we will adopt the nomenclature outlined in Stipp et al. [55].Within the Eriboll quartzite and the tectonically overlying Lewisian gneiss, Domain 1 records deformation structurally below the MT and in rocks affected by movement along the Lochan Riabhach Thrust (LRT). Domain 1 spans a structural distance of approximately 250 m, extending from the lower limit of crystalplastic deformation in the footwall of the LRT to approximately 100 m structurally below the MT (Figure 4(a)). Strain is accommodated chiefly by crystal plastic deformation of quartz and mica as well as subsidiary brittle fracture in quartz, mica, and feldspar. Dynamic recrystallization in quartz is dominated by bulge nucleation, indicated by serrated grain boundaries and bulges, as well as very limited subgrain rotation, evidenced by the development of core and mantle microstructures with mantling subgrains roughly equal in size and dimension to recrystallized grains and an abundance of low-angle misorientations (Figures 4(g) and 7(a)–7(c), S2). Percent of recrystallized quartz increases structurally up from the undeformed Eriboll Fm. in the footwall of the LRT, where detrital grains are preserved at the lowest structural levels, to complete recrystallization at <20 m below the lithologic MT. Where present, feldspar generally forms large (500 to >1000 μm) porphyroclasts which show variable intensity of brittle fracture typically increasing structurally up towards the MT. Fractures in quartz and feldspar are commonly filled with precipitated quartz and/or calcite, indicating solution-precipitation creep involving these phases (Figure 7(c)). Phyllosilicates, including white mica and chlorite, are the primary phases defining the foliation and generally wrap around larger feldspar porphyroclasts.The characteristics differentiating Domain 2 from Domain 1 are the near-complete dynamic recrystallization of quartz, chiefly by SGR, and extensive reduction in grain size. We subdivide Domain 2 into two subdomains based on foliation intensity, grain size, and interconnection of phyllosilicate layers (Figures 7(d) and 7(e)). Domain 2a (Figures 4(f) and 7(d)), characterized by finer grain sizes and strong lamellar folia of alternating quartz-rich and homogenized, fine-grained, polyphase (quartz + feldspar + white mica ± chlorite ± minor accessory) material, extends from approximately 100 m structurally below the MT to >100 m structurally above the MT (Figure 4(a)). Domain 2b, extending structurally up to approximately 200 m above the MT, is characterized by increased grain size and anastomosing phyllosilicate networks that commonly wrap around feldspar porphyroclasts (Figures 4(e) and 7(e)). Matrix material in Domain 2b records less mixing (homogenization) of fine-grained quartz + feldspar + mica compared to Domain 2a (e.g., Figures 7(e) and 7(f)). Recrystallized quartz-dominated lamellae in Domain 2b also show variable buckle folding whereas quartz-dominated lamellae in Domain 2a show no evidence of folding and are mostly parallel to subparallel to the macroscopic foliation (Figures 7(d) and 7(e)). In all, Domains 2a and 2b extend for a structural distance of approximately 300 m above the MT (Figure 4(a)).Within Domain 2, quartz textures record pervasive dislocation-driven dynamic recrystallization chiefly by SGR, indicated by (1) development of core and mantle microstructures with mantling subgrains roughly equal in size and dimension to recrystallized grains; (2) development of a pervasive oblique shape preferred orientation (SPO) of recrystallized grains; and (3) misorientation angle distributions within dynamically recrystallized quartz (Figure S2). Limited evidence in the form of quartz-filled pressure shadows in porphyroclasts and rare quartz fill in fractured garnets and feldspar porphyroclasts record a relatively minor component of dissolution-reprecipitation creep (i.e., pressure solution; Figure 7(e)). Where quartz is mixed with other phases, generally mica and feldspar, the resulting mixture is significantly finer-grained due to the pinning of grain boundaries (Figures 7(d) and 7(e)). Because of the small grain size and abundance of phase boundaries that may act to promote quartz dissolution rates [55, 56], quartz in regions dominated by fine-grained, polyphase material (Figures 7(d) and 7(e)) likely underwent increased deformation by pressure solution, although we lack direct evidence to support this. In pure quartz domains where grain boundaries are unaffected by nonquartz phases, grains show a ubiquitous SPO generally inclined at 10-50° to the foliation in the direction of shear (Figures 4(e) and 7(f)).Feldspars occur as equant to elongate clasts with diameters of up to >1000 μm. Feldspar long axes are parallel to the foliation and clasts are commonly wrapped by micas and other phyllosilicates (e.g., chlorite). There is a correlation between feldspar shape and surrounding material; whereas feldspar grains surrounded primarily by quartz tend to fracture, feldspar grains surrounded by a polyphase matrix are elongate (Figure S1). The presence of elongate clasts in a polyphase matrix is suggestive of crystalplastic deformation or spallation of the feldspar; however, there is only limited direct evidence (e.g., core and mantle structure, bulging, or sutured grain boundaries) to support crystal plastic deformation.Discontinuous microscale shear bands, inclined to the primary foliation, are common in Domain 2b (Figure 8(a)). These appear to be coeval with the primary foliation: there is no difference in microstructure in the bands, and they are defined primarily by the deflection of the mica foliation. The relative abundance and intensity increase structurally up from very high strain rocks in which shear bands have been obliterated to a maximum at a structural distance of 200-300 m above the MT. Structurally above this, both intensity and abundance decrease until the transition to Domain 4, above which shear bands are generally absent. Most well-developed shear bands indicate a top-WNW sense of shear although rare, less developed bands indicate top-ESE, consistent with a strain geometry dominated by simple shear but with a minor component of flattening.The structurally higher part of Domain 2 contains a zone of Lewisian gneiss <4 m thick, in contact with Moine schist structurally above and below. This Lewisian inlier is likely either an imbricate thrust slice, in which case the lower contact is a fault and the upper contact is a nonconformity, or the core of a tight to isoclinal fold which incorporated basement rock, in which case both the upper and lower contacts are nonconformable. We observe no exposure of a brittle fault or high-strain zone. At the microscale, the grain size, shape, and recrystallization mechanism in recrystallized quartz do not vary drastically across this region. Below, we address the rheologic implications of this Lewisian inlier with respect to effective shear zone width.Domain 3 is marked by the transition from quartz recrystallizing by subgrain rotation to high-T GBM. Quartz grains in this domain are significantly coarser grained (Table 1) and preserve an irregular, amoeboid texture characteristic of high-T GBM (Figures 4(d), 7(f), and 7(g)). These amoeboid grains include minor subgrain development and commonly show undulose extinction, indicating limited buildup of dislocations in the crystal lattice. At higher structural levels within Domain 3, straight grain boundaries and stable 120° grain triple junctions [59] mark recovery and likely grain growth driven by minimization of surface energy (γ-GBM of [60]). Based on the relative structural position of dominant recrystallization mechanisms, we interpret γ-GBM to have overprinted dynamic high-T GBM microstructures (i.e., grains were annealed), although it is plausible that the two modes coexisted.Feldspar and mica are also coarser grained than in Domains 1 and 2; single mica grains >500 μm are common, as are feldspar porphyroclasts >1 mm in diameter. Feldspars occur in two distinct populations: plagioclase (generally sodic) occurs primarily as porphyroclasts in variable proportions whereas orthoclase occurs as both porphyroclasts and as subordinate grains incorporated into the matrix. Within Domains 3 and 4, some plagioclase feldspar grains are irregularly zoned with more sodic cores (~An40-50) and irregular calcic (~An60-70) overgrowths; these observations are consistent with other chemical analyses of feldspars from within the Moine Nappe [35, 38]. Feldspars show variable degrees of dynamic recrystallization, where recrystallized, new grains tend to be a calcic plagioclase, regardless of the composition of the grain they originated from. Within the basement gneiss slice that crops out immediately above the BHT, recrystallized feldspars have distinctive lozenge shapes, with grain long axes parallel to the foliation and grain sizes on the order of 100 to >500 μm.Domain 4 occupies the structurally highest levels of the Moine Nappe and continues up into the Ben Hope Nappe. Domain 4 is similar to Domain 3 although quartz in Domain 4 has undergone pervasive annealing and probable grain growth, resulting in a larger grain size (Figures 4(c) and 7(h), Table 1). Quartz preserves a variable to strong CPO although the dynamically recrystallized microstructure has been overprinted by annealing of grains (indicative of recovery and γ-GBM). The most abundant phases besides quartz are feldspar and mica, which have similar compositions, grain sizes, and textures to those in Domain 3.The Stipp and Tullis [62] and Cross et al. [61] piezometers are calibrated to grain sizes up to ~50 μm, where microstructures indicate dynamic recrystallization primarily by BLG and SGR. The calibration has been extrapolated to grain sizes up to >120 μm, corresponding to deformation primarily by SGR and high-T GBM, but yields only minimum differential stress estimates for these large grain sizes [60, 68]. We also calculate stresses for microstructures which clearly show evidence of recovery (e.g., γ-GBM in Domain 4) and accept that these calculations are only crude estimates of minimum differential stress.We measured dynamically recrystallized grain sizes of quartz in 19 samples using both electron backscatter diffraction (EBSD) and Fiji optical analysis software, an extended toolbox for ImageJ (http://www.fiji.sc; [69]). Thin sections were cut and analyzed parallel to the lineation and perpendicular to the foliation. EBSD acquisition details and data cleaning routine are detailed in Appendix A.For coarser-grained samples (>100 μm), optical images were acquired and grain boundaries defined in Fiji to quantify grain size distribution. Multiple photomicrographs were taken with differently angled polarizers to more accurately distinguish grain boundaries.All grain size measurements are expressed as the diameter of a circle with an equivalent area to calculated grain polygons. A minimum of 350 grains were used to calculate the mean grain size within a sample. We calculated the grain size distribution frequency peak, as outlined by Lopez-Sanchez and Llana-Fúnez [70]. However, we found that our EBSD-based grain size analyses contained an abundance of small grains which result in a positively skewed distribution and a frequency peak significantly lower than the arithmetic mean or root mean square (RMS) grain size. For this reason and for consistency with the piezometric calibrations, final recrystallized grain size for each sample is taken as the RMS of all measurements after cleaning, with errors reported as 1σ (Table 1).We used EBSD data from all 19 samples to determine crystallographic preferred orientations (CPO) of recrystallized quartz as evidence for recrystallization by dislocation creep, qualitative conditions of deformation, and active slip systems throughout the structural section of the Strabeg transect. c-, a-, and m-axis pole figures (PF) and X-direction inverse pole figures (IPF-X) were constructed from a calculated orientation distribution function using MTEX (http://www.mtex-toolbox.github.io) based on a one point-per-grain statistical calculation. PFs are oriented in the X-Z plane with the foliation oriented parallel to the X-direction, thus interpreted to lie close to the shear plane in the direction of shear. PFs were plotted as lower hemisphere, equal-area projections, whereas IPFs were plotted as X-direction upper hemisphere projections. Individual scales were used for each PF and IPF to bring out CPO intricacies in low-intensity fabrics that would otherwise be lost if a common scale were applied. CPO intensity was measured using the ODF-based m-index of Skemer et al. [71] and j-index [72]. Each PF and IPF was constructed using only dynamically recrystallized grains; host grains are identified following the grain orientation spread discrimination technique and are excluded [61]. The quartz crystallographic data we present are derived from both monophase quartz and polyphase regions and were constructed from a number of grains greater than or equal to # grains (EBSD) from Table 1.At all structural levels within the Moine Nappe, quartz grains exhibit evidence of grain boundary pinning by both phyllosilicates and fine-grained feldspars. These polyphase aggregates systematically contain demonstrably finer grain sizes compared to areas of pure quartz, (Figures 7(d) and 7(e)) consistent with observations elsewhere (e.g., [73–75] and references therein; [76]); for this reason, we attempt to record grain size measurements from areas free of nonquartz phases (e.g., recrystallized quartz veins, quartz-rich lenses). In some cases, chiefly in the coarser-grained rocks at higher structural levels in Domains 3 and 4, it is difficult to obtain a statistically significant number of grains from monophase regions. In this case, we include some grains that have pinned boundaries and accept that errors associated with these measurements may be significantly higher than those in monophase regions.At lower structural levels within Domain 2a where total strain is likely higher, phyllosilicate-rich or fine-grained polyphase interconnected layers alternate with monophase quartz or feldspar dominated layers, defining the primary foliation. Polyphase layers show evidence of higher shear strains compared to the pure quartz or quartz + feldspar layers (Figure 8(b)). Similarly, the presence of buckle-style folds in quartz layers at higher structural levels within Domain 2b indicates a viscosity contrast between these layers and the surrounding polyphase matrix (Figure 7(e)).Based on these two primary lines of evidence, we interpret the quartz and quartz + feldspar layers as more competent, with more strain accommodated in the weaker polyphase layers. These weak polyphase layers may deform by a combination of dislocation creep and grain size sensitive creep, including grain boundary sliding (GBS), especially parallel to the long axis of phyllosilicates. Because the areas where we collected grain size measurements are possibly stronger, our stress determinations may overestimate the average stress in the system.We determined deformation temperatures (T) and pressures (P) for 11 samples using the Ti-in-quartz (TitaniQ) thermobarometer of Wark and Watson [77], as calibrated by Thomas et al. [78, 79], in conjunction with thermodynamic modeling of Si-in-phengite [80] and TiO2 activity ([81]; Figure 9). Temperature and pressure calculations can be attributed to a specific quartz- and mica-dominated microstructure, thereby determining the conditions at which the microstructure was formed. Both quartz and white mica record progressive recrystallization and reduction in grain size along the transect, suggesting that both phases recrystallized and reequilibrated to ambient conditions together. As such, the temperatures and pressures we calculate represent the last stage of deformation before the rock left the active shear zone (Figure 6), and may not be the same those calculated using traditional thermobarometry on the metamorphic assemblage as a whole. For 9 samples that record crossed-girdle c-axis topologies, we use the quartz c-axis opening angle thermometer calibration of Faleiros et al. (2016) for additional temperature estimates, chiefly to compare to our TitaniQ-based temperature estimates as well as previous opening angle temperatures from the area ([83–86] and references therein).For each sample, we calculate T, P, and a(TiO2) using a combination of Ti-in-quartz (Figure 10(a)), Si-in-phengite (Figure 10(b)), and titania activity (a(TiO2)) pseudosection modeling (Figures 9(a) and 9(b)); details of these analytical techniques and methods are outlined in Appendix B. a(TiO2) is contoured in P-T space based on the bulk composition of each sample (see [81]). Due to the temperature dependence of titanium activity in our samples, modeled a(TiO2) generally increases with temperature (Figures 9(b) and 10(c)). From the solubility equation for Ti in quartz (e.g., Equation (B.1); [79]), the position of the equilibrium line in P-T space for a given Ti concentration in quartz ([Ti]) will shift to lower temperatures with increasing a(TiO2) in the system. By plotting the positions of the equilibrium line for the measured [Ti] as a function of a(TiO2), and contouring for a(TiO2) from 0 to 1, we can determine the points in P-T space where the equilibrium lines at different a(TiO2) intersect the corresponding contours. We then graphically determine where this array intersects the modeled Si-in-phengite isopleth (corresponding to the measured Si PFU). Errors are reported as 1σ of the measured analytical values for Si-in-phengite PFU and Ti-in-quartz concentration (Figure 9(b)).Grain sizes along the Strabeg transect range from ~9±4 μm at the structurally lowest levels, where recrystallization by BLG dominates, to ~127±55 μm just below the transition from Domain 3 to 4 (sample LS-105), to ~175±87 μm at the structurally highest levels, where recrystallization occurs chiefly by high-T GBM (Table 1, Figure 11(a)). These values correspond to differential stresses ranging from ~119 to 15 MPa, respectively, using the 1 μm step size calibration of Cross et al. [61] (Figure 11(b)). For structurally higher samples in which grain sizes were measured both optically and by EBSD, we observe a marked decrease in average recrystallized grain size measured by EBSD compared to optical measurements from the same sample. White [75] also reported different grain sizes determined by electron and optical microscopy and suggested that such measurements not be interposed. Optically measured recrystallized grain sizes range from ~68±25 μm at a structural distance of 866 m, to ~143±73 μm just below the transition from Domain 3 to 4 (sample LS-105), to ~255±121 μm at the structurally highest levels (Figure 11(a)). These values correspond to differential stresses ranging from ~23 to 8 MPa using the piezometer of Stipp and Tullis [62] (Figure 11(b)).Our EBSD-based grain size measurements from the lowest structural levels are similar to previous optical determinations of recrystallized grain size from the region. White [75, 87] measured grain sizes of 14.6 μm from the footwall of the MT at Eriboll, Ord and Christie [88] recorded grain sizes as small as 12.7 μm in the footwall of the MT in the Assynt Culmination, and Weathers et al. [89] determined grain sizes of 10-20 μm from the Assynt Culmination and Eriboll (Figures 1 and 2). These measurements were taken chiefly from within quartzites of the Eriboll Fm. in the footwall of the MT. Additionally, Francsis [83] measured recrystallized grain sizes optically 5 km to the south of the Strabeg transect; these measurements ranged from 26.2±10 μm at 80 m below the MT, up to 203.5±96.1 μm at 2294 m above the MT, in the hanging wall of the BHT. These grain size measurements are larger than those we measured by EBSD, but are close to our optical measurements.All samples show some degree of a CPO in recrystallized quartz, consistent with dislocation creep as the primary deformation mechanism. CPO intensities, measured by the m-index [71] and j-index [72], show significant variability (Figure 12). All CPOs are inclined in an orientation consistent with top-WNW shearing. CPOs along the Strabeg transect are dominated by Y-maxima, crossed-, and single girdles, consistent with the activity of basal , rhomb , and prism slip systems; we see no evidence for prism [c] slip at these structural levels. Slip systems are likely at least partially temperature-dependent with basal , rhomb , and prism representing progressively higher temperatures. They may also depend on finite strain, with prism favored by higher strains (Figure 12, [14, 90] and references therein; [91]). Temperatures, based on active slip systems, generally increase structurally upward from the LRT to the BHT although the effect of temperature in isolation on CPO topology remains unclear [14].A general trend emerges in the shape of the CPO through the structural section (Figure 12). At the lowest structural levels around the LRT (Domain 1), CPOs are defined by weak c-axis crossed-girdles suggesting activity of basal , rhomb , and prism slip systems. At structural levels immediately above and below the MT (Domain 2a, b), c-axes show somewhat stronger crossed-girdles and single girdles. Single girdles are generally stronger and may show weak complementary crossed-girdle legs. CPOs in the lower structural levels of Domain 3 are characterized by strong maxima normal to the foliation (Y-maxima), which are indicative of prism slip. Structurally higher (i.e., higher structural levels of Domain 3 and Domain 4), textures transition to single girdles with elongate Y-maxima parallel to the long axis of the girdle, indicative of prism and rhomb slip. Secondary maxima generally expressed along the pole figure periphery indicates smaller contributions from the basal slip system. As in Domain 2, generally weak maxima exist in some samples along the pole figure periphery that represent crossed-girdle legs. Strong Y-maxima in the immediate hanging wall of the BHT and at the structurally lower levels of Domain 3 may result from large shear strains [90, 91] or enhanced hydrolytic weakening (e.g. [84, 92]).As illustrated in Figure 12, many of the crystallographic textures plot as single girdles with absent or very weak crossed-girdle legs that may not be expressed in the contouring. These patterns differ from previously published crystallographic data from northwest Scotland (e.g., [45, 84–86] and references therein) which commonly show crossed-girdle c-axis patterns, used to determine temperatures based on crossed-girdle opening angle. The paucity of crossed-girdle patterns in our EBSD-based c-axis data can likely be attributed to the techniques used for fabric measurement and contouring (R. Law, personal communication); whereas EBSD-based crystallographic data are produced by one point-per-grain analyses including all grains within a large area, measurements by universal stage, utilized in many previous studies, require individual measurements of grains that occupy the entire section thickness, and may introduce subjectivity.Like other studies that have employed the TitaniQ thermobarometer in deformed terranes (e.g., [93–96]), our analyses reveal low Ti concentrations in dynamically recrystallized quartz. Despite low Ti concentrations, the data follow a generally well-defined trend, increasing structurally up from 0.58 ppm near the MT, to 2.57 ppm in the hanging wall of the BHT (Figure 10(a)), whereas Si-in-phengite shows a broadly increasing trend over the same structural section from 3.23–3.29 PFU (Figure 10(b)). Utilizing the modeling approach detailed in Appendix B, Ti concentrations correspond to temperatures and pressures ranging from approximately 350–450°C and 270–560 MPa (2.7–5.6 kbar; Figures 4(b) and 10(c), Table 1). Quartz c-axis opening angle temperatures broadly increase structurally up, albeit with significantly more scatter, from 334–555° C (Figure 12, Table 1). Both TitaniQ and c-axis opening angle temperatures agree with trends identified by previous workers, who have found structurally upward-increasing field gradients within individual nappes [45, 97]. Our calculated TitaniQ temperatures are also generally lower than temperatures estimated by quartz recrystallization mechanism; recrystallization by BLG, SGR, and GBM are suggested to occur within temperature ranges of ~300-400°C, 400-525°C, and >525°C, respectively [55, 98]. Along the Strabeg transect, rocks deforming by BLG have calculated temperatures of ~350°C, recrystallization by SGR corresponds to temperatures of ~350–380° C, and recrystallization by high-T GBM range from ~370–450°C. It is worth noting, however, that the recrystallization mechanism temperature estimates of Stipp et al. [55] are based on syn-kinematic mineral assemblages, representing “close to peak” temperatures in a system that continued deforming while cooling, and therefore may be capturing a different part of the P-T-t path than TitaniQ estimates.TitaniQ-derived deformation temperatures calculated here tend to be significantly lower than published garnet-biotite Fe-Mg exchange (GARB) metamorphic temperatures, quartz c-axis opening angle deformation temperatures, and multisystem P-T analyses [43–45, 48, 97]. We offer the following possible explanations for this discrepancy. (1)Temperatures derived from TitaniQ are strongly dependent on a(TiO2), and small changes in a(TiO2), especially at low values (i.e., a(TiO2) <0.3), can result in significant differences in P-T conditions. Although the method we follow yields a simultaneous, unique solution for P, T, and a(TiO2), it is possible that analytical errors arising from XRF, SIMS, or EPMA may result in a(TiO2) values that are systematically too high, and hence temperatures that are too low. For our TitaniQ-based temperatures to come within the error of multisystem and GARB values, a value of a(TiO2) of <0.1 is necessary. However, based on the temperature dependence of a(TiO2), the presence of syn-deformational titanite, and the homogeneous distribution of Ti at both the grain- and sample-scales, we consider a(TiO2) values this low to be unlikely.(2)A more fundamental flaw in our understanding of the mechanics of Ti mobility and substitution into quartz affected by crystal-plastic deformation may also be possible. Ashley et al. [99] suggest that low [Ti] in dynamically recrystallized quartz could be a result of local reequilibration from subgrain boundaries and dislocation arrays migrating through quartz grains. The reequilibration in this case is suggested to be buffered or regulated by the composition of the intergranular medium which is typically Ti-undersaturated with respect to the overall assemblage and may not represent the actual a(TiO2). More recent experimental work however indicates that Ti concentrations are reequilibrated during recrystallization, reflecting bulk a(TiO2) [100, 101].(3)Another possible explanation for the discrepancy in temperatures stems from what portion of the P-T-t history a thermometer or thermobarometer captures. Metamorphic temperatures calculated from metamorphic thermobarometers or multisystem equilibria (GARB included) likely record “peak” or “near-peak” prograde metamorphic temperatures. Within rocks of the Moine Supergroup, garnets are present as porphyroblasts of variable size, morphology, and chemistry and are commonly chemically zoned with relative proportions of Mn higher in the cores and Fe and Ca higher in the rims (see [33, 43, 45, 48, 97]). Optically, zoning is commonly defined by linear or spiral inclusion trails either in the cores or rims that are discordant to the primary foliation. This physical and chemical zoning indicates that garnets record growth over multiple episodes, likely at variable P-T-X. At structurally lower levels along the Strabeg transect garnets tend to be anhedral or skeletal, suggesting that they could be out of equilibrium. In contrast, if [Ti] reequilibrates with dynamic recrystallization, TitaniQ temperatures should record the conditions when plastic deformation and dynamic recrystallization ceased (i.e., when the rock left the actively-deforming shear zone).(4)Based on our interpretation of shear zone evolution, deformation temperatures recorded in the quartz microstructures should be well below peak conditions. c-axis opening angle temperatures are inconsistent with this interpretation whereas our TitaniQ temperatures, albeit low, are consistent. Although the similarity between opening angle temperatures and petrologic thermobarometers (e.g., [84] their Figure 24) is compelling, considerable uncertainty remains regarding the effects of strain geometry, recrystallization mechanism, strain rate, and water content on c-axis opening angles (see [84] for further discussion). Furthermore, existing c-axis opening angle calibrations are based almost exclusively on temperature estimates derived from peak or near-peak metamorphic assemblages ([84] and references therein; Faleiros et al., 2016); although these may represent conditions during deformation, they are not necessarily representative of the last deformation conditions the rocks last experienced before being “locked in”. As such, we are hesitant to assign temperatures calculated from c-axis opening angles as being representative of any specific (or consistent) time in the deformation history (e.g., [84]).(5)Lastly, based on microstructural observations, the trace of the MT (i.e., base of the Moine Nappe) exposes different structural levels along strike ranging from very shallow, mylonite-on-foreland (e.g., Knockan Crag – Figure 1) to high-temperature GBM microstructures within mylonitic Moine schist lying on mylonitic Oystershell rock (a phyllonite thought to be derived from Lewisian basement gneisses that commonly crops out within the MTZ) along the north coast [34, 38, 46, 102]. So, although the Moine Nappe is a coherent tectonic unit, pressure and temperature conditions vary both along and across strike, as do conditions at the base of the nappe. This is plausibly a result of differential syn- and postdeformation erosion and exhumation. In this case, it is likely that previously published estimates are measuring temperatures and pressures attained at different structural levels and at different times within the Moine NappeTemperatures derived from TitaniQ are strongly dependent on a(TiO2), and small changes in a(TiO2), especially at low values (i.e., a(TiO2) <0.3), can result in significant differences in P-T conditions. Although the method we follow yields a simultaneous, unique solution for P, T, and a(TiO2), it is possible that analytical errors arising from XRF, SIMS, or EPMA may result in a(TiO2) values that are systematically too high, and hence temperatures that are too low. For our TitaniQ-based temperatures to come within the error of multisystem and GARB values, a value of a(TiO2) of <0.1 is necessary. However, based on the temperature dependence of a(TiO2), the presence of syn-deformational titanite, and the homogeneous distribution of Ti at both the grain- and sample-scales, we consider a(TiO2) values this low to be unlikely.A more fundamental flaw in our understanding of the mechanics of Ti mobility and substitution into quartz affected by crystal-plastic deformation may also be possible. Ashley et al. [99] suggest that low [Ti] in dynamically recrystallized quartz could be a result of local reequilibration from subgrain boundaries and dislocation arrays migrating through quartz grains. The reequilibration in this case is suggested to be buffered or regulated by the composition of the intergranular medium which is typically Ti-undersaturated with respect to the overall assemblage and may not represent the actual a(TiO2). More recent experimental work however indicates that Ti concentrations are reequilibrated during recrystallization, reflecting bulk a(TiO2) [100, 101].Another possible explanation for the discrepancy in temperatures stems from what portion of the P-T-t history a thermometer or thermobarometer captures. Metamorphic temperatures calculated from metamorphic thermobarometers or multisystem equilibria (GARB included) likely record “peak” or “near-peak” prograde metamorphic temperatures. Within rocks of the Moine Supergroup, garnets are present as porphyroblasts of variable size, morphology, and chemistry and are commonly chemically zoned with relative proportions of Mn higher in the cores and Fe and Ca higher in the rims (see [33, 43, 45, 48, 97]). Optically, zoning is commonly defined by linear or spiral inclusion trails either in the cores or rims that are discordant to the primary foliation. This physical and chemical zoning indicates that garnets record growth over multiple episodes, likely at variable P-T-X. At structurally lower levels along the Strabeg transect garnets tend to be anhedral or skeletal, suggesting that they could be out of equilibrium. In contrast, if [Ti] reequilibrates with dynamic recrystallization, TitaniQ temperatures should record the conditions when plastic deformation and dynamic recrystallization ceased (i.e., when the rock left the actively-deforming shear zone).Based on our interpretation of shear zone evolution, deformation temperatures recorded in the quartz microstructures should be well below peak conditions. c-axis opening angle temperatures are inconsistent with this interpretation whereas our TitaniQ temperatures, albeit low, are consistent. Although the similarity between opening angle temperatures and petrologic thermobarometers (e.g., [84] their Figure 24) is compelling, considerable uncertainty remains regarding the effects of strain geometry, recrystallization mechanism, strain rate, and water content on c-axis opening angles (see [84] for further discussion). Furthermore, existing c-axis opening angle calibrations are based almost exclusively on temperature estimates derived from peak or near-peak metamorphic assemblages ([84] and references therein; Faleiros et al., 2016); although these may represent conditions during deformation, they are not necessarily representative of the last deformation conditions the rocks last experienced before being “locked in”. As such, we are hesitant to assign temperatures calculated from c-axis opening angles as being representative of any specific (or consistent) time in the deformation history (e.g., [84]).Lastly, based on microstructural observations, the trace of the MT (i.e., base of the Moine Nappe) exposes different structural levels along strike ranging from very shallow, mylonite-on-foreland (e.g., Knockan Crag – Figure 1) to high-temperature GBM microstructures within mylonitic Moine schist lying on mylonitic Oystershell rock (a phyllonite thought to be derived from Lewisian basement gneisses that commonly crops out within the MTZ) along the north coast [34, 38, 46, 102]. So, although the Moine Nappe is a coherent tectonic unit, pressure and temperature conditions vary both along and across strike, as do conditions at the base of the nappe. This is plausibly a result of differential syn- and postdeformation erosion and exhumation. In this case, it is likely that previously published estimates are measuring temperatures and pressures attained at different structural levels and at different times within the Moine NappeFor the structural thickness of a shear zone to remain constant through time, the shear zone must not undergo significant thinning or volume loss. We argue here that the shear zone deformed primarily by plane strain and simple shear (noncoaxial) and did not undergo significant volume loss. In principle, this can be tested by a variety of techniques that allow the kinematic vorticity number (⁠Wk⁠) to be estimated. Thigpen et al. [85], for example, use rigid grain analysis to calculate Wk values between ~0.6–0.7 for rocks within the Moine Nappe on the Eriboll Peninsula, corresponding to ~60–50% pure shear (coaxial). However, in numerous deformed terranes, calculation of Wk by rigid grain analysis appears to underestimate the component of noncoaxial strain relative to other methods [103–105] and uncertainties associated with these methods may be significant [106]. Law (2010) reports values of Wk from within 100 m structurally above and below the MT at the Stack of Glencoul, using rigid grain analysis for the Moine mylonites, and two additional techniques involving the geometry of the CPO for the mylonitic Cambrian quartzites below the Moine thrust. The values range from 0.75–0.65 (45–55% coaxial shear) to 0.99–0.90 (10–30% coaxial shear), and generally increase (i.e., a larger component of simple shear) with proximity to the MT. A significant component of coaxial shortening in such high-strain rocks presents serious compatibility issues, however. X-Z finite strain ratios in from detrital and recrystallized grains in the Eriboll Fm. commonly range between 10 and 19 (Law, 2010). Assuming no volume loss, and Wk≈0.77⁠, an X-Z ratio of 19 requires 65% shortening normal to the shear plane, and hence a stretch of 2.1 in the direction of shear (Law, 2010).The situation in the Moine mylonites is much more extreme. Strain data are lacking, but if we take a very conservative estimate of 1 km displacement across the basal 100 m of mylonite, giving a component of simple shear strain γ of 10, take Wk≈0.75 as estimated by Law (2010), and assume plane strain and no volume loss, then shortening normal to the shear plane is 88%, and the pure shear related stretch in the direction of shear is 8.2. Unless the entire thrust pile above the mylonite zone experiences the same amount of stretch, this requires extrusion of many kilometers of mylonite at the thrust front. This type of extrusion model has been invoked to explain the emplacement of the Greater Himalayan Sequence [107–109], but it requires a reversal of the shear sense across the mylonite zone, and we see no evidence for this. Furthermore, there is no evidence for thinning of the Caledonian orogen as a whole by a factor of 10 or more, which would be required to avoid extrusion of the shear zone. Lastly, although kinematic vorticity analyses commonly indicate general shear, quartz c-axis fabrics (e.g., this study, [85, 86, 110]) show Type 1 crossed-girdles consistent with plane strain and primarily simple shear [111, 112]. As such, we assume plane strain and simple shear dominated, acknowledging that there may be subsidiary components of general shear.The structural continuity, distribution of microstructures, and a metamorphic field gradient that increases structurally up collectively suggest that our samples from the Strabeg transect record the progressive evolution of a single Scandian-aged shear zone. The structurally lowest rocks cropping out immediately below the lithologic MT record the narrowest, most localized, highest stress, and lowest temperature sections of the shear zone. Conversely, structurally higher rocks from near the top of the Moine Nappe, which record higher deformation temperatures and lower stresses, record the deeper, wider portions of the shear zone (Figure 6). Rocks in the lower Ben Hope Nappe record conditions of deformation of the Scandian shear zone at greater depths than rocks from the top of the Moine Nappe. Therefore, structural distances calculated from samples within the Ben Hope Nappe represent cumulative thicknesses of the active parts of the Moine and Ben Hope Nappes. We include these rocks in this analysis acknowledging that the calculation of shear zone width at these highest structural levels yields only an approximate value, as we cannot constrain the displacement on the BHT.As strain localizes up dip in an idealized and simplified reverse-sense fault system, hanging-wall rocks near the upper margin of the shear zone will leave the shear zone as they move up dip, and the shear zone narrows. Their microstructures will therefore be “locked in”, recording the conditions of the shear zone at the depth they left it (Figure 6). If deformation is dominated by simple shear in which strain is homogeneously distributed (i.e., the shear zone at any given depth deforms at the same stress, temperature, and strain rate), the width of the shear zone for a given microstructure and conditions of deformation will be recorded as the structural distance from the projected fault plane to the sample of interest. With these assumptions, we make a space-for-time substitution to reconstruct shear zone geometry, internal structure, and rheology.We present a model for shear zone geometry as a function of depth based on an assumed fault dip (15°), plus calculated shear zone thickness and depth. Depths are estimated from pressure calculations (Table 1, Figure 10(c)), based on a density of 2.75 g cm-3 for rocks of the Moine Supergroup (Rollin, 1994). We neglect the effect of tectonic overpressure, as our stress measurements indicate that this did not exceed 100 MPa (1 kbar), which is within the uncertainties on our pressure estimates. Our reconstruction, based on thickness-depth data from 10 samples along the Strabeg transect, is illustrated in Figure 13. Because of the large errors associated with calculated pressures, not all samples plot in a sequence of increasing structural thickness with increasing depth, as would be expected in an ideal scenario. Additional uncertainty in total shear zone thickness arises from the thickness of the footwall material incorporated into the shear zone (teal-colored zone in Figure 13). The lower limit of shearing is poorly constrained, but this uncertainty is likely to be only a fraction of the total shear zone thickness. We base this on the relatively minor (i.e., 10 m-scale) thickness of the Lewisian basement that is incorporated along the MT and BHT (Figures 1, 2(a), and 2(b)). Similar to what is observed in the hanging wall Moine schist, the amount of basement incorporated into the shear zone likely increases with increasing depth.Even with these uncertainties, this model illustrates a general trend of a wider shear zone at depth. We estimate a thickness of ~2.5 km at ~20 km depth, and extrapolating downwards along the projected fault dip results in a shear zone structural thickness >5 km at ~25 km depth. We base our synoptic shear zone (Figure 6) on this modeled profile.Experimental rock studies have been paramount in our understanding of rock strength and rheology in regions of both brittle and ductile deformation. However, the difference between experimental deformation conditions and geologic conditions for temperature, stress, and strain rate is large, and we must therefore rely on scaling relationships to apply experimental results to geological conditions. These relationships require validation from field-based studies on naturally-deformed rocks to determine how well experimental constraints approximate deformation at natural conditions. In the following section, we use calculated deformation temperatures, pressures, and differential stresses to compare our natural data to currently published flow laws for dislocation creep in quartz. We then use strain rates predicted from published flow laws and compare them to the geometrical strain rates calculated independently from field data.Flow laws are plotted in T-σ space with strain rate contouring from 10-10 to 10-16 s-1 (Figure 14). Data from the Strabeg transect generally lie between strain rates of 10-15 and 10-13 s-1 for Hirth et al. [113] and between 10-16 and 10-14 s-1 for Tokle et al. [114]. Data show a trend of increasing strain rates at lower temperatures and higher stresses, reflecting the shear zone narrowing due to localization of strain and resulting tendency towards higher strain rates.The Tokle et al. [114] flow law is proposed specifically for prism slip whereas rocks along the Strabeg transect clearly show evidence for activation of multiple slip systems (Figure 12). For quartz that shows contributions from basal , rhomb , and prism slip systems (i.e., single girdle CPOs), Tokle et al. [114] suggest grain boundary sliding (GBS) as a deformation mechanism that connects the prism limiting and basal limiting dislocation creep regimes. We see no evidence for GBS in the quartz microstructure of samples with single girdle CPOs (e.g., parts of Domain 3 and 4). Dynamically recrystallized grain sizes in these samples are significantly larger than those where GBS has been proposed in other naturally-deformed quartz-rich rocks [119–122].A value for imposed plate velocity is calculated from the total displacement (shortening) and duration of thrusting on two faults below the MT in the Assynt Culmination, located ~30 km south of the Strabeg transect (Figure 1). This calculated value is then compared to generalized tectonic velocities for the region. Shear zone thickness is taken as the structural (orthogonal) distance to the projected fault plane, plus the thickness we determine of the shear zone in the footwall. These thicknesses are based on four detailed structural and microstructural transects parallel to the direction of displacement, and we justify the thickness calculations below.In the above sections, we have discussed, in detail, the calculation of shear zone thickness relative to the lithologic MT. Examination and quantification of rock microstructures indicates that this lithologic contact is of little rheological significance and acts primarily as a passive marker from which we measure the structural distance. We have presented evidence for moderate to high strains preserved in rocks from the footwall of the lithologic MT. Therefore, for calculations which concern the total thickness of the active shear zone, we add the distance from the lithologic MT (defined as 0 m) to LS-26 (172 m below the MT) to each thickness measurement at and above the MT (for LS-27, at 58 m below the lithologic MT, we calculate a shear zone thickness=172–58 m⁠). LS-26 shows moderate strains compared to structurally higher rocks indicating that it was likely at the lower shear zone margin (Figure 7(c)). There is no exposure of the brittle MT along the Strabeg transect, and we estimate that the minimum thickness of the shear zone at the deformational depths recorded by the structurally lowest samples was likely on the order of 100–150 m.Displacement rate (⁠V⁠) is calculated by dividing total thrust convergence (km) by duration of thrusting (Myr). Elliott and Johnson [34] estimate 20–25 km and 28 km of displacement on the Glencoul and Ben More thrusts in the Assynt Window, respectively. The timing of deformation is well-constrained based on U-Pb geochronology on a suite of alkali intrusions. Syn-kinematic (Loch Ailsh Pluton, early parts of the Loch Borralan Pluton, and the Canisp Porphyry sills) and postkinematic (Loch Borralan Pluton) intrusions constrain thrusting to have been active between 430.6±0.3 Ma and 429.2±0.5 Ma⁠, although it could possibly have initiated earlier [36]. Taking an estimate for shortening (50 km) and time span (0.6–2.2 Myr) yields a calculated displacement rate of 23–83 mm yr-1. As a conservative estimate, we use the minimum displacement rate of 23 mm yr-1 but also calculate an upper limit based on 35 mm yr-1 (~50% increase in displacement rate). These timing constraints are from the Assynt Window, which is 40–50 km south of the Strabeg transect, but the continuity of structures along strike strongly suggest contemporaneity.The tectonic rate of orogen-normal motion for the Scandian phase of the Caledonian Orogeny in NW Scotland is constrained between 30–60 mm yr-1 between Laurentia and Baltica based on plate tectonic reconstruction models [18]. Our local calculated rates are in general agreement with these tectonic-scale estimates.To use this displacement rate to calculate strain rates, we make several assumptions. First, we assume that the displacement rate did not vary significantly in time or along strike. This is especially important since the displacement rate is calculated based on thrusting below the MT, requiring the displacement rate to be constant over a period of c. 5–10 Myr prior to motion along the Glencoul and Ben More thrusts. Second, we assume that strain was accommodated along a single active fault (shear) zone at any given time. It is, however, likely that minor components were partitioned along subsidiary structures, which is why we elect to use the minimum value for the estimated displacement rate. Although assumptions are made to independently calculate strain rate and we accept that these are first-order estimations, it is important to realize that order-of-magnitude strain rates will not be significantly affected by even moderate errors in the values for velocity and/or shear zone thickness. We are confident that we can constrain the displacement rate to within ± ~50% and shear zone thickness to ± ~20%, which will not drastically affect calculated strain rates.As discussed above, microstructures at any given structural distance from the fault plane likely preserve the conditions present in the shear zone at that given thickness (and time). Therefore, we assign temperature, pressure, and stress to a specific structural thickness, which we then attribute to a calculated strain rate.Although some estimates are within error, flow law-based strain rates (from [110, 111]) are consistently lower for given temperature, pressure, and stress conditions compared to independent field-based calculations, sometimes by >1 order-of-magnitude (Figure 15, Table 2). Note that if differential stresses were lower than those calculated (due to strain partitioning between quartz-rich and polyphase regions), or calculated displacement rates were higher (i.e., not the minimum estimate we use), the discrepancy in experimental versus natural strain rates would become even larger. These differences may indicate (a) that dislocation creep in quartz is not the primary control on rheology, (b) inaccuracies in estimates of field-based strain rate, and/or (c) selected flow laws do not accurately model rock rheology at geological conditions. We address each of these possibilities below. (a)Based on our optical and textural analyses, we conclude that quartz is the primary phase controlling viscous rheology in most parts of the shear zone. Psammitic Moine schist is a quartz-rich rock and it is probable that a rock with a higher proportion of feldspar (e.g., a granitic or granodioritic composition) will be stronger, reflecting the rheology of the feldspar, or of a polyphase mixture of feldspar and quartz [123]. We do however observe differences in rock rheology related to composition and grain size variability at the thin section-scale (Figure 8(b)). Interconnectivity of phyllosilicates can result in weaker rock strength due to easy glide between phyllosilicate basal planes [124–127]. Additionally, reduction in grain size due to pinning in a polyphase material may lead to a switch to grain size sensitive creep in quartz [128, 129].(b)As discussed above, even moderate uncertainties in shear zone width or displacement rate do not substantially affect our order-of-magnitude estimates in strain rate. Furthermore, our field-based strain rates (Figure 15) are within the range of other independent estimates of strain rates from plate boundary-scale fault systems (Sassier et al., 2009; [129, 130]).(c)Significant variability exists between published calibrations of flow laws for dislocation creep in quartz [113, 114, 131–135]. Variability in values of H, n, and r in equation (2), which may stem from differences in starting materials, experimental conditions (including deformation apparatus), poorly constrained fluid content, among other uncertainties, can result in order-of-magnitude differences in predicted strain rate. More recent work also introduces a pressure sensitivity for activation enthalpy (H), adding further complexity [133]. We contend that experimental-based constitutive laws describing rock rheology should be thoroughly tested, and if necessary altered, to better fit well-constrained field-based data, as suggested by Hirth et al. [113].Based on our optical and textural analyses, we conclude that quartz is the primary phase controlling viscous rheology in most parts of the shear zone. Psammitic Moine schist is a quartz-rich rock and it is probable that a rock with a higher proportion of feldspar (e.g., a granitic or granodioritic composition) will be stronger, reflecting the rheology of the feldspar, or of a polyphase mixture of feldspar and quartz [123]. We do however observe differences in rock rheology related to composition and grain size variability at the thin section-scale (Figure 8(b)). Interconnectivity of phyllosilicates can result in weaker rock strength due to easy glide between phyllosilicate basal planes [124–127]. Additionally, reduction in grain size due to pinning in a polyphase material may lead to a switch to grain size sensitive creep in quartz [128, 129].As discussed above, even moderate uncertainties in shear zone width or displacement rate do not substantially affect our order-of-magnitude estimates in strain rate. Furthermore, our field-based strain rates (Figure 15) are within the range of other independent estimates of strain rates from plate boundary-scale fault systems (Sassier et al., 2009; [129, 130]).Significant variability exists between published calibrations of flow laws for dislocation creep in quartz [113, 114, 131–135]. Variability in values of H, n, and r in equation (2), which may stem from differences in starting materials, experimental conditions (including deformation apparatus), poorly constrained fluid content, among other uncertainties, can result in order-of-magnitude differences in predicted strain rate. More recent work also introduces a pressure sensitivity for activation enthalpy (H), adding further complexity [133]. We contend that experimental-based constitutive laws describing rock rheology should be thoroughly tested, and if necessary altered, to better fit well-constrained field-based data, as suggested by Hirth et al. [113].The most significant difference between predicted and field-based strain rate is in samples LS-72 and LS-74, which are derived from the zone above the Lewisian inlier in Domain 2. Both samples record temperatures and stresses lower than those from samples structurally above or below (Table 1). If this inlier is an imbricate slice and acted as a mechanically strong block, then the effective shear zone width represented by both LS-72 and LS-74 would decrease by ~25-30%, resulting in faster strain rates closer to those predicted based on sample temperature, pressure, and stress. The effect of decreasing shear zone width on structurally higher samples would be minor as the thickness of the imbricate slice is a smaller proportion of the total shear zone width. The width of this secondary zone is likely only a fraction of the wider primary shear zone, which would rectify lower strain rate estimates (for given stress, temperature, and pressure conditions) calculated from flow laws. A secondary localization is also consistent with lower calculated temperatures; we do not however observe a smaller recrystallized grain size, which is also predicted by this model (Table 1).The strength of the upper crust is thought to be controlled primarily by frictional processes along active faults following a Mohr-Coulomb criterion for frictional sliding. Empirical and experimental estimates of the coefficient of friction (μ) generally range between 0.6–0.85 for undamaged crustal materials [136]. More realistic estimates indicate that the upper crust is much weaker than predicted by Byerlee’s Law because of low values of the effective coefficient of friction of fault gouges and clay-rich fault rocks (e.g., μ<0.1⁠). These low values of the effective coefficient of friction are likely temperature dependent due to the thermal stability of clay minerals, and increase closer to the BDT as clays become unstable and/or frictionally stronger phases are precipitated ([16] and references therein). Because of the transition from frictionally weak to frictionally strong materials close to the BDT, Byerlee-type friction can still be used to approximate rock strength in this region [16].Assuming a simplified system where rock strength is controlled primarily by μ, frictional strength is depth-dependent due to the increase in normal stress (pressure) with increasing depth. At temperatures of ~300°C for quartz-rich rocks, thermally-activated creep processes become the dominant deformation mechanism, following a power-law relationship between stress and strain rate (equation (2)). Viscous creep processes are highly temperature-dependent, resulting in an exponential decrease of crustal strength with depth. In these models, the strongest region of the crust is predicted to be the transition between frictional and viscous rheology (see [16, 17]). In the following section, we construct a first-order, naturally-constrained, crustal strength profile for a contractional fault system by plotting shear stress and deformation depth data from rocks along the Strabeg transect in conjunction with frictional strength as predicted by Byerlee’s Law. Note that stresses measured by paleopiezometry (Table 1) are calibrated in uniaxial compression (⁠σ2=σ3⁠) and are expressed in terms of differential stress (⁠σd=σ1–σ3⁠). To compare these stresses to those driving brittle faulting, we convert them to shear stresses in a plane stress environment by dividing the values of differential stress by √3 as outlined in Paterson and Olgaard [137].Rocks at and below the trace of the MT at the Strabeg transect record quartz microstructures indicative of viscous deformation, but lack evidence for extensive frictional or brittle behavior, likely because the structural level of the BDT on the MT has been eroded along much of the fault trace. Faults closer to the foreland (west), however, record deformation conditions at the BDT. Therefore, we quantify paleostress on a sample (GT-3) from the immediate hanging wall of the Glencoul Thrust (GT) at Loch Glencoul (red star in Figure 1) which places Lewisian gneiss on a thin veneer of An t-Sron siltstones and sandstones, which in turn conformably overlie Eriboll quartzite [47]. Coexisting brittle (e.g., quartz fracture and offset along brittle shear bands) and ductile (e.g., incipient dynamic recrystallization of quartz by BLG) structures clearly place this sample around the BDT when the microstructure formed (Figures 8(c) and 8(d)). Although the precise depth that sample GT-3 records is difficult to determine, we calculate an approximate depth of ~11 (+4/-2) km based on a temperature of ~280±20°C for the lower limit of crystal plastic behavior in quartz and a geothermal gradient of 25±5°C km−1⁠. This depth estimate is consistent with previous estimates of 200–250°C and 200–300 MPa in the immediate footwall of the MTZ (i.e., to the west of GT-3; [39]) and is also consistent with depths for samples from the Strabeg transect which approach the BDT. EBSD analysis on sample GT-3 yields an average recrystallized grain size of 3.9 ± 1.5, resulting in σd=225 (+92/-46) MPa based on the Cross et al. [61] piezometer, which is equivalent to a shear stress in a plane stress environment of σs=130 (+53/-26) MPa.Following the Andersonian model for fault classification, principal stresses driving deformation in a thrust regime are oriented such that the least compressive principal axis, σ3⁠, is vertical and is taken as the effective pressure (equal to the lithostatic pressure less the pore fluid pressure). σ1⁠, the largest compressive stress, is horizontal, acting in the direction of shortening. Assuming plane stress, σ2=σ1+σ3/2⁠. Because of the orientation of these stresses relative to the Earth’s surface, shear stress along a fault, an analog for crustal strength, is predicted to be larger for a reverse regime compared to corresponding shear stresses in a normal or strike-slip regime for a given depth [138]. In a dry system where σ3 is equal to the lithostatic pressure, rock strength in a contractional regime without preexisting faults (i.e., μ=0.85⁠) is predicted to exceed 350 MPa. As discussed above, this is an unreasonable estimate of bulk rock strength as thrust faults have been shown to have very low (e.g., <0.1) effective coefficients of friction ([139]; see also discussion in [16]). This estimate was also made assuming a dry system with no effect of pore fluid pressure. The effect of pore fluid pressure in rocks that follow a Byerlee-type frictional rheology is to lower the effective normal stress; indeed, high pore fluid pressures have long been invoked as a mechanism to explain apparently low values of effective friction along thrust faults. The presence of syn-deformational fluids along the GT and MT is evidenced by precipitation of quartz and pervasive chloritization and sericitization of nominally anhydrous minerals.The effect of pore fluids in ductile rocks is more difficult to predict as thermally-activated processes (e.g., dislocation creep and dynamic recrystallization) likely result in a change in the area of frictional contact and therefore the effect of pore fluid pressure (Pf; see discussion in [67]). We therefore modify our estimates for Byerlee-type frictional behavior through the introduction of the term α (⁠1≥α≥0 as a function of asperity yield stress, modifying the Pf) following Hirth and Beeler [67]. We use the same values to calculate an asperity yield stress but use a strain rate of 10-13 s-1 as calculated from Hirth et al. [113] for the structurally lowest rocks in the Strabeg transect.Based on paleopiezometric-derived estimates of shear stress on rocks deformed within the BDT, maximum shear stress is unlikely to have exceeded ~180 MPa (maximum shear stress within error for GT-3 is 183 MPa). For modeled shear stresses of Byerlee-controlled rocks to be consistent with values that we observe, μ=0.50⁠, and a ratio of pore fluid pressure to lithostatic pressure, λ=0.36⁠, are required (Figure 16).This study presents a reconstruction of the geometry, internal structure, and rheology of a plate boundary-scale shear zone from ~10–20 km depth. We draw the following conclusions: (1)Temperatures and pressures of deformation are consistent with a tectonically-inverted field gradient (in which isograds dip to the east) that preserves a record of shear zone evolution accompanied by exhumation.(2)Quartz appears to be the primary phase controlling shear zone rheology, deforming chiefly by dislocation creep. Quartz recrystallization mechanisms within the active shear zone evolve through time from high-T GBM to BLG as temperature decreases and strain localizes. The change in recrystallization mechanism corresponds roughly with a change in active slip systems from prism dominated at higher temperatures and lower stresses to a combination of prism , rhomb , and basal at lower temperatures and higher stresses.(3)Shear zone geometry in a contractional, plate boundary-scale fault system has been independently constrained and shown to broaden with depth, to a thickness of ~2.7 km at ~20 km depth.(4)Independent, field-based estimates of strain rate decrease from approximately 10-11–10-12 from the BDT to 20 km depth, consistent with a shear zone model that localizes strain at lower temperatures and pressures, producing higher strain rates in narrower portions of the shear zone.(5)Rock microstructures indicate that dislocation creep in quartz is the primary deformation mechanism controlling rock rheology across the Strabeg transect and likely throughout most of the Scandian shear zone. However, independent, field-based estimates of strain rate are generally higher than strain rates predicted by existing constitutive relationships for dislocation creep in quartz, often by greater than one order-of-magnitude.(6)Calculated depths and stresses are plotted in conjunction with frictional rock strength to construct a naturally-constrained stress profile through the middle- to lower-crust in a thrust environment. We estimate that shear stress decreases from 130 to <10 MPa from the BDT to 20 km depth. Shear stress measurements compare well with those determined from a normal-sense shear zone in the Whipple Mountains, California, by Behr and Platt [15]. Note that we modified the stress estimates from Behr and Platt [15] so as to not reflect the proposed Holyoke and Kronenberg [66] stress recalibration (discussed above) that the authors originally used. Our estimated peak shear stress of 130 MPa at the BDT is somewhat higher than that in the Whipple Mountains (107 MPa shear stress), as is expected given the difference in tectonic regime. The profile shows that for values of μ<0.50⁠, ductile rocks from immediately below the BDT were deformed at higher stresses than rocks deforming by frictional mechanisms at higher structural levels. This suggests that the strength of the crust is controlled by this shallow ductile region of the middle crust, as suggested by Behr and Platt [16].(7)We present a method for application of TitaniQ to psammitic, semipelitic, or otherwise low a(TiO2) mylonites by simultaneous solution of deformation temperature, pressure, and a(TiO2). This method requires thermodynamic modeling of bulk rock composition, measurements of Ti-in-quartz, and an independent thermobarometer.Temperatures and pressures of deformation are consistent with a tectonically-inverted field gradient (in which isograds dip to the east) that preserves a record of shear zone evolution accompanied by exhumation.Quartz appears to be the primary phase controlling shear zone rheology, deforming chiefly by dislocation creep. Quartz recrystallization mechanisms within the active shear zone evolve through time from high-T GBM to BLG as temperature decreases and strain localizes. The change in recrystallization mechanism corresponds roughly with a change in active slip systems from prism dominated at higher temperatures and lower stresses to a combination of prism , rhomb , and basal at lower temperatures and higher stresses.Shear zone geometry in a contractional, plate boundary-scale fault system has been independently constrained and shown to broaden with depth, to a thickness of ~2.7 km at ~20 km depth.Independent, field-based estimates of strain rate decrease from approximately 10-11–10-12 from the BDT to 20 km depth, consistent with a shear zone model that localizes strain at lower temperatures and pressures, producing higher strain rates in narrower portions of the shear zone.Rock microstructures indicate that dislocation creep in quartz is the primary deformation mechanism controlling rock rheology across the Strabeg transect and likely throughout most of the Scandian shear zone. However, independent, field-based estimates of strain rate are generally higher than strain rates predicted by existing constitutive relationships for dislocation creep in quartz, often by greater than one order-of-magnitude.Calculated depths and stresses are plotted in conjunction with frictional rock strength to construct a naturally-constrained stress profile through the middle- to lower-crust in a thrust environment. We estimate that shear stress decreases from 130 to <10 MPa from the BDT to 20 km depth. Shear stress measurements compare well with those determined from a normal-sense shear zone in the Whipple Mountains, California, by Behr and Platt [15]. Note that we modified the stress estimates from Behr and Platt [15] so as to not reflect the proposed Holyoke and Kronenberg [66] stress recalibration (discussed above) that the authors originally used. Our estimated peak shear stress of 130 MPa at the BDT is somewhat higher than that in the Whipple Mountains (107 MPa shear stress), as is expected given the difference in tectonic regime. The profile shows that for values of μ<0.50⁠, ductile rocks from immediately below the BDT were deformed at higher stresses than rocks deforming by frictional mechanisms at higher structural levels. This suggests that the strength of the crust is controlled by this shallow ductile region of the middle crust, as suggested by Behr and Platt [16].We present a method for application of TitaniQ to psammitic, semipelitic, or otherwise low a(TiO2) mylonites by simultaneous solution of deformation temperature, pressure, and a(TiO2). This method requires thermodynamic modeling of bulk rock composition, measurements of Ti-in-quartz, and an independent thermobarometer.EBSD analyses were performed on a JEOL-7001F scanning electron microscope equipped with an EDAX Hikari EBSD detector at the University of Southern California Center for Nanoimaging. We used an accelerating voltage of 20 kV, probe current of 14 nA, working distance of 15 mm, and step sizes from 500 nm to 8 μm, where step size is at most ¼ the diameter of the smallest grain. Map coverage was variable, based on recrystallized grain size and step size; in coarse-grained samples, multiple maps were stitched together for a total map size of ~3×15 mm⁠, whereas in finer-grained samples, maps were as small as ~2×2 mm⁠. Map data were collected, cleaned, and plotted using OIM 7 software package by EDAX. Cleaning in OIM 7 consisted of a grain confidence index standardization, followed by a neighbor point confidence index correlation and a neighbor point orientation correlation. No grain dilation procedure was applied. Grains were defined using the OIM grain reconstruction routine; high-angle grain boundaries were defined by a minimum misorientation of 10° between neighboring grains and subgrain boundaries allowed to complete down to a misorientation of 2° based on EBSD angular precisions and community conventions [137–139]. We followed the routine of Cross et al. [58] to discriminate recrystallized and relict grains based on the grain orientation spread (GOS) trade-off curve threshold within each sample. Although the GOS has been suggested to not be an accurate metric to discriminate recrystallized and relict grains since newly recrystallized grains continually accumulate intragranular strain [140], we applied this filter for consistency with the calibration of Cross et al. [58].In all analyses, quartz was the only phase indexed. In cases where other phases were present in the map, and to eliminate misindexing due to damage to the sample surface, we removed indexed points with an average confidence index <0.4. Because of our chosen step size of ¼ the diameter of the smallest grain, grains with <16 pixels were also removed as they are likely artefacts of the cleanup routine. EBSD analyses regularly revealed mottled or spotted patterns of pixels within grains; these patterns have misorientations of 60±5° around <0001>, likely recording Dauphiné twin boundaries as well as regions of systematic misindexing. These regions were removed in postprocessing to maintain consistency with the paleopiezometer calibration [58].The TitaniQ thermobarometer utilizes the temperature and pressure dependence of the 48Ti for 28Si substitution in quartz to calculate P–T conditions. Higher temperatures or lower pressures allow for increased Ti concentration within the quartz crystal structure. Kohn and Northup [141] and Spear and Wark [142] demonstrated that Ti content in quartz reequilibrates as a result of dynamic recrystallization, suggesting that TitaniQ will actually yield deformation temperatures. Later work, however, suggested that recrystallization by GBM is necessary to facilitate Ti reequilibration, and that at temperatures below ~500° C, where recrystallization by BLG and SGR likely dominate, Ti concentrations are not reset [91]. On the basis of lower Ti concentrations in recrystallized grains compared to host porphyroclasts and low overall Ti concentrations, Ashley et al. [96] claimed that TitaniQ cannot be applied to determine the deformation temperature of quartz recrystallized by SGR. In contrast, however, more recent experimental work has demonstrated that dynamic recrystallization in quartz enhances the kinetics of Ti equilibration, regardless of recrystallization mechanism, confirming that TitaniQ does indeed record deformation temperatures [98].The degree to which Ti substitutes for Si is also dependent on the activity of TiO2 in the system; at titanium activity (a(TiO2)) less than unity, the availability of Ti to substitute decreases, thus reducing the concentration of Ti in quartz. Ghent and Stout [143] estimate the following a(TiO2) for assemblages in which Ti-bearing phases are in equilibrium: rutile TiO2=1⁠; ilmenite FeTiO3=0.8⁠; titanite CaTiSiO5=0.6⁠. However, using these values for a(TiO2), numerous workers have reported anomalously low temperatures (e.g., [87–90]).To address this issue, we implement a(TiO2) modeling across P-T space combined with contouring of TitaniQ XTiO2quartzand Si-in-phengite isopleths to accurately constrain activities for each sample (Figure 9(b); see also [78] for a complete discussion of the modeling approach). Using this approach, we calculate values of a(TiO2) for Moine psammites in the range 0.20-0.35 (Table 2), considerably lower than the broad estimates suggested by Ghent and Stout [143]. They are however in agreement with thermodynamic modeling by Ashley and Law [78] who calculate a(TiO2) for greywacke (i.e., psammitic) compositions of <0.3 and by Kidder et al. [92] who suggest a value of aTiO2=0.1 for mylonites from the Alpine Fault. These lower activities result in higher temperatures for a given Ti concentration.Due to the relatively low Ti concentrations, samples are best measured on a Secondary Ion Mass Spectrometer (SIMS). Prior to analysis, samples were examined by cathodoluminescence (CL) in the panchromatic and blue-UV wavelengths to look for Ti heterogeneity and/or zoning in quartz (e.g., Wark and Spear, 2005; [142, 145]). Within the Moine Schist, CL revealed no detectable heterogeneity, suggesting homogeneous Ti distribution in quartz. Within the Lewisian gneiss, recrystallized quartz is generally darker than the larger gneissic grains, indicating that Ti concentration in recrystallized grains is lower. This is consistent with observations that dynamic recrystallization resets Ti concentration in quartz [93–95].Analyses were conducted on a Cameca 6f SIMS at Arizona State University (ASU). A 16O- beam was accelerated to -12.5 kV with a primary beam current of ~15 nA and a stationary beam with a diameter of 10–30 μm. For standards, three silica glasses with concentrations of 0, 100, and 500 μg/g (ppm) were synthesized and characterized at the University of Edinburgh (https://www.ed.ac.uk/geosciences/facilities/ionprobe/standard-materials-available/tiquartzstandards). Study of these samples using the ASU Cameca 6f SIMS at the conditions described above provided a calibration curve to correlate Ti+/Si+ ion ratios with TiO2 concentrations (Figure A1). For unknown samples, analyses started with a 300-second sputter to remove the conductive Au coating, ensuring the ion beam was contacting the rock sample. This was followed by measurements of 27Al, 40Ca, 30Si, 48Ti, and 49Ti over 30 cycles per site. Depending on sample complexity, between 7–10 sites were chosen per sample; site locations were based on CL imaging, proximity to Ti-bearing phases, and quartz microstructure. In each measurement, we monitored two titanium isotopes 48Ti and 49Ti because of the unresolvable interference of 48Ca (a minor isotope) on 48Ti. If a Ca-rich area is unintentionally analyzed (e.g., through accidental overlap of the analyzed area on a plagioclase crystal), the 49Ti signal will suggest a lower concentration. While the lower-intensity from this minor titanium isotope will result in a larger uncertainty, the accuracy of the analysis will be better than using the sum of 48Ti and 48Ca. 27Al and 40Ca isotopes were used to monitor for microinclusions within the quartz as described by Kohn and Northrup [141]. Data cleaning and post-processing consisted of removal of errant values and spikes or inconsistencies in 27Al and 40Ca counts that would indicate contact with a microinclusion or grain boundary.After data cleaning, a final, representative sample Ti concentration was calculated by taking the mean of each site; individual sites with Ti concentrations >1σ and which failed the Student’s T-test were considered outliers, disregarded, and not included in the final mean calculation. Analytical results are tabulated in Table 1 and Figure 10(a).Because the TitaniQ calibration we use is sensitive to both pressure and temperature, we model Si-in-phengite isopleths to independently constrain P-T conditions based on the composition of white mica in the muscovite-celadonite solid solution [77]. The Si content per formula unit (PFU) of phengite, a high celadonite content white mica favored by high P and low T, increases with increasing pressure from 3.0 (pure muscovite) to ~3.9 (high-Si phengite).Si-in-phengite contents were measured for each sample that has a Ti-in-quartz analysis (Table S2). Analyses were performed on a JEOL JXA-8200 electron probe microanalyzer (EPMA) at the University of California, Los Angeles. An accelerating voltage of 15 kV, beam current of 15 nA, and spot diameter of 5 μm were used throughout. Neither high-contrast backscatter imaging nor multiple EPMA line transects analyses per grain revealed compositional zoning within white mica grains. Analytical results are tabulated in Table 1 and Figure 10(b).X-ray fluorescence (XRF) bulk rock analyses were performed for each sample that has Ti-in-quartz and Si-in-phengite measurements. Lithologically homogeneous, unweathered portions of samples were powdered in an agate ball mill. From this powder, ~2 g was separated and loss on ignition calculated. XRF analyses of major elements were measured on a Bruker M4 Tornado Micro-XRF Spectrometer at the California Institute of Technology. All P is assumed to be confined predominantly to apatite; P2O5 was removed from the bulk chemistry and remaining oxide ratios normalized to 100%. All Fe is assumed to be FeO (2+ oxidation state) and corresponding XRF data were corrected for this assumption; no correction was made for Fe2+/Fe3+ ratio. The results are tabulated in Table S3.Thermodynamic modeling is carried out for the system MnO-Na2O-CaO-K2O-FeO-MgO–Al2O3-SiO2-H2O-TiO2 (MnNCKFMASHT) in Perple_X [146], which calculates stable phases in P-T space based on minimization of Gibb’s free energy. We use the 2004 update to the Holland and Powell [147] thermodynamic database and the following solution models: garnet, Gt(HP); chlorite, Chl(HP); phengite, Pheng(HP) for potassic phengite; chloritoid, Ctd(HP); staurolite, St(HP) from Holland and Powell (2004); biotite, Bio(TCC) allowing for Tschermak exchange [148]; ideal solution models for hydrous cordierite (hCrd) and ilmenite-geikielite-pyrophanite (IlGkPy) from Holland and Powell [147]; high structural state feldspar (feldspar) from Fuhrman and Lindsley [149]. The system is modeled as saturated in SiO2 and H2O and excludes hedenbergite (hed), stilpnomelane (stlp and mnsp) as none of these phases are expected in rocks of this composition nor are they observed in the higher-grade Moine rocks. Melt is not included as P-T conditions are mostly below the minimum melting temperature, and we do not observe evidence for melting at these structural levels (Figure 9(a)).The authors declare that they have no conflicts of interest.We would like to sincerely thank Sarah Roeske for editorial handling. Our thanks to Rick Law, Jeffrey Rahl, and 2 anonymous reviewers for thorough and insightful reviews that greatly improved the content and organization of this manuscript. Special thanks are extended to Rick Law, for especially helpful reviews and discussions during the whole period of this research project. We are grateful to Richard Hervig and Lynda Williams at the SIMS facility at Arizona State University for assistance with the TitaniQ measurements. This research was funded in part by NSF grant EAR-1650173 to J. Platt and a Dornsife Doctoral Fellowship to A. Lusk.Figure A1: secondary ion mass spectrometry (SIMS) calibration curves for Ti-in-quartz using 48Ti and 49Ti isotopes (forced to pass through the origin). Figure S1: photomicrograph illustrating the difference in feldspar grain shapes between quartz + feldspar-dominated matrix (top) where feldspar grains tend to be equant and angular, and fine-grained mica-dominated matrix (bottom) where feldspar grain shapes are ovoid and elongate parallel to the macroscopic foliation (horizontal). Figure S2: misorientation profiles of EBSD maps in Figures 4(c)–4(g). Correlated misorientations can be compared to a random distribution as evidence for the active recrystallization mechanism. Figure S3: outcrop photos of Moine conglomerates used for strain analyses. Strain intensity, D=lnX/Y2+lnY/Z2 is quoted in text.

中文翻译：

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板块边界剪切带的深层结构和流变学：来自苏格兰西北部古苏格兰剪切带的约束

在地震发生带以下，断层表现为分布延性应变的区域，其中矿物主要通过晶体塑性和扩散过程变形。我们目前从苏格兰西北部的加里东侧额冲系统中进行案例研究，以更好地约束脆性-延性转变（BDT）以下反向感知剪切力主要区域的几何形状，内部结构和流变学。现在暴露在地表的岩石保留了一系列剪切带条件，反映了变形过程中剪切带的逐渐发掘。基于场的垂直于穆恩推力带的结构距离测量，该距离标志着剪切带的近似基底，以及对活动滑动系统的微观结构观察以及石英的变形和再结晶机制，与差动应力，变形温度和压力的定量估计值配对。这些被用来重建从约10至20 km深度的斯堪甸剪切带的内部结构和几何形状。我们记录了一个剪切带，该剪切带从> 2.5 km的厚度向上定位到<200 m，温度范围为〜450–350°C，应力差为15–225 MPa。我们将变形条件的估计值与独立计算的应变率结合使用，以比较实验得出的本构关系与自然变形岩石中观察到的条件。最后，压力和转换后的切应力用于通过该收缩造山带构造地壳强度剖面。我们计算出在BDT变形的最浅岩石中的最大剪切应力约为130 MPa，在约20 km的深度下降到<10 MPa。我们的结果与以前的研究基本一致，后者发现BDT是地壳的最强区域。切割地壳和上地幔的收缩断层系统是板块汇聚和大陆碰撞的必要结果[1]。在任何时候，板块的大部分相对运动都局限在相对较窄的高应变区域[2]。在上地壳中，这些区域表现为离散的脆性断层或具有摩擦流变学的断层系统。在脆性-延性转变（BDT）下，该转变描述了从显性脆性和摩擦行为向以晶体塑性和扩散过程为主的变形的转变，人们认为它们会扩展到广泛分布的应变区域，通常称为延性剪切区域。在板块边界尺度的环境中，对于富含石英的晶体大陆壳，这些剪切带的宽度可能超过20 km（取决于断层状态和地热梯度）[3-8]，而在上地幔中甚至更宽[9]。对加利福尼亚州的圣安德烈亚斯系统的研究表明，一些走滑断层继续作为离散的，狭窄的断层带继续向下延伸到莫霍面[10-12]，而SKS分裂和异种岩数据表明，圣安德烈亚斯变换系统可能形成一个〜上地幔的剪切带约100 km [13]。在新西兰的高山断裂带上，已描述了一个由地壳中部深度形成的1-2 km厚的镍铁矿带，这表明至少这些尺寸的地壳中部剪切带[14]​​。这两个系统例证了有关板块边界尺度断层系统深部结构和几何形状的重大不确定性。尽管这些研究和其他研究在理解BDT以下断层系统的深层根源方面取得了重大进展，但仍然缺少关键信息。这包括（1）收缩和走滑断层系统中应力随深度的变化，尽管在正常断层系统上已经取得了相当大的进步（例如[15]）；（2）横穿岩石圈的剪切带的几何形状，厚度和内部结构；（3）这些区域的机械性能（即流变性），包括时空变化。为延性剪切带的几何形状和流变性开发一个自然约束模型，对于更好地理解控制板块相互作用和断裂的过程具有广泛的意义。岩石圈尺度的断层可能表现为区域之间具有解耦或复杂反馈的系统，这些区域的行为主要由上地壳的瞬变，粘滑，摩擦事件和中，下地壳的稳态占主导的延性行为决定。BDT周围的岩石可能保留了大部分的地壳强度，因此在地表附近断层的加载和活化中起着重要作用[16，17]。因此，至关重要的是表征BDT内部和下方深处发生的情况，以更好地了解地壳在脆性区域内的行为。最终，需要建立基于自然系统的野外观测资料来构建模型，并为地壳流变学的实验研究提供验证。板块边界剪切带上的大位移以及挖掘它们的过程的复杂性可能使其难以用深度重建这种剪切带的结构。在上面概述的示例中，两者都是走滑系统，这意味着除非斜滑或断层后抬升和侵蚀，否则在中低地壳水平变形的岩石不太可能暴露出来。在常识断层系统中，沿断层系统冷却并挖掘出底盘岩石，并沿其运动进行挖掘，通常在动态微结构中保留分区，以记录应变局部化以及剪切带的时空演化。与常识系统不同 反向感知系统通常掩埋岩石，将冷岩石向下平移到下盘壁，并使地壳变厚。为了保留记录有反向感官演化的岩石微结构，必须对悬壁岩进行顺变形挖掘，以防止动态微结构的静态叠印。在这里，我们介绍了一个从加里东前冲力系统的综合场，微结构和分析研究。为了更好地了解从BDT到下地壳的岩石圈规模的收缩剪切带的几何形状，结构和流变学特性，在苏格兰西北部。为此，我们提出了变形的差分应力（σd），压力（P）和温度（T）的估算值，以及从连续剪切带剖面重建现场流变学，内部结构的现场和微观结构观察结果，加里东造山带从西爱尔兰北部一直延伸到斯瓦尔巴特群岛，并记录了一次碰撞事件，可能是高山或喜马拉雅山的尺寸[18，19]，从寒武纪晚期到最新泥盆纪[20]的时间跨度将近200 Ma。广义上讲，加里东造山运动是下古生界伊帕特斯海域关闭的结果，该海带位于几个大洋俯冲带内，随后发生了劳伦蒂亚，波罗的海，阿瓦龙尼亚以及大洋弧和其他较小的地形碰撞[18，21–23] ]。在苏格兰西北部，表达了加里东造山运动的两个主要阶段：格兰坪（475-460 Ma）和斯堪第纳（445-425 Ma）（[24]及其中的参考文献）。格兰屏阶段，归因于海洋弧的碰撞，标志着东部Laurentian被动边缘的结束和寒武纪至奥陶纪陆架相岩的沉积，最终形成了蛇绿岩和Barrovian型变质作用的位置[21]。斯堪的纳期形成了造山带的许多延性推力，这是波罗的海与劳伦西亚（约435-420 Ma）相撞的结果，紧接着是阿瓦隆（约425 Ma）[18， [22-24]。加里东造山带的前陆包括太古宙至中元古代基底片麻岩复合体，不整合地覆盖着元古代和坎布罗-奥陶纪沉积岩。基底的刘易斯综合体包括多次变形的片麻岩，其中包括受Badcallian（c。2450 Ma）和后来的Laxfordian（c。1800 Ma）造山事件影响的3000–2700 Ma的准类质，沉积物和沉积物。刘易斯群的岩石不均匀地覆盖着Torridonian群的元古代（约1200-1050 Ma）大陆红层和Cambro-Ordovician Laurentian陆架层序岩，包括Eriboll组（石英岩），T-Sron组（细中-粒状碎屑岩）和Durness集团的碳酸盐岩。Lewisian片麻岩和Eriboll组石英岩是研究区内唯一出现的前陆岩石。Lewisian片麻岩由长石（正长石+次要钠长石）+石英+白云母+附子类矿物+亚氯酸盐+不透明物组成。不受延性应变影响的Eriboll地层石英岩具有相当的石英晶粒，其晶粒尺寸最大为> 1 mm。长石+白云母的次要成分也存在。加里东造山带的逆行变质内陆地带主要由Moine Supergroup的岩石构成，构造上交错有与Lewisian相关的基底片麻岩，并被Caledonian花岗岩类侵入（图1）。在苏格兰西北部，腹地岩石构成了四个主要的延性冲断层。从结构最低到结构最高的是Moine，Ben Hope，Naver和Skinsdale Nappes。这些延展性的冲断片保留了变质级的内部梯度，其内部结构从穆伊纳皮构造的最低部分的下部格林西斯相增加到本·霍普，纳韦尔和斯金斯代尔纳普斯上部的大型角闪石相[26-28]；该场梯度被解释为与西向（当前方向）的斯坎迪冲断有关[29]。穆恩超群包括变形严重的元古代变质沉积物，主要由滑石和泥质组成，并有少量大理石和变砾岩[30，31]。莫伊纳超群岩石可能更遥远，等同于在莫伊纳斯冲断带和加里多尼亚前陆出露的托里东群岩石的时间[32]。传统上，广泛的沉积沉积物的Moine超群（以下称为Moine schist）可分为三个不同的组：Morar，Glenfinnan和Loch Eil，尽管在当前研究领域中，所有Moine schist都包括在Morar组中。莫拉尔族的岩石在组成上主要为假岩质，包括变质的石英+白云母+长石（阿尔比特+正钙石）+附子类矿物±黑云母±石榴石±不透明，具有包括钛铁矿，锆石，磷灰石，和独居石。尽管在研究区域没有裸露物，但富含云母，长石，石榴石，附子和稀有的星形石的豆状体层在晶状体中长出。亚氯酸盐存在于整个序列中，通常是黑云母和/或石榴石的逆向分解产物。斜长石以遗留的沉积卟啉菌和较小的颗粒形式存在于基质中，而长石钾主要混入基质中，但以较低结构水平的卟啉菌形式存在。石榴石存在时，从全面到全面[33]和骨骼都有不同的形态。百米厚的角闪石透镜（角闪石+石英+长石±石榴石±白云母±黑云母±钛矿±附子类矿物）在本·霍普纳皮的基部和莫因片岩中稀有的内陆出现。苏格兰西北西北部的斯堪的纳变形可以追溯到穆恩推力带（MTZ），该带状带描绘了从加里东造山带前陆到腹地的过渡，向东延伸到腹地，最深达40 km，从中到中较低的地壳结构水平被暴露出来。考虑到建议的向北和向南的海上延展，MTZ和上覆腹地岩石的暴露大约延伸了NS至少200 km（图1），并且可能超过450 km [34]。MTZ形成一条带状的前陆岩石带，由下方结构最低的Sole Thrust和上方的Moine Thrust束缚。同系运动侵入体中的同运动云母的K-Ar和Rb-Sr定年[35]和同运动侵入体中的锆石的U-Pb定年[29，36]将活性限制在〜435-425 Ma之间。该时间与报道的白云母上的Rb-Sr年龄和角闪石和白云母的40Ar / 39Ar冷却年龄一致[37]。推力大致是WNW定向的，由普遍的伸展和矿物的排列记录下来，紧密到等斜的褶皱旋转成与排列平行的[38-40]。图2（a）是在Moine Thrust（MT）底盘中Strabeg的定居点，横跨Eriboll半岛南部延伸的SSE以及Ben Hope Thrust到Ben Hope的山顶（在此称为Strabeg样带）;图2（a） ）和2（b））。该区域的选择是根据MT的清晰岩性表达（图3），相对简单的构造地层（图4）以及沿大部分样带的广泛，连续的暴露。沿着沿着110°-290°趋势线的线截取，该线平行于伸展线的平均趋势和推断的运输方向[38-40]。总的来说，该断面跨地面9公里，相当于3公里以上的结构厚度。样带的较低结构水平记录了绿片岩级变质，而构造较高的结构水平记录了在中，下闪石相下的变质[43-45]。沿该样带出现了三个主要的延性冲断（图1、2和4）。 （一种））。结构最低的Lochan Riabhach推力（LRT）在前陆Eriboll组石英岩上形成了路易斯阶片麻岩。在上面的结构上，Moine Thrust（MT）将Moine Nappe的Moine片岩置于变长的变质路易斯化片麻岩和Eriboll组石英岩上。本霍普推力（BHT）沿本霍普西侧暴露，将莫伊纳岩片岩以及构成本霍普纳普岩的基底片麻岩（可能是刘易斯岩）和角闪石薄层覆盖在莫伊纳皮岩的莫伊纳岩片上（图2）正常断层以前是从洛普霍普（Loch Hope）的头部撞击到NS上的（图1和2及其参考）。由于在样带的此部分中没有暴露，这些隐秘结构具有未知的方向和位移。由于这些结构之间没有明显的间隙或重复的岩性或微观结构，我们得出的结论是，沿着这些断层的偏移以及由此造成的构造距离差异很小。冲断的顺序通常向前陆传播，早期的腹地冲断片在年轻的冲断作用下“背负式”输送[34，38，46 ]。详细地讲，尤其是在造山带尺度上，该系统可能会发生更复杂的演化，其顺序是逆推力作用和旧推力的重新激活[47，48]。然而，在研究区域内，褶皱的几何形状和相互作用与局部简单的前陆传播模型一致[49]。此外，MT是Moine片岩与前陆Cambro-Ordovician和Lewisian岩石之间的主要构造边界，因此，它被解释为是该更广泛的地壳尺度剪切带系统在深度上的近似基底脱离，尽管脚壁岩石参与了变形[26]。最后，地质年代学证据表明，苏格兰古苏格兰在整个斯堪的纳期都经历了积极的侵蚀和冷却作用（建议在425 Ma之后进行同形冷却和侵蚀； [50]及其参考文献）。我们支持这些观点，并继续进行解释，即沿Strabeg样带暴露的断层是同一剪切带深度的一部分，该剪切带在研究区域内反复向前陆传播。因此，我们将BHT，MT和LRT视为代表Scandian剪切带的不同结构水平（图5）。同时挖掘出因这些推力而举起的腹地推力板，保留岩石的微观结构并暴露同一剪切带的深层（图5和图6）。结构距离被视为从投影MT平面到感兴趣点的叶垂线垂直距离。计算沿Strabeg样条线的当今结构距离，以便将我们的样本作为一个整体作为剪切带的背景，并为在剪切带处于活动状态时重建剪切带的几何形状提供基础。距离是使用MT的岩性表达式（即，Moine片岩和下面的路易斯片麻岩之间的接触）作为参考平面来计算的（图4（a））。尽管岩性接触可能与局部性最高，应变最高的岩石不一致，但它在剪切带内提供了适当的被动边界。假设MT在感兴趣区域下方以恒定的倾角延伸为平面特征。这由DRUM，MOIST和LISPB地震研究支持，这些图像反射器被解释为以恒定角度切穿上，中地壳的推力平面[51-53]。根据现场测量结果和公布的英国地质调查图（Loch Eriboll表114 W），我们假定推力面在15°ESE下倾。我们还对感兴趣点和MT轨迹之间的高程变化进行了校正。为使结构距离测量有效，我们假设叶面平行于或平行于剪切平面。这是基于这样的事实，即剪切区域中的叶面以渐进应变向剪切平面旋转。我们在两个基本的Moine巨砾岩露头上测量了应变强度（图1），得出D = 2.5和D = 2.3 ?，其中D是对数Flinn图上定义的应变量纲的无量纲度量（图S3）。在Moine片岩中使用长石卟啉菌的最近邻技术对应变进行量化的其他尝试均未成功，这可能是由于初始的假定条件是：碎屑随机分布所致。尽管在Moine片岩中缺乏广泛的定量有限应变估计，但我们认为有限剪切应变通常大到足以近似平行于剪切平面的叶面，因此验证了我们对结构距离的计算（参见[26，54]以供进一步讨论）。基于> 从Strabeg断面的50个薄断面中，我们已经确定了四个不同的但渐进的微观结构域（图4（a）和4（c）–4（g））。这些域记录了渐进的剪切带演化和应变局部化，并根据石英的再结晶机理，流变行为（例如，适应应变的相）以及较小程度的岩性进行了细分。在下面的部分中，我们将介绍这些域的每个区域的微结构和定义特征，重点是石英的微结构和重结晶机理。整个横断面，石英通过凸核（BLG），亚晶粒旋转（SGR）和高温晶粒重结晶边界迁移（高T GBM）。如Stipp等人所述，BLG，SGR和GBM。[55]大致对应于Hirth和Tullis的实验方案1、2和3 [56]，分别。读者应注意，Hirth和Tullis的方案3 [56]与Stipp等人的SGR / GBM过渡带更好地相关。[55]。对于本手稿的其余部分，我们将采用Stipp等人中概述的术语。[55]。在Eriboll石英岩和构造上覆盖的Lewisian片麻岩中，Domain 1记录了MT下方和受Lochan Riabhach推力（LRT）运动影响的岩石中的结构变形。域1跨越大约250 m的结构距离，从LRT底壁的结晶塑性变形的下限延伸到MT下方大约100 m的结构（图4（a））。应变主要通过石英和云母的结晶塑性变形以及石英，云母和长石的次生脆性断裂来承受。石英中的动态重结晶主要由凸起的形核，锯齿状的晶界和凸起，以及非常有限的亚晶粒旋转所指示，这由核和幔微结构的发展所证实，其亚晶粒的尺寸和尺寸与再结晶晶粒和充裕的晶粒大致相等。低角度误取向的示意图（图4（g）和7（a）–7（c），S2）。重结晶石英的百分比从未变形的Eriboll Fm结构上增加。在LRT的下盘处，碎屑保留在最低的结构水平，以在岩性MT以下<20 m处完成重结晶。长石在存在时通常会形成大的（500至> 1000μm）卟啉，它显示出不同的脆性断裂强度，通常在结构上朝MT逐渐增加。石英和长石中的裂缝通常充满沉淀的石英和/或方解石，表明涉及这些相的溶液-沉淀蠕变（图7（c））。硅酸盐包括白云母和亚氯酸盐，是决定叶相的主要相，通常包裹在较大的长石卟啉碎屑中。畴2与畴1的区别在于石英的近乎完全的动态重结晶，主要是通过SGR，以及晶粒的大量减少。尺寸。根据叶面强度，粒度和层状硅酸盐层的相互连接，我们将域2细分为两个子域（图7（d）和7（e））。域2a（图4（f）和7（d）），其特征是具有更细的晶粒尺寸和浓厚的层状叶片，交替分布的富含石英和均质的细晶粒，多相（石英+长石+白云母±亚氯酸盐±次要附件）材料从MT下方的大约100 m结构延伸到MT上方的> 100 m结构（图4（a））。区域2b在结构上延伸至MT上方约200 m，其特征是晶粒尺寸增大，并且长条硅酸盐网状结构（通常长石长卟啉弹性体包裹在一起）吻合（图4（e）和7（e））。与域2a相比，域2b中的基质材料记录的细粒石英+长石+云母的混合（均质化）更少（例如，图7（e）和7（f））。在域2b中重结晶的石英占主导地位的薄片也显示出可变的屈曲折叠，而在域2a中的石英占主导地位的薄片没有显示出折叠的迹象，并且基本上平行于亚平行于宏观的叶状体（图7（d）和7（e））。在所有，域2a和2b在MT上方延伸了约300 m的结构距离（图4（a））。在域2中，石英质地主要由SGR记录了普遍的位错驱动的动态重结晶，如（1）岩心和地幔微观结构，其地幔亚晶粒的大小和尺寸与再结晶晶粒大致相等；（2）发展出重结晶晶粒的普遍的倾斜形状优选取向（SPO）；（3）动态重结晶石英内部的取向差角分布（图S2）。有限的证据以卟啉晶状体中充满石英的压力阴影形式存在，而破裂的石榴石和长石卟啉岩中稀有石英填充物则表现出溶解-再沉淀蠕变相对较小的成分（即压力溶液；图7（e））。在石英与其他相（通常是云母和长石）混合的情况下，由于晶界的钉扎，所得混合物的晶粒明显细化（图7（d）和7（e））。由于较小的晶粒尺寸和丰富的相边界可能会促进石英的溶解速率[55，56]，因此可能会发生由细粒多相材料（图7（d）和7（e））为主的区域中的石英尽管我们缺乏直接的证据来支持这一点，但压力解决方案会增加变形。在晶界不受非石英相影响的纯石英域中，晶粒显示出普遍存在的SPO，通常在剪切方向上相对于叶面倾斜10-50°（图4（e）和7（f））。延长直径大于1000μm的碎屑。长石的长轴与叶面平行，并且碎屑通常被云母和其他页硅酸盐（例如绿泥石）包裹。长石形状与周围物质之间存在相关性。而主要被石英包围的长石晶粒容易断裂，而被多相基质包围的长石晶粒则伸长（图S1）。在多相基质中存在细长的碎屑，暗示了长石的结晶塑性变形或剥落。然而，仅有有限的直接证据（例如核心和地幔结构，隆起或缝合的晶界）来支持晶体塑性变形。在初次叶面倾斜的不连续的微尺度剪切带在区域2b中很常见（图8（a ））。这些似乎与初级叶期同时存在：条带的微观结构没有差异，它们主要是由云母叶片的挠度决定的。相对丰度和强度从非常高应变的岩石开始在结构上增加，在该应变岩石中，剪切带在MT上方200-300 m的结构距离处被消除到最大。从结构上讲，强度和丰度都会降低，直到过渡到畴4为止，在畴4之上通常不存在剪切带。大部分发达的剪切带显示了WNW顶切变的感觉，尽管很少见，发展较弱的带显示了ESE顶切变，这与以简单剪切为主的应变几何一致，但具有较小的展平成分。结构2的结构较高部分包含厚度小于4 m的路易斯型片麻岩带，在结构上和下与莫因片岩接触。这个路易斯式的内层可能是一个盘状的逆冲断层，在这种情况下，下部接触是断层，上部接触是不整合，或者可能是密闭的等轴向褶皱的核心，其中合并了基岩，在这种情况下，上部和下部联系人不符合要求。我们没有发现任何脆性断层或高应变区。在微观范围内，重结晶石英的晶粒尺寸，形状和重结晶机理在该区域没有显着变化。下面，我们讨论了该Lewisian矿床在有效剪切带宽度方面的流变学含义。第3区的特征是从由亚晶粒旋转引起的石英重结晶到高T GBM的转变。该区域中的石英晶粒粗大得多（表1），并保持不规则，高T GBM的变形虫质地特征（图4（d），7（f）和7（g））。这些变形虫晶粒包括较小的亚晶粒发育，并且通常显示出无光的消光，表明晶格中位错的累积有限。在畴3内较高的结构水平上，直的晶界和稳定的120°晶粒三重结[59]标志着恢复和可能由于表面能最小化而驱动的晶粒生长（γ-GBM为[60]）。基于主导的再结晶机制的相对结构位置，我们认为γ-GBM具有叠印的动态高T GBM微观结构（即晶粒已退火），尽管这两种模式共存是合理的。长石和云母的晶粒也较粗糙比域1和2中的要多；直径大于1毫米的长云母卟啉石通常大于500μm。长石存在于两个不同的种群中：斜长石碱（通常为钠盐）主要以可变比例的卟啉形成，而直长石既以卟啉形成，又作为并入基质的次要颗粒出现。在域3和4中，一些斜长石长石晶粒不规则地划分为更多的苏打核（〜An40-50）和不规则的钙质（〜An60-70）过度生长。这些观察结果与Moine Nappe内长石的其他化学分析结果一致[35，38]。长石显示出不同程度的动态重结晶，在重结晶时，新晶粒往往是钙质斜长石，而与它们起源的晶粒组成无关。在BHT上方的地下片麻岩片中，重结晶的长石具有独特的菱形，晶粒长轴平行于叶面且晶粒尺寸在100至> 500μm的数量级.4区占据了Moine Nappe的结构最高水平，并一直延伸到Ben Hope Nappe。畴4与畴3相似，尽管畴4中的石英经历了普遍的退火和可能的晶粒长大，从而导致了更大的晶粒尺寸（图4（c）和7（h），表1）。尽管动态再结晶的微观结构已经通过晶粒退火而被套印（指示回收率和γ-GBM），但石英仍保留了强大的CPO变量。除石英外，最丰富的相是长石和云母，它们的成分，晶粒大小和织构与畴3中的相近。Stipp和Tullis [62]和Cross等。[61]测压计已校准至最大〜50μm的粒径，其中的微观结构表明主要由BLG和SGR进行的动态再结晶。该校准被推断为最大> 120μm的晶粒，主要对应于SGR和高T GBM引起的变形，但是对于这些大晶粒仅产生最小的差应力估计[60，68]。我们还计算了清楚显示恢复迹象的微观结构的应力（例如，域4中的γ-GBM），并接受这些计算只是最小微分应力的粗略估算。我们使用两种电子测量了19个样品中石英的动态重结晶晶粒尺寸背向散射衍射（EBSD）和斐济光学分析软件，这是ImageJ的扩展工具箱（http://www.fiji.sc; [69]）。切下薄片并平行于线并垂直于叶面进行分析。附录A中详细介绍了EBSD的采集细节和数据清洗程序。对于粒度较大的样品（> 100μm），采集了光学图像，并在斐济定义了晶界以量化晶粒尺寸分布。用不同角度的偏光镜拍摄了多个显微照片，以更准确地区分晶界。所有晶粒尺寸测量值均表示为与所计算晶粒多边形相等面积的圆直径。最少使用350个晶粒来计算样品中的平均晶粒尺寸。如Lopez-Sanchez和Llana-Fúnez所述，我们计算了晶粒尺寸分布的频率峰值[70]。然而，我们发现，基于EBSD的晶粒度分析包含大量小晶粒，这些晶粒导致正偏分布，并且频率峰值显着低于算术平均或均方根（RMS）晶粒度。因此，为了与测压校准一致，将每个样品的最终重结晶晶粒尺寸作为清洁后所有测量值的RMS，误差报告为1σ（表1）。我们使用了所有19个样品的EBSD数据来确定晶体学重结晶石英的最佳取向（CPO）作为位错蠕变，变形的定性条件以及整个Strabeg横断面结构段的活动滑动系统的再结晶证据。c-，a-，M轴极图（PF）和X轴反极图（IPF-X）是基于MTEX（http://www.mtex-toolbox.github.io）根据一个点数统计计算。PF沿着XZ平面定向，而叶面平行于X方向定向，因此可以解释为在剪切方向上靠近剪切平面。PF绘制为下半球等面积投影，而IPF绘制为X方向上半球投影。每个PF和IPF均使用单独的标度，以显示低强度织物中CPO的复杂性，如果使用通用标度，这些标度可能会丢失。使用Skemer等人的基于ODF的m指数测量CPO强度。[71]和j-index [72]。每种PF和IPF均仅使用动态重结晶晶粒来构建。主体晶粒是根据晶粒取向扩散鉴别技术确定的，并被排除在外[61]。我们目前提供的石英晶体学数据均来自单相石英和多相区域，并由表1中大于或等于＃晶粒（EBSD）的许多晶粒构成。在莫伊纳皮内的所有结构水平上，石英晶粒均显示出证据层状硅酸盐和细粒长石对晶界钉扎的影响。与纯石英区域相比，这些多相聚集体系统地包含明显更细的晶粒尺寸（图7（d）和7（e）），与其他地方的观察结果一致（例如[73-75]和其中的参考文献； [76]）；为此原因，我们尝试从无石英相的区域（例如，重结晶的石英脉，富含石英的透镜）记录粒度测量值。在某些情况下，主要是在区域3和4中具有较高结构水平的粗粒岩石中，很难从单相区域获得统计上显着数量的晶粒。在这种情况下，我们包括一些具有固定边界的晶粒，并接受与这些测量相关的误差可能明显高于单相区域中的误差。在结构域2a内较低的结构水平（总应变可能较高）下，富含页硅酸盐或细小。粒状的多相互连层与单相石英或长石为主的层交替，定义了主要的叶状构造。与纯石英或石英+长石层相比，多相层显示出更高的剪切应变（图8（b））。类似地，在畴2b内较高结构水平的石英层中存在屈曲式褶皱，表明这些层与周围的多相基质之间存在粘度差异（图7（e））。基于这两个主要证据，我们解释石英和石英+长石层的能力更强，在较弱的多相层中可以容纳更多的应变。这些位错蠕变和位错蠕变和对晶粒尺寸敏感的蠕变（包括晶界滑动（GBS），尤其是平行于页硅酸盐的长轴）的结合可能会导致变形。由于我们收集粒度测量值的区域可能更坚固，我们的应力确定可能会高估系统中的平均应力。我们使用Wark and Watson的钛石英（TitaniQ）热压计[77]确定了11个样品的变形温度（T）和压力（P），这是由Thomas校准的等。[78，79]，结合硅藻土[80]和TiO2活性的热力学模型（[81]；图9）。温度和压力的计算可以归因于特定的石英和云母为主的微结构，从而确定微结构形成的条件。石英云母和白云母都记录了沿着该断面的渐进重结晶和晶粒尺寸减小，表明这两个相一起重结晶并重新平衡到环境条件。因此，我们计算的温度和压力代表了岩石离开活动剪切带之前的最后变形阶段（图6），并且可能与使用传统的热压法对整个变质组合计算得出的温度和压力不同。对于9个记录交叉腰带c轴拓扑的样本，我们使用Faleiros等人的石英c轴开口角温度计校准。（2016）进行其他温度估算，主要是与我们基于TitaniQ的温度估算以及该地区先前的开角温度（[83-86]及其参考）进行比较。对于每个样本，我们计算出T，P和a（TiO2）结合使用钛-石英（图10（a）），硅-英石（图10（b））和二氧化钛活性（a（TiO2））伪截面建模（图9（a） ）和9（b））；这些分析技术和方法的详细信息在附录B中概述。a（TiO2）在PT空间中根据每个样品的整体成分绘制轮廓（请参见[81]）。由于我们样品中钛活性的温度依赖性，模拟的a（TiO2）通常随温度而增加（图9（b）和10（c））。根据钛在石英中的溶解度方程（例如，方程（B.1）； [79]），对于给定的石英中钛浓度（[Ti]），平衡空间在PT空间中的位置将随着温度的降低而降低在系统中增加a（TiO2）。通过绘制测得的[Ti]的平衡线位置与a（TiO2）的函数关系，并绘制a（TiO2）从0到1的轮廓，我们可以确定PT空间中不同a处平衡线的点。 （TiO2）与相应的轮廓相交。然后，我们以图形方式确定此阵列与建模的辉石等腰线等值线相交的位置（对应于测得的Si PFU）。误差报告为Si-in-英铁PFU和Ti-in-石英浓度的测量分析值的1σ（图9（b））。沿Strabeg横断面的晶粒尺寸在结构最低水平处约为9±4μm ，其中BLG的重结晶占主导地位，刚好在从结构域3过渡到4（样品LS-105）的过渡以下，约为〜127±55μm，在结构最高水平上约为〜175±87μm，其中重结晶主要由高T GBM发生（表1，图11（a））。使用Cross等人的1μm步长校准，这些值分别对应于〜119至15 MPa范围内的微分应力。[61]（图11（b））。对于用光学方法和EBSD测量晶粒尺寸的结构较高的样品，与相同样品的光学测量结果相比，我们观察到用EBSD测量的平均重结晶晶粒尺寸明显降低。怀特[75]也报告了不同的gr通过电子和光学显微镜确定的尺寸，并建议不要进行此类测量。光学测量的重结晶晶粒尺寸范围为：在866 m结构距离处为〜68±25μm，仅在从畴3过渡到4（样品LS-105）的过渡以下处为〜143±73μm，在结构域处为〜255±121μm。结构上最高的水平（图11（a））。这些值对应于使用Stipp和Tullis的压强计测得的〜23至8 MPa的差异应力[62]（图11（b））。我们从最低结构水平进行的基于EBSD的晶粒尺寸测量与以前的光学测定相似。从该区域再结晶的晶粒尺寸。White [75，87]在Eriboll，Ord和Christie [88]处测得的MT后壁的晶粒尺寸为14.6μm，在Assynt Culmination中记录的MT后壁的晶粒尺寸小至12.7μm，和Weathers等。[89]通过Assynt Culmination和Eriboll确定了10-20μm的晶粒尺寸（图1和2）。这些测量主要是从Eriboll Fm的石英岩内部进行的。在MT的后壁。另外，弗朗西斯[83]在Strabeg样面以南5公里处光学测量了重结晶晶粒的尺寸。这些测量值的范围从MT下方80 m处的26.2±10μm，到BHT悬挂壁中MT上方2294 m处的203.5±96.1μm。这些晶粒尺寸测量值比我们通过EBSD测量的尺寸大，但与我们的光学测量结果相近。所有样品均显示出重结晶石英中一定程度的CPO，这与位错蠕变为主要变形机制相一致。通过m指数[71]和j指数[72]测量的CPO强度显示出显着的可变性（图12）。所有CPO均以与WNW顶部剪切一致的方向倾斜。沿Strabeg样带的CPO受Y最大值，交叉和单束带的支配，这与基底，菱形和棱柱滑动系统的活动一致；我们看不到棱镜[c]在这些结构水平上滑动的证据。滑移系统可能至少部分依赖于温度，基底，菱形和棱镜表示逐渐升高的温度。它们也可能取决于有限应变，而棱镜受到较高应变的青睐（图12，[14、90]和其中的参考文献； [91]）。尽管隔离温度对CPO拓扑的影响尚不清楚，但基于主动滑移系统的温度通常会从LRT到BHT在结构上升高[14] .CPO的整体趋势在整个结构截面中都出现了（图12）。在轻轨（Domain 1）周围的最低结构水平上，CPO由弱的c轴交叉环定义，表明基，菱形和棱镜滑动系统活动。在MT上方和下方的结构层（域2a，b）上，C轴显示出更强的交叉围带和单围带。单腰带通常更结实，并且可能显示出较弱的互补交叉腰带腿。域3较低结构级别的CPO的特征是垂直于叶的强最大值（Y最大值），这表示棱镜滑动。在结构上较高（即，域3和域4的结构水平较高）下，纹理过渡到具有伸长的Y最大值（平行于腰带的长轴）的单个腰带，指示棱镜和菱形滑移。通常沿极图外围表示的次要最大值表示基底滑移系统的贡献较小。像在域2中一样，沿着极图外围的一些样本中通常存在弱的最大值，这些极小值表示交叉腰带。BHT的直接悬挂壁和结构域3的结构较低水平处的强Y最大值可能是由于较大的剪切应变[90，91]或增强的水解弱化作用（例如[84，92]）引起的。如图12所示。 ，许多晶体织构以不带或非常弱的交叉带状腿的单腰带绘制，这些轮廓可能无法在轮廓中表达出来。这些模式与苏格兰西北部先前发表的晶体学数据（例如[45，84–86]及其参考文献）不同，这些数据通常显示出交叉腰带的c轴模式，用于根据交叉腰带的打开角度确定温度。在我们基于EBSD的c轴数据中，交叉腰带图案的匮乏可能归因于用于织物测量和轮廓绘制的技术（R. Law，个人交流）；基于EBSD的晶体学数据是通过每点的分析得出的，包括大面积内的所有晶粒，通过通用阶段进行的测量已用于许多先前的研究中，需要对占据整个截面厚度的晶粒进行单独测量，并且可能引入主观性。就像其他在变形的地形中使用TitaniQ热压计的研究（例如[93–96]）一样，我们的分析显示，动态重结晶石英中的Ti浓度较低。尽管Ti浓度很低，但数据遵循了明确定义的趋势，在结构上从MT附近的0.58 ppm增加到BHT的悬挂壁上的2.57 ppm（图10（a）），而在同一结构截面上，硅锰矿在3.23–3.29 PFU范围内显示出广泛的增长趋势（图10（b））。利用附录B中详述的建模方法，Ti浓度对应于大约350-450°C和270-560 MPa（2.7-5.6 kbar；图4（b）和10（c），表1）范围内的温度和压力。石英c轴张开角温度从334–555°C的温度范围内总体上呈上升趋势，尽管散布明显得多（图12，表1）。TitaniQ和c轴开角温度均与以前的工作人员发现的趋势一致，他们发现单个尿布内部结构的场梯度逐渐增大[45，97]。我们计算出的TitaniQ温度通常也低于通过石英重结晶机制估计的温度。建议通过BLG，SGR和GBM进行的重结晶分别在约300-400°C，400-525°C和> 525°C的温度范围内发生[55，98]。沿Strabeg样带，BLG变形的岩石计算出的温度约为350°C，SGR的再结晶对应的温度约为〜350–380°C，而高T GBM的再结晶的温度约为370–450°C。但是，值得注意的是，Stipp等人的重结晶机理温度估算值。[55]基于运动学上的矿物组合，代表了系统中“接近峰值”的温度，该系统在冷却时持续变形，因此可能捕获了与TitaniQ估计不同的PTt路径。此处计算得出的TitaniQ衍生的变形温度往往明显低于已发表的石榴石-黑云母Fe-Mg交换（GARB）变形温度，石英c轴开角变形温度和多系统PT分析[43-45、48、97]。对于这种差异，我们提供以下可能的解释。（1）TitaniQ衍生的温度强烈依赖于a（TiO2），并且a（TiO2）的微小变化，尤其是在低值下（即，a（TiO2）<0.3），可能会导致PT条件的显着差异。尽管我们采用的方法可同时生成P，T和a（TiO2）的唯一解，但XRF，SIMS或EPMA产生的分析误差可能会导致a（TiO2）值系统地过高，因此温度太低。为了使基于TitaniQ的温度在多系统误差和GARB值范围内，a（TiO2）的值必须小于0.1。但是，基于a（TiO2）的温度依赖性，同构钛铁矿的存在以及Ti在晶粒和样品尺度上的均匀分布，我们认为a（TiO2）值这么低不太可能。 （2）在我们理解钛迁移率的机理以及受晶体塑性变形影响的石英的替代中，更根本的缺陷是可能的。Ashley等。[99]表明，动态再结晶石英中的低[Ti]可能是亚晶界和位错阵列通过石英晶粒迁移引起的局部再平衡的结果。建议这种情况下的重新平衡是由晶间介质的组成来缓冲或调节的，该晶间介质的组成通常相对于整个组装体是钛-不饱和的，并且可能不代表实际的α（TiO2）。然而，最近的实验工作表明，Ti的浓度在重结晶过程中重新平衡，反映出大量的a（TiO2）[100，101]。（3）关于温度差异的另一种可能的解释是由温度计或热压计记录的PTt历史记录的哪一部分引起的。根据变质热压计或多系统平衡（包括GARB）计算出的变质温度可能记录“峰值”或“接近峰值”的渐进变质温度。在Moine Supergroup的岩石中，石榴石以可变大小，形态，化学和化学方面，通常在化学区域中，铁芯中Mn的相对比例较高，而轮辋中Fe和Ca的相对比例较高（参见[33、43、45、48、97]）。从光学上讲，分区通常由与初生叶脉不符的纤芯或轮缘中的线性或螺旋形夹杂物痕迹定义。这种物理和化学分区表明石榴石记录了多个事件的增长，可能是在可变PTX处。在沿Strabeg样带的石榴石结构上较低的水平上，石榴石往往是无角的或骨骼的，这表明它们可能不平衡。相反，如果[Ti]随着动态再结晶而重新平衡，则TitaniQ温度应记录塑性变形和动态再结晶停止（即，岩石离开主动变形剪切区时）的条件。（4）根据我们对剪切带演化的解释，石英微结构中记录的变形温度应远低于峰值条件。c轴打开角度的温度与此解释不一致，而我们的TitaniQ温度虽然低，但却是一致的。尽管开角温度和岩石热压计之间的相似性令人信服（例如，[84]其图24），但是关于应变几何形状，重结晶机制，应变率和水含量对c轴开角的影响仍然存在相当大的不确定性（参见[84]进行进一步讨论）。此外，现有的c轴张开角校准几乎完全基于从峰或近峰变质组合得出的温度估算值（[84]和其中的参考文献； Faleiros等人，2016）；尽管这些可能代表变形期间的条件，但不一定代表岩石在“锁定”之前最后经历的最后变形条件。因此，我们不愿将根据c轴张开角计算出的温度指定为代表变形历史中任何特定（或一致）时间的时间（例如[84]）。（5）最后，基于微观结构观察， MT的痕迹（即，Moine推覆的基部）沿罢工暴露出不同的结构水平，范围从非常浅的陆上my石（例如，Knockan岩屑–图1）到位于其上的lon陷Moine片岩内的高温GBM微结构。北部海岸的质牡蛎壳岩（一种千枚陨石，被认为是从路易斯河基底的片麻岩中产生的，通常在MTZ内长出）[34，38，46，102]。因此，尽管Moine Nappe是一个连贯的构造单元，但是压力和温度条件在整个行程内和整个行程中都会发生变化，以及在Nappe底部的条件也一样。这可能是由于变形和变形后不同程度的腐蚀和发掘而造成的。在这种情况下，以前发布的估算值可能会测量在Moine Nappe中不同结构水平和不同时间所达到的温度和压力。源自TitaniQ的温度强烈依赖于a（TiO2），而a（TiO2）的变化很小，特别是在较低的值（即，a（TiO2）<0.3）下，会导致PT条件的显着差异。尽管我们采用的方法可同时生成P，T和a（TiO2）的唯一解决方案，但XRF，SIMS，或EPMA可能导致（TiO2）值系统性太高，因此温度太低。为了使基于TitaniQ的温度在多系统误差和GARB值范围内，a（TiO2）的值必须小于0.1。但是，基于a（TiO2）的温度依赖性，同构钛铁矿的存在以及Ti在晶粒和样品尺度上的均匀分布，我们认为a（TiO2）值这么低不太可能。在我们理解Ti迁移率的机理以及受晶塑性变形影响的石英替代中，更根本的缺陷也是可能的。Ashley等。[99]表明，动态再结晶石英中的低[Ti]可能是亚晶界和位错阵列通过石英晶粒迁移引起的局部再平衡的结果。建议这种情况下的重新平衡是由晶间介质的组成来缓冲或调节的，该晶间介质的组成通常相对于整个组装体是钛-不饱和的，并且可能不代表实际的α（TiO2）。然而，最近的实验工作表明，Ti的浓度在重结晶过程中重新平衡，反映出大量的a（TiO2）[100，101]。温度差异的另一种可能的解释是温度计或热压计捕获了PTt历史的哪一部分。根据变质热压计或多系统平衡（包括GARB）计算出的变质温度可能记录“峰值”或“接近峰值”的渐进变质温度。在Moine Supergroup的岩石中，石榴石以可变大小，形态，化学和化学方面，通常在化学区域中，铁芯中Mn的相对比例较高，而轮辋中Fe和Ca的相对比例较高（参见[33、43、45、48、97]）。从光学上讲，分区通常由与初级叶不协调的岩心或轮缘中的线性或螺旋形夹杂物痕迹来定义。这种物理和化学分区表明石榴石记录了多个事件的增长，可能是在可变PTX处。在沿Strabeg样带的石榴石结构上较低的水平上，石榴石往往是无角的或骨骼的，这表明它们可能不平衡。相反，如果[Ti]随着动态再结晶而重新平衡，则TitaniQ温度应记录塑性变形和动态再结晶停止（即，岩石离开主动变形剪切区时）的条件。根据我们对剪切带演化的解释，石英微结构中记录的变形温度应远低于峰值条件。c轴打开角度的温度与此解释不一致，而我们的TitaniQ温度虽然低，但却是一致的。尽管开角温度和岩石热压计之间的相似性令人信服（例如，[84]其图24），但是关于应变几何形状，重结晶机制，应变率和水含量对c轴开角的影响仍然存在相当大的不确定性（参见[84]进行进一步讨论）。此外，现有的c轴张开角校准几乎完全基于从峰或近峰变质组合得出的温度估算值（[84]和其中的参考文献； Faleiros等人，2016）；尽管这些可能代表变形期间的条件，但不一定代表岩石在“锁定”之前最后经历的最后变形条件。因此，我们不愿将根据c轴张开角计算出的温度指定为代表变形历史中任何特定（或一致）时间的时间（例如[84]）。最后，根据微观结构观察， MT（即，Moine Nappe的基底）沿走向暴露出不同的结构水平，范围从非常浅的陆上my石（例如，Knockan Crag –图1）到位于my石牡蛎壳岩石上的Mylonitic Moine片岩内的高温GBM微结构。 （一种千枚榴石（据认为是从路易斯河时期的基底片麻岩中获得的，通常在MTZ内生长））[34，38，46，102]。因此，尽管Moine Nappe是一个连贯的构造单元，但是压力和温度条件在整个行程内和整个行程中都会发生变化，以及在Nappe底部的条件也一样。这可能是由于变形和变形后不同程度的腐蚀和发掘而造成的。在这种情况下，以前发布的估算值很可能会测量在莫奈薄纱内不同结构水平和不同时间所达到的温度和压力为使剪切区的结构厚度随时间保持恒定，剪切区一定不能经历明显的变薄或体积损失。我们在这里认为，剪切带主要是由于平面应变和简单剪切（非同轴）而变形，并且没有经历明显的体积损失。原则上，这可以通过多种技术进行测试，这些技术可以估算运动涡度数（⁠Wk⁠）。Thigpen等。例如，[85]使用刚性晶粒分析来计算Eriboll半岛上的Moine Nappe内岩石的Wk值在〜0.6–0.7之间，相当于〜60–50％的纯剪切力（同轴）。但是，在许多变形的地层中，相对于其他方法，通过刚性晶粒分析计算Wk似乎低估了非同轴应变的分量[103-105]，并且与这些方法相关的不确定性可能很大[106]。Law（2010）报告了Wk值，该值来自Glencoul烟囱MT上下100 m范围内的Wk值，其中使用了硬质分析法分析了Moine镍铁矿，并采用了另外两种技术，涉及位于该岩棉以下的镁铁质寒武纪石英岩的CPO几何形状。推力。该值的范围从0.75–0.65（45–55％同轴剪切）到0.99–0.90（10–30％同轴剪切），并且通常在接近MT时增加（即，简单剪切的较大部分）。然而，在这种高应变岩石中，同轴缩短的重要组成部分存在严重的相容性问题。Eriboll Fm中碎屑和重结晶晶粒的XZ有限应变比。通常在10到19之间（法律，2010年）。假设没有体积损失，并且Wk≈0.77⁠，XZ比率为19则需要垂直于剪切平面缩短65％，因此在剪切方向上的拉伸为2.1（Law，2010）。更极端。缺乏应变数据，但是如果我们非常保守地估计基岩100 m上的1 km位移，给出简单剪应变γ为10的分量，则取Wk≈0。由Law（2010）估计为75，假设平面应变且没有体积损失，则垂直于剪切平面的缩短为88％，与剪切方向有关的纯剪切相关拉伸为8.2。除非在mylonite区上方的整个推力桩经历相同的拉伸量，否则这需要在推力前部挤出许多公里的mylonite。已经使用这种类型的挤压模型来解释大喜马拉雅层序的形成[107-109]，但它需要逆转该mylonite区域的剪切力，我们对此没有证据。此外，没有证据表明整个加里东造山带变薄了10倍或更多，这是避免剪切区域挤压所必需的。最后，尽管运动学涡度分析通常表明总体剪切，石英c轴织物（例如，本研究[85，86，110]）显示了与平面应变和主要是简单剪切一致的类型1交叉环束[111，112]。因此，我们假设平面应变和简单剪切作用占主导地位，并承认可能存在普通剪切作用的辅助分量。结构的连续性，微观结构的分布以及在结构上向上增加的变质场梯度共同表明，我们从Strabeg横断面记录的样本单个斯堪的纳时代剪切带的渐进演化。刚好在岩性MT下方切出的结构最低的岩石记录了剪切带的最窄，最局部，最高应力和最低温度的部分。相反，在莫伊纳皮峰顶部附近的结构较高的岩石，记录了较高的变形温度和较低的应力，记录了剪切区更深，更宽的部分（图6）。本霍普纳普河下游的岩石记录的斯堪的安剪切带的变形条件在深度上比从莫伊纳皮河顶部的岩石更大。因此，从本·希望·纳普内的样本计算出的结构距离代表了穆伊纳河和本·希望·纳普斯活动部分的累积厚度。在分析中我们将这些岩石包括在内，这表明在这些最高结构水平上的剪切带宽度计算只能得出一个近似值，因为我们不能限制BHT上的位移。系统，剪切带上边缘附近的悬壁岩石随着它们向上倾斜而离开剪切带，并且剪切带变窄。因此，它们的微观结构将被“锁定”，记录剪切区离开其深度时的状态（图6）。如果变形由应变均匀分布的简单剪切决定（即，在给定深度处的剪切区域在相同的应力，温度和应变速率下发生变形），则在给定的微观结构和变形条件下剪切区域的宽度将记录为从投影断层平面到感兴趣样品的结构距离。基于这些假设，我们进行了时空替换，以重建剪切带的几何形状，内部结构和流变性。我们基于假定的断层倾角（15°），加上计算出的剪切带厚度和深度，提出了一个剪切带几何形状随深度变化的模型。深度是根据压力计算得出的（表1，图10（c）），基于Moine Supergroup岩石的密度为2.75 g cm-3（Rollin，1994）。我们忽略了构造超压的影响，因为我们的应力测量表明该压力不超过100 MPa（1 kbar），这在我们的压力估算值的不确定性之内。我们基于沿Strabeg断面的10个样本的厚度-深度数据进行的重构如图13所示。由于与计算压力有关的大误差，并非所有样本都按深度增加结构厚度的顺序绘制在理想情况下可以预期。总剪切区厚度的其他不确定性是由于掺入剪切区（图13中为浅色区）的底壁材料的厚度引起的。剪切下限的约束较弱，但是这种不确定性可能只是剪切区总厚度的一小部分。我们基于沿MT和BHT合并的Lewisian地下室的相对较小（即10 m尺度）的厚度（图1、2（a）和2（b））。与在壁挂式Moine片岩中观察到的情况相似，掺入剪切带的基底数量可能会随着深度的增加而增加，即使存在这些不确定性，该模型也说明了深度剪切带变宽的总体趋势。我们估计在约20 km的深度处约2.5 km的厚度，沿预测的断层倾角向下推算，在〜25 km深度处的剪切带结构厚度> 5 km。我们在此模拟剖面基础上建立了天气切变带（图6）。在我们了解脆性和延性变形区域的岩石强度和流变学方面，实验岩石研究至关重要。但是，温度，应力和应变率的实验变形条件和地质条件之间的差异很大，因此我们必须依靠比例关系将实验结果应用于地质条件。这些关系需要对自然变形岩石进行基于野外研究的验证，以确定实验约束在自然条件下近似于变形的程度。在以下部分中，我们使用计算出的变形温度，压力和微分应力，以将我们的自然数据与当前发布的关于石英中位错蠕变的流动定律进行比较。然后，我们使用根据已发布的流定律预测的应变率，并将其与独立于现场数据计算出的几何应变率进行比较。在T-σ空间中绘制流定律，应变率的轮廓范围为10-10到10-16 s-1（图14）。对于Hirth等人，来自Strabeg断面的数据通常在10-15 s-1和10-13 s-1的应变率之间。[113]以及Tokle等人的10-16至10-14 s-1之间。[114]。数据显示出在较低温度和较高应力下应变率增加的趋势，反映出由于应变局部化而导致的剪切带变窄以及由此导致的较高应变率的趋势。[114]流量定律是专门针对棱镜滑动提出的，而沿Strabeg断面的岩石清楚地表明了激活多个滑动系统的证据（图12）。对于石英，其显示出基底，菱形和棱柱滑动系统（即单带状CPO）的贡献，Tokle等人。[114]建议晶界滑动（GBS）作为一种变形机制，将棱镜极限和基极位错蠕变机制联系起来。我们没有发现具有单束带CPO的样品的石英微观结构中存在GBS的证据（例如，域3和4的一部分）。这些样品中的动态重结晶晶粒尺寸明显大于其他天然变形的富含石英的岩石中建议使用GBS的晶粒尺寸[119-122]。板块速度的值是根据在Strabeg断面以南约30 km的Assynt Culmination中MT下方两个断层的总位移（缩短）和推力持续时间计算得出的（图1）。然后将该计算值与该区域的广义构造速度进行比较。剪切带厚度取为到投影断层平面的结构（正交）距离，再加上我们确定的底盘剪切带厚度。这些厚度基于平行于位移方向的四个详细的结构和微观结构断面，我们证明了以下厚度计算的合理性。在以上各节中，我们详细讨论了相对于岩性MT的剪切带厚度的计算。岩石微观结构的检查和定量表明，这种岩性接触的流变学意义不大，并且主要充当我们测量结构距离的被动标记。我们已经提供了从岩性MT底盘的岩石中保留的中等到高应变的证据。因此，对于涉及活动剪切带总厚度的计算，我们将从岩性MT（定义为0 m）到LS-26（MT下方172 m）之间的距离，加上在MT处及以上的每个厚度测量值（对于LS-27，在岩性MT下方58 m处，我们计算出剪切带厚度= 172–58 m？）。与结构较高的岩石相比，LS-26表现出中等应变，表明它可能位于较低的剪切带边缘（图7（c））。沿Strabeg断面没有脆性MT的暴露，我们估计在结构上最低的样品记录的变形深度处，剪切带的最小厚度可能约为100-150 m。 ⁠）通过将总推力收敛（km）除以推力持续时间（Myr）来计算。Elliott和Johnson [34]估计在Assynt窗的Glencoul和Ben More推力上的位移分别为20-25 km和28 km。基于U-Pb年代学对一套碱性侵入岩的变形时间进行了很好的约束。运动学（Loch Ailsh Pluton，波拉兰Pluton湖的早期部分和Canisp斑岩窗台）和运动学（Loch Borralan Pluton）侵入体将逆冲作用限制在430.6±0.3 Ma和429.2±0.5 Ma之间，尽管它可能早些启动了[36]。对缩短时间（50 km）和时间跨度（0.6–2.2 Myr）进行估算，得出的位移率为23–83 mm yr-1。作为保守估计，我们使用最小位移速率23 mm yr-1，但也基于35 mm yr-1计算上限（位移速率增加约50％）。这些时间限制来自于Strabeg断面以南40–50 km的Assynt窗，但沿走向的结构的连续性强烈地表明了同期性。西北西加里东期造山带的斯堪的安期造山带正常运动的构造速率根据板块构造重建模型，苏格兰被限制在劳伦蒂亚和波罗的海之间的30-60 mm yr-1之间[18]。我们当地计算的比率与这些构造规模的估计值总体上是一致的。为了使用这个位移率来计算应变率，我们做几个假设。首先，我们假设位移率在时间上或沿行程没有明显变化。这是特别重要的，因为位移率是根据MT以下的推力来计算的，因此要求位移率在c周期内保持恒定。在沿着Glencoul和Ben More冲断运动之前，要先走5-10 Myr。其次，我们假设在任何给定时间沿单个活动断层（剪切）带都容纳了应变。但是，次要组件可能会沿着辅助结构进行划分，这就是为什么我们选择使用最小值作为估算的位移率。尽管我们假设可以独立计算应变率，但我们接受的是一阶估算，重要的是要意识到，速度和/或剪切区厚度的值即使有中等误差也不会显着影响量级应变率。我们有信心可以将位移率限制在±〜50％以内，并将剪切带厚度限制在±〜20％以内，这不会严重影响计算出的应变率。如上所述，在距断层平面任何给定结构距离的微观结构都有可能在给定的厚度（和时间）下，保持剪切区内的条件。因此，我们将温度，压力和应力分配给特定的结构厚度，然后将其归因于计算出的应变率。尽管有些估计值在误差范围内，但基于流定律的应变率（来自[110，111]）始终较低在给定温度，压力下 与独立的基于场的计算相比，应力条件有时大于> 1数量级（图15，表2）。请注意，如果差分应力低于计算得出的应力（由于富含石英的区域和多相区域之间的应变分配），或者计算得出的位移速率较高（即，不是我们使用的最小估计值），则实验与自然应变速率之间的差异将变得更大。这些差异可能表明：（a）石英的位错蠕变不是流变学的主要控制因素；（b）基于场的应变速率的估计不准确；和/或（c）选定的流动规律不能在地质学上准确地模拟岩石流变学条件。我们在下面介绍了每种可能性。（a）根据我们的光学和质地分析，我们得出结论，石英是剪切带大部分区域中控制粘性流变学的主要相。寄居岩片岩是富含石英的岩石，长石比例较高的岩石（例如，花岗质或花岗二元组成）可能会更强，反映出长石或长石与石英[123]。但是，我们确实在薄截面尺度上观察到与成分和晶粒尺寸变异性相关的岩石流变学差异（图8（b））。由于层状硅酸盐基面之间容易滑动，层状硅酸盐的相互连通性可能导致岩石强度较弱[124-127]。此外，由于固定在多相材料中而导致晶粒尺寸减小，可能会导致转向石英中对晶粒尺寸敏感的蠕变[128，129]。（b）如上所述，即使剪切区宽度或位移率的中等不确定性也不会显着影响应变率的数量级估计。此外，我们基于现场的应变率（图15）在板边界尺度断层系统的应变率的其他独立估计范围内（Sassier等，2009； [129，130]）。（c）显着变异性在发表的关于位错蠕变的流动定律校准之间存在着石英[113，114，131–135]。公式（2）中H，n和r值的变异性可能源自原料的差异，实验条件（包括变形设备），流体含量约束不良以及其他不确定性，可能导致数量级预测应变率的差异。最近的工作还引入了对激活焓（H）的压力敏感性，增加了更多的复杂性[133]。我们认为，描述岩石流变学的基于实验的本构定律应进行彻底测试，并在必要时进行更改，以更好地适应受严格约束的基于现场的数据，正如Hirth等人所建议的那样。[113]。根据我们的光学和组织分析，我们得出结论，石英是剪切区大部分区域中控制粘性流变学的主要相。寄居岩片岩是富含石英的岩石，长石比例较高的岩石（例如，花岗质或花岗二元组成）可能会更强，反映出长石或长石与石英[123]。但是，我们确实在薄截面尺度上观察到与成分和晶粒尺寸变异性相关的岩石流变学差异（图8（b））。由于层状硅酸盐基面之间容易滑动，层状硅酸盐的相互连通性可能导致岩石强度较弱[124-127]。此外，由于钉扎在多相材料中而导致晶粒尺寸减小，可能会导致转向石英中对晶粒尺寸敏感的蠕变[128，129]。如上所述，即使剪切区宽度或位移速率的中等不确定性也基本上不会影响我们应变率的数量级估计。此外，我们基于现场的应变率（图15）在板边界尺度断层系统的应变率的其他独立估计范围内（Sassier等，2009； [129，130]）。标定石英中位错蠕变的流动规律[113，114，131–135]。公式（2）中H，n和r的值的变异性，这可能是由于起始材料，实验条件（包括变形设备），流体含量控制不佳以及其他不确定性方面的差异而导致的预测应变率的数量级差异。最近的工作还引入了对激活焓（H）的压力敏感性，从而增加了复杂性[133]。我们认为，描述岩石流变学的基于实验的本构定律应进行彻底测试，并在必要时进行更改，以更好地适应受严格约束的基于现场的数据，如Hirth等人所述。[113]。预测应变率与基于现场的应变率之间最显着的差异在于样本LS-72和LS-74，它们来自域2中路易斯维斯内层上方的区域。两种样品的温度和应力均低于结构上或低于结构（表1）的样品。如果此内部是一个片状薄片并充当机械强度较高的块，则由LS-72和LS-74表示的有效剪切区宽度将减少〜25-30％，从而导致更快的应变速率接近于基于样品温度，压力和应力。减小剪切区宽度对结构上较高的样品的影响很小，因为纤齿状薄片的厚度占总剪切区宽度的比例较小。该次要区域的宽度可能只是较宽的主要剪切区域的一小部分，这将纠正根据流量定律计算出的较低的应变速率估计值（对于给定的应力，温度和压力条件）。次要定位也与较低的计算温度相符。然而，我们没有观察到较小的再结晶晶粒尺寸，该模型也对此进行了预测（表1）。认为上地壳的强度主要受沿活动断层的摩擦过程控制，遵循Mohr-Coulomb摩擦滑动准则。对于未损坏的地壳材料，经验和实验估计的摩擦系数（μ）通常在0.6-0.85之间[136]。更现实的估计表明，上地壳比伯利利定律所预测的要弱得多，因为断层泥和富含粘土的断层岩石的有效摩擦系数值较低（例如，μ<0.1？）。这些有效摩擦系数的低值可能归因于粘土矿物的热稳定性，与温度有关，并且随着粘土变得不稳定和/或沉淀出摩擦力更强的相而更接近BDT（[16]和其中的参考文献）。由于从靠近BDT的弱摩擦材料到强摩擦材料的过渡，Byerlee型摩擦仍可用于估算该区域的岩石强度[16]。假设简化系统的岩石强度主要由μ控制，则摩擦强度由于法向应力（压力）随深度的增加而增加，因此它与深度有关。对于富含石英的岩石，在约300°C的温度下，热活化蠕变过程成为主要的变形机制，遵循应力与应变率之间的幂律关系（等式（2））。粘性蠕变过程高度依赖于温度，导致地壳强度随深度呈指数下降。在这些模型中，预计地壳的最强区域是摩擦流变学和粘性流变学之间的过渡（参见[16，17]）。在下面的部分中，我们通过绘制沿Strabeg断面的岩石的切应力和变形深度数据以及Byerlee定律所预测的摩擦强度，来构造收缩断层系统的一阶自然约束地壳强度剖面。请注意，用古测压法（表1）测得的应力是在单轴压缩中校准的（？σ2=σ3？），并以微分应力表示（？σd= σ1–σ3？）。为了将这些应力与驱动脆性断层的应力进行比较，我们通过用Paterson和Olgaard [137]中概述的√3除以√3将平面应力环境中的应力转换为剪切应力。在Strabeg断面记录了指示粘性变形的石英微结构，但缺乏广泛的摩擦或脆性行为的证据，可能是因为MT上BDT的结构水平已沿着许多断层迹线腐蚀了。但是，靠近前陆（西部）的断层记录了BDT的变形情​​况。因此，我们对格伦库尔湖（图1中的红色星体）格伦库尔推力（GT）的直接悬挂壁上的样品（GT-3）上的古应力进行了量化，该样品将路易斯阶片麻岩置于An T-Sron粉砂岩的薄单板上，砂岩 依次顺次覆盖在Eriboll石英岩上[47]。当形成微观结构时，共存的脆性（例如，石英断裂和沿脆性剪切带的偏移）和延性（例如，通过BLG引起的石英的动态再结晶）结构清楚地将样品置于BDT周围（图8（c）和8（d）） ）。尽管很难确定样品GT-3记录的精确深度，但我们根据〜280±20°C的温度为晶体塑性行为的下限计算了约11（+ 4 / -2）km的深度。石英，地热梯度为25±5°Ckm-1⁠。该深度估计值与先前在MTZ的直接下盘（即，GT-3的西部； [39]）下的200–250°C和200–300 MPa的估计值一致，并且与来自接近BDT的Strabeg样面。对样品GT-3的EBSD分析得出的平均重结晶晶粒尺寸为3.9±1.5，根据Cross等人的观点，得出σd= 225（+ 92 / -46）MPa。[61]压强仪，等效于σs= 130（+ 53 / -26）MPa的平面应力环境中的剪应力。按照安德森模型进行故障分类，推力方向中驱动变形的主应力定向为最小压缩主轴σ3⁠是垂直的，并视为有效压力（等于岩石静压力减去孔隙流体压力）。σ1⁠，最大的压应力，是水平的，作用在缩短方向上。假设平面应力为σ2=σ1+σ3/2⁠。由于这些应力相对于地球表面的方向，沿着断层的剪切应力是地壳强度的模拟，对于给定深度，与正常或走滑状态下的相应剪应力相比，反向状态下的应力预测值更大[138]。在σ3等于岩石静压力的干燥系统中，在没有先断层（即μ=0.85⁠）的收缩状态下的岩石强度预计将超过350 MPa。如上所述，由于推力断层已经显示出非常低的（例如，<0.1）有效摩擦系数（[139]；另请参见[16]中的讨论），这是对岩石总强度的不合理估计。该估计也是在假设干燥系统不影响孔隙流体压力的情况下进行的。遵循Byerlee型摩擦流变学的岩石中的孔隙流体压力的作用是降低有效法向应力。确实，长期以来，人们一直将高孔隙流体压力作为一种机制来解释沿冲断层的有效摩擦值很低的现象。石英的沉淀以及名义上无水矿物的普遍氯化作用和绢云母化证明了GT和MT沿同变形流体的存在。韧性流体中孔隙流体的影响更难以通过热活化过程（例如位错）来预测。蠕变和动态再结晶）可能会导致摩擦接触面积发生变化，从而影响孔隙流体压力（Pf；请参见[67]中的讨论）。因此，在Hirth和Beeler [67]之后，我们通过引入术语α（≥1≥α≥0作为粗糙屈服应力的函数，修改了Pf）来修改对Byerlee型摩擦性能的估计。我们使用相同的值来计算粗糙变形屈服应力，但使用Hirth等人的计算得出的应变速率为10-13 s-1。[113] Strabeg断面中结构最低的岩石。基于古测度估算的BDT内变形岩石的剪切应力，最大剪切应力不可能超过〜180 MPa（GT-3的最大剪切应力在误差范围内）是183 MPa）。为了使Byerlee控制的岩石的模拟剪应力与我们观察到的值一致，μ=0.50⁠，并且需要孔隙流体压力与岩石静压力之比λ=0.36⁠（图16）。重建约10–20 km深度的板块边界尺度剪切带的几何形状，内部结构和流变学。我们得出以下结论：（1）变形的温度和压力与构造反转场梯度（等梯度向东倾斜）一致，该梯度保留了伴随着发掘的剪切带演化的记录。（2）石英似乎是控制剪切的主要相带流变学，主要由于位错蠕变而变形。随着温度降低和应变局部化，活动剪切区内的石英重结晶机制会随着时间从高T GBM演变为BLG。再结晶机制的变化大致与活动滑移系统的变化相对应，从在较高温度和较低应力下占主导的棱镜到在较低温度和较高应力下由棱镜，菱形和基体组成的组合。（3）收缩区的剪切带几何形状，板块边界尺度断层系统已被独立地约束，并且显示出随着深度的增加而变宽，在〜20 km的深度处达到〜2.7 km的厚度。（4）独立的基于现场的应变率估计从大约10-11–10减小从BDT到20 km深度为-12，这与剪切带模型一致，该模型将应变定位在较低的温度和压力下，从而在剪切带的较窄部分产生较高的应变率。（5）岩石微观结构表明，位错蠕变是石英的控制整个Strabeg断面以及可能遍及斯堪的纳大部分剪切带的岩石流变的主要变形机制。但是，独立的，基于场的应变率估计值通常要比现有的本构关系预测的石英位错蠕变的应变率要高，（6）将计算出的深度和应力与摩擦岩石强度一起绘制出来，以在推力环境中通过中下地壳构造自然约束的应力分布。我们估计，从BDT到20 km深度，剪应力从130降低到<10 MPa。剪切应力的测量结果与由Behr和Platt [15]从加利福尼亚州Whipple山脉的常理剪切带确定的结果相比较。请注意，我们修改了Behr和Platt [15]提出的应力估计，以不反映作者最初使用的拟议的Holyoke和Kronenberg [66]应力重新校准（如上所述）。我们估算的BDT的峰值剪切应力为130 MPa，比Whipple山脉的峰值剪切应力（107 MPa剪切应力）高一些，正如预期的那样，考虑到构造方式的差异。剖面图表明，对于μ<0.50？的值，BDT紧下方的延性岩石在较高应力下的变形要比在较高结构水平下通过摩擦机制变形的岩石高。这表明，地壳的强度受中地壳的该浅延性区域控制，如Behr和Platt所建议的[16]。（7）我们提出了一种将TitaniQ应用于氨基甲酸酯，半pepelitic或其他低磷的方法。同时变形温度，压力和a（TiO2）的解 这种方法需要对大块岩石成分进行热力学建模，对石英中钛的测量以及独立的热压计。变形的温度和压力与构造反转场梯度（等梯度向东倾斜）一致，该梯度保留了伴随着发掘的剪切带演化的记录。石英似乎是控制剪切带流变学的主要相，主要是通过剪切来改变的。位错蠕变。随着温度降低和应变局部化，活动剪切区内的石英重结晶机制会随着时间从高T GBM演变为BLG。重结晶机制的变化大致对应于活动滑移系统的变化，从在较高温度和较低应力下占主导的棱镜到在较低温度和较高应力下棱镜，菱形和基体的组合。板块边界尺度断层系统已经被独立地约束，并且显示出随着深度的增加而变宽，在〜20 km的深度处达到〜2.7 km的厚度。独立的基于现场的应变率估计从大约10-11–10-12减小BDT深度为20 km，这与在较低温度和压力下将应变局部化的剪切带模型一致，从而在剪切带的较窄部分产生较高的应变率。岩石微结构表明，石英的位错蠕变是控制岩石流变学的主要变形机制。横跨Strabeg样带，可能遍及整个斯堪的纳剪切带。但是，独立的，基于场的应变速率估计值通常要比现有的本构关系预测的位错蠕变高，通常将计算出的深度和应力与摩擦岩石强度一起绘制，从而在推力环境中通过中下地壳构造自然约束的应力分布。我们估计，从BDT到20 km深度，剪应力从130降低到<10 MPa。剪切应力的测量结果与由Behr和Platt [15]从加利福尼亚州Whipple山脉的常理剪切带确定的结果相比较。请注意，我们修改了Behr和Platt [15]提出的应力估计，以不反映作者最初使用的拟议的Holyoke和Kronenberg [66]应力重新校准（如上所述）。我们估算的BDT的峰值剪切应力为130 MPa，比Whipple山脉的峰值剪切应力（107 MPa剪切应力）高一些，如预期的那样，考虑到构造方式的差异。剖面图表明，对于μ<0.50？的值，BDT紧下方的延性岩石在较高的应力下变形，而在较高的结构水平下，由于摩擦机制变形的岩石变形更大。这表明，地壳的强度由中地壳的这个浅韧性区域控制，如Behr和Platt所建议的[16]。我们提出了一种将TitaniQ应用于磷酰胺，半pepelite或其他低a（TiO2）的方法。同时变形温度，压力和a（TiO2）溶液。这种方法需要对大块岩石成分进行热力学建模，对石英中钛的测量以及独立的热压计。EBSD分析是在配备有EDAX Hikari EBSD检测器的JEOL-7001F扫描电子显微镜上进行的，该检测器位于南加州大学纳米影像中心。我们使用20 kV的加速电压，14 nA的探针电流，15 mm的工作距离以及500 nm至8μm的步长，其中步长最多为最小晶粒直径的1/4。根据重结晶的晶粒尺寸和台阶尺寸，地图覆盖范围是可变的；在粗粒度的样本中，将多张地图缝合在一起，总地图大小约为3×15毫米，而在细粒度的样本中，地图则小至约2×2毫米。使用EDAX的OIM 7软件包收集，清理和绘制地图数据。OIM 7中的清洁工作由谷物置信度指数标准化，其次是邻居置信度指数相关性和邻居点定向相关性。没有应用晶粒膨胀程序。使用OIM晶粒重建程序定义晶粒。高角度晶界的定义是相邻晶粒之间的最小错位为10°，而基于EBSD角精度和社区惯例，亚晶界可以完全向下直到2°的错位[137-139]。我们遵循Cross等人的程序。[58]基于每个样品中的晶粒取向扩散（GOS）折衷曲线阈值来区分重结晶晶粒和残渣晶粒。尽管由于新的重结晶晶粒不断积累晶内应变，所以已建议使用GOS来判别重结晶晶粒和残渣晶粒不是一个准确的度量[140]，我们应用此过滤器是为了与Cross等人的校准保持一致。[58]。在所有分析中，石英是唯一的相位索引。如果地图中存在其他相，并且为了消除由于样品表面损坏而造成的索引错误，我们删除了平均置信指数<0.4的索引点。由于我们选择的步长为最小晶粒直径的1/4，因此<16像素的晶粒也被去除，因为它们很可能是清理程序的伪像。EBSD分析会定期发现谷物中像素的斑点或斑点图案；这些模式在<0001>附近的方向错误为60±5°，可能记录了Dauphiné孪晶边界以及系统错误定位的区域。在后处理中将这些区域除去，以保持与古眼压计校准的一致性[58]。TitaniQ温度晴雨表利用48Ti的温度和压力依赖性来替代石英中的28Si，以计算P–T条件。较高的温度或较低的压力允许在石英晶体结构内增加Ti的浓度。Kohn和Northup [141]以及Spear和Wark [142]证明，由于动态重结晶，石英中的Ti含量重新平衡，这表明TitaniQ实际上会产生变形温度。然而，后来的工作表明，GBM重结晶对于促进Ti的再平衡是必要的，并且在低于〜500°C的温度下，BLG和SGR的重结晶很可能占主导地位，Ti的浓度不会复位[91]。由于重结晶晶粒中的Ti浓度低于寄主卟啉，并且总体Ti浓度较低，Ashley等。[96]声称TitaniQ不能用于确定由SGR重结晶的石英的变形温度。但是，与此相反，最近的实验工作表明，石英中的动态重结晶增强了Ti平衡的动力学，而与重结晶机理无关，这证明TitaniQ确实记录了变形温度[98]。Ti替代Si的程度也很明显。取决于系统中TiO2的活性；如果钛活度（a（TiO2））小于1，则钛替代物的可用性降低，从而降低了石英中Ti的浓度。Ghent和Stout [143]估计以下含钛相的a（TiO2）：金红石TiO2 =1⁠; 钛铁矿FeTiO3 =0.8⁠; 钛矿CaTiSiO5 =0.6⁠。然而，使用这些值表示a（TiO2），许多工人报告了异常的低温（例如[87–90]）。为解决此问题，我们在PT空间上实现了a（TiO2）建模，并结合了TitaniQ XTiO2石英和Si-in的轮廓片-等长线准确地限制了每个样本的活动（图9（b）；有关建模方法的完整讨论，另请参见[78]）。使用这种方法，我们计算出的money滑石的a（TiO2）值在0.20-0.35之间（表2），大大低于Ghent和Stout [143]提出的广泛估计。但是，它们与Ashley和Law [78]的热力学模型相一致，后者计算了<0.3的葛瑞瓦克（即密胺）组成的a（TiO2），以及Kidder等人的方法。[92]他们提出来自高山断层的镍铁矿的aTiO2 = 0.1的值。这些较低的活动会导致给定Ti浓度下的较高温度。由于Ti浓度相对较低，因此最好在二次离子质谱仪（SIMS）上测量样品。在分析之前，通过阴极发光（CL）在全色和蓝色UV波长下检查样品，以寻找石英中Ti的异质性和/或分区（例如，Wark和Spe​​ar，2005； [142，145]）。在Moine Schist内，CL没有发现可检测到的异质性，表明石英中Ti分布均匀。在刘易斯片麻岩中，重结晶石英通常比较大的片麻岩晶粒更暗，这表明重结晶晶粒中的Ti浓度较低。这与动态再结晶重置石英中Ti浓度的观察结果一致[93-95]。在亚利桑那州立大学（ASU）的Cameca 6f SIMS上进行了分析。16O光束的初级光束电流为〜15 nA，固定光束的直径为10–30μm，因此加速至-12.5 kV。作为标准，在爱丁堡大学合成了三种浓度分别为0、100和500μg/ g（ppm）的石英玻璃并进行了表征（https://www.ed.ac.uk/geosciences/facilities/ionprobe/standard -材料可用/ tiquartz标准）。在上述条件下使用ASU Cameca 6f SIMS对这些样品进行的研究提供了将Ti + / Si +离子比与TiO2浓度相关联的校准曲线（图A1）。对于未知样品，分析从300秒溅射开始，以去除导电的Au涂层，确保离子束与岩石样品接触。随后测量27Al，40Ca，30Si，每个站点超过30个循环的48Ti和49Ti。根据样品的复杂程度，每个样品选择7–10个位点。站点的位置基于CL成像，与含钛相的接近度以及石英的微观结构。在每次测量中，由于48Ca（次要同位素）对48Ti的不可分辨的干扰，我们监测了两个钛同位素48Ti和49Ti。如果无意地分析了富含钙的区域（例如，通过斜长石晶体上被分析区域的意外重叠），则49Ti信号将提示浓度较低。尽管这种次要的钛同位素产生的较低强度会导致较大的不确定性，但分析的准确性将优于使用48Ti和48Ca之和。如Kohn和Northrup [141]所述，使用27Al和40Ca同位素监测石英中的微夹杂物。数据清理和后处理包括消除错误值和27Al和40Ca计数中的尖峰或不连续性，这表明与微夹杂物或晶界接触。数据清理后，通过取平均值计算出最终的代表性Ti浓度。每个站点；Ti浓度>1σ且未通过Student T检验的单个站点被视为异常值，被忽略，并且不包括在最终均值计算中。分析结果列于表1和图10（a）中。由于我们使用的TitaniQ校准对压力和温度均敏感，因此我们基于在样品中的白云母成分对Si-in-phengite等值线进行建模以独立约束PT条件。白云母-硅藻土固溶体[77]。硫铁矿的每配方单位（PFU）中的Si含量，高云母含量的白云母受高P和低T的影响，随着压力从3.0（纯白云母）升高到〜3.9（高Si硅镁铁矿）而增加。对于每个具有Ti-石英内分析（表S2）。在加利福尼亚大学洛杉矶分校的JEOL JXA-8200电子探针微分析仪（EPMA）上进行了分析。整个过程中使用了15 kV的加速电压，15 nA的束电流和5μm的光斑直径。高对比度反向散射成像或每个颗粒的多个EPMA线横断面分析都没有揭示白云母颗粒内的成分分区。分析结果列于表1和图10（b）中。对具有Ti-in-Quartz和Si-in-phengite测量结果的每个样品进行X射线荧光（XRF）块岩分析。岩性均匀 将未风化的部分样品在玛瑙球磨机中粉化。从该粉末中分离出〜2g，并计算出燃烧损失。主要元素的XRF分析是在加利福尼亚理工学院的Bruker M4 Tornado Micro-XRF光谱仪上进行的。假定所有的P主要限于磷灰石。从本体化学物质中除去P2O5，并将剩余的氧化物比率标准化为100％。假定所有的Fe均为FeO（2+氧化态），并为此假设校正了相应的XRF数据。没有对Fe 2+ / Fe 3+的比例进行校正。结果列在表S3中。对Perple_X [146]中的MnO-Na2O-CaO-K2O-FeO-MgO-Al2O3-SiO2-H2O-TiO2（MnNCKFMASHT）系统进行了热力学建模，计算了PT中的稳定相。基于吉布自由能最小化的空间。我们使用针对Holland和Powell [147]热力学数据库的2004年更新以及以下解决方案模型：石榴石，Gt（HP）；亚氯酸盐，Chl（HP）；钙镁矿，钾盐；类胡萝卜素，Ctd（HP）；人造石，来自荷兰和鲍威尔的St（HP）（2004）；黑云母，允许Tschermak交换的生物（TCC）[148]；来自荷兰和鲍威尔的含水堇青石（hCrd）和钛铁矿-辉石-辉石沸石（IlGkPy）的理想溶液模型[147]；来自Fuhrman和Lindsley的高结构态长石（长石）[149]。该系统被建模为在SiO2和H2O中饱和，并且排除了菱锰矿（hed），stilpnomelane（stlp和mnsp），因为在这种组成的岩石中这些相都不是预期的，在更高品位的Moine岩石中也没有观察到。不包括熔体，因为PT条件大多低于最低熔体温度，而且我们没有观察到在这些结构水平上融化的证据（图9（a））。作者声明他们没有利益冲突。我们要衷心感谢Sarah Roeske的编辑工作。感谢Rick Law，Jeffrey Rahl和2位匿名审稿人的深入而有见地的审稿，这些审稿极大地改善了此手稿的内容和组织。特别感谢里克·劳（Rick Law），在整个研究项目期间进行了特别有益的评论和讨论。我们感谢亚利桑那州立大学SIMS实验室的Richard Hervig和Lynda Williams为TitaniQ测量提供的帮助。这项研究部分由NSF授予J.Platt的EAR-1650173以及A.Lusk的Dornsife博士奖学金资助。钛离子在石英中的二次离子质谱（SIMS）校准曲线，使用48Ti和49Ti同位素（强制穿过原点）。图S1：显微照片，显示了石英+长石为主的基质（上）（长石趋于均匀且呈角形）和细粒云母为主的基质（底部）（长石呈卵形且细长）之间的长石晶粒形状差异平行于宏观叶（水平）。图S2：图4（c）–4（g）中EBSD映射的错误取向轮廓。可以将相关的取向错误与随机分布进行比较，以作为主动重结晶机制的证据。图S3：用于应变分析的Moine砾岩露头照片。文字中引用了应变强度D = lnX / Y2 + lnY / Z2。