When a page, represented by the interval $[0,1],$ is folded right over left $ n$ times, the right-hand fold contains a sequence of points. We specify these points and the order in which they appear in each fold. We also determine exactly where in the folded structure any point in $[0,1]$ appears and, given any point on the bottom line of the structure, which point lies at each level above it.

New detailed mapping and related field studies, together with re-assessment of prior investigations, have revealed that three groups of faults, orientated broadly NE, N and NW, have been the primary controls on stratigraphical, structural and geomorphological evolution in the upper Firth of Clyde since their initiation by proto-Variscan stresses in Late Devonian time. Extended control has been achieved through repeated episodic reactivation, during which existing lines of fracture were rejuvenated and others of similar orientation initiated. Movements on two (if not all three) groups of faults persisted until middle Palaeogene time at least. The faults have been augmented by two sets of irregularly distributed, open, plunging folds, broadly N–S and E–W in their axial orientations. Some N–S folds may be attributed to oblique or strike-slip movement on reactivated caledonoid faults, others to intermittent transpression, probably in Namurian–Westphalian times, affecting mainly the northeastern Midland Valley but stretching beyond the massif of the Clyde Lava Plateau to register a weakened presence as far W as the upper Firth. The N–S folds and dextral strike-slip movements on some faults may be far-field expressions of the Uralian Orogeny, whereas earlier, sinistral displacements on NE faults and the development of small, later and less-significant E–W folds may be related to different phases of long-lived Variscan compression from the S.

The boundary between the Rhoscolyn and New Harbour formations on Holy Island, Anglesey, has been described as a high strain zone or as a thrust. The boundary is here described at four localities, with reference to the contrasting sedimentary and deformational character of the two formations. At one of these localities, Borth Wen, sandstones and conglomerates at the top of the Rhoscolyn Formation are followed, without any break, by tuffs and then mudstones of the New Harbour Formation. It is concluded that there is clear evidence of depositional continuity across the boundary here, and that both formations subsequently shared a common two-phase deformation. The first (D1) was manifestly different in intensity and scale in the two formations, whereas the second (D2) produced very similar structures in both. The other three localities provide continuity of sedimentary and tectonic features at this boundary in a traverse along the length of Holy Island, leading us to identify two previously unrecognized major D1 folds in addition to the Rhoscolyn Anticline. At one of these localities (Holyhead), we confirm the presence of Skolithos just below the boundary, supporting radiometric evidence for a lower Cambrian or later age for the Rhoscolyn Formation. A turbidite interpretation for both the Rhoscolyn and New Harbour formations best fits the available evidence. A deep-water depositional environment is still compatible with the sporadic presence of Skolithos burrows, but less so with reported observations of hummocky and swaley cross-stratification lower down the South Stack Group.

We describe the geometry and kinematics of a Jurassic to Early Cretaceous transpressive sinistral strike-slip system within a metamorphic basement inlier of the Mesozoic magmatic arc near Bahia Agua Dulce at latitudes 31–32°S in north-central Chile and discuss possible relations with the Atacama Fault System further north. Sinistral transpression overprints structures of an accretionary system that is represented by the metamorphic basement. Sub-vertical semi-ductile NNW-striking strike-slip shear zones are the most conspicuous structures. Chlorite and sericite grew, and white mica and quartz dynamically recrystallized, suggesting low-grade metamorphic conditions during semi-ductile deformation. Folds at the 10–100 metre scale developed before and during strike-slip shearing. The folds are deforming a former sub-horizontal transposition foliation that originated during prior accretion processes. The folds have axes sub-parallel to the strike-slip shear zones and sub-vertical axial surfaces indicating a component of shortening parallel to the shear-zone boundaries, suggesting an overall transpressive deformation regime. Transpressive strike-slip deformation also affects Middle Triassic (Anisian) basal breccias of the El Quereo Formation. 40Ar–39Ar laser ablation ages of synkinematically recrystallized white mica in one of the shear zones provide an age of 174–165 Ma for the waning stages of semi-ductile strike-slip shearing. The semi-ductile shear zones are cut by mafic and rhyolite dykes. Two rhyolite dykes yield 40Ar–39Ar ages of 160.5 ± 1.7 Ma and 131.9 ± 1.7 Ma, respectively. The latter dyke has been affected by brittle faulting. Fault-slip analysis shows that the kinematics of the faulting event is similar to the one of the semi-ductile shearing event, suggesting that sinistral transpression continued after ~130 Ma. Timing, kinematics and geographic position suggest that the shear zones at Bahia Agua Dulce represent a southern continuation of the prominent Atacama Fault System that affected the Jurassic/Early Cretaceous arc over its ~1400 km length.

Pre-/early folding fracture patterns were recognized in several anticlines from three structural domains in the Simply Folded Belt of the Fars arc. These fracture sets were characterized in terms of opening mode and relative chronology and used to reconstruct the main compressional trends related to the early Zagros collisional history. The palaeostress reconstructions based on these fracture sets were further refined by combination with newly collected or already available fault-slip and calcite twin data. As an alternative to previous models of rigid block rotations or regional stress rotation, we propose that the complex pattern of pre-folding fractures and the contrasting palaeostress orientations through time in the different domains investigated are related to the presence of basement faults with N–S and WNW trends, above which basement and cover were variably coupled during stress build-up and early deformation of the Arabian margin. Beyond regional implications, this study draws attention to the need to carefully consider pre-existing fractures, possibly unrelated to folding, to build more realistic conceptual fold–fracture models.

The Old Red Sandstone on Anglesey, North Wales, presumed Lower Devonian in age, is folded and locally cleaved, but the intensity of this deformation has previously been understated. We describe two S-verging anticline–syncline pairs, one with a strongly overturned middle limb, their associated minor folds and an axial-planar cleavage. The intensity of the deformation calls into question a proposed link to Variscan fault displacements, and the angular unconformity below the Old Red Sandstone precludes the deformation being part of a continuous ‘late Caledonian’ phase. We consider this deformation of the Old Red Sandstone to be mid-Devonian, correlating with the Acadian phase in mainland Wales. It is predated by a Silurian shortening deformation on Anglesey that is possibly related to the closure of the Iapetus Ocean, absent in mainland Wales and the Lake District, but perhaps preserved also on the Isle of Man.

Quartzites tend to be compositionally homogeneous, and because of this, deformation related fabric elements (foliations and lineations) are poorly developed in them. This makes structural analysis of deformed quartzites challenging. The measurement of anisotropy of magnetic susceptibility (AMS) is useful for recognizing structural imprints in rocks that lack mesoscopic fabrics and the present study is carried out with an aim to demonstrate the robustness of AMS in analysing such deformation imprints in quartzites. AMS data of samples from folded quartzites located in an approximately 10 km2 area around Galudih (eastern India) are presented. Although on a regional scale, superposed deformation and ductile shearing are known from the area, the investigated quartzites do not preserve mesoscopic evidence of these large-scale features and have developed folds that plunge gently towards the SE with a vertical NW–SE-striking axial plane. The magnetic foliation recorded from AMS analysis is parallel to the axial plane, while the orientation of the magnetic lineation varies from SE through vertical to NW. This is similar to the large-scale fold axis variations recorded in various regional domains mapped over an area of about 200 km2. It is concluded that although the imprint of regional superposed deformation is not obvious on the mesoscopic scale in the quartzites around Galudih, this imprint can be detected from the magnetic fabric. The present study thus highlights the usefulness of AMS in analysing superposed folds in quartzites.

The elliptical and hyperbolic outcrop patterns characteristic of periclinal folds can be used to classify structures according to different curvature attributes. Elliptical patterns indicate domal-basinal structures with synclastic curvature, that is, principal curvatures of the same sign. Hyperbolic patterns are diagnostic of anticlastic curvature (saddle-like structures). Such outcrop geometries are geological examples of Dupin's indicatrix, the geometrical figure obtained by sectioning a curved surface on a plane parallel and almost coincident with the tangent plane. The aspect ratio of Dupin's indicatrix is theoretically related to the ratio of the principal curvature values for the part of the structure being considered. This new method allows quantitative assessment of structures on maps and on remote sensing images. Illustrations are given from Wyoming, USA, and Yorkshire, England.

The Kenmore inlier exposes the most intensely deformed part of a major Laxfordian shear zone whose NE margin occurs at Diabaig, N of Loch Torridon. The Laxfordian (post-Scourie dyke) deformation commences with two very intense deformations D1 and D2, producing LS fabrics in dykes and gneisses associated with heterogeneous, locally very large, and typically prolate strains under amphibolite-facies metamorphism. D2 also produced widespread mesoscopic folds. The finite strain was measured at 135 localities using grain-aggregate shapes in Scourie dykes. The combined D1-D2 elongation lineation plunges gently to NW or SE, and the planar fabric appears to have been sub-horizontal before the D3 deformation, which produced NW-SE upright folds under retrogressive metamorphism.

The D1-D2 structure is attributed to a major sub-horizontal shear zone with a top-to-NW movement, a minimum vertical width of 2·5 km and estimated minimum displacement of c. 19 km. The upper (NE) wall of the shear zone at Diabaig exhibits dextral-normal (NE-down) D1 movements. The D2 structures are attributed to superimposition of sub-horizontal movements on earlier inclined D1 fabrics as the shear zone evolves. The D3 refolding reflects a change to a dextral transpressive regime.

Five generations of structures (F1–F5), excluding faults, can be recognised in granitoid and trondhjemitoid migmatites with quartzofeldspathic neosome development associated with F1–F4 structures. Areal variation in metamorphic grade is shown by the zonal development of muscovite-sillimanite, potassium feldspar-sillimanite and potassium feldspar-cordierite assemblages in the palaeosomes. The climactic metamorphism, associated with MS2–MP2 mineral growth, occurred at between 675°C, 4 kb and 825°C, 6·5 kb. These pressure-temperature conditions are consistent with at least some neosome development having resulted from partial melting. The occurrence of a relatively shallow metamorphic geotherm and the resultant products are assessed in relation to metamorphic conditions known from elsewhere in the Svecokarelides.