Rift zone-parallel extension during segmented fault growth: application to the evolution of the NE Atlantic

. The mechanical interaction of propagating normal faults is known to influence the linkage geometry of first-order faults, and the development of second-order faults and fractures, which transfer displacement within relay zones. Here we 10 use natural examples of growth faults from two active volcanic rift zones (Koa ʻ e, Island of Hawai ʻ i and Krafla, northern Iceland) to illustrate the importance of horizontal-plane extension (heave) gradients, and associated vertical axis rotations, in evolving continental rift systems. Second order extension and extensional-shear faults within the relay zones variably resolve components of regional extension, and components of extension and/or shortening parallel to the rift zone, to accommodate the inherently three-dimensional (3D) strains associated with relay zone development and rotation. Such a configuration 15 involves volume increase, which is accommodated at the surface by open fractures; in the subsurface this may be accommodated by veins or dikes oriented oblique-and normal to the rift axis. To consider the scalability of the effects of relay zone rotations, we compare the geometry and kinematics of fault and fracture sets in the Koa ʻ e and Krafla rift zones with data from exhumed contemporaneous fault and dike systems developed within a >5x10 4 km 2 relay system that developed during formation of the NE Atlantic Margins. Based on the findings presented here we propose a new conceptual 20 model for the evolution of segmented continental rift basins on the NE Atlantic margins.


Introduction
The primary, regional scale segmentation of extensional terranes is controlled by the development of networks of normal fault systems and the partitioning of strain across them.Normal faults comprise multiple discontinuous, non-collinear segments, with overlaps and segment linkage forming characteristic stepping geometries at a broad range of scales (e.g.Cartwright et al., 1996;Peacock et al., 2000;Acocella et al., 2005;Long and Imber, 2011;Henstra et al., 2015).Fault growth models have been derived using natural examples and numerical, or scaled-analogue modelling techniques, where normal faults grow through stages in which discontinuous segments interact and link across relay zones to form composite structures with fault displacement deficits initially accommodated by soft-linkage rotation and/or material folding (e.g.Trudgill andCartwright, 1994 Gupta andScholz, 2000;Peacock, 2002;Long and Imber, 2010).
Mechanical interaction (i.e., where the mechanical behaviour of a fault segment is altered in the presence of another segment by the elastic interaction of their respective stress fields, see e.g., Segall and Pollard, 1980;Willemse et al., 1996) between discontinuous fault segments can have an important influence on fault system evolution, including the geometry of first-order (i.e. largest scale of observation) faults, and the development and distribution of second-order (i.e.ancillary) faults and fractures within developing inter-fault (relay) zones.Segmentation is a feature common to all scales of faults and fault development (e.g.Walsh et al., 2003;Long and Imber 2011) and the conservation of regional strain across networks of discontinuous segments has been well-established (e.g.Peacock and Sanderson, 1991;Peacock, 2002;Fossen and Rotevatn, 2016).Normal fault displacement is typically considered with emphasis on the vertical motion (fault throw), which can be measured using offset bedding, either in the field, laboratory, or using high-resolution seismic imaging.In horizontallylayered materials, displacement (throw) gradients on adjacent coherent normal faults are commonly accommodated by relay structures (e.g., Peacock and Sanderson, 1991;Childs et al., 1995;Long and Imber, 2010), requiring horizontal axis bending of the host layering (Fig. 1).The bounding faults of a relay zone also exhibit opposing horizontal displacement (heave) provides useful and abundant offset markers for measurement.There are fewer studies that have made detailed analysis of horizontal motions -the fault heave -due to the challenges in defining it accurately.Local deficits in fault throw are identified using comparisons with a theoretical final displacement profile for a fully linked set of faults accommodating regional extension, which show a centrally located displacement maxima.Such deficits can be accommodated by the development of new synthetic faults in the relay zone, and/or by folding about a horizontal axis, producing the relay ramp.
Any deficits in fault heave, on the other hand, require vertical axis rotation (Fig. 1C, E), which can be accommodated by the formation of new faults (i.e.hard-linkage: e.g.Gawthorpe and Hurst, 1993;Hus et al., 2006), or bending within the plane of bedding (i.e.soft-linkage: e.g.Childs et al., 1995;Faulds and Varga, 1998).The evolution of such structural elements will have a profound influence on the evolving tectono-stratigraphic architecture of rift basins (e.g.Lambiase and Bosworth, 1995;Sharp et al., 2000;Hus et al., 2006) as well as contributing to the sealing potential or fluid flow properties of fault zones (e.g.Morley et al., 1990;Manzocchi et al., 2010;Seebeck et al., 2014).

Methodology
Surface-breaching normal faults in the Koaʻe and Krafla fault systems cut sub-horizontal bedded lavas, which exhibit vertical columnar joint sets at a range of scales.Previous work has established that faults in layered basaltic sequences, at low confining pressures, develop as networks of extension fractures, which open along favorably oriented, pre-existing cooling joints in the lava pile, driven by tensile stresses ahead of blind normal faults (e.g.Grant and Kattenhorn, 2004;Martel and Langley, 2006).Eventual linkage of fault and fracture networks at depth results in the development of surfacebreaching, sub-vertical normal faults that exhibit components of horizontal and vertical displacement.The polygonal geometry of reactivated cooling joints allows displaced walls to be matched across the aperture of open fractures at multiple points along individual traces for: (1) extension fractures (i.e.mode-I fractures with no throw); (2) extensional-shear fractures (i.e.mixed-mode fractures with open and lateral shear components of offset, but no throw); and (3) normal faults (i.e.throw across subvertical, surface-breaching fault segments).Measurements of extension direction, extension magnitude (i.e.opening, or aperture), mode (i.e.mode-I or mixed-mode: Fig. 2) and individual trace azimuth were gathered using traditional compass techniques (Fig. 2).Cut-off line positions for surface-breaching fault segments and hanging wall monoclines were mapped remotely using satellite imagery (GoogleEarth TM and World-View2) and topographic datasets (aerial LiDAR; Hawaiʻi only).The resulting combined dataset contains approximately 2500 measurements and covers up to three orders of length magnitude.Where applicable, fault throw was estimated, either in the field, or remotely using highresolution topographic datasets.It should be noted that a majority of the structures encountered in the study areas are extension fractures that do not involve a shear component, typical of deformation patterns seen in many near surface rift zones (e.g.Grant and Kattenhorn, 2004;Casey et al., 2006).
Fault and intrusion geometry and kinematic data was collected over several field seasons for Kangerlussuaq and the Faroe Islands, from over 400 localities (Walker, 2010;Walker et al., 2011).Structures were mapped using a combination of field observation and remote sensing analysis.Fault slip data from localities was grouped based on observed cross-cutting relationships where possible, or grouped by fault strike where direct cross-cutting relationships were not clear.Kinematic inversions were performed using the methods described in Walker et al. (2011).

Field study areas
4.1 Kilometre-scale segmented fault systems

The Koaʻe fault system, Hawaiʻi
The Koaʻe fault system is ~12 km long and ~3 km wide and is located on the south flank of Kīlauea Volcano, the youngest intraplate volcanic system on the Island of Hawaiʻi.The Koaʻe system connects two prominent rift zones: the Southwest and East Rift Zones, (SWRZ and ERZ: Fig. 3A) to form a near-continuous rift system that accommodates regional NNW-SSE extension (Dzurisin et al., 1984;Wright and Klein, 2006;Poland et al., 2012).
Based on orientation, extension direction, and spatial distribution, we identify two dominant fault and fracture sets in the Koaʻe fault system: (1) ENE-WSW (ERZ-parallel) striking first-order fractures and normal faults that accommodate the regional NNW-SSE extension (sets A, C and D; Fig. 3B); and (2) NW-SE (ERZ-oblique) striking fractures that accommodate a more localised NE-SW extension (set B; Fig. 3B).The NW-SE (ERZ-oblique) striking fractures (set B) are not ubiquitous throughout the Koaʻe fault system.Instead they are restricted to zones of underlap between 1 st -order rift faults: here, in the underlap between two major ENE-WSW (ERZ-parallel) striking normal faults: sets A and C (Fig. 2 and 3).NW-SE striking fractures are therefore described as second-order structures, ancillary to first-order bounding rift faults (set A and C).All measured fractures in this NW-SE striking set (set B) show purely extensional opening (Figure 3B), resulting in a local extension direction that is ~40° clockwise of the regional (NNW-SSE) extension.We found no evidence for cross-cutting relationships between ENE-WSW and NW-SE striking fracture sets (sets A, C and B, respectively, Fig. 3Ci, ii).Measurements of fresh ground cracks following the last major rifting event that affected the Koaʻe (December 1965) identified fresh ENE-WSW striking extension fractures (here labelled set D: Fig. 3B, Ciii; Swanson et al., in press), at which time fault and fracture sets A, B, and C had already been mapped; we infer here that these existing sets either formed in a cyclic sequence, or formed contemporaneously.
The ENE-WSW striking sets comprise first-order normal faults that dip dominantly to the north and demonstrate maximum throws of ~5-12 m, and footwall fractures with maximum apertures of ~4-5 m (sets A and C; Fig. 4).Individual surface-breaching normal fault segments show trace lengths of up to ~200 m, and exhibit discontinuous fault-parallel monoclinal flexures in fault hanging walls.Fault sets A and C (Fig. 3 and 4) are separated by ~800 m (measured in a NNW-SSE axis, parallel to the fault dip), and underlap by 200 m.The NW-SE striking fracture set are limited to this zone of underlap, and record smaller strains, with no surface-breaching fault segments, and fractures with trace lengths <200 m and apertures <2.5 m (set B: e.g.Fig. 4B).We interpret this zone of underlap to be a relay zone, bound by fault sets A and C.
Figure 4 shows the summed surface extensional strains for each fracture set in the mapped area, as a function of the total plane-normal extension (i.e., extension measured in the dip azimuth), and the resolved contribution to NNW-SSE (regional) extension.Extension on set B fractures is in deficit compared to the surrounding regions with a total measured heave (aperture) peak of ~3.5 m compared to ~6 m for the northern bounding set A and 4.5 m for the southern bounding set C (Fig. 4B).A vertical displacement (throw) deficit is also recognized (Fig. 4C) from aerial LiDAR datasets with up to ~12 m of displacement measured across fault A and up to ~4 m across fault C and the monocline along fracture set B. The relative contributions of the components of rift zone-normal and rift zone-parallel extension also follow this distribution with a centrally located minimum of 3 m (rift zone-normal extension) on linking set B. This minimum is bound to the north by ~5 m of rift-normal extension on set A and ~4 m on set C to the south.Calculated rift zone-parallel extension is minor on southern bounding set C (up to 1.2 m) and peaks are approximately equal on the linking set B and northern bounding set A (up to 2.5 m).Although set B accommodates a component of rift zone-normal extension, this set contributes relatively little to the regional extensional strain as a whole (Fig. 4B,C).

The Krafla fissure swarm, Iceland
Iceland sits at the junction between the northern termination of the Reykjanes Ridge, and the southern termination of the Kolbeinsey Ridge, with present-day rifting on the island accommodated by the Neo-Volcanic Zone.We focus here on the well-exposed Gjastykki valley, 10 km North of Krafla, within the Krafla fissure swarm (Fig. 5).Regional NW-SE extension in the Krafla fissure swarm is accommodated dominantly on surface-breaching normal faults with maximum throws of 10-30 m; monoclinal surface flexures occur as discontinuous structures in some fault hanging walls, but are rare compared to the Koaʻe fault system.The focus of this study area is a relay zone surrounding the tips of en echelon rift zone-parallel normal faults that strike NNE-SSW (Fig. 5B, C).Faults and footwall fractures in the Krafla system can be separated into three structural sets based on their orientation, extension direction and extension mode ( (Fig. 5C These later structures connect NW-SE striking sets B' and A' and accommodate rift zone-normal extension.Hence, rift-parallel striking faults and fractures, which cut, and are cut by, obliquely oriented sets, are the first and final stage of observed deformation in the rift zone, respectively (Fig. 5E).No consistent cross-cutting relationships are observed between rift-oblique and rift-normal striking structures (Fig. 5E), suggesting that they formed contemporaneously.
Figure 6 shows the summed extensional strains for each fracture set in the mapped area, as a function of the planenormal extension, and the resolved contribution to WNW-ESE (regional) extension.Rift-oblique striking fault and fracture sets (set A', B': Fig. 5C, 6A) are well-developed and branch away from the tips of rift-parallel striking faults, with tensile openings of up to ~8 m (Fig. 6B) and estimated maximum throws of ~ 20 m.Rift-normal striking fractures (set D: Fig. 5C, 6A) represent the smallest strains in the relay zone with maximum fracture apertures of up to 2 m (Fig. 6B) and no vertical displacement (throw).Based on the total measured extension profile (grey dotted line in Fig. 6B), which represents a fully linked fault array that accommodates regional extensional strain, the underlap zone does not appear to be in deficit compared to the surrounding regions.There is an approximately centralized total aperture peak of ~14 m, compared to 8 m for southern bounding set B and 13.5 m for northern bounding sets A and C (Fig. 6B).When the directional components of this total measured extension are plot, however, we are able to define a pronounced heave deficit in the relay zone (blue and red dashed lines on Fig. 6B).Resolved rift zone-normal extension is greatest on northern bounding sets B and C (~12 m), followed by southern bounding set B (~10 m), with a low of ~9 m total aperture for linking fault and fracture sets (A', B', D, B-C: Figure 6B) in the overlap zone.Rift zone-parallel extension within the relay zone is significant for the area at ~ 8 m, compared to a maximum of 1 m for southern bounding set B and a maximum of 5.5 m for northern bounding sets A and C.

Summary and interpretations for the Koaʻe and Krafla fault systems
Regional extension in the Koaʻe and Krafla fault systems is accommodated by segmented rift zone-parallel faults that are discontinuous and underlapping at the present-day topographic surface.Relay zones, located between the lateral terminations of first-order bounding rift faults, transfer displacement across second-order, ancillary faults and fractures that strike obliqueand normal to the bounding fault segments.Displacement (extension)-length profiles show an extension deficit in the regional extensional strain, relative to a theoretical displacement profile for fully linked fault array (Figure. 4B and 6B).Fracture sets that strike at a low angle to the main rift zone (<45°) show extensional-shear opening (e.g.Krafla: Fig. 5), and must therefore accommodate a combined rift zone-normal extension direction (i.e.contributing to the regional extension), and a component of rift zone-parallel shortening.Fracture sets that strike at high angles (i.e.>45°) to the main rift-parallel faults are dominantly extensional, and therefore provide a smaller contribution to the regional extension, but nevertheless represent a significant component of rift zone-parallel extensional strain.Simultaneous orthogonal extension directions produce an area of inherently 3D strain within the relay zones.
Observed rift-oblique extensional-shear fault and fracture sets are dominantly synthetic to each other, rather than bimodal (i.e., conjugate).As such, we infer that they facilitate a vertical axis rotation between the main rift faults, similar to a bookshelf-like faulting mechanism (Mandl, 1987).A bookshelf rotation about a vertical axis would involve a rift zonenormal material thickening, but must also involve a rift zone-parallel material thinning (cf.bookshelf rotations about a horizontal axis, which accommodate horizontal extension and vertical thinning).Fractures with strikes orthogonal to the main rift faults in the Krafla study area, however, display extensional openings that may counteract this shear-induced shortening, leading to an overall volume increase within the rift zone.At the surface, this volume increase is accommodated by open cracks, but may be accommodated in the subsurface by normal faults and dike emplacement oblique to, and normal to the rift axis.

Tens-of-kilometer-scale segmented basin systems: the NE Atlantic passive margins
The pre-break-up configuration of the NE Atlantic involved the development of offset spreading segments (the Reykjanes and Aegir systems; Fig. 7B-D) that accommodated a regional NW-SE extension, culminating in break-up and formation of the contiguous NE Atlantic (Gernigon et al., 2012).The Faroe Islands and Kangerlussuaq were located either side of the SW termination of the Aegir spreading ridge segment, and NE termination of the Reykjanes ridge segment, respectively (Fig. 7A), and both ridges record the initiation of oceanic spreading in the Early Ypresian (~55-53 Ma: Gernigon et al., 2012) (Fig. 7C).Prior to NE Atlantic spreading, the Faroes and Kangerlussuaq were located about 80 km apart (Ellis and Stoker, 2014).The two regions can therefore be considered remnants of a very large (~5x10 4 km 2 ) breached relay system between the eventual ridge segments.
Both areas are dominated by Cenozoic North Atlantic Igneous Province lavas and intrusions, and both exhibit sequential deformation phases that are constrained as having formed prior to, and contemporaneous with, Atlantic opening (Walker et al., 2011;Roberts and Walker, 2016;Guarnieri, 2015.Here we present a combination of new geometric and kinematic data for the Kangerlussuaq region of East Greenland, and published data for Kangerlussuaq and the Faroe Islands, based on field-and remote-mapping of upper crustal (1-6 km depth maximum) faults and intrusions.We do not seek to directly compare the scale or regional dynamics of continental margins with volcanic island faulting or mid-ocean ridges, but rather the kinematic evolution of segmented fault systems.Our comparison is between the surface expression of fault sets (Koaʻe and Krafla), and near-surface brittle deformations on the Atlantic margins.We do not seek here to address full crustal thickness stretching models.

Kangerlussuaq, East Greenland Atlantic margin
Igneous activity in the Kangerlussuaq region of East Greenland (Fig. 8A), associated with continental break-up is thought to have occurred in three phases: 62-59 Ma, 57-54 Ma and 50-47 Ma (Tegner et al., 1998), with emplacement of the 7 km wide, layered gabbroic Skaergaard intrusion at ~56 Ma (Wotzlaw et al., 2012).Deformation is characterized by geometrically and temporally-linked suites of cross-cutting faults and dikes, hosted within the Archaean basement and Cretaceous-Cenozoic stratigraphy (Fig. 8B, C).Importantly, faults and dikes cut the Skaergaard intrusion, and compositionally similar macrodikes (e.g., the Miki Fjord macrodike: Fig. 8A, C) that are thought to be contemporaneous with emplacement of the Skaergaard intrusion (Holm et al., 2006;Holwell et al., 2012), giving a well-constrained maximum age for the deformation.
The ~500 m thick Miki Fjord macrodike strikes parallel to the margin and Reykjanes ridge segment (i.e., NE-SW; Fig. 8A, C), and accommodates margin-normal (NW-SE) extension.The macrodike is cut and offset by ESE-WNW obliqueextensional faults, which show lateral displacements of at least ~100 m (e.g.Fig. 8C), and form a conjugate set with ENE-WSW-striking faults, that accommodates margin-oblique (N-S) extension (Fig. 8Di).These faults also cut the Skaergaard intrusion (Fig. 8B) and strike parallel to conjugate dikes, with which they show a mutual cross-cutting relationship.
Skaergaard additionally hosts margin-normal (N-S to NW-SE) faults and dikes, accommodating margin-parallel (NE-SW) extension (Fig. 8B, Dii), which are cut by the margin-oblique structures (Fig. 8B).Locally, margin-parallel dikes are observed in the Skaergaard intrusion, which cut both of those sets (see also Irvine et al., 1998).

The Faroe Islands, European Atlantic margin
Deformation in the Faroe Islands (Fig. 9A) is characterized by sets of cross-cutting faults and intrusive igneous sheets that  Roberts and Walker (2016) showed that although dating of set 2 (ENE and ESE striking) faults suggest they are Mid-Eocene in age, there was potential for overlap with the ages of set 3 faults (Eocene and Miocene).Roberts and Walker (2016) were unable to constrain ages for set 1 faults, primarily due to high concentrations of common Pb, and very low U concentration within the tested calcite.Margin-parallel (NE-SW striking) faults accommodate extension parallel to the regional extension (i.e.NW-SE).The apparently oldest structures strike NW-SE and are parallel to postulated margin-normal strike-slip (transfer) fault zones reported along the margin (e.g., Ellis et al., 2009).In the Faroe Islands, this set accommodates minor (~1%) extension parallel to the margins, and not strike-slip displacement.The prevalent strain recorded on the Faroe Islands, in terms of distribution and scale of displacements, is associated with the phase of N-S extension, in which ENE-WSW and ESE-WNW conjugate dikes and strike-slip faults accommodate large lateral displacements (potentially up to hundreds of metres).

Summary and interpretations for Kangerlussuaq and the Faroe Islands
Faults and intrusions in Kangerlussuaq and the Faroe Islands record a consistent vertical axis rotation in extensional strains through time, during a period of regional-scale NW-SE extension (Walker et al., 2011).Structures that strike at a high-angle to the NE-SW trending rift segments (i.e.NW-SE striking structures) accommodate NE-SW (rift-parallel) extension (Fig. 8D, 9E), rather than the dominantly strike-slip displacements that have been inferred from seismic and potential field datasets (e.g., Rumph et al., 1993;Ellis et al., 2009).Structures that strike at angles oblique to the rift segments (i.e.ENEand ESE-striking faults and intrusions) accommodate a component of rift-sub-parallel shortening, and extension oblique to the regional extension vector (Fig. 8D, 9E).Very few structures within the mapped areas accommodate rift-normal extension (NW-SE): the Miki Fjord macrodike accommodates up to ~500 m horizontal extension, and approximately in a NW-SE direction (Fig. 8C).These structures appear to be cut by, and cut, other structural sets, suggesting they represent the first and final observed structures within the study areas.

Rift zone-parallel extension associated with normal fault and rift systems
The potential for displacement transfer and locally anomalous (with respect to far-field stresses), three-dimensional strains during fault linkage has been recognized in field studies (e.g.Ferrill et al., 1999;Ferrill and Morris, 2001;Koehn et al., 2008Koehn et al., , 2010;;Morris et al., 2014), scaled analogue models (e.g.Tentler and Acocella, 2010; see Fig. 1), and numerical simulations (e.g.Segall and Pollard, 1980;Crider and Pollard, 1998;Kattenhorn et al., 2000;Maerten et al., 2002).For instance, Kattenhorn et al. (2000) demonstrated that, depending on the remote stress state, it is possible for a range of ancillary fault or fracture orientations to develop, recording variable amounts of extension parallel to the first-order faults.It is likely that such ancillary deformations record a component of bending strain (e.g.deformation bands in the Delicate Arch relay ramp, Arches National Park, Utah: see Rotevatn et al., 2007).
Bending strains are commonly analyzed in the vertical plane where bedding is horizontal, but bending in the horizontal plane is challenging to identify due to a paucity of reference points.Normal faults in this study demonstrate vertical plane bending, about a horizontal axis, but associated with this extension is an observable component of bending in the horizontal plane, about a vertical axis.The development of strains associated with this bending do not develop instantaneously, rather each set may grow incrementally with slip accumulation on the bounding first-order faults as the relay zone distorts, nor are they restricted to one scale of observation.Such incremental, non-plane strains within evolving relay zones may be responsible for local instances of basin inversion, and reverse and strike-slip faulting in otherwise extensional regimes, and complex compartmentalization characteristics (e.g.Lin and Okubo, 2016;Sachau et al., 2016).Importantly, for basin faults with displacements at the km-scale, significant amounts of horizontal bending and rotation is possible, driving associated strains that may go undetected.
The effect of horizontal heave displacement gradients requires vertical axis rotations (Ferrill and Morris, 2001), and may operate independently of scale (e.g.Morris et al., 2014), in the same manner as other fault characteristics.For instance, worldwide catalogues of relay zone geometry have demonstrated a power-law scaling relationship that covers approximately 8 orders of magnitude (e.g.Peacock, 2003;Long and Imber, 2011).Evidence for heave gradients and locally non-coaxial strains are described at the at the tens of km separation scale in the East African Rift (e.g.Koehn et al., 2008Koehn et al., , 2010;;Sauchau et al., 2016) and the hundreds of km-scale in the Baikal rift zone (Hus et al., 2006) and the Hold With Hope relay zone in NE Greenland (Peacock et al., 2000).These examples show many characteristics similar to those observed in the Koaʻe and Krafla study sites, including (1) segmented bounding faults; (2) progressive development of obliquely oriented ancillary fault structures internal to the relay zone that accommodate non-coaxial strains; and (3) rift zone-parallel connecting faults.
Evidence for vertical axis rotations at the rift zone scale (i.e.tens to hundreds of km) have previously been attributed to bookshelf-type faulting models (e.g. Green et al., 2014; Fig. 10A).In such models, a vertical axis rotation can contribute to rift zone-normal extension.In horizontal axis rotations, via bookshelf faulting, a shear couple in the vertical plane represents a horizontal extension, and a vertical shortening (i.e.crustal thinning).In vertical axis rotation, shortening would require a horizontal material thinning along the rift zone: In plane strain, this would not require vertical crustal thinning.Vertical axis rotations by this mechanism, with a shear couple in the horizontal plane requires horizontal shortening (Fig. 10).For a rigid block model, the rotation has the effect of causing a material thickening orthogonal to the rift zone (e.g.Fig. 1E). Figure 1E shows that this rotation also results in material extension parallel to the rift axis, allowing addition of new material as a volume increase; during non-rigid body rotations (e.g., Fig. 10), second-order faults may act to facilitate the coupled components of rift zone-normal extension and rift zone-parallel shortening (e.g., Fig. 10B).For faults in the Krafla study area we infer that rift zone-parallel shortening is counteracted, contemporaneously, by the extensional component of obliquely oriented extensional shear faults, and rift-normal striking extension fractures at the free surface (e.g., Fig. 10Biii).At depth, this volume increase could occur as veins and/or dikes.

A vertical axis rotation model for rift basin segmentation in the NE Atlantic
Structures in the Faroe Islands and East Greenland share a common geometric, kinematic, and temporal evolution (Fig. 8 and  9), formed before, and during, continental break-up.Structures accommodate extensional strains at a range of angles relative to the regional extension vector (NW-SE) associated with a vertical axis rotation in the maximum horizontal stress (Figs 8  and 9).Here we apply a geometry and kinematic comparison between the observed structures on the Atlantic margins, and smaller scale structures that evolved in regions of extension deficit and rotation in the Koaʻe and Krafla fault systems to consider, by analogy, whether vertical axis rotation during extension presents a viable model for strain evolution at the tensof-kilometre scale.We focus on the Krafla system, as the extensional strain accommodated there has produced surface breaching structures that are closely comparable to the Atlantic margin.
To make the comparison of relative fault orientations and kinematics between the Krafla analogue and the NE Atlantic margins, we have rotated the Krafla rift datasets into the orientation and overlap configuration of the Atlantic European margin basin systems: i.e. a NE-SW trending, right-stepping rift.Thus, a right-stepping mirror image of the leftstepping Krafla rift is used (Fig. 12A) and compared with the Reykjanes-Aegir system, with the rift-parallel striking faults rotated into parallelism with those of the NE Atlantic margin (Fig. 12B, C).Data rotation is undertaken in two ways here for comparison: (1) by rotating the measured planar data for the Krafla system into an orientation that matches the strike of basin-and sub-basin faults along the Faroe-Shetland Basin; and (2) by rotating the measured planar data for the Krafla system so that the average strike of the rift-parallel structures match the measured strike of rift-parallel structures in the Faroe Islands and East Greenland.The two styles of rotation result in a difference in second order fault orientation of 30°, which is significant for data comparison.However, both types of rotation lead to the second-order data becoming parallel with either ENE or ESE-striking structures mapped in the Faroe Islands and Kangerlussuaq (Fig. 12A-D).All of the study areas show kinematically near-identical fault sets, with a 20-28° spread in extension directions across datasets.Removing one or the other of the reoriented Krafla sets reduces the spread to 12-20°.Importantly, each dataset comprises: rift-parallel striking faults that open normal to the rift axis (red in Fig. 12E); rift-oblique striking structures that accommodate extension oblique to the rift zone (blue in Fig. 12E); rift-normal striking structures that accommodate extension parallel to the rift zone (yellow in Fig. 12E).Rift zone-parallel extension in the Krafla study area is accommodated by extension mode fractures at the surface that strike orthogonal to the bounding rift faults.Equivalent subsurface structural sets exposed in the Faroe Islands and in East Greenland are normal faults and dikes.Notably, evidence for this style of inter-rift system architecture has also been noted in the East Africa Rift where, in younger portions of the rift, obliquely oriented dikes accommodate rift zone-parallel extension in the intervening relay zone between rift segments (tens of km scale: e.g.Muirhead et al., 2015).
Rift-parallel striking fault sets along both margins represent the first and final structural set.Timing relationships of fault sets on the Faroe Islands and in East Greenland imply a progressive vertical axis stress rotation at the regional scale, which is consistent with models that predict break-up involved a series of initially underlapping rift systems during rift propagation (Ellis and Stoker, 2014; Fig. 7B-D).Although the history of fault sets in the Krafla relay zone is less clear, the interpreted pattern fits well with the strains observed at a larger scale along the NE Atlantic margins (Fig. 12).We therefore propose that a vertical axis rotation model (associated with heave gradients) can account for margin-normal striking normal faults, dikes, and lineaments in segmented rift systems, and presents a viable alternative to a polyphase extension and reorganization, or strike-slip -transfer -models, that have been applied previously (e.g., Ellis et al., 2009).Our new model, however, cannot and should not be applied along the entire length of the European margin in a simple way.Along this margin segmentation styles vary considerably, from large-scale, localized transform faults, e.g. the Jan Mayan Fracture Zone, or the Senja Fracture Zone in the Norwegian-Greenland sea (e.g.Skogseid and Eldholm, 1987;Gernigon et al., 2009), to distributed, discontinuous continental style accommodation zones along the Møre-Faroes-Rockall portion of the margin.
Variations in the along-strike segmentation and scaling of fault populations have been well-documented in both continental rift (e.g.Hayward and Ebinger, 1996;Scholz and Contreras, 1998;Faulds and Varga, 1998) and oceanic fault populations (e.g.Carbotte and Macdonald, 1994;Macdonald, 1998).Variations have previously been attributed to changes in crustal thickness, strain rate (i.e.heat diffusion/magma supply), segment configuration, and the presence of pre-existing "weak" structures (e.g.Cowie, 1998;Corti et al., 2003;Tentler and Acocella, 2010;Gerya, 2012Gerya, , 2013)).Scaled-analogue models of normal fault populations have demonstrated that increases in effective elastic layer thickness results in a dominance of small and widely distributed faults (Ackermann et al., 1997(Ackermann et al., , 2001)).With increasing total extension, these authors noted that faults increased in number and length, producing a close and regularly spaced network.More recent scaled-analogue modeling of ridge-transform fault configurations also suggest that fault style and scaling is a function of strain rate and crustal thickness, with relatively thick lithosphere producing oblique zones of rifting and relatively thin lithosphere resulting in the development of transform faults that link the offset accreting segments (Gerya, 2012(Gerya, , 2013)).With estimated crustal thicknesses in the NE Atlantic varying from ~3-10 km in the Norwegian-Greenland Sea to ~10-35 km in the Rockall Basin and the Greenland-Iceland-Faroes Ridge (Smallwood and White, 2002;Gernigon et al., 2009), variations in axis-parallel segmentation patterns are to be expected (e.g.Hayward and Ebinger, 1996).Localized and large-scale fracture zones along the NE Atlantic margins only occur where crustal thicknesses fall below 10 km, elsewhere we find thick crust and distributed fault systems that are dominated by accommodation zone-style stress transfer, rather than regional-scale strike-slip faults.The protracted extensional history of the region and superposition of NE Atlantic rifting on Paleozoic rift systems, themselves influenced by Caledonian and/or older fabrics, mean that pre-existing structural weaknesses are likely to be widespread along the margin (e.g.Doré et al., 1999), and the style of segmentation appears to vary considerably.Although the controls on segmentation style in the NE Atlantic are beyond the scope of this study to investigate, it is nevertheless important to consider the potential role of factors such as pre-existing structures, strain rate or crustal thickness when applying any single model to the entire margin.

Conclusions
• Discontinuous normal faults in the Koaʻe and Krafla fault systems accommodate regional horizontal extensional strains via a combination of fault throw and heave on first-order rift faults.Obliquely oriented second-order deformation is driven by extension gradients and vertical axis block rotation within the intervening relay zones.
• Second-order faults and fractures serve to accommodate components of the regional extension and, variably, a component of shortening and extension in a direction parallel to-and oblique to the rift zone.
• Fault population heterogeneity within relay zones is attributed to locally non-coaxial stress states associated with mechanical interaction and resulting fault displacement gradients, rather than regional-scale polyphase tectonic episodes or changes in the remote stress field.
• Relay zones are considered to occur across most scales of segmented extensional systems; thus, we infer that vertical axis block rotations and the associated local deformation, which accommodate deficits in fault heave, occurs within the same range of scales.The distribution of second-order structures is controlled by the scale of segmentation.
• A displacement deficit-rotation model is applied to the NE Atlantic margins, in which second-order fault sets locally accommodate margin-parallel extension and shortening, during vertical axis rotation.We show that this is a viable alternative model to explain the upper crustal geometry, kinematics, and timing of structures, versus existing strike-slip (transfer) segmentation models for the case study presented, but urge caution in applying the model along the length of a given system.
, D): (1) NNE-SSW striking (parallel to the rift axis: set A, B, C) first-order fractures and normal faults, that accommodate rift zone-normal (WNW-ESE) extension; (2) NW-SE striking (rift-oblique: set A', B') normal faults and mixed-mode (extensional-shear) fractures that accommodate rift zone-oblique (ENE-WSW) extension; and (3) WNW-ESE striking (rift-normal: set D) fractures that accommodate rift zone-parallel (NNE-SSW) extension.The distribution of NW-SE (set A',B') and WNW-ESE (set D) striking fractures is limited to a zone of underlap ahead of two first-order rift-parallel normal faults (set A and B).Both the NW-SE and WNW-ESE sets are cut by a NNE-SSW striking normal fault showing up to 2 m of throw and set of fractures with up to 3 m of aperture (set B-C).
reflect reorientation of the local extension vector during and following emplacement of the Faroe Islands Basalt Group (57-54 Ma: Passey and Jolley, 2009; Fig.9B).Based on fault and fracture geometry and kinematics (including paleostress analysis), together with cross-cutting relationships,Walker et al. (2011) identified three main structural sets (Fig.9C, D, E).These are (oldest to youngest): (1) N-S and NW-SE striking normal faults and dikes (margin-normal strike; Fig.9C, Ei) that accommodate E-W to NE-SW extension; (2) ENE-WSW to ESE-WNW conjugate dikes and strike-slip faults (marginoblique strike; Figure9C, D, Eii) that accommodate N-S extension; and (3) NE-SW and NNE-SSW-striking strike-obliqueslip faults (margin-parallel strike; Fig.9D, Eiii) that accommodate NW-SE extension.Walker et al. (2011) interpreted the fault and intrusion sets as representing a progressive anti-clockwise rotation in the extension direction before, during and following continental break up.Set 1 (NW and N striking) faults are associated with thickness variations in the Faroe Islands Basalt Group(Passey and Jolley, 2009) suggesting that they are Paleocene in age.Using U-Pb geochronology for calcitebearing fault rocks,

Figure 2 .
Figure 2. Measurement of fracture geometry and kinematics.(A) Mode-I (extensional) opening across pre-existing cooling joint surfaces allows the traditional measurement of extension direction and magnitude (aperture) and fracture trace azimuth.The fracture in the image shows an aperture of 0.2 m, and an opening direction of 142°, orthogonal to the azimuth of the fracture (052°); (B) Mixed-mode (extensional-shear) opening across a cooling joint.The fracture in the image shows an 5

Figure 3 .
Figure 3. (A) Simplified structural elements map of Kīlauea Volcano's, showing the study area within the Koa`e fault system (KFS).ERZ: East Rift Zone.SWRZ: Southwest Rift Zone.HFS: Hilina Fault System.Inset shows relative position of A, on the south coast of Island of Hawai`i; (B) WorldView image of the study area showing the distribution and orientation of mapped fractures.White arrows indicate dip directions of monocline limbs and fault scarps; (C) Lower hemisphere stereographic projections showing measured fault/fractures as planes and measured extension directions for each of the three structural sets; (D) Proposed schematic evolution of fault sets: (i) Propagation of the main rift-fault set (set A and C); (ii) interaction between sets A and C produces deficits of heave displacement, requiring vertical axis block rotation in the relay zone, and local reorientation of extension direction (set B); (iii) development of new rift-parallel structures (set D: Swanson et al., in press).Bounding box is aligned with 1st-order rift faults (set A and C).

Figure 4 .
Figure 4. (A) Distribution of mapped fractures in the study area; (B) Profile of horizontal displacement (heave) vs length for mapped fractures.Dotted grey line indicates cumulative aperture for each set.Dashed blue lines indicate the calculated component of rift zone-normal extension on each fracture set.Dashed red lines indicate the calculated component of rift zone-parallel extension on each fracture set.Dotted orange line represents a hypothetical total displacement profile for a 5

Figure 5 .
Figure 5. (A) Map of Iceland highlighting the major tectonic elements: Reykjanes Ridge (RR); the Kolbeinsey Ridge (KR); South Iceland Seismic Zone (SISZ); West Volcanic Zone (WVZ); East Volcanic Zone (EVZ); Neo-Volcanic Zone (NVZ: the axial rift zone); Askja volcanic centre (As); Fremri-Namur volcanic centre (Fr); Krafla volcanic centre (Kr); Theistareykir volcanic centre (Th); the Tjörnes Fracture Zone (TFZ) comprising the Dalvik lineament (DF), the Husavik-Flatey Fault (HF) and the Grimsey lineament (GF); (B) Location of study area in the Gjastykki Valley within the Krafla fissure swarm.White arrows indicate dip direction for fault scarps in the area; (C) Mapped structures in the study area, colorcoded based on orientation and kinematics: (1) rift zone-parallel faults and fractures (red); (2) rift zone-oblique faults and fractures (blue); and (3) rift zone-normal fractures (yellow); (D) Lower hemisphere stereographic projections showing measured extension directions for each of the three structural sets; (E) Proposed schematic evolution of fault sets: (i) Propagation of the main rift-fault sets A and B; (ii) interaction between sets A and B leads to a horizontal displacement deficit and vertical axis block rotation in the relay zone, and induced local reorientation of extension direction accommodated on variably oriented ancillary faults and fractures; (iii) continued propagation of the main rift faults (A, B and C) leads to the development of new rift-parallel structures.Bounding box is aligned with 1st-order rift faults (set A and B).

Figure 6 .
Figure 6.(A) Distribution of mapped faults and fractures in the study area; (B) Profile of horizontal displacement (extension, or heave) vs length for mapped fractures.Dotted black line indicates the total measured extension for structures in each set.Dashed blue lines indicate the calculated component of extension on each fracture set that occurs in a direction orthogonal to the rift zone.Dashed red lines indicate the calculated component of extension on each fracture set that occurs in a direction parallel to the rift zone.Extension across the system as a whole is represented by a hypothetical displacement

Figure 8 .
Figure 8. (A) Geological map of the Skaergaard intrusion and surrounding area (redrawn from Holwell et al., 2012).Contours indicate 50 m elevation intervals from sea level; (B) Margin-normal striking faults and dikes cut the Skaergaard intrusion, which are in turn cut by margin-oblique striking faults and dikes; (C) Margin-oblique striking faults cut the margin-parallel Miki Fjord macrodike; (D) Lower hemisphere stereographic projections for relative-age-constrained examples of the three main fault sets observed.

Figure 9 .
Figure 9. (A) Onshore structural element map of the Faroe Islands; (B) Inferred extension directions indicating an islandwide anticlockwise rotation in extension direction through time; (C) Margin-oblique faults cut margin-normal faults; (D) Margin-parallel faults cut rift-oblique faults and dikes; (E) Lower hemisphere stereographic projections for relative-ageconstrained examples of the three main fault sets observed.

Figure 10 .
Figure10.Horizontal plane 2D conceptual models for inter-fault/inter-rift relay rotation.(A) Bookshelf rotation model showing (i-iii) progressive rotation leading to rift normal extension, and rift-parallel shortening; (B) Schematic models for structures observed in the study areas presented here: (i) conjugate extensional shear faults, (ii) extension fractures, and (iii) a combination of extension fractures and conjugate extensional shear faults.If faults develop throw, as in the Krafla example, the system becomes non-plane strain.Models are not to scale.