Structure and topology of a brittle-ductile fault swarm at Crawford Knob, Franz Josef, New Zealand

ABSTRACT

We present surface and structural models of a swarm of dm-scale subparallel faults exposed in a ∼2000 m² glaciated outcrop near Franz Josef Glacier, in the Southern Alps of New Zealand. These structures are inferred to have slipped at ∼20 km depth in the hanging-wall Alpine Schist of the Alpine Fault under conditions that were variably brittle to ductile as the Pacific Plate was tilted and uplifted. Using field mapping, real-time kinematic GPS and digital images from a remotely piloted aircraft system, we have created a digital surface model of the outcrop and orthophotographs at a ground resolution of ∼1 cm to map compositional layering in the metasediments and the array of brittle-ductile faults displacing them. In order of decreasing relative age (and average thickness), displaced markers in the schist include primary psammite and pelite beds, quartz veins, and a deformational foliation. The surface models have been used to create 2-D transects and a 3-D model where faults are projected down-dip, to determine the connectivity, topology and intersection types of the fault swarm. Lithological variations, particularly the interface between pelitic and psammitic schist, were a primary control on the topology of the fault network and the spacing between faults.

KEYWORDS:

• Brittle-ductile rheology
• fault networks
• mapping
• RPAS
• drone
• RTK
• Southern Alps
• Alpine Schist

Introduction

The transition from pressure-dependent frictional behaviour in the upper, brittle part of the crust to strongly temperature- and rate-dependent behaviour at greater depths is marked by changes in rock structure, rheology, and fluid activity that are closely tied to the seismic cycle (e.g. Sibson 1983; Evans et al. 1990; Kohlstedt et al. 1995; Huc et al. 1998; Rolandone et al. 2004; Ellis and Stöckhert 2004; Handy et al. 2007; Nüchter and Stöckhert 2008; Hirth and Beeler 2015; Marchesini et al. 2019). Observations of hypocentre depths and variations in slip stability in fault gouge suggest that earthquakes often nucleate just above the brittle-ductile transition, near where brittle strength reaches its maximum (Sibson 1983; Scholz 1988; Van Dinther et al. 2013; Mitchell et al. 2016; Niemeijer et al. 2016). Outcrops containing crustal rocks only recently exhumed from the mid-crust that preserve the imprint of the brittle-ductile region are rare but can provide important clues about these processes. This study summarises three-dimensional (3-D) structural mapping and analysis of one such example in New Zealand, an outcrop at Crawford Knob in the Southern Alps that has been exhumed from mid-crustal depths during the past several million years.

Tectonic setting

Crawford Knob is in the hanging-wall of the Alpine Fault, the predominant surface expression of transpressional plate boundary slip between Pacific and Australian plates in the South Island of New Zealand (Figure 1). The obliquely convergent relative plate motion of ca. 37 mm/yr since at least 3 Ma (DeMets et al. 1994) has given rise to the Southern Alps, bounded to the west by the ∼30–50° SE -dipping dextral-reverse Alpine Fault, which locally attains late Quaternary strike-slip rates of 23–25 mm/yr, and dip-slip rates of 8–12 mm/yr (Norris and Cooper 2001; Sutherland et al. 2006; Little et al. 2007). Fault motion and accompanying erosion has exhumed Mesozoic quartzofeldspathic schist in the hanging-wall, with the metamorphic grade of the exhumed rocks decreasing from amphibolite facies adjacent to the mylonites of the Alpine Fault to prehnite-pumpellyite facies at the Main Divide 15–20 km eastward. Antithetic, reverse-oblique slip has occurred on northwest-dipping faults distributed eastward across the orogen (Cox and Findlay 1995; Little 2004; Cox et al. 2012).

Figure 1. A, Tectonic index map of New Zealand, showing motion of the Pacific Plate relative to Australia (black arrow, from DeMets et al. 1994), the Alpine Fault (in red), and the location of the enlargement that is part B of this figure. B, Location of the study area (Crawford Knob, indicated by a blue dot) in the non-mylonitic Alpine Schist near Franz Josef Glacier in the central Southern Alps. The faults are part of an exhumed corridor of steeply-dipping brittle-ductile faults (after Little et al. 2007).

Crawford Knob is a well-exposed glaciated platform of multiply-deformed Alpine Schist on the north-eastern flank of Franz Josef Glacier (Figure 1; Figure 2) at 1200–1600 m elevation. The greenschist-facies Alpine Schist in this region contains a swarm of closely spaced faults of late Neogene age dipping near-vertically (Little 2004; Little et al. 2005; 2007) and occupying a 1-2 km wide fault corridor. The faults strike subparallel to one another and to the Alpine Fault, but at acute angles to compositional layering and the steeply dipping foliation in their host rock, which they offset in a systematic manner. The faults cause variably brittle to ductile offsets of compositional markers and cross-cutting quartz veins in the schist, structures that are interpreted to have been active at different levels in the crust of the Pacific Plate during its exhumation along the Alpine Fault (Figure 1). This fault swarm has only been observed in the central part of the Southern Alps, the region experiencing the highest rates of tectonic uplift and exhumation (Wightman 2005; Wightman and Little 2007). The fault swarm extends for ca. 20 km along-strike in the Franz Josef–Fox area and represents an exhumed, fossil, brittle–ductile transition zone (BDTZ; Little et al. 2002; Wightman and Little 2007) that separates deeper schist from relatively undeformed greywacke and semischist sequences above it (Cox and Findlay 1995; 2012; Beysacc et al. 2016). Its formation has been attributed to westward translation of the Pacific Plate relative to the Australian Plate above a locally steepened Alpine Fault ramp, causing a sharp bending of Pacific Plate crust accompanied by back-shearing (Little et al. 2005; Figure 2). The swarm of faults is interpreted to have played a significant role in accommodating this upward bending as well as dextral-strike slip (Little 2004). The faults may also have enhanced the channelling of metamorphic fluids upward through the Alpine orogen (Wightman and Little 2007). The outcrop thus provides a window into mid-crustal deformation processes in a transpressional orogen (Wightman 2005; Hill 2005; Wightman et al. 2006; Wightman and Little 2007; Grigull et al. 2012).

Figure 2. A, Cartoon showing the brittle-ductile fault corridor interpreted as a zone of backshearing that transiently deforms mid-crustal rocks of the Pacific Plate as they are tilted across the base of the Alpine Fault ramp (after Little 2004). B, Schematic block diagram (looking NNE) showing kinematics of faults in the corridor. Oblique-slip on the subparallel array of steep faults accommodates a net up-to-the-NW angular shear of the Pacific Plate (∼22°, after Wightman and Little 2007) as well as a subequal magnitude of dextral angular shear. The faults cut and offset the metamorphic foliation in the Alpine Schist (dashed planes) and a set of generally east-dipping quartz veins (solid blue layers). C, Schematic view of one of the quartz veins, showing the typically brittle-to-ductile nature of their offset.

Scope and focus of the paper

Previous field and modelling studies of Crawford Knob have provided valuable context regarding deformation conditions and processes affecting the brittle-ductile faults at the centimetre to meter scale, and their physical interactions with quartz veins. However, these studies have not explored the arrangement and interactions of the faults to one another or to lithological layers at length scales of metres to hundreds of meters, or controls on fault spacing. This paper aims to provide this information. The superb exposure provided by the glaciated outcrop at Crawford Knob provides an opportunity to map the fault swarm in detail, and to analyse the degree to which the faults are planar, parallel, or evenly spaced, to describe fault geometries in 3-D, measure fault population statistics, characterise any apparent fault interactions, and to test the link (if any) between host rock properties and the spacing and geometry of faults in the swarm. We test the hypothesis that the frequency, thickness, and volumetric extent of different types of lithological layering within the schist influence mean fault spacing and explore the development of the fault network through interactions between discrete fault strands.

Summary of Crawford Knob geology and previous work

The fault swarm deforms Alpine Schist consisting mainly of biotite-grade quartzofeldspathic metagreywacke (psammite or meta-sandstone) with subordinate meta-argillite (pelite). Rocks intermediate in texture and colour between psammite and pelite (referred to here as semi pelite/psammite), laminated schist (alternating bands of pelite and psammite < 5 cm thick), strongly veined pelite (pelite that has been intruded by numerous quartz veins to make up 20–50% of the rock), and large (10’s of cm in diameter) quartz masses are also present. The dominant foliation in the schist strikes northeast at a mean azimuth of ∼045° and dips, on average, very steeply (80° or more) to the southeast. A recent paleogeothermometric transect of the Alpine Schist that includes the Franz-Josef Glacier indicates that biotite zone rocks near Crawford Knob experienced peak metamorphic temperatures of ∼400–524°C within ∼2 km to the SE of the ∼1 km-wide brittle-ductile fault swarm, and 525–536°C within 2 km to the NW of the swarm (Beyssac et al. 2016). As pointed out by these authors, these paleotemperature estimates relate to the steeply dipping, biotite-grade, peak-metamorphic fabric that is termed ‘S₃’ by Little et al. (2002). The S₃ Mesozoic foliation also deforms a pervasive set of 1–5 cm-thick quartz veins that mostly strike north and dip east at a moderate angle (Wightman and Little 2007), and crenulates an older, higher-strain foliation of shallower dip (known as ‘S₂’), that is typically subparallel to relict bedding and was later cut and offset in the Neogene by the brittle-ductile faults at temperatures of 400–530°C (Wightman 2005; Wightman and Little 2007; Grigull et al. 2012, see below).

The brittle-to-ductile faults strike ∼243° (dipping steeply NW), at an acute angle to the central Alpine Fault’s average strike of 055° (dipping SE). They crosscut the dominant foliation at an acute (clockwise) strike angle of ∼18°. The faults dip steeply to the northwest (or are subvertical) and are spaced ∼1-2 m apart on average. Individual faults are mostly smooth and planar, and their traces extend 10–100s of metres vertically and horizontally across the flat-crested but steep-flanked outcrop. The near-vertical faults strike at a high angle to the flanks of Franz Josef Glacier, occur on both sides of that deep valley (also others to the west and east), and there are few obvious rockfalls or landslides associated with them. There is no evidence that the faults, which are mineralised with greenschist-facies assemblages, formed as a result of the removal of glacial support, or were reactivated at that time (Figure 3). The fault surfaces commonly have fine quartzcalcite ± chlorite mineral fibres (infill veins), interpreted to have grown in the slip direction, that everywhere plunge to the SW at moderate angle (mean of ∼30°).

Figure 3. Outcrops of schist below Crawford Knob. A, subvertical aerial photograph from approximately 50 m above ground level showing exposed schist locally mantled by patches of gravel or alpine vegetation. Note tents from field camp on far right-hand side of the image for scale. B, Oblique view south from ground level of outcrop (view direction and position shown in A and people for scale) showing smooth, glacially sculptured outcrop surface, pelite and psammite layers in the schist (dark- and light-coloured bands, respectively), quartz veins (white masses); and brittle-ductile faults (red dashed traces). The irregular dark stain on the left-hand side of the photograph is water (also visible in panel A).

Where the faults obliquely intersect relict bedding, quartz veins, or foliation-parallel compositional bands, they typically offset these planar markers by cm to dm (maximum ∼1.5 metres) in a sense that is consistently dextral and/or northwest-up (generally reverse) (Figure 4). The abundant quartz veins are ductilely deformed but retain approximately planar form, and dip moderately to the east, on average. The veins have been shown to have been displaced parallel to the slip lineation on the faults by an average of ∼15 cm (Wightman 2005; Wightman and Little 2007). Zones or layers of psammitic (quartzofeldspathic) schist are mostly offset abruptly and brittlely by these faults. By contrast, thick (>1 cm) quartz veins (mostly dipping east as mentioned above) are commonly sheared gradationally and ductilely across these faults. This contrast in rheological behaviour between psammite and quartz veins indicates conditions near the brittle-viscous (brittle-ductile) transition zone, with the quartz veins behaving more ductilely than the psammite (Grigull et al. 2012). Thinner (e.g. mm-thick) quartz veins are commonly offset in a hybrid manner that is expressed by a mixture of brittle and ductile slip (Wightman and Little 2007; Grigull et al. 2012).

Figure 4. Outcrop exposure of faults. A, Two faults displacing a 2-3 cm-thick quartz-calcite vein. B, Wider view showing several faults that dextrally offset a thick relict bed of pelite (brown-coloured band) as well as numerous cm-thick quartz veins (white stripes). C, Example of mineral fibre lineations (red arrows) defined by quartz-calcite-chlorite vein material that infills some fault planes (fault plane dipping NNW, lineation plunging ∼30^o SW).

Brittle offsetting of the quartz veins is more common towards the structural top (southeast side) of the fault swarm. None of the faults here are coated with frictional wear products such as cataclasite or gouge, suggesting they slipped as a result of an aseismic creep process (Wightman and Little 2007). Instead, most of the faults are infilled with a thin (1-2 mm-thick) vein of quartz-calcite ± chlorite. As mentioned above, this vein is commonly fibrous, defining a syn-kinematic fault-surface lineation that plunges to the SW. The width of the fault-surface veins records a small but persistent component of fault dilation. Estimates of paleotemperature based on oxygen-isotope and Titanium-in-Quartz geothermometry for these veins suggest they were emplaced at temperatures of ∼400–530°C (Wightman 2005; Wightman and Little 2007; Grigull et al. 2012).

Based on arguments from fluid inclusion analyses, geothermometry, cooling ages and prevailing stress conditions, Wightman (2005) concluded that the fault swarm formed in a zone of transiently elevated differential stresses in the hanging wall of the Alpine Fault, structurally above the Fault’s transition from a subhorizontal basal decollement to a moderately southeast-dipping ramp. In this region, a transient increase in differential stresses accompanied by high fluid pressures is proposed to have triggered a short-lived pulse of brittle failure and fault dilation, especially in psammite rocks, at depths of 21 ± 5 km (estimated from ⁴⁰Ar-³⁹Ar cooling ages from 400°C, and an assumed convergence rate, Alpine Fault dip, and geothermal gradient in this region; Wightman 2005; Wightman et al. 2006; Grigull 2011; Beyssac et al. 2016). Wightman (2005) concluded that fluid pressure dropped significantly post-failure, suggesting a cycling of fluid pressure during the active ‘life’ of a fault.

Materials and methods

Field observations and creation of 3-D digital outcrop model

In 2014 and 2018 we carried out detailed fault trace mapping and structural measurements at Crawford Knob, expanding on previous studies to analyse fault interactions in the swarm at length scales of tens to hundreds of metres. Using real-time kinematic (RTK) GPS, we mapped individual fault traces across the outcrop as a series of precisely digitised fault points (nodes) to create a detailed digital map of fault traces. Along (and near) each mapped fault trace, we took supporting structural measurements on the outcrop of the attitude of faults, foliations, fault surface fibre lineations and quartz veins using a traditional analogue field compass or digital compass system. Field mapping of geological features located with RTK GPS focused on the most accessible (least steep) parts of Crawford Knob’s glaciated exposures (Figure 3). To identify faults, we visually inspected the outcrop to locate the faults and then surveyed points along each fault trace using the RTK to map them across the outcrop face. We only mapped fault traces that offset markers (mostly quartz veins) by ≥1 cm. For these traces, a fault termination location was mapped at the point where offset reduces to <1 cm. We also mapped fault splay intersection points. Virtually every fault that we observed on the outcrop with a trace length > 1-2 m has an observable shear offset of a nearby quartz vein or other marker, even if it is small.

As a part of the fault trace mapping, we also mapped points around the larger (dm-wide or greater) quartz vein masses. Several transects of the outcrop (roughly orthogonal to layering) were made with a measuring tape to map host rock lithologic bands (pelite-rich or psammite-rich layers, and quartz veins). The transects were used to ground-truth aerial surveys that attempted to map these lithologic bodies remotely (see below).

Digital photographs were collected with a remotely piloted aerial system (RPAS, commonly known as a drone) and used to create high-resolution 3-D maps of outcrop surfaces. We used a DJI Mavic Pro quadcopter aircraft to capture 5,552 photographs and processed those images with Structure from Motion (SfM) software to create orthophotographs and digital surface models (DSM). Six surface models were created over the study area (Figure 5): (1) a lower-resolution survey of the entire Crawford Knob study area with a ground sample distance (GSD; the size on the ground represented by one pixel in the digital image or cell in the surface model) of 60 mm; (2) a higher-resolution survey covering much of the Crawford Knob study area (blue dashed region; GSD = 17 mm); (3) the ‘Glacial Platform’ outcrop (red dashed region; GSD = 4.3 mm) which is an outcrop of particular focus; (4) an area referred to as ‘Kea Rock’ (green dashed region; GSD = 12 mm); (5) an area referred to as ‘Critter Ridge’ (yellow dashed region; GSD = 18 mm); and, (6) an ultra-high-resolution survey (GSD = 0.7 mm) over a small 5 m wide outcrop located ∼20 m northeast of the Glacial Platform site. The SfM models were georeferenced to several ground control points located using the RTK GPS system that was also used in the fault trace mapping above (see Hill et al. 2020). In Geographical Information System (GIS) digital mapping software, our derived models can be viewed as orthophotographs (geographically located and rectified vertical aerial photographs), as DSMs, or both. The models provide a topographic base on which to place the structural map (Figure 6).

Figure 5. Map of the remotely piloted aerial survey (RPAS) area at Crawford Knob. A, Project location (brown box) near Franz Josef Glacier, west of the main divide of the Southern Alps and southeast of the Alpine Fault. B, the Crawford Knob study area showing the RPAS survey areas; the lower-resolution site survey of the study area (blue dashed rectangle), the Glacial Platform outcrop site (red dashed outline), and other detailed model areas (Kea Rock and Critter Ridge, green and yellow dashed outlines, respectively), from this study. Map data are from LINZ, Heron (2018) and Langridge et al. (2016). Except for ‘Franz Josef Glacier’, ‘Almer Glacier’ and ‘Crawford Knob,’ the above-mentioned location names are informal ones used only for this study.

Figure 6. Orthophotograph, digital surface model (DSM) and digital 3-D outcrop model of the Glacial Platform site. A, orthophotograph with GSD of 4.3 mm over the outcrop site with inset panels B and C, enlarged views showing lithological layering in the schist, faults and quartz veins. D, digital surface model showing the elevation of the outcrop and hillshade model that highlights areas of smooth glacially eroded outcrop and gravel deposits at the site. E, Perspective view of 3-D model that uses the DSM with a draped orthophotograph to create a digital outcrop that can be used to map fault planes, schist layering, quartz veins and outcrop extent in GIS.

Data from the SfM modelling (orthophotographs and DSMs), RTK GPS survey results, field observations and notes, and structural measurements were compiled into a GIS database. These data could be viewed and compared spatially in the GIS and 3-D modelling software and were used to map faults, veins, and schist layering.

Constructing a 2-D orthorectified map of the outcrop and fault network

The GIS database and 3-D model were used to construct a 2-D orthorectified map of the outcrop and fault network. Combination of measurements of fault points from RTK GPS and RPAS was aided by the good spatial correlation (i.e. points measured using both techniques within millimetres of each other) due to the use of common ground control points and other calibrations points.

Faults were mapped in the GIS as polylines using the RTK fault nodes with additional nodes added during the digitisation process from fault traces observed on the on the RPAS derived orthophotographs, thus improving the overall resolution of mapped fault traces in the GIS. Fault traces could also be extended beyond the safely accessible and RTK-surveyed parts of the outcrop by digitising them on the orthophotographs. In these instances, faults were identified and mapped where they visibly offset a quartz vein or other lithological boundary on the images (Hill et al. 2020).

By combining remote interpretation of the orthophotographs with direct surveying on the outcrop using RTK data, we made a map of not only the fault traces but also schist lithologies on the outcrop, and local areas of surficial gravel that mantle the outcrop. Within the exposed areas, polylines were digitised along the contacts between several different recognised rock types. The regions enclosed by these contacts were assigned to one of six lithological classes: psammite, pelite, semi-pelite/psammite (visually identified as a uniform indeterminate schist composition with intermediate texture and colour between psammite and pelite), laminated schist (alternating bands of pelite and psammite < 5 cm thick, too small to be individually mapped at the scale of this interpretation), strongly veined pelite (pelite that has been intruded by numerous quartz veins to make up 20-50% of the rock), and large quartz masses (Figure 7). Distinguishing lithology differences from orthophotography requires partly subjective decisions based on colour and texture, but our numerous outcrop observations at ground level have trained and guided our interpretation. We also made allowance for differences in the degree of shading across the images and the different visual appearances of wet and dry rock.

Figure 7. Orthophotograph images showing representative examples of each of the six lithological classes that we recognised in our mapping of the schist.

The light-colored quartz veins (including the larger quartz masses) were mapped into the GIS by analysis of the red, green, and blue (RGB) colour channels in the orthophotographs. An average of the RGB values (a number from 0–255 representing the colour intensity in the image) for each pixel was calculated (see Hill et al. 2020), with the white coloured areas commonly associated with quartz veins highlighted in the average colour intensity map (Figure 8C). Combining our interpretation of the colour intensity data with a much smaller number of RTK-surveyed margins of quartz veins allowed us to map the distribution of quartz veins across the entire outcrop.

Figure 8. Geological map of the Glacial Platform outcrop site. Fault traces are colour-coded according to the mapping process used to locate them (mapped in situ with RTK GPS, shown in black; or virtually in GIS, shown in red). Rock type in the schist is assigned to six lithological classes (see legend and the main text). Black arrows depict the local dip direction of the generally sub-vertical faults. Inset Maps: A, enlarged part of the map showing a fault offsetting lithological layers in the schist. B, enlarged view of high-resolution orthophotographic image derived from RPAS data. The image shows faults offsetting lithological layers (dark and light bands) in the schist. C, RGB analysis used to identify white-coloured pixels in quartz veins (here rendered in pink), psammitic schist (yellow-green), and pelite (blue). D, enlarged part of the map showing representative detail at the metre scale, including coding of fault termination types (see adjoining legend), and local dip-directions and dip angles of faults (arrow symbols). Locations of Transect A and Transect B are shown with heavy black lines, with the several inferred fault-spacing domains approximately located by text labels. The topography of the outcrop outside of the geologically mapped area is depicted in greyscale as a hillshade DSM.

In our merging of the RTK-surveyed and orthophotographically-interpreted fault traces with GIS software, we noticed several cases where faults that had been confidently observed and mapped by RTK on the outcrop were ‘invisible’ on the imagery. These situations arose where there were few optically resolvable quartz veins to be offset by the fault (thus revealing its presence), and/or little or no lithological contrast to be expressed in the image as a colour change across the fault or as an optically resolvable dark line coincident with its trace. These observations highlight the importance of supporting digital interpretations with field observations.

Results

A 2-D orthorectified map of the outcrop and fault network

Using the suite of methods described above, we compiled a plan view geological map of the Glacial Platform field site (Figure 8; Supplementary Dataset 1 in electronic repository). The map depicts the location of faults, lithological boundaries, and large quartz vein masses. Faults directly observed in the field and mapped using RTK are distinguished from those interpreted only on the digital orthophotography.

Several features of the faults are obvious on the 2-D map (Figure 8), such as the approximate uniformity in their mean strike and spacing. Most fault segments strike ∼243°, transecting the schist foliation at an angle of ∼018° (Figures 9E and 8B). In detail, a few faults locally strike within 5° of the strike of the dominant Alpine Schist foliation. Most of these instances are where otherwise obliquely intersecting faults are deflected along the contact between psammite and pelite for short distances.

Fault orientations

We combined our field structural measurements with structural data that had been measured during previous field mapping of the Crawford Knob outcrop (Wightman 2005; Wightman and Little 2007; Grigull 2011; Grigull et al. 2012). These data plotted as poles and density of pole points in stereograms (Figure 9) illustrate the mean steeply southeast-dipping orientation of the dominant Alpine Schist foliation (Figure 9A) and mean steeply east-dipping quartz veins (Figure 9B). The veins predate that foliation and both features are cut and offset by the brittle-ductile faults. The faults strike northeast (average strike 243°), are steeply dipping, and are remarkably consistent in attitude across the study area, with a standard deviation from all combined strike measurements across the fault network of only ±4.5° (Figure 9C), while the average standard deviation in strike along each individual fault (computed using strike measurements of mapped fault trace segments) is only ±1°. On average, the mineral fibres on the fault planes pitch moderately to the southwest (Figure 9D).

Figure 9. Lower hemisphere equal-area stereographic projections of structural orientations measured in the field at Crawford Knob. Parts A, B, and C plot poles to planar data (black dots), contours of the poles, and a great circle to depict the mean attitude of the planes (identified with label as a strike/dip/dip direction). A, predominant Alpine Schist foliation. B, deformed quartz-rich veins embedded in the Alpine Schist. C, brittle-ductile faults cross-cutting the Alpine Schist foliation and the veins. D, plots and contours calcite-quartz fibre lineations coating fault planes (black dots) and specifies the mean direction of these (red dot with labelled trend/plunge). E, plots the mean attitude of each of the above structures as a great circle or lineation together with the contoured poles of the measured faults (same as in C). Data plots and calculations were made using Stereonet 10 (Allmendinger 2020); contour intervals of 5 calculated using 1% of area; mean plane and line values from Bingham analysis; conical best fit half apical angle (CBFHA).

Because the outcrop surface has a knob-like shape with steep flanks, the curved trajectory of the fault traces across this sculptured massif can be used to compute best-fit fault dips directly from an analysis of three or more (or most commonly all) of the surveyed fault nodes (see Hill et al. 2020). In this calculation we are assuming that the faults are planar and have a fixed attitude everywhere beneath the outcrop surface. We consider these assumptions to be valid, since as noted previously, the fault strikes are remarkably constant where exposed at the outcrop surface (with an average standard deviation in strike per fault of only 1°). The geometrically computed fault plane attitudes are averages over a greater (e.g. 2–30 m) length scale than the point field measurements of fault attitude made with a compass (shown in Figure 9C). The computed planes, when compiled, yield the same mean fault attitude as the field measured ones, although the former data have a higher standard deviation. We used best-fit fault dips determined from the fault trace analysis in cases where direct field measurements for a particular fault were not available.

Fault spacing and offsets

While fault spacing is typically between 1-2 m, locally the spacing between adjacent faults (away from intersection points) may be as small as several centimetres or as large as several metres. For example, a > 8m- wide zone (measured perpendicular to mean fault strike; indicated by orange arrow and labelled ‘Reduced fault density’ near inset panel C on Figure 8) does not contain any faults, and this sparsity of faults continues towards the southern end of the outcrop. Faults can in some places be interpreted to continue beneath zones of gravel cover to link to other faults along-strike. While there is not enough exposure continuity across the map area for us to be certain, perusal of Figure 8 suggests that local areas of narrower or wider than average fault spacing do not persist along-strike over distances > ∼30 m. A visual inspection of the map suggests that changes in fault spacing may be related to thickness or spacing of pelite layers occurring in the otherwise mostly psammitic schist (brown vs. pale yellow shading in Figure 8). We explore this hypothesis in more detail later.

At the resolution of the orthophotographic images (5 mm pixel size), one can recognise the offset of individual quartz veins and pelite bands across faults, provided the markers are thicker than 10 mm and their offsets are >5 mm. At the Glacial Platform site, 1032 such offsets (all of them dextral and/or up-to-the NW) were measured, 598 determined from displaced compositional layering boundaries (pelite – psammite contacts) and 434 from displaced quartz veins (e.g. Figure 10). Because we measured fault offsets in a GIS program, the 3-D separations of these markers on the (typically inclined) outcrop surface were projected onto the horizontal plane of the map datum. This reduced the apparent magnitude of each fault separation by systematically converting the actual offset distances along the inclined slope into a shorter horizontal ones in the map plane (Appendix 1). After this step, the averaged apparent dextral offset for the 265 individual faults (where multiple offset measurements were included for some faults) is 0.19 m ± 0.03 (2σ), slightly higher than the average computed by Wightman (2005) and Wightman and Little (2007), with most offsets being less than 30 cm (Figure 11). Since the fault traces on the outcrop surface are typically not parallel to the SW-inclined, 3-D slip direction, any offsets observed on the horizontally projected outcrop face are separations, not true fault slips. However, because of the regular geometrical arrangement of the faults and markers to one another at Crawford Knob, including their remarkably consistent attitudes (Figure 9), most of the separations (offsets) measured on the outcrop surface can be inferred to closely approximate (within ±∼10%) the actual 3-D fault slip magnitudes, with the ratio of observed separation to true slip varying slightly with the marker attitude and slope angle (see Appendix 1). Despite this approximate statistical concordance between 3-D offset and 3-D slip, the systematic foreshortening of each 3-D separation onto the horizontal map datum probably biases our GIS-measured separations towards slightly underestimating true slip magnitudes. Thus, we argue that the mean horizontal offset calculated in the GIS map (Figure 11) is a reasonable approximation (or slight underestimate of) the average (dextral-oblique) slip of the faults in the swarm. Finally, since the distribution in Figure 11 is skewed (not normal) with some large offset outliers, the median offset (10.4 cm) may be a more appropriate indicator for typical fault offset, with 50% of fault-averaged offsets between 6.6 and 21 cm.

Figure 10. Outcrop photograph from RPAS illustrating offset quartz veins and lithological boundaries across faults. Example offset features paired by colour for each fault and of faults terminating at lithological boundaries and fault stepovers. Offsets are measured in the GIS (in the horizontal plane).

Figure 11. Histogram of average apparent offset in the horizontal plane of mapped faults at the Glacial Platform site. These offsets of quartz veins and foliation planes/lithological layers were measured using orthophotographs in the GIS. The counts represent the average horizontal offset obtained from multiple offset data for each fault (n = 265 individual faults, based on a total of 1032 offset marker observations). The median offset is 0.104 m and 50% of offsets lie between 0.066 and 0.21 m.

Extrapolating faults to depth along two transects: fault spacing analysis

Cross-sections across the northwestern part of the main outcrop were constructed along transects A and B in Figure 8. On these, the faults and the lithological layers cut by them were extrapolated as planar features to depth (Figure 12). As noted previously, projection to depth below the outcrop surface relies on the assumption that fault strikes and dips remain constant. The depicted fault dips are based on our direct surface measurements of fault attitude, and/or on our analytical solutions for the plane of best-fit coinciding with the RTK-surveyed array of nodes on the fault trace (provided it spans a > 1 m range of elevations on the 3-D outcrop surface). In accord with our structural data, pelitic schist layering was assumed to dip 79° to the SE, subparallel to the mean foliation attitude about which that compositional layering is tightly folded (Figure 9A). The outcrop surface contains numerous fault terminations (isolated nodes (‘I’-nodes) and ‘Y’ junctions). While we were unable to predict ‘I’-nodes at depth, faults at the surface were projected into the subsurface until they intersected an adjacent fault. At this intersection, one of the two splays was interpreted to terminate in a ‘Y’-junction. Appendix 2 contains a more detailed description of our procedure.

Figure 12. Simplified geological cross-sections for Transect A (above) and Transect B (below) viewed from the northeast (for location see Figure 8). No vertical exaggeration. The boundaries of the labelled fault domains are defined by spatial changes in mean fault spacing as revealed on a cumulative fault frequency plot (see Appendix 2). Domains 1 and 4; 2 and 5; and 3 and 6 (respectively) are approximate along-strike equivalents to each other between the two transects (see Figure 8).

The cross-sections illustrate the apparently spaced arrangement of the faults, and their consistently steep dips, and show that most fault segments probably intersect with a contiguous fault at depth to create a network in 3-D. Nevertheless, many projected faults do not intersect over vertical length-scales of >10 m. While projections to these depths are highly uncertain, it is interesting that the steep dipping faults are projected to continue to these depths, while more shallowly dipping faults – often associated with stepover or bifurcations mapped at the surface- are predicted to intersect at depth.

Using trigonometry, the apparent fault spacings as observed along the two transects (Figure 12) were corrected (reduced) to true spacing values as would have been measured exactly orthogonal to the mean fault attitude (Terzaghi-correction). After that, we statistically analysed the corrected spacing data using the several methods outlined in Sanderson and Peacock (2019) and Marrett et al. (2018), as is detailed in Appendix 2. Our goal was to evaluate whether the faults are regularly spaced about a predictable spacing value (that is, are they quasi-periodic and anti-clustered). Transect A has a mean fault spacing (and standard deviation) of 1.44 ± 2.17 m and Transect B of 1.15 ± 0.97 m. As noted previously, fault spacing is not constant, and it varies across the outcrop, as is also evident from Figure 8. As part of our analysis (Appendix 2), cumulative frequency plots were used to divide the projected sections into different domains, within each of which there was a more nearly constant fault spacing than for the transect as a whole (labelled on Figure 8). The northwest end of both transects have a slightly higher-than-average fault spacing and the spacing is more variable, whereas the middle of each transect has more uniform fault spacing; at the southeast ends, both transects are characterised by large and variable spacings. More rigorous statistical tests can be used to verify that despite the observed variability in individual spacings, as a whole the faults in Transects A and B can be characterised at >95% confidence as being quasi-periodic rather than randomly spaced (Appendix 2).

The narrowest fault spacing domains in Figure 8 occur in the centre of each transect (Domains 2 and 5 which are along-strike of each other). These domains correlate with an abundance of pelite-psammite interfaces. In contrast, the domains that have much wider fault spacing (at the southeast end of the transects) coincide with a region that is dominated by thick psammite layers with fewer pelite-psammite interfaces (Appendix 2).

Extrapolating faults to depth: a 3-D fault network model with analysis of fault intersections

We used a similar procedure in 3-D as that applied in 2-D for Figure 12 to construct a 3-D fault network model for the main outcrop area (i.e. the area that is well-constrained by RTK GPS and RPAS measurements). The 3-D fault network model can be downloaded from Supplementary Dataset 2 in the electronic repository.

Each fault segment mapped at the outcrop surface was projected to depth using a best-fit estimate of fault dip and strike that was derived from a 3-D geometrical analysis of each digitised array of fault trace points. The projections to depth using these average dip and strike values per fault are a simplification of geological reality since each fault may locally vary in strike and dip, particularly where the fault is branching or steps over onto another structure (though as noted earlier, the variation in strike along each fault has an average standard deviation of only ±1°). Obviously, we cannot extend the fault structures to depths >10s of metres because their attitudes become increasingly uncertain, and they may intersect or experience discontinuities such as splays and stepovers (e.g. Figure 12). Short fault segments along-strike (lengths < a few metres) may be splays that coalesce at depth, and we consider them not as likely to persist to as great a depth as are longer, more continuous ones having along-strike lengths up to 30 m. Examination of fault traces over the 3-D outcrop surface- particularly comparing faults exposed within the semi-horizontal outcrop surface (south) to those exposed at its steep northern-most slope (Figure 3B) suggest that fault spacing and lengths have similar attributes horizontally and vertically. To reflect this, we limited the depth of our subsurface fault projections to obtain a 1:1 ratio between the mapped length of a fault and its projected maximum depth. After first projecting the faults downward to this extent, we then calculated the position and orientation of any junctions between converging fault planes using Coreform-Cubit 2020 software, which outputs the vertices of the calculated fault-fault intersection lines. We assumed that each fault intersection at depth results in the discontinuation of the shorter or less steeply-dipping of the two faults. In the final 3-D fault model these truncated faults end at their intersection line with the other fault.

The 3-D model (Supplementary Dataset 2) was used to extract the computed orientation (trend and plunge) of each 3-D fault plane intersection line (Appendix 3). These orientations show a dominance of sub-horizontal to gently plunging intersections trending northeast or southwest (Appendix 3). The pattern reflects the following basic geometrical properties of the fault network: (1) the faults have a consistent ENE strike, varying by no more than 20°; and (2) the faults are persistently sub-vertical (dips of 75–90°), but have dip directions that are either to the NW or SE. A key inference based on this analysis is that the fracture permeability caused by the intersecting faults is predicted to be largest in the E-W (sub-horizontal) direction (Figure A3.1).

Fault lengths and termination types

Analysis of the 2-D map (Figure 8) and field observations reveal that some faults continue across the whole outcrop (up to 30 m along-strike), some die out as isolated endpoints, while others bifurcate into two splays or undergo a step-over to link into nearby fault (e.g. Figure 8D; Figure 10). Note that, since we can only observe the outcrop surface, it is possible that the fault strands involved in the terminations we label ‘stepovers’ actually coalesce into or out of the outcrop plane in the third dimension; that is, they are actually bifurcations that just happen to be sliced at an oblique angle by the outcrop plane (as shown in the cross-sections on Figure 12).

The map-view bifurcations (i.e. splaying) and the stepovers locally create zones, typically <20 cm wide, in which there is a smaller-than-average apparent fault spacing (e.g. Figure 8; also Appendix 2). These regions commonly include faults that have shorter-than-average apparent length (e.g. 1-2 m long, Figure 13A). For the shortest observed apparent fault lengths, the cumulative frequency curve shows a flattened shape, suggestive of a log-normal distribution (Figure 13B), although at least some of this apparent flattening of the curve must reflect that the fact that we did not attempt to measure any faults expressed by an offset of <1 cm – that is, the smallest faults were artificially excluded from the data. At the large end of the fault length scale, the maximum observed length is ca. 30 m. This is an arbitrary boundary that reflects intersection of our longest faults with the outcrop edge, beyond which they are unmapped.

Figure 13. A, Histogram of apparent fault trace lengths where the number of faults between 0-1 m, 1-2 m, etc, are binned and plotted. Orange colour represents minimum (uncensored) fault length for faults that intersected the edge of the outcrop (i.e. the fault trace disappeared under gravel, such that the total fault length was greater than measured), whereas blue colour indicates lengths only for censored faults that were fully contained within the outcrop (i.e. we could measure the entire length with fault termination points at either end). The minimum and maximum censored fault lengths are (0.36, 20 m); whereas if we include uncensored faults these values are (0.5, 32 m). B, Cumulative frequency plot with the y-axis plotting the number of censored (thick blue line) and uncensored (thin dashed line) faults having a length greater than or equal to the length that is specified along the x-axis. These curves suggest a log-normal fault length distribution, although the flattened curve shape at small lengths (< 0.5 m) probably at least in part reflects undersampling as discussed in the text. The orange line shows the censored fault log-log fit between 5 and 15 m where faults are not under-sampled, with an equation (for cumulative number of faults y with length ≥ x) of y = 1478 x^−2.134 (R-squared = 0.98). This corresponds to a power-law fit with an exponent of ∼ 3, as discussed in the text.

We can estimate overall connectivity of faults depicted in the 2-D fault map from the relative abundance of the several termination types. Out of a total of 336 fault terminations that we mapped, 64% of them terminate in isolated (simple) points, 21% at bifurcations and 15% at stepovers (Appendix 4; Table A4.1; e.g. Figure 8D). Bifurcations (Y-junctions) are defined as hard linkages between splays that intersect at a mappable point on a fault trace, with the splays merging rather than one offsetting the other. Most converge at a small dihedral angle in map view (<15°). There is a preponderance of east-facing bifurcations (58%) in the 2-D fault map. Stepovers are defined as two subparallel faults, both of which terminate across a narrow zone of overlap between the faults. These fault segments do not intersect one another on the outcrop surface but end at isolated termination points that are closely spaced to one another. Right step-overs are dominant (65%) in the 2-D fault map.

Based on the ratio of isolated terminations (isolated simple nodes and stepover nodes) to bifurcations (Y-junctions where one fault ends against another), we calculate an average of 0.82 connections per fault in the 2-D fault network (Appendix 4; using the topological equations in Sanderson and Nixon 2015). This result indicates a relatively small connectivity between faults, as we also found in our earlier analysis of the two cross-sections (Figure 12; Appendix 2).

Fault termination points: effects of lithology

During field mapping and from our 2-D fault map analysis, we noted that many of the faults terminated on or close to lithological boundaries, especially the margins of thick pelite layers (Figure 10). To assess whether this apparent association between fault terminations and lithology is statistically significant, we compiled a database of fault termination points and noted whether the terminations occurred in pelite-rich schist, in psammite schist, in a quartz vein or mass, or at the contact between two of these rock types. We defined a termination point at a contact if it occurred within 2 cm of that boundary (Appendix 4; Table A4.5). Of the 336 fault terminations that were mapped across the outcrop, 40% occurred inside psammite (the dominant rock type) and 57% at contacts. Almost 40% of terminations occur at psammite-pelite contacts and 18% at schist-quartz vein contacts (Appendix 4, Figure A4.4). Contacts (including their 2 cm buffer) constitute only 2.6% of the mapped area, showing that the null hypothesis (that terminations intersect lithological contacts purely by chance) can be firmly rejected at the 5% level (p-value < 0.05; Appendix 4). In other words, we can be at least 95% confident that there is a statistically significant association between faults terminating and lithological contacts (especially the margins of thick pelite beds).

Discussion

Control on fault network topology by lithological contrasts

Strength anisotropy controlled by lithology can affect the geometry of fault networks (e.g. Childs et al. 1996; Beacom et al. 2001) and the relative interplay between brittle and ductile deformation during fault growth (e.g. Misra et al. 2015). Changes in mean fault spacing as a function of lithology on the two transects (Appendix 2), the statistically significant correlation between fault terminations and lithological contacts, and our direct field observations indicate that the fault network topology was strongly influenced by rock types, particularly by transitions between psammitic and pelitic schist, or between (any) schist type and thick quartz veins. Field observations reveal that the dominant psammitic schist was mostly displaced brittlely along the sharply defined fault planes by shear-extensional (mixed mode I-II, I-III) slip, where the extensional opening was a very small component (1-2 mm; Wightman and Little 2007). In addition, a smaller component of ductile shearing may also deform schist, particularly: (1) at the deeper structural levels of the swarm, (2) within restraining stepover zones, and (most commonly) in pelite-rich layers, where the shearing occurs parallel to the foliation (Grigull et al. 2012). At the cm-scale, field observations indicate that faults are commonly deflected around the ends of 1–3 cm-thick quartz veins that are cut by the fault. These veins are typically offset by a combination of brittle slip and ductile shearing (Figure 4A) although thicker quartz veins may be sheared in an entirely continuous and ductile way. By contrast, where a fault elsewhere transects quartz veins that are 1–5 mm-thick, they are invariably displaced brittlely (Wightman 2005; Hill 2005; Wightman et al. 2006; Wightman and Little 2007; Grigull et al. 2012). All these observations point to a strong lithological control on the spacing and interaction between individual faults within the fault array over scales of centimetres to decimetres.

Grigull et al. (2012) numerically modelled an individual fault passing through variable-thickness quartz veins and showed that while the strength ratio between viscous quartz and frictional schist (respectively) must have been close to 1, the degree of ductile strain in a deformed quartz vein depended on the viscous strength contrast between it and the host schist that encloses the vein. Based on our new observations we suggest that subtle strength contrasts (in brittle and/or ductile environments) between pelitic and psammitic schist may similarly have controlled the degree to which the faults were able to propagate through pelitic layers. In cases where faults terminate at the boundary of a pelite layer (e.g. Figure 10), we infer that at least some of the shearing was absorbed into foliation-parallel, distributed shear inside the pelite. This may help to explain many cases where faults were seen to die out at a pelite contact and then ‘re-emerge’ along-strike as a new fault cutting schist that on the opposite side of the pelite layer (Figure 10).

Based on our observations, we infer that regions with many intercalated layers of pelitic and psammitic schist hosted faults at a higher than average density and connectivity, and a smaller than average spacing (e.g. Domains 1, 2, 4 and 5 on the transects in the northwest part of Figure 8). Owing to the acute angle between the strike of foliation and compositional layering in the schist vs. the strike of the younger faults cutting these structures, the fault clusters must have continued outside of the thinly intercalated zones, where they encounter thicker schist and pelite layers along-strike or down-dip. Where a fault intersected the boundary of a thick pelite, it commonly terminated there (e.g. Figure 10), with some of the fault slip being redirected into distributed shear inside the pelite layer. This fault censorship process increased the mean fault spacing in the regions dominated by thickly interlayered psammitic and pelitic schist.

At the outcrop (1–10 m) scale of observation, it is not uncommon to observe faults terminating at the edge of sparsely distributed globular-shaped quartz vein masses, most of which are <1 m in diameter (e.g. Figure 8D). This relationship suggests that these lithological contrasts played a mechanical role in arresting fault growth. Such quartz masses are more likely to intersect faults at a larger angle compared to the schist foliation and pelite-psammite boundaries, which may enhance their efficacy in terminating faults. However typical psammite and pelite layers (and their mutual contacts) in the schist are laterally extensive, commonly extending >30 m along-strike (and presumably a similar distance vertically). The different attitudes and length-scales of interaction of faults with the quartz vein masses vs. schist, psammite vs. pelite contacts may have exerted multi-scale control on the fault network topology (e.g. Schrank et al. 2008). According to this view, the spacing between most faults was influenced (regularised) by alternation of the two most common rock types in the schist (e.g. Appendix 2; Figure 8), whereas smaller-scale bifurcations and stepovers may have been controlled by smaller length-scale heterogeneities, for example the sparsely distributed, < 1 m-thick masses of quartz vein rock.

Fault length distribution and effect on fault connectivity

The cumulative fault length plot (Figure 13B) has the form of a log-normal distribution (Davy 1993). A characteristic length scale provided, for example, by lithological layering, can give rise to a log-normal distribution where fault lengths less than the characteristic spacing are rare (Odling et al. 1999). This is consistent with evidence for lithological control on the spacing and termination of faults in the brittle-ductile swarm at Crawford Knob. However, artificial truncation of fault samples at length-scales that are smaller than the resolution of the measuring technique can cause a power-law distribution to mimic a log-normal one (Eisnstein and Baecher 1983; Segall and Pollard 1983; Rizzo et al. 2017). Our dataset is certainly censored at the maximum length end of the distribution (by the faults intersecting the outcrop edge on scales of ∼ 30 m) and was to some degree under-sampled for fault lengths < 0.5 m due to the practical limitations in our mapping techniques. We applied Fracpaq (Healy et al. 2017) over a subset of our network including 92 fault traces. Using the Maximum Likelihood Estimator to account for non-Gaussian noise, Fracpaq calculated an almost equal probability (using the Kolmogorov-Smirnoff test for goodness of fit) for power-law (98.64%; estimated power-law exponent of 2.6, lower length cutoff of 3.45 m) and log-normal (99.32%; μ = 1.3, σ = 0.89) fault length distributions. For the entire outcrop, where faults intersecting the outcrop edge have been censored, a power-law fit in the well-sampled interval of fault lengths between 5 and 15 m has a cumulative frequency slope of just over 2 (Figure 13B, slope = −2.13) giving a power-law frequency exponent near 3 (Bonnet et al. 2001).

Effect of fault topology on fluid flow and permeability

The Crawford Knob faults are infilled with a thin (1-2 mm-thick), planar vein of quartz-calcite ± chlorite, and record a small but persistent component of fault dilation (mode I opening) that took place during the brittle failure event that formed the structures. This fracturing was accompanied by substantial fluid flow and a drop in fluid pressure (Wightman 2005). Unlike fractures that form predominantly by mode I opening, where the fracture aperture is proportional to fracture length, there appears to be no relationship between infill thickness (fault aperture) and fault lengths in the brittle-ductile fault array; instead, infill thicknesses are fairly uniform across the entire fault network. This uniformity of width may occur because the faults deformed predominantly by shearing with only a small degree of opening.

The transiently open fracture network could have enhanced rates of fluid flow by allowing that fluid to pass between open and connected faults. Fluid flow through the fault network would have been enhanced up-dip (∼vertically) and along-strike (ENE-WSW) along the fault planes, while additional fracture permeability caused by the intersecting of adjacent faults would have been greatest in the ENE-WSW sub-horizontal direction (Figure A3.1). However, analysis of the 2-D fault network indicates a relatively low mean inter-fault connectivity C_L < 1 (as defined by Sanderson and Nixon 2015), below the percolation threshold for an orientation-clustered network (C_L > 2; e.g. Manzocchi 2002) at which large-scale fluid transmission through the fault network should occur. In contrast, Wightman (2005) estimated that a fluid flux of up to 14.8 m³/m²/s per fault was necessary to precipitate quartz into the veins. The low fault connectivity can be reconciled with this evidence for high fluid flux in several ways. First, a swarm of near-parallel faults with a (transient) opening component can still affect average permeability even if they are not well connected, provided matrix permeability is greater than zero so that elevated fluid pressure gradients between closely-spaced open fractures promote fluid flow (e.g. Pozdniakov and Tsang 2004). Second, our 2-D connectivity estimate may underestimate 3-D connectivity- for example, stepovers in 2-D may connect as bifurcations in 3-D. Third, while fault connectivity is low, the degree of connectivity may not have been uniform at the scale of the outcrop; for example, the smaller average fault spacings and lengths in domain 2 cf. domains 1 and 3 (Figure 8; Figure 12; Appendix 2) have more linked connections; in such regions, closely-spaced faults may have had enhanced fluid permeability. Finally, the connectivity estimate based on fault nodes does not fully represent the scale limitation of our measurements, since a significant proportion of the faults we mapped (60% of them) intersect at least one outcrop boundary. To explore this further, we used the code Fracpaq (Healy et al. 2017; Rizzo et al. 2017) to estimate the open-fracture 2-D permeability tensor for a rectangular 2-D subset of our dataset chosen to avoid outcrop boundaries. Fracpaq uses the connectivity/node mapping and fault statistics to create simulated fracture meshes which are optimum replica of the observed fracture network. In each fracture mesh, fracture centres are randomly positioned; their orientations are based on the field map and the lengths are simulated using a Monte-Carlo process from the best-fit log-normal distribution. Fracture abundance is based on the mean density value from the real map and fluid flow in the matrix is neglected. The permeability calculation requires a fracture aperture (here set to a constant of 1 mm based on infill vein thicknesses) and a connectivity factor which must be estimated by the user. Even setting the connectivity factor very low (0.01), the Fracpaq procedure predicts that the transient 2-D permeability of the fault array during the opening phase was highly anisotropic, with a maximum permeability of 10⁻¹³ m² aligned with the average fault strike direction, and minimum permeability more than 2 orders of magnitude lower and perpendicular to the fault strike direction. For comparison, typical basement permeabilities in New Zealand are < 10⁻¹⁶ m² for depths greater than 1-2 km (e.g. Upton and Sutherland 2014) and permeability measurements on the host biotite-grade schist near Franz Josef glacier average 10⁻¹⁷–10⁻¹⁸ m² (Wightman 2005 Table 5.4). The elevated transient permeability along-strike and up-dip within the fault planes can help to explain the large fluid flux calculated to have caused vein infilling in the fault array which acted as conduits to tap deep to mid-crustal metamorphic fluids (Wightman 2005; Wightman and Little 2007).

Bulk finite shear of crust accommodated by accumulated fault slips

The ratio of mean per-fault slip at Crawford Knob (∼19 cm, probably a minimum value) to the observed mean apparent fault spacing (∼1.25 m, Appendix 2) can be used to estimate an apparent (minimum) bulk finite shear strain accommodated by slip across the mapped array of subparallel faults of ∼0.15. This estimate pertains to the 3-D slip direction, which we infer to pitch ∼30° to the SW (Figure 9D). Decomposing this shear strain value into strike-slip and dip-slip components, at Crawford Knob one obtains a dextral-slip shear strain estimate of ∼0.13, and a vertical-slip (NW-up) shear strain estimate of ∼0.08. Wightman and Little (2007) used a 3-D analytical method to calculate mean dextral and vertical shear strain components for the brittle-ductile faults along field transects at several different sites in the central Southern Alps (including near Crawford Knob but outside of our map area). Like our measurements at Crawford Knob, they calculate an average per-fault slip for the entire data set of faults of 14.1 ± 1.2 cm, and infer an average a net-slip vector pitching 36° SW. Their average calculated fault spacing is, however, much narrower than ours, mostly only 15–30 cm – a difference that accounts for them calculating a much larger average finite shear strain than we have for Crawford Knob (they calculate 0.46 ± 0.12 for dextral-slip and 0.41 ± 0.14 for vertical slip, as averaged across their entire data set). Noting the unusually large spacing of faults at Crawford Knob, they attributed this difference to the mechanical effects of the thick pelitic layers there.

The exhumed faults at Crawford Knob show no evidence for gouge, pseudotachylite or other products of seismic fault slip. Nevetherless it is instructive to compare the predicted focal mechanism and seismic magnitude (if each fault slipped seismically) to present-day seismicity in the Alpine Fault hangingwall, particularly if we assume that the fault array was connected to a brittle (and possibly seismic) fault at shallower levels while it deformed. A back-projection of the Crawford Knob fault array location prior to exhumation from 20 km depth would place it towards the northeast, near the Arthur’s Pass region. Wightman and Little (2007) used the slip kinematics at Crawford Knob to predict a dextral-reverse focal mechanism, broadly compatible with the composite focal mechanism computed from the first motions of seven M_L ≥ 5.0 aftershocks of the Mw 6.7 1994 Arthur’s Pass earthquake (Abercrombie et al. 2000). Fault slip of 15 cm on a single fault strand rupturing an area of 30 × 30 m would have an equivalent Mw of ca. 2.4, observable within modern seismic networks near where Michailos et al. (2019) mapped seismicity to depths of ca. 22 km.

Conclusions

Our study has explored a rare field example of a well-preserved fault swarm, interpreted to have formed due to upramping and tilting of the Pacific Plate onto the Alpine Fault ramp at mid-crustal depths. The swarm’s unique characteristics result from its rapid exhumation from the mid crust along a transpressive plate boundary fault (the Alpine Fault) exposing a shear zone that deformed under conditions where slight lithological variations expressed both brittle and ductile behaviour. The topology and structure of the fault array provide valuable information concerning fault interactions, connectivity, and mechanics at the brittle-ductile transition in New Zealand’s schist basement.

We have constructed 2-D and 3-D maps of a brittle-ductile fault array and analysed the attitude, spacing, length, slip, and styles and controls on termination and linkage of these faults. While the maximum along-strike length of the outcrop of ∼ 30 m imposes some limits to our analysis, and the 3-D fault model cannot be extrapolated more than about 10 m down-dip, our results demonstrate that the faults have a low connectivity. However, the small opening component of fault displacement (creating an average fault aperture of ∼ 1 mm) is predicted to have created significant transient fluid permeability anisotropy in the along-strike direction of the fault swarm in 2-D (and by inference, up-dip as well). We have demonstrated that:

1. while the faults are regularly spaced at the 1-2 m scale, spacings are locally variable (and can be separated into fault domains including narrow damage zones with smaller spacing). This spacing appears to be at least partially related to the presence or absence of contrasts in lithology within the schist, especially those caused by intercalations of pelite in the otherwise dominantly psammitic rock.

2. apparent fault lengths range from < 1 m to > 30 m. Fault lengths appear to have a log-normal distribution indicative of a minimum cutoff length-scale controlled by the afore-mentioned lithological contrasts.

3. faults begin/end: (a) where they intersect another fault at an angle (at a Y-bifurcation, or splay); (b) where they step over onto another fault; or (c) as an isolated point where slip reduces to zero.

4. lithological contrasts between psammitic and pelitic schist, and between schist and quartz veins, exert a significant control on the distribution of these types of fault junctions and terminations.

5. a topological analysis of the 2-D fault map suggests that, despite low connectivity per fault, permeability and fluid flow were transiently enhanced along-strike and up-dip.

Data Availability Statement

The authors confirm that the data supporting the findings of this study are available within the article and its supplementary materials. The appendices are available for download at https://doi.org/10.6084/m9.figshare.22492936. Two supplementary data collections containing fault geometry and lithology (Supplementary Dataset 1) and the 3-D fault model (Supplementary Dataset 2) supporting the findings of this study are openly available at https://doi.org/10.21420/8VT4-2J73.

Acknowledgements

This study was funded by core funding to GNS Science and Victoria University of Wellington. The authors would like to thank the Department of Conservation for the help in permitting and providing radios; the Local Air Users Group at Franz Josef for their cooperation in providing permit conditions that allowed us to fly a remotely piloted aircraft in an area used by many helicopter companies; Neville Palmer and Garth Archibald for RTK GPS equipment preparation and training; and Te Runanga o Makaawhio (Komiti Taiao) for permission to access the field area. We acknowledge fruitful discussions with Simon Cox, David Prior, Virginia Toy, Steve Kidder, Andrew Cross, Cecile Massiot, Ruth Wightman, Susanne Grigull, and many others over the years. Mark Rattenbury, Cecile Massiot, Jack Williams and an anonymous reviewer provided constructive comments on the manuscript.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by the GNS Te Riu-a-Māui/Zealandia Programme (Strategic Science Investment Fund, contract C05X1702).