Extension parallel to the rift zone 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 firstorder faults, and the development of second-order faults and fractures, which transfer displacement within relay zones. Here we use natural examples of growth faults from two active volcanic rift zones (Koa‘e, island of Hawai‘i, and Krafla, northern Iceland) to illustrate the importance of horizontalplane extension (heave) gradients, and associated vertical axis rotations, in evolving continental rift systems. Secondorder 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 involves volume increase, which is accommodated at the surface by open fractures; in the subsurface this may be accommodated by veins or dikes oriented obliquely 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‘e and Krafla rift zones with data from exhumed contemporaneous fault and dike systems developed within a > 5 × 104 km2 relay system that developed during formation of the NE Atlantic margins. Based on the findings presented here we propose a new conceptual model for the evolution of segmented continental rift basins on the NE Atlantic margins.

Abstract. The mechanical interaction of propagating normal faults is known to influence the linkage geometry of firstorder faults, and the development of second-order faults and fractures, which transfer displacement within relay zones. Here we use natural examples of growth faults from two active volcanic rift zones (Koa'e, island of Hawai'i, and Krafla, northern Iceland) to illustrate the importance of horizontalplane extension (heave) gradients, and associated vertical axis rotations, in evolving continental rift systems. Secondorder 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 (3-D) strains associated with relay zone development and rotation. Such a configuration involves volume increase, which is accommodated at the surface by open fractures; in the subsurface this may be accommodated by veins or dikes oriented obliquely 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'e and Krafla rift zones with data from exhumed contemporaneous fault and dike systems developed within a > 5 × 10 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 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 on 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, in which 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 and Cartwright, 1994;Gupta and Scholz, 2000;Peacock, 2002;Long and Imber, 2010).
Mechanical interaction (i.e. in which 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 interfault (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 Published by Copernicus Publications on behalf of the European Geosciences Union.

1162
A. Bubeck et al.: Extension parallel to the rift zone during segmented fault growth 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 highresolution seismic imaging. In horizontally layered materials, displacement (throw) gradients on adjacent 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) gradients, which requires a component of vertical axis rotation to maintain the connection between the hanging wall and footwall (e.g. Ferrill and Morris, 2001). Few studies have addressed this rotational strain (see e.g. Koehn et al., 2008) and the resulting horizontal extension profile between faults or the potential for non-plane stresses and strains within the relay zone. Unlike horizontal axis rotation, it cannot be accommodated by layer-parallel or flexural slip between layers (unless layering is vertical) and thus requires the material to bend or stretch within the layer plane.
We present field examples of growth faults from two active volcanic rift zone segments -the Koa'e (island of Hawai'i) and Krafla (northern Iceland) fault systems -to demonstrate the inherently three-dimensional (3-D) strains associated with extensional strain gradients within evolving relay zones. The Koa'e fault system represents an early stage rift that connects the East and Southwest rift zones of Kīlauea Volcano to produce a continuous zone of extension that facilitates southward flank motion. The Krafla fissure swarm represents a well-established and highly extended portion of the Neovolcanic Zone of Iceland: a subaerially exposed segment of the NE Atlantic spreading ridge. Faults in both study areas are interpreted to be upward-propagating (e.g. Tentler, 2005;Martel and Langley, 2006) syn-volcanic growth faults (e.g. Macdonald et al., 1996;Dauteuil et al., 2001;Holland et al., 2006). The two case studies represent early and advanced stages in normal fault linkage during rifting.
In both case studies the expression of surface strains records minor (≤ 20 %) extension, in which respect they can be considered analogous to the surface expression of evolving extensional systems. The aim of this paper is to demonstrate the importance of displacement variation as a function of fault heave, rather than throw, and highlight the potential for the development of non-plane strains and volume change on the scale of the intervening relay zones. We consider the potential for such 3-D strains to form a viable alternative model to explain complex fault sets in laterally propagating rift systems: here we contrast structures in the Koa'e and Krafla regions to upper crustal (e.g. ∼ 1-6 km depth) structures of a scale that is at least 1 order of magnitude greater, developed along the NE Atlantic margins. For comparison, new and existing kinematic and geometric data are presented for Kangerlussuaq (east Greenland) and the Faroe Islands (European) portions of the NE Atlantic margins. Based on these examples, we suggest a new conceptual model for the evolution of segmented continental rift basins, with specific reference to the NE Atlantic margin.
2 Background: displacement transfer and relay zones in segmented normal fault systems Two-dimensional analyses of the stresses surrounding en échelon faults and dikes have demonstrated that mechanical interaction of opposing elastic stress fields produce areas of highly perturbed stress, which exert a control on the growth, slip distribution, and geometry of faults (e.g. Segall and Pollard, 1980;Sempere and Macdonald, 1986;Cowie and Scholz, 1992;Crider and Pollard, 1998). To maintain the extensional strain across the fault system as a whole (i.e. representing a fully linked, mature system), the volume ahead of the fault tips is required to accommodate the opposing along-strike displacement gradients on the first-order bounding fault structures. This may be accommodated in this interfault region, or relay zone, through components of elastic and inelastic strain (e.g. Peacock andSanderson, 1991, 1994;Childs et al., 1995;Long and Imber, 2010), and depending on the degree of overlap and separation of individual segments, may lead to different styles of deformation (e.g. Tentler and Acocella, 2010;Long and Imber, 2011;Childs et al., 2017) ( Fig. 1a, b). Using scaled-analogue models, Tentler and Acocella (2010) showed that a large underlap (relative to fracture length) between fracture segments produces elongated relay zones with new linking fractures opening ahead of the tips, striking subparallel to the bounding fractures ( Fig. 1d(i)). Decreasing the underlap of the bounding fractures (Fig. 1d(iiiv)) results in the growth of open fractures in the relay zones that strike at increasingly higher angles to the main structures. The propagation of these high-angle fractures generates a local component of extension, and volume increase, in a direction parallel or at low angles to the strike of the bounding fractures. At the same time, the component of extension orthogonal to the bounding structures decreases. At larger overlap geometries (Fig. 1d(v)), linking fractures strike at a lower angle, resulting in a reduction of the local component of bounding fracture-parallel extension and an increase in the fracture-normal component. The model configurations of Tentler and Acocella (2010) represent single stages of propagation and linkage, rather than the full progression. In nature, however, the process should graduate through some or all of these stages, as the bounding structures propagate toward each other and link, subjecting the relay zone to distortions as a function of the changing fault cut-off line lengths associated with slip accumulation (Fig. 1c, d).
It is typical to consider the distortions associated with normal fault displacement in terms of the vertical motion: the throw (e.g. Fig. 1d). This is perhaps due to the association  of normal faults with gently dipping or horizontal bedding, which provides useful and abundant offset markers for measurement. There are fewer studies that have made a detailed analysis of horizontal motions -the fault heave -due to the challenges in defining them 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, however, 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 Surface-breaching normal faults in the Koa'e and Krafla fault systems cut sub-horizontal bedded lavas, which exhibit vertical columnar joint sets on 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 favourably 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 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 ™ and World-View2) and topographic datasets (aerial lidar; Hawai'i only). The resulting combined dataset contains approximately 2500 measurements and covers up to 3 orders of length magnitude. Where applicable, fault throw was estimated, either in the field, or remotely using high-resolution topographic datasets. It should be noted that the 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 nearsurface rift zones (e.g. Grant and Kattenhorn, 2004;Casey et al., 2006). Fault and intrusion geometry and kinematic data were 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 were 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). The Koa'e 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 Hawai'i. The Koa'e 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 Koa'e fault system: (1) ENE-WSW-striking (ERZ parallel) first-order fractures and normal faults that accommodate the regional NNW-SSE extension (sets A, C, and D; Fig. 3b) and (2) NW-SE-striking (ERZ-oblique) fractures that accommodate a more localized NE-SW extension (set B; Fig. 3b). The NW-SE-striking (ERZ-oblique) fractures (set B) are not ubiquitous throughout the Koa'e fault system. Instead they are restricted to zones of underlap between first-order rift faults: here, in the underlap between two major ENE-WSW-striking (ERZ-parallel) normal faults: sets A and C (Figs. 2 and 3). NW-SE-striking fractures are therefore described as second-order structures, ancillary to first-order bounding rift faults (sets A and C). All measured fractures in this NW-SE-striking set (set B) show purely extensional opening (Fig. 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; Fig. 3c(i, ii)). Measurements of fresh ground cracks following the last major rifting event that affected the Koa'e (December 1965) identified fresh ENE-WSW-striking extension fractures (here labelled set D; Fig. 3b, c(iii); Swanson et al., 2017), 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.

Mixed-mode (extensional-shear) fracture
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; terpret 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-zonenormal and rift-zone-parallel extension also follow this distribution with a centrally located minimum of 3 m (rift-zonenormal 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 ex-tension 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 Neovolcanic Zone. We focus here on the well-exposed Gjástykki 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 Koa'e fault system. The focus of this  study area is a relay zone surrounding the tips of en échelon 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, d): (1) NNE-SSW-striking (parallel to the rift axis: sets A, B, C) first-order fractures and normal faults, which accommodate rift-zone-normal (WNW-ESE) extension; (2) NW-SEstriking (rift-oblique: sets A', B') normal faults and mixedmode (extensional shear) fractures that accommodate riftzone-oblique (ENE-WSW) extension; and (3)  . 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 stages of observed deformation in the rift zone, respectively (Fig. 5e). No consistent cross-cutting relationships are observed between riftoblique-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 (sets A', B'; Figs. 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; Figs. 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 plotted, however, we are able to define a pronounced heave deficit in the relay zone (blue and red dashed lines in 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; Fig. 6b) in the overlap zone. Rift-zone-parallel extension within the relay zone is significant for the area at ∼ 8 m, com-pared 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 Koa'e and
Krafla fault systems Regional extension in the Koa'e 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 obliquely and normal to the bounding fault segments. Profiles of displacement (extension) length show an extension deficit in the regional extensional strain, relative to a theoretical displacement profile for fully linked fault array (Figs. 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 riftzone-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 3-D 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 riftzone-normal material thickening but must also involve a riftzone-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.

Segmented basin systems on a scale of tens of kilometres: 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 (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 Faroe Islands and Kangerlussuaq were located about 80 km apart (Ellis and Stoker, 2014). The two regions can therefore be considered remnants of a very large (∼ 5×10 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 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 (Koa'e 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, 57-54, 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 oblique-extensional faults, which show lateral displacements of at least ∼ 100 m (e.g. Fig. 8c)  conjugate set with ENE-WSW-striking faults, which accommodates margin-oblique (N-S) extension ( Fig. 8d(i)). 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, d(ii)), 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 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 ( www.solid-earth.net/8/1161/2017/ dikes and strike-slip faults (margin-oblique strike; Fig. 9c, d, e(ii)) that accommodate N-S extension; and (3) NE-SW and NNE-SSW-striking strike-oblique-slip faults (marginparallel strike; Fig. 9d, e(iii)) that accommodate NW-SE extension. Walker et al. (2011) interpreted the fault and intrusion sets as representing a progressive anticlockwise 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 , suggesting that they are Paleocene in age. Using U-Pb geochronology for calcitebearing fault rocks, 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 (Figs. 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. ENE-and ESE-striking faults and intrusions) accommodate a component of rift-subparallel shortening and extension oblique to the regional extension vector (Figs. 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, approximately in a NW-SE direction (Fig. 8c). These structures appear to be cut by, and cut, other structural sets, suggesting that 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., , 2010Morris 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 analysed 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 does 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, 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 on the kilometre scale, significant amounts of horizontal bending and rotation are 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 on a separation scale of tens of kilometres in the East African Rift (e.g. Koehn et al., 2008Koehn et al., , 2010Sauchau et al., 2016) and on a scale of hundreds of kilometres 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 characteris-  tics similar to those observed in the Koa'e 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 on the rift zone scale (i.e. tens to hundreds of kilometres) has 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 nonrigid 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-zoneparallel 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. 10b(iii)). 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 (Figs. 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 geometric 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 Koa'e and Krafla fault systems to consider, by analogy, whether vertical axis rotation during extension presents a viable model for strain evolution on a scale of tens of kilometres. 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, rightstepping 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). Here data rotation is undertaken in two ways 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 matches 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), and rift-normal-striking structures that accommodate extension parallel to the rift zone (yellow in Fig. 12e). Rift-zoneparallel 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 African Rift, where, in younger portions of the rift, obliquely oriented dikes accommodate rift-zone-parallel extension in the intervening relay zone between rift segments (scale of tens of kilometres; 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-c). Although the history of fault sets in the Krafla relay zone is less clear, the interpreted pattern fits well with the strains observed on 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 strikeslip -transfer -models, that has 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 Mayen Fracture Zone, or the Senja Fracture Zone in the Norwegian-Greenland seas (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 and/or 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 result 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 modelling of ridgetransform fault configurations also suggests that fault style and scaling is a function of strain rate and crustal thickness, with a relatively thick lithosphere producing oblique zones of rifting and a relatively thin lithosphere resulting in the  (Gerya, 2012(Gerya, , 2013. With estimated crustal thicknesses in the NE Atlantic varying from ∼ 3-10 km in the Norwegian-Greenland seas 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 regionalscale 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 Koa'e 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 toand 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, occur 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. Data availability. Raw data for study sites on the Faroe Islands are published in Walker (2010) and Walker et al. (2011). Field locations may be found in Figs. 3,5,8,and 9. Raw data are not currently available due to ongoing data analysis but will be made available to the broader community in due course. For specific requests in the meantime, please contact A. Bubeck (ab753@le.ac.uk).
Author contributions. Data from Hawai'i and Iceland were collected by AB. Data from the Faroe Islands and Greenland were collected by RW. RH and JI provided valuable discussion. CM and DH assisted with data collection and contributed to the discussion. AB prepared the paper with contributions from all co-authors.
Competing interests. The authors declare that they have no conflict of interest.