Abstract
In this study, fracture systems developed within faulted, high-porosity sandstones in the decommissioned mines of Alderley Edge, Cheshire, UK are characterized using lidar (Light Detection And Ranging)-based analysis. The geometry of the mine workings prove to be conducive to the extraction of fracture attributes, whilst providing a degree of exposure of a notable Triassic-aged reservoir outcrop analogue (Helsby Sandstone Formation) not afforded at the surface.
To test the fidelity of the approach, fracture statistics generated from lidar-derived digital outcrop models are compared to an equivalent dataset collected using conventional manual surveys, with digital outcrop and manually acquired fracture attributes used to populate discrete fracture network models. These are upscaled to provide equivalent porous medium properties, enabling the impact of uncertainties introduced into fracture modelling workflows by lidar-based techniques to be assessed.
Whilst broadly comparable to fracture attributes obtained using manual surveys, the systematic underrepresentation of fracture properties is observed within lidar-derived dataset, resulting in the underestimation of fracture network flow capacity. The study results suggest that, whilst enhancing data acquisition rates and coverage of exposure surfaces, the use of digital discontinuity analysis may introduce additional biases into fracture datasets, increasing the level of uncertainty within resultant modelled networks.
The characterization of subseismic-scale structure is a perennial problem within petroleum reservoir modelling. Advances in three-dimensional (3D) seismic imaging and analysis over the past several decades now afford the construction of geometrically accurate static and dynamic reservoir models, with depositional and structural architectures constrained at resolutions of tens to hundreds of metres (e.g. Grötsch & Mercadier 1999; Caers et al. 2001). In spite of these developments, structural heterogeneities manifest at scales below conventional seismic thresholds (c. 2×101 m: Waggott et al. 2005) may profoundly influence reservoir character. Unresolved mesoscale structural entities – such as shear fractures (faults), dilatational fractures and compression structures – impart significant anisotropy within the rock mass, resulting in permeability regimes typically several orders of magnitude greater or lower than those of enveloping matrix continuum (Aydin 2000).
A common strategy to reduce reservoir uncertainty is to employ the use of analogues. The power of using cognate surface outcrops lies in their ability to extend scales of observation below conventional seismic thresholds, whilst adding complexity to 1D well data (Jones et al. 2008). However, whilst numerous examples exist where outcrop analogues have provided lucid insights about the structural and diagenetic styles of their reservoir equivalents (e.g. Koestler & Ehrmann 1991; Odling et al. 1999; Gale et al. 2004; Sharp et al. 2006), conventional methods of fracture characterization at outcrop scale suffer manifest deficiencies, with direct sampling of the rock face (i.e. via cell mapping/scanline surveys) biased, inefficient and subject to edge effects (Kemeny et al. 2006), and with fracture mapping from 2D photo-images resulting in poorly resolved datasets (especially with regards to orientation: e.g. Ghosh & Mitra 2009).
In the present work, it is proposed that data capture and analysis techniques currently being developed within the burgeoning field of digital outcrop geology could provide a viable alternative to conventional means of fracture characterization commonly applied to reservoir analogue studies. Here, a combination of terrestrial lidar and calibrated digital imagery is used to map exposures of the Mid-Triassic-aged (Anisian) Helsby Sandstone Formation (HSF) of the Cheshire Basin, UK. A salient analogue for reservoir objectives in the East Irish Sea Basin, ascertaining the properties of the fracture network of the HSF has considerable practical application. Exposures of the HSF within the West Mine, Alderley Edge, Cheshire form the principal targets for data capture (Fig. 1). The use of subsurface exposures is motivated by the favourable geometries that the mine workings exhibit in terms of fracture property extraction, with the upwardly recurved, cylindrical rock surfaces limiting data shadows, aiding enhanced visualization of the fracture network, whilst providing optimal conditions for the extraction of geometrical fracture attributes.
High-resolution digital outcrop model of the West Mine main chamber, Alderley Edge, Cheshire. The model is a 3D reconstructed triangular mesh surface generated using terrestrial laser-scanner-derived ‘point cloud’ data (groups of vertices defined by X, Y, Z co-ordinates representing an exposure surface). The high degree of realism in the above model is achieved by mapping referenced digital imagery to the triangular mesh surface. The lateral extent of the image is approximately 12 m.
A comprehensive areal survey was conducted on the photorealistic point cloud dataset and texture mapped triangular irregular network (TIN) outcrop model derivatives. Eigen-analysis-based methods (Fernández 2005; García-Sellés et al. 2011) are employed to aid the identification of fracture traces and facets, with fracture orientations constrained using a simple three-point approach. Furthermore, a series of linear transect surveys (virtual scanlines: sensu Voyat et al. 2006) across TINs of the West Mine exposures are employed in order to determine fracture trace length and spacing. Fracture sets are delineated using a suite of qualitative and quantitative methods, with orientation statistics subsequently calculated for each of the identified sets. Mean fracture spacing, trace length and density are then determined for individual sets, with the appropriate geometrical and censoring corrections applied.
In order to assess the validity of the approach, the orientation statistics of identified sets are compared to an equivalent dataset collected through a series of conventional scanline surveys conducted on surface exposures around the Alderley Edge locality. In similitude, the fidelity of the lidar-generated trace lengths, spacing and densities are compared to a commensurate dataset, acquired using manual scanlines precisely referenced to corresponding virtual linear transect surveys within the West Mine main chamber. Finally, fracture statistics obtained for field- and digital-outcrop-derived sets are used to construct representative discrete fracture network models, which are subsequently upscaled to provide equivalent porous medium properties for both manually and virtually characterized networks. Thereby enabling the differential in the petrophysical attributes of the corresponding fracture arrays to be assessed.
Advantages of using subsurface digital outcrop models
The use of mine workings, such as those used in the present study, offer considerable advantages over conventional surface exposures for digital outcrop fracture characterization. For example, several workers have noted the effects of range shadows in lidar point clouds due to a restricted line of sight, and have highlighted the need to conduct scans from multiple positions to ensure the exposure is fully resolved (e.g. Kemeny et al. 2006; Buckley et al. 2008). However, unless a synoptic vantage point is afforded by the local topography, it is common for subhorizontal fractures at elevated positions up the rock face to be occluded during scanning, resulting in the potential for view-limited censoring and vertical orientation bias to be introduced (Sturzenegger & Stead 2009a; Lato et al. 2010). The cylindrical geometry of mine workings serve to limit the effects of occlusion, with the scanner line of sight to subhorizontal fractures maintained with greater continuity up the outcrop face.
Further benefits relate to enhanced visualization of fracture systems. By capturing exposures within enclosed spaces such as mine workings, tunnels or cave systems, fracture networks may be viewed contemporaneously in both the vertical and horizontal plane. The resultant point clouds or TIN mesh derivatives are, in essence, morphologically analogous to drill core samples (i.e. they are cylindrical), albeit up-scaled by several orders of magnitude. These digital outcrop ‘pseudo-cores’ offer clear advantages to the analyst, including the ability to better gauge the spatial distribution, as well as the degree of persistence and connectivity of the fracture network.
Finally, perhaps the most significant advantage that such exposures offer to digital-outcrop-based fractured reservoir analogue studies pertains to the measurement of trace orientations. It is common for terrestrial lidar-based fracture studies to constrain orientations and delineate sets solely on the basis of fractures with well-developed surfaces (e.g. Kemeny et al. 2006; Sturzenegger & Stead 2009b; Larsen et al. 2010). Even when fracture traces are considered, it is usually in order to resolve other characteristics such as trace length, apparent spacing and linear/areal density (e.g. Gillespie et al. 2011).
In the context of deriving statistics for fracture modelling workflows, this practice is problematic. Whilst several measures of discontinuity abundance exist (e.g. fracture frequency (P10), fractures per unit length; 3D fracture density (P30), fractures per unit volume; 3D fracture intensity (P32), fracture area per unit volume: Dershowitz 1985; Dershowitz & Herda 1992), in order to constitute a viable input for fracture modelling, fracture densities must be established for individual sets across a given scanline or cell (Munier 2004). Unless all of the fractures along the survey transect or within the survey area have well-developed fracture planes (which, based on the authors’ experience is unlikely), fracture orientations, and thus set membership for the target population, cannot be fully resolved from outcrop models using fracture facets alone. Moreover, if only fracture planes are accounted for, discontinuity types developed only as fracture traces are, by default, omitted from the modelling procedure. This is of particular concern when attempting to characterize faulted high-porosity sandstones, such as those encountered in the present study, where deformation bands, expressed exclusively as surficial traces, may represent a major control over the petrophysical character of analogous reservoir sequences (Manzocchi et al. 1998).
The orientation of a fracture trace may be determined rudimentarily from an outcrop model by selecting three known X, Y, Z co-ordinates across its length, and then calculating the orientation of the plane fitted to the selected nodes (‘three-point approach’: e.g. McCaffrey et al. 2008; the present study). In addition, more sophisticated averaging methods, such as planar regression (e.g. Banerjee & Mitra 2004; García-Sellés et al. 2011), may be employed towards the same objective. A feature common to the aforementioned approaches is that the reliability of the fitted plane is strongly dependent on the distribution of the selected nodes (Fernández 2005). Thus, as selected vertices approach colinearity, the number of possible solutions for the orientation of the fitted plane, θ, tends towards infinity (Fig. 2a). Conversely, as the selected vertices become equilaterally distributed (and thus coplanar), θ is reduced to a unique solution (Fig. 2b). The majority of surface exposures may be likened to the case illustrated in Figure 2a (i.e. they are essentially planar), and thus pre-empt the possibility of obtaining reliable fracture trace orientations. In contrast, the tunnel-like cylindrical walls that constitute many subsurface exposures, such as those used within the present study, are broadly analogous to the case illustrated in Figure 2b. As a result, outcrop models derived from such exposures have a greater potential of yielding reliable measurements of fracture trace orientation and, as a consequence, will maximize the possibility of gaining meaningful fracture densities from terrestrial lidar-derived datasets.
(a) Illustration of the three-point approach used to resolve the orientation of a subvertically orientated fracture from a trace expressed across a perfectly planar surface. The selected nodes are distributed in a colinear fashion, resulting in a near infinitesimal number of solutions to the fracture orientation (θ). As a consequence, the orientation of the trace cannot be resolved. (b) Illustration of the three-point approach used to determine the orientation of a fracture trace on a perfectly cylindrical surface. The selected nodes are equilaterally distributed around the objects centre of mass, resulting in a unique solution to θ.
Geological setting
Alderley Edge lies proximal to the NE margin of the Cheshire Basin, an asymmetrical half-graben structure bounded by major syndepositional normal faults along its eastern perimeter (Rowe & Burley 1997). Forming as a midpoint between the Needwood Basin to the SE and the East Irish Sea Basin (EISB) petroleum province to the NW, the Cheshire Basin is part of a complex north–south-trending Permo-Triassic rift system that transects much of the western UK (Fig. 3a). The basin fill comprises over 4000 m of sediments locally, with the predominantly arenaceous red-bed deposits of the Sherwood Sandstone Group (SSG) and argillaceous units of the Mercia Mudstone Group (MMG) constituting the dominant fraction (Warrington et al. 1999) (Fig. 3b, c).
(a) Onshore and offshore outcrop of Permo-Triassic rocks in central and northern England and Wales, showing the location of the Cheshire Basin at regional scale. (b) Structure of the Cheshire Basin, with the outcrop of the Sherwood Sandstone Group and the location of the present study area indicated. (c) Permian–Jurassic stratigraphy of the Cheshire Basin. (a) Modified from Jackson et al. (1995) and Mountney & Thompson (2002). (b) Modified from Plant et al. (1999). (c) Redrawn (with additions) from Plant et al. (1999).
The Alderley Edge area is formed as a 3 km-wide tilted horst block structure that dips SW towards the Cheshire Plain (Rowe & Burley 1997) (Fig. 4). Outcropping in the northern and central parts of the horst, respectively, are the dominantly aeolian Wilmslow Sandstone Formation and the mixed fluviatile–aeolian Helsby Sandstone Formation (HSF) of the SSG, which are juxtaposed against units of the MMG by large displacement normal faults to the east and the west (Thompson 1991). In addition, a complex array of subsidiary structures may be observed at the site, with subparallel sets of north–south- and WNW–ENE-trending small displacement normal faults (commonly <20 m: Rowe & Burley 1997) occurring alongside a range of smaller-scale heterogeneities.
Fence diagram illustrating the structure of the Alderley Horst. The location of the present study area; the main chamber of the West Mine is also indicated. Fault locations and bedding-plane contacts derived from the detailed mapping of Thompson (1965). Fault displacements and orientations based on Thompson (1965) and the authors’ measurements. Local stratigraphical units after Thompson (1965), with lithological descriptions after Thompson (1965) and Carlon (1979), and based on the authors’ observations. Cross-section of the main chamber of the West Mine after Warrington (1965).
Subvertical joints (i.e. tension fractures exhibiting null shear displacement: Nur 1982) are the most pervasive structures visible in outcrop across the horst, and are presented by two distinct group sets. First, systematic joints may be identified as laterally continuous, planar discontinuities, forming two cross-cutting, orthogonally arranged, north–south-/east–west-oriented joint sets (Fig. 5a). In vertical section, bedding interfaces appear to be the major control on the arrest of joint propagation in the more strongly bedded, heterolithic units (e.g. the fluvial units of the HSF and the marginal marine Tarporley Siltstone Formation), with stratabound jointing architectures common in such lithologies. However, bedding contacts appear to offer only limited mechanical control over joint arrest within the more monotonous, aeolian units present within the horst block (e.g. the West Mine and Beacon Lodge members of the HSF). The more common development of systematic joints as unconfined discontinuities in these lithologies implies a lesser degree of mechanical anisotropy in the aeolian units when compared to their fluviatile or marine equivalents (Odling et al. 1999).
(a) Subvertical joints developed within the roof of the West Mine, Alderley Edge, with large systematic joints indicated. (b) Fracture map derived from (a), illustrating the geometry and connectivity of both systematic (thick lines) and non-systematic joints (thin lines). Discontinuities clearly relating to roof collapse or those that are indiscernible from the original 4288×2848 pixel image have been omitted from the fracture map. (c) Close-up view of discontinuities illustrated in (b) with termination styles indicated: A, abutting; B, blind; C, crossing; D, diffuse. Terminology after Barton et al. (1987) and Laubach (1992).
A second group of smaller-scale, yet more numerous, non-systematic joints may also be observed within the Alderley locality. These are often characterized by curviplanar, undulating or irregular geometries, propagated at angles ranging from subparallel to oblique to the systematic joints (Fig. 5b). In addition to the geometrical complexity of their surficial traces, termination styles of non-systematic joints are inherently multiform, with such discontinuities having crossing or diffuse intersections with other non-systematic joints or terminating within the rock mass as blind traces (Fig. 5c). Furthermore, non-systematic joints commonly abut systematic joints, indicating that the former group post-dates the latter (e.g. Cruikshank & Aydin 1995).
Developed within both fluvial and aeolian sandstone horizons, deformation bands are a further notable discontinuity type present at the study site (e.g. Fossen & Bale 2007). Whilst sometimes occurring in isolation, these structures become locally prominent around normal faults, manifest as conjugate pairs cutting obliquely through the main failure plain (Fig. 6a). Where faults achieve displacements of several to tens of metres, deformation bands occur in dense clusters, forming anatomizing networks within a narrow damage zone (typically <10 m: Rowe & Burley 1997) around the fault core.
(a) Conjugate set of deformation bands developed in the footwall and hanging wall of a small displacement normal fault in the West Mine main chamber. The hammer is for scale. Dashed lines indicate the projected path of the deformation bands from the hanging wall to footwall. (b) Optical photomicrograph in plane polarized light showing the intersection between the conjugate set of deformation bands illustrated in (a). The zone of intense cataclasis (ZIC: boundary indicated by the thin dashed lines) is characterized by grain communition and diminution in sorting, as well as partial cementation with barite, resulting in localized porosity reduction (porosity labelled Φ).
Also spatially associated with faults and their damage zones is the extensive mineralization and porosity reduction of the Alderley Horst. Diagenetic phenomena, such as hematite reduced grains and barite cemented discontinuities (Fig. 6b), are widespread throughout the site, with more localized emplacement of polymetallic mineral assemblages (Cu–Pb–Zn–Fe sulphides) also commonly observable (Rowe & Burley 1997). This latter group of metalliferous cements have been the focus for ore extraction at Alderley Edge, motivating several sporadic periods of mining that have left an extensive system of mines across the area (Carlon 1979). It is within the largest such working, the West Mine, that digital outcrop data were captured during this study.
A number of similarities may be drawn between the Alderley Horst and the reservoir objectives within the East Irish Sea Basin (EISB), which make the area a pertinent candidate for reservoir outcrop analogue studies. For example, the horst is analogous to tilted fault block structures within the EISB, and has similar instances of porosity reducing diagenesis (i.e. fault-related diagenetic cementation and sandstone hosted Cu–Pb–Zn–Fe sulphides: Naylor et al. 1989; Rowe & Burley 1997). Furthermore, the HSF, which enjoys extensive exposure within the Alderley Edge Mines, is recognized as a salient sedimentological analogue for reservoir sequences in the EISB, and forms the onshore equivalent of the principle reservoir unit of the Lennox field, the Ormskirk Sandstone Formation (Meadows & Beach 1993; Mountney & Thompson 2002). Thus, the Alderley Horst presents the opportunity to study fracture characteristics within an equivalent structural, diagenetic and sedimentological setting to those encountered within the EISB, with the mine workings providing exposures with a geometrical arrangement that is conducive to the extraction of fracture attributes from digital outcrop datasets.
Methodology
Data acquisition
The lidar platform used in this study was a RIEGL LMS-Z420i long-range terrestrial laser scanner, with an operable range of 2–1000 m (2–600 m for geological materials), a data acquisition rate of up to 11 000 points per second and a quoted accuracy of 10 mm (RIEGL 2010). The scanner was powered using 12 V batteries and operated using RiScan Pro v.1.4.2, run from a Trimble Yuma Windows-based ruggedized tablet computer. In addition, a Nikon D300 12.3 MP (megapixel) digital single lens reflex camera with a calibrated 14 mm lens was mounted on the scanner, enabling the simultaneous capture of high-resolution imagery, auto-referenced to the point cloud. Furthermore, the platform was equipped with a stand-alone flashgun to facilitate the capture of photo-imagery within the subsurface environment.
The point cloud dataset was acquired from nine scan positions in the mine, selected with the intention of minimizing the occlusion of subvertical fracture facets (Kemeny et al. 2006) (Fig. 7). In order to facilitate the registration of multiple scans, retro-reflective targets were placed around the mine workings to form a network of common control points (Buckley et al. 2008). A laser level was used to align several targets within a single plane, to enable the horizontal attitude of the registered scans to be defined. Furthermore, two of these targets were aligned to magnetic north, with the aid of a compass clinometer and laser level, to allow registered scans to be referenced to a local magnetic co-ordinate system. Thereby enabling measurements from the outcrop model to be compared directly with manually collected orientation data (van Knapen & Slob 2009). Furthermore, additional reflectors were used to mark the origins of survey transects, to enable virtual and manual scanlines to be accurately matched at a later point.
Plan of the West Mine main chamber, with the location of scan positions indicated. The dashed lines indicate overhanging sections within the mine workings. Original mine plans courtesy of P. Deakin. Fault locations based on the authors’ measurements.
A total of 15 360° rotational scans were executed, with scanner circumvolutions conducted in both the vertical (n=9) and horizontal (n=6) axial plane in order to honour the upwardly recurved geometry of the mine workings (Fig. 8). The resultant 15 point clouds covered an area of approximately 12 500 m2 and were comprised of over 2×108 points, with a sampling interval of 2.5 cm. Furthermore, a total of 120 high-resolution photo-images were simultaneously collected during the scanning process.
(a) Scanner set-up for vertical (left) and horizontal (right) scans. The inclination of the scanner is modified using a tilt mount. (b) Scanner rotations in relation to the dominant strike of the mine workings for horizontal (left) and vertical (right) scans. (a) is modified from RIEGL (2010).
Digital outcrop model construction
The construction of outcrop models follows the approach presented by Fabuel-Perez et al. (2010) and comprises three discrete phases, namely: the alignment and merger of individual scans; the consolidation of point clouds prior to surface reconstruction and optimization; and the texture mapping of triangular irregular network meshes with referenced photo-imagery.
Point cloud merger was achieved using the IMAlign module within InnovMetric Polyworks v.9. Having completed the merge process, a simple rotation of the newly registered scans was performed to achieve alignment to magnetic north. Further checks to the fidelity this alignment were performed using Virtual Reality Geological Software (VRGS), a software package developed in-house for processing, visualizing and analysing geological datasets acquired using digital outcrop techniques. Detailed survey plans of the mine were projected into VRGS in order validate the azimuthal alignment, with scanned entities within the point cloud of known vertical attitude (e.g. free hanging ropes) used to correct the alignment within the horizontal plane.
Subsequent to the merger of individual scans, operations were carried out to consolidate the individual point clouds into a single merged dataset, both to reduce computational expenditure and to reduce areas of excessively high or low point density. Initially, peripheral areas in the individual point clouds suffering low point densities were removed by establishing range maxima of 20 m from the scan origin. Having established optimal dimensions for individual scans, a declustering operation was performed, with the point clouds resampled to 2.5 cm spacings.
Within the study, TIN surfaces form the primary basis for fracture property extraction. The motivation behind using TINs over point clouds as the principle analytic medium is that discontinuity facets tend to be manifest more clearly on reconstructed surfaces (Turner et al. 2006). The incipient phase in TIN construction is the removal of artefacts (i.e. reflected points) and superfluous entities (i.e. floors, ropes, ladders, etc.) within point clouds using point editing methods. A Delaunay triangulation is then performed on the edited point clouds to produce the TIN (e.g. Kemeny et al. 2006), with an optimization procedure applied, eliminating the appearance of sliver tetrahedra.
The construction of photorealistic outcrop models requires each vertex within the TIN meshes to be mapped with registered photography, creating a reconstructed surface with individual pixels from images linked by Cartesian co-ordinates to their corresponding vertices (Fabuel-Perez et al. 2010). However, due to poor lighting conditions, many of the images captured in the mine required remediation through digital image-processing techniques. Consequently, a suite of methods, including Piecewise Linear Transformation Functions (contrast stretching) and power-law transformations, were employed to increase the fidelity of imagery prior to texture mapping.
Digital discontinuity analysis
Recent advances in digital outcrop analysis now permit the automated and semi-automated extraction of near-planar geological surfaces (most ostensibly faults, fractures and bedding planes) directly from point clouds and TIN meshes. In this regard, workers have put forward a number of methods for the unsupervised identification of fracture facets from outcrop models, including geometrical segmentation through region growing (e.g. Kemeny et al. 2006) and fuzzy-k means clustering (e.g. van Knapen & Slobb 2009). Whilst offering clear advantages with respect to efficacy of data acquisition, an inherent limitation to auto-extraction procedures is that they are incapable of resolving fracture facets that are markedly discontinuous or that exhibit a high degree of curvature. A point reflected in the selection of well-consolidated lithotypes containing strongly developed, planar fractures as test beds for the aforementioned approaches (i.e. intensively jointed meta-sandstones and hard carbonates). Furthermore, if applied without careful visual assessment and vetting of extracted facets, such methods harbour the potential to introduce artefact surfaces formed by non-geological processes into fracture datasets (e.g. excavations/blast-induced fractures).
The discontinuous expression of the fracture network within the West Mine, coupled with the frequent occurrence of extraction-related surfaces, severely restricts the usefulness of unsupervised classification techniques. In lieu of such methods, geometrical attributes calculated using moment of inertia analysis are employed in the present study, both to enhance reconstructed surfaces, and to guide the identification of fracture facets and traces prior to manual digitization.
Moment of inertia analysis
Equivalent to the orientation-tensor method for defining fabric shape (e.g. Woodcock 1977), the moment of inertia of a group of adjacent points/vertices may be used as a proxy for their vector sum by using the axis of their maximum moment of inertia as the pole to the best-fit plane (Fernández 2005). The potential of using moment of inertia analysis for resolving fracture properties has previously been recognized, with workers using derivative attributes (i.e. dip, azimuth and coplanarity) as criteria for the identification of discontinuity surfaces (e.g. García-Sellés et al. 2011). A further application, presented here, is the selected targeting of planar surfaces on TIN meshes for smoothing operations.
Selective smoothing
The inherent measurement error of terrestrial laser scanners introduces ranging noise into point cloud datasets, with recorded points commonly exhibiting negative or positive displacement normal to the targeted surface. As a result of this ranging error, adjoining triangular facets within TIN meshes are erratically oriented, severely limiting the fidelity of reconstructed outcrop model surfaces (Fig. 9a). Consequently, the indiscriminate smoothing of outcrop models is a requisite processing stage prior the extraction of fracture facets (Turner et al. 2006), resulting in the attenuation of discontinuity edges. In the present work, fracture morphology on reconstructed surfaces is maintained through the use of attribute filters, whereby areas of low coplanarity (i.e. fracture edges) are preferentially excluded prior to surface averaging (Fig. 9b). Having smoothed inferred discontinuity facets, low coplanarity regions are reinstated, resulting in triangular meshes that exhibit minimal ranging noise whilst retaining acutely defined fracture edges (Fig. 9c).
Methods of surface optimization and digital discontinuity analysis using moment of inertia-derived surface attributes. (a) Targeted smoothing of TIN surfaces: triangular mesh with coplanarity attribute displayed. (b) Vertices of low coplanarity are filtered and smoothing operations conducted. (c) Surface is restored after smoothing operations. (d) Increases in frequency density for dip and (e) dip azimuth may indicate the presence of subparallel fracture sets. Note that frequency spikes for tetrahedra azimuths of approximately 220° and dips of around 10° often coincide on the outcrop model surface. (f ) Orientation frequency distributions may be used to guide the filtering of outcrop model attributes, resulting in the semi-automated extraction of fracture surfaces and patches (compare with Fig. 1). Note that a threshold limit of 10 vertices has been placed on extracted fracture patches. (g) Linear areas of low coplanarity indicate the presence of fracture traces.
Feature extraction
In addition to a surface optimization, orientation-tensor-based methods hold great potential to assist the analysis of fracture network properties. Indeed, the non-random propagation behaviour of fracturing observed within most lithological and structural settings, as well as the generic characteristic of discontinuities to develop continuous planar surfaces (Hoek 1964; Pollard & Aydin 1988), provides a diagnostic rationale that may be implemented by harnessing geometrical surface attributes (e.g. García-Sellés et al. 2011).
For example, the frequency distributions of vertical and lateral orientation components (i.e. surface dip and dip azimuth), calculated using moment of inertia analysis, may provide an immediate indication of the presence of fracture sets amongst a wider population of discontinuities. The occurrence of multiple subparallel fractures is reflected by a marked increase in dip/dip azimuth frequency densities, cross-correlatable over the outcrop model surface (Fig. 9d, e). Frequency distributions of surface orientations may then be used to guide semi-automated feature extraction, with targeted filtering of geometrical surface attributes used to isolate fracture ‘patches’ (sensu Kemeny et al. 2006) and facets (Fig. 9f).
Further to the extraction of surface planes, tensor-analysis-generated attributes may also aid the identification of fracture traces from digital outcrop models. A problem associated with the use of RGB coloured TIN surfaces is that images are effectively downsampled to the vertex spacing of the triangular array. As a result, features such as fracture traces expressed at scales lower than the resampled image may appear ambiguous, becoming irresolvable across the outcrop model surface. Whilst the optical signature of such features may be lost on the RGB coloured TIN, the geometrical expression may be retained and enhanced through selective smoothing of TIN surfaces, with traces identifiable as continuous linear regions of low coplanarity on the outcrop model surface (Fig. 9g).
In the present study, the methods described above are used in conjunction with visual assessment of RGB coloured point clouds and TIN surfaces to identify fracture facets and traces. However, owing to the commonly abstruse nature of fracturing within the West Mine, the direct extraction of fracture attributes (e.g. orientation, length and spacing) is conducted manually through supervised digitization.
Data collection
Areal survey
A systematic areal survey was conducted across the worked face of the West Mine outcrop models to collect a fracture orientation dataset from which set distributions could be ascertained. To reduce computing requirements, the survey was limited to small areas, with outcrop models generated from single scans surveyed individually (e.g. Fabuel-Perez et al. 2010). In order to constrain fracture orientations, a simple three-point approach was applied, with a best-fit plane projected through three selected vertices of each measured fracture facet or trace. A total of 1377 fracture orientation measurements were collected during the survey (Fig. 10).
(a) Merged point cloud of the West Mine main chamber, illustrating the extent of the digital outcrops used for the areal fracture survey. (b) Individual fracture orientation measurements (n=1377) collected through a comprehensive areal fracture survey of the exposure surfaces within the West Mine main chamber. NB: Polygon size relates to the spacing of points selected to calculate each fracture orientation.
Virtual scanlines
Five virtual scanlines were generated across outcrop model surfaces (two vertical and three horizontal), referenced to retro-reflective control points positioned during scanning (Fig. 11). The collection procedure was similar to that of Voyat et al. (2006), with polylines constructed across the outcrop model face used to demarcate the transect line and Euclidean measuring tools employed to establish fracture spacing and trace length. In similitude to the virtual areal survey, the orientations of individual fracture facets and traces were determined by picking point sets from outcrop model surfaces.
Virtual scanlines conducted in the West Mine Alderley Edge, referenced using retro-reflective common control points. Individual fractures are extrapolated to the digital scanline in order to resolve linear discontinuity spacing.
Manual scanlines
In order for the impact of uncertainties into fracture datasets by digital discontinuity analysis, an equivalent database of fracture statistics was collected. A direct comparison of digitally and manually derived fracture trace length and spacing was achieved using a dataset collected from five conventional scanline surveys, referenced to the previously described retro-reflective control points within the West Mine. However, owing to the large data volumes required for the identification of fracture sets and calculation of orientation statistics, coupled with the slow data acquisition rate inherent to manual surveys, a direct comparison of orientation measurements was not feasible within the scope of this study. This situation was compounded by the limited number of fractures that were accessible to manual measurement at the base of the West Mine exposures. To supplement the orientation datasets collected within the West Mine, a further 34 scanline surveys were undertaken at 10 locations around the Alderley Edge area (Fig. 12, Table 1).
The solid bedrock geology of Alderley Edge, with the location of manual scanline survey sites indicated. After Thompson (1991) with modifications.
Summary of all manual scanline surveys undertaken for the study
The procedure for all scanline surveys broadly followed that of ISRM (1978) and Priest (1993). With the intention of limiting orientation bias, wherever possible, multiple surveys were conducted along exposures with different orientations, with vertical scanlines used on rock faces that were suitably accessible (ISRM 1978). A total of 726 fractures were recorded from 39 surveys, with 631 orientation measurements collected.
Data analysis
Fracture set delineation and orientation statistics
In addition to qualitative assessment of set distributions outlined previously, more robust stereographic techniques were used to delineate fracture sets from both manually and virtually derived orientation datasets. Initial efforts focused on the use of density contour plots of orientation data (scalar product method), with the segregation of the fracture populations achieved through visual assessment of orientation distributions (e.g. Hitchmough et al. 2007). Further to this, the clustering algorithm of Wallbrecher (1978) was used to formally define fracture set membership. In order to make a quantitative comparison between fracture sets defined from virtual and manual datasets, statistical parameters of spherical distributions were determined for both populations, with the direction of vector sum, measure of cylindricity, degree of preferred orientation and the estimation of the concentration parameter calculated for the corresponding fracture arrays (Table 2).
Statistical parameters for spherical distributions calculated for both manual and virtual fracture sets
Trace length
Given that fracture size exerts significant control over gross network connectivity, the curtailment of fracture trace lengths due to the finite window of observation requires correction (Priest & Hudson 1981; Priest 1993). In the present work, a Kaplan–Meier (product limit) estimator (Kaplan & Meier 1958) was used to account for the censoring of fractures extending beyond the extent of the exposure for both manually and virtually acquired datasets. The Kaplan–Meier estimator provides the non-parametric maximum likelihood estimation of the cumulative distribution function (CDF) of corrected fracture trace length (e.g. Lindsay & Rothrock 1995; Odling 1997). Being a non-parametric technique, the Kaplan–Meier estimator has the advantage of providing an estimate of the CDF of corrected trace length that is insensitive to the shape of the underlying distribution of the fracture population from which the random sample was drawn.
Within the present modelling workflow, however, discontinuity length distributions are a required input for the construction of discrete fracture networks. Initially, parent distributions were estimated on a set by set basis using histograms determined for fracture trace length (e.g. Hitchmough et al. 2007). In addition, a more robust identification procedure was employed, with probability plots constructed for individual sets used to assess the goodness of fit of measured distributions to empirically observed trace length probability densities (exponential, e.g. Robertson 1970; lognormal, e.g. Barton 1978; hyperbolic, e.g. Segall & Pollard 1983). Furthermore, in order to test the significance of trace lengths conforming to a specific distribution, the Anderson Darling (AD) test statistic was calculated for each of the aforementioned probability densities (P) (Shorak & Wellner 1986). Based on the AD test criteria, the null hypothesis that the data come from a specific distribution is rejected if the P value is less than the α value of 0.05, with the optimally fitted distribution identified using the highest values of P (i.e. with a tendency towards P=1).
Fracture spacing and density
In addition to the truncation of discontinuity traces, a further bias introduced by scanline sampling procedures relates to fracture spacing. The apparent spacing of fractures orientated subnormal to the rock face is always greater than the true value, growing proportionally with increasing parallelism to the strike of the exposure (Terzaghi 1965). Having applied this procedure, corrected values of fracture spacing were then converted to linear fracture density (P10) using a reciprocal function. Finally, values of P10 for each set were converted to volumetric fracture density (Hitchmough et al. 2007). In the absence of evidence to the contrary, fractures were assumed to be four-sided polygons of constant aspect ratio (e.g. Hitchmough et al. 2007), with fracture area for each set taken as the square of the corrected mean trace length.
Discrete fracture network modelling
The purpose of fracture modelling in the present context is to assess the level of asymmetry in equivalent porous medium values between modelled networks derived using conventional and digital discontinuity datasets. The construction and upscaling of discrete fracture networks was conducted using the DFN module in the PETREL reservoir simulation software.
Faults with visibly determinable displacements and laterally continuous bedding-plane joints extending beyond the limits of the study area were modelled deterministically, with the geometrical arrangement of both structure classes delineated from merged point clouds via manual digitization (e.g. van Lanen et al. 2009) (Fig. 13). These elements were then used as the template for the structural base model within PETREL, with the geometry of the modelled domain defined by the lateral and vertical extent of the West Mine outcrop models. Smaller-scale structures determined using both manual and virtual methods were then modelled stochastically (Fig. 14), with the geometrical characteristics of predetermined fracture sets governed by the discontinuity statistics derived using the methods outlined in the previous sections (Table 3). A limit corresponding to the smallest measured trace length in each set was placed on fracture size, below which fractures were modelled implicitly. Further to this, randomly oriented fractures were not considered in the present workflow.
(a) Major faults and (b) bedding contacts in the West Mine interpreted from merged point clouds.
Discrete fracture network models generated in PETREL 2010 using (a) manual and (b) lidar-derived fracture statistics data.
Model parameters and corresponding inputs for the DFN procedure
The upscaling process requires the definition of other fracture attributes that are impractical or impossible to collect using digital-outcrop-based techniques (i.e. aperture/fracture permeability). A mean fracture aperture value of 400 μm was adopted, based on estimates by Hitchmough et al. (2007) for discontinuities developed in surface exposures of the Sherwood Sandstone Group within the Cheshire Basin. Fracture transmissivity was then obtained from values of mean aperture using the cubic law (Snow 1968), with fracture permeability subsequently calculated (e.g. Chesnaux et al. 2009). Finally, the Oda method (Oda 1985) was employed to upscale the DFN to equivalent porous medium properties across a 200×200×50 m grid composed of 25 m3 cells, with values of fracture porosity and permeability obtained for both fracture networks. A point of criticism that may be levelled at the Oda method is that it assumes that the upscaled fracture network is fully connected and may, therefore, overestimate the degree of communication within a modelled fracture array. However, whilst more sophisticated upscaling methods exist that provide a realistic account of fracture network connectivity (e.g. flow-based modelling: Chesnaux et al. 2009), the use of the Oda method in the present study is driven by the greater degree of computational efficiency that the procedure offers.
Results
Fracture set delineation
Manual scanline surveys and the areal survey of the West Mine outcrop model yielded 631 and 1377 individual orientation measurements, respectively, the results of which are displayed in Figure 15a. Stereographic density contour plots of poles to planes indicate the presence of three major sets within both manually and virtually derived fracture populations, namely: those containing east–west-oriented subvertical fractures; north–south-oriented subvertical fractures; and NE–SW-oriented subhorizontal fractures (Fig. 15b). Confirmation of these groupings is provided by way of cluster analysis, which indicates that 81 and 79% of the total fracture population (TFP) of manual and virtual datasets, respectively, fall within three major sets conforming to those described from density contour plots of orientation data (Fig. 15c):
Set 1: NE–SW-oriented subhorizontal discontinuity sets;
Set 2: north–south-oriented subvertical discontinuity sets;
Set 3: east–west-oriented subvertical discontinuity sets.
(a) Manual and virtual fracture orientations from all surveys projected as poles to planes. (b) Density contour stereonets displaying all manual and virtual fracture orientations. The density plots indicate the presence of three major fracture sets, namely: those containing east–west-oriented subvertical fractures; north–south-oriented subvertical fractures; and NE–SW-oriented subhorizontal fractures. (c) The results of cluster analysis, confirming the occurrence of the three major discontinuity sets described above. The inner small circle is the cone of confidence of Fisher (1953) of the direction of vector sum at the 99% confidence level. The outer red circle is the spherical aperture (Wallbrecher 1979), a measure of cluster variance. NB: Smaller clusters below 10% of the total fracture population are omitted.
Of these, Set 1 forms the dominant clusters within both fracture populations (41% of the TFP for both groups), with Set 2 accounting for 13 and 22% of manually and virtually derived populations, and Set 3 accounting for 27 and 16% of the equivalent manual and virtual orientation datasets, respectively.
Fracture orientation statistics
The results of the statistical analysis of manual and virtual fracture orientations are summarized in Table 4. Measures of cylindricity (ω) indicate that clusters from both manually and virtually derived sets are similarly distributed, with sets from both populations conforming to a von Mises–Fisher distribution (i.e. ω≤50% for all sets: Wallbrecher 1986). Furthermore, the calculated direction of vector sum indicates a strong agreement between the mean orientations of equivalent sets, with a maximum separation of only 7° in the horizontal plane (i.e. Set 3) and 3° in the vertical (i.e. Set 1), and with the direction of vector sum for Set 3 in the vertical plane being coincident. This is in addition to both measures of variance, which indicate that Set 1 has the least dispersion of all clusters from both populations, and Set 3 having the greatest. Measures of variance do, however, reveal notable differences between the two equivalent populations, with all clusters from the digital-outcrop-derived datasets exhibiting greater dispersion than their manually determined equivalents.
Summary of orientation statistics for manually and virtually derived fracture populations
Mean trace length, spacing and fracture density
A summary of calculated mean trace length, spacing and fracture density for both manually and virtually derived datasets is presented in Table 5. Values of uncorrected mean trace length derived from digital outcrop data are lower than their manually determined equivalents, with an average reduction in length of 24%. In similitude, product limit estimator corrected values of mean trace length are, on average, lower than those determined by manual scanlines (mean 11% reduction), although the Kaplan–Meier amended value for Set 1 was notably greater from the lidar population. However, this occurrence is an artefact of the correction procedure, where corrected mean trace length is restricted if the largest observed fracture is censured (Zhong & Hess 2009). Furthermore, geometrically corrected fracture spacing estimated from virtual scanlines is greater than measured from manual transects, with an average increase of 74%. As a result, volumetric fracture counts derived from digital outcrop data capture and analysis are, on average, 18% lower than values of P30 determined by conventional scanline surveys.
Calculated fracture trace length, spacing and density
Fracture trace length distributions
Visual assessment of frequency distributions from histograms indicates that the distribution of fracture trace lengths across a linear transect approximates to a lognormal distribution (Fig. 16). This qualitative assessment is confirmed by analysis of density distributions on probability plots (Fig. 17), with maximal P values corresponding to lognormal distributions for all recognized sets (Table 6).
Trace length frequency distributions from manual and virtual scanlines. Complete traces are fractures with both termination points discernable on the exposure surface, with censored traces being fractures with at least one termination point being obscured by the edge of the exposure.
Probability plots for the lognormal distributions of trace lengths measured from manual and virtual scanlines. The dashed black line is best of fit line to the data points, with solid lines representing the 95% confidence interval.
Summary of Anderson Darling (AD) test statistics and P values (lognormal distributions) for manual and virtual scanlines
However, the higher probability of longer traces intersecting the linear transects during scanline surveys results in a distribution that is skewed towards longer trace lengths. The lognormal distribution cannot therefore accurately represent the true trace length distribution across the areal extent of the rock exposures under investigation (Priest 1993, p. 161). Using the relationship between trace length distributions measured by linear transect and the areal distribution across the rock face presented by Priest (1993), we may infer that the lognormal trace length distribution calculated from the West Mine linear transect data equates to a negative exponential trace length distribution across the entirety of the rock face.
DFN petrophysical properties
Equivalent porous medium property values for upscaled discrete fracture networks are summarized in Table 7. Upscaled fracture porosity for manually and virtually derived fracture networks show broad-scale agreement, falling within the same order of magnitude. Nevertheless, fracture porosity is reduced for the DFN generated using digital outcrop data, being approximately a third lower than the discrete network constructed using data obtained from manual scanlines. Whilst upscaled values of fracture permeability in the three principle directions of anisotropy (ki, kj, kk) are also broadly comparable between both DFNs, lower values of k are observed from the network constructed using virtual fracture attributes, with a reduction in permeability ranging from 15 (ki) to 52% (kk).
Upscaled equivalent porosity and permeability generated for manually and virtually derived DFNs
Interpretation and discussion
The results from the study suggest that the application of high-resolution digital discontinuity analysis to exposures with geometries favourable to the extraction of geometric fracture attributes is able to produce datasets comparable to those collected using direct surveys. Furthermore, the approach presented here is capable of resolving fracture characteristics with sufficient fidelity to act as conditioning data for DFN models, making it a plausible alternative to conventional means of deriving inputs for fracture modelling workflows.
The comparison of set distributions from manual and virtual discontinuity datasets reveals excellent agreement, with the recognition of three orthogonally arranged major fracture sets in both cases also corresponding to observations made by Hitchmough et al. (2007), concerning the wider distribution of fracturing across the Cheshire Basin. The degree of equivalence between the mean orientations of the corresponding fracture sets is markedly high, exemplified by the diminutive maximal separation in 
, which in all instances falls within or marginally outside the estimated error for individual measurements made with a compass-clinometer (±2.5° vertical error and ±7.5° azimuthal error: Windsor & Robertson 1994). So, whilst ostensibly negligible, the magnitude of this deviation may in part be due to an apparent rotation in the digital outcrop-derived orientation data anticlockwise to the west (see Table 4, Fig. 15). Although having potentially resulted from perturbations in the local stress field and/or lithological variability across the horst (e.g. Finkbeiner et al. 1997; Yale 2003), the systemic nature of this anomaly suggests that it may be due to an error incurred during the alignment of the point cloud to magnetic north. Thus, the implementation of a more stringent referencing procedure (e.g. using a high-precision compass theodolite) may serve to increase the level of agreement between the two equivalent datasets.
There are, however, a number of noteworthy discrepancies between virtual and manual fracture orientation populations. For example, the proportion of the total fracture population assigned to Set 2 is considerably higher within the digital outcrop-derived dataset, with a corresponding reduction in the fraction of the TFP designated to Set 3. The more frequent occurrence of fractures from Set 2 within the virtual dataset may be attributed to the dominant strike of the West Mine (i.e. WNW–ESE), with the higher degree of orthonormality of north–south-oriented fractures to exposure walls resulting in a greater propensity for such discontinuities to be manifest on model surfaces (Terzaghi 1965). Therefore, in this instance, the results from manual scanline surveys are to be viewed as being a more reliable indicator of the true distribution of the fracture network, having been acquired from a more varied range of exposure orientations (Priest 1993).
Measures of variance (
/R%) suggest further divergence between the two orientation datasets, with the higher degree of dispersion within fracture populations derived from lidar data indicative of the lower degree of precision inherent to digital-outcrop-based analysis techniques. Whilst the rapid data acquisition rate of lidar-based methods facilitate the collection of statistically dense datasets, the increased level of dispersion is likely to impact on modelled network connectivity (Berkowitz et al. 2000), potentially resulting in the underestimation of simulated fracture permeability within a given fracture array.
The reduction in mean trace length, spacing and fracture density observed for virtual fracture sets signifies the introduction of uncertainties within the digital discontinuity dataset, and holds direct implications for the petrophysical character of resultant modelled networks. In addition to the degree of regimentation that exists within a fracture network, gross connectivity acts largely as a function of the size and intensity of fracturing (Berkowitz et al. 2000; Singhal & Gupta 2010), with the diminution of either parameter likely to result in the underrepresentation of network flow capacity.
The systematic underestimation of trace lengths from the lidar-derived triangular meshes within this study emanates from the apparent curtailment of fracture traces on outcrop model surfaces, resulting in the true termination points of discontinuities becoming irresolvable. Contrary to the curtailment of fracture trace lengths by exposure edges (Priest 1993), the presently described phenomenon is effective where fractures terminate within intact rock. Curtailment occurs when both the geometrical expression and the optical signature of the distal ends of fractures falls below the vertex–image-sampling interval of the representative outcrop model surface. The frequent occurrence of non-abrupt termination styles (i.e. crossing/blind: Barton et al. 1987) within the West Mine (e.g. Fig. 9g) makes this particular form of bias especially pervasive.
Further to this, the marked reduction in fracture density observed within the digital discontinuity dataset also relates to resolution-dependent censoring. Other authors have noted the truncation of fractures formed below some discrete minimum observable scale within lidar-based datasets (e.g. Sturzenegger & Stead 2009b), analogous to fracture network scaling problems recognized from remotely sensed imagery (e.g. Odling 1997). Whilst such effects are apparent on the West Mine outcrop models, the omission of discontinuities is commonly more selective, with the reduction in fracture spacing (and thus density) largely resulting from the exclusion of deformation bands in virtual scanline surveys. Although strongly manifest traces (e.g. large dilational fractures) are readily discernable from outcrop models with the aid of eigen-analysis-derived attributes, the limited areal thickness (i.e. <1 cm: Fowles & Burley 1994) of such features means that they occur at a scales below that of the resampled imagery, with their negligible surface expression inhibiting detection using surface displays of coplanarity.
The effects of resolution-dependent censoring are clearly evident in the upscaled DFN conditioned with virtual fracture attributes, with a broad-scale reduction in equivalent porous medium values apparent. The most striking discrepancy between the two fracture models is the markedly lower value of vertical permeability (kk) for the lidar-derived fracture network, resulting in a more laterally isotropic, vertically flattened permeability tensor. This divergence in network properties is due to the extensive diminishment in fracture area per unit volume for discontinuities aligned to kk, emanating from the combined censoring of fractures within Set 2 and Set 3.
Whilst providing general insights into the impact of censoring-related uncertainties on the petrophysical character of virtually derived fracture networks, the results of DFN upscaling should be treated with caution. The greatest deficiency of the modelling procedure relates to the representation of deformation bands, which, for the sake of parsimony, were modelled as open fractures. Given the commonly observed dilation of pore spaces associated with deformation bands in high-porosity sandstones (e.g. Fowles & Burley 1994), a more robust treatment of such features would involve their segregation from other fracture types and their representation as permeability baffles. The dominant occurrence of deformation bands as north–south- and east–west-oriented subvertical discontinuities within the vicinity of the present study area (Hitchmough et al. 2007) suggests that the omission of deformation bands from virtual scanlines would result in the lateral compression of the permeability tensor under this more stringent modelling schema. Therefore, the inability of current digital-outcrop-based methods to resolve such features in high-porosity faulted sandstones hold implications for reservoir modelling workflows, with models populated with virtual fracture attributes potentially incapable of realistically accounting for the degree of compartmentalization within a simulated reservoir interval.
Given both the curtailment and truncation of fractures described here acts largely as a function of image resolution, an obvious solution to limit the effects of censoring on digital outcrop models is to directly reference multiple high-quality images to the triangular mesh surfaces (Cline et al. 2011). However, the precise referencing of large quantities of optical remotely sensed data to triangular mesh surfaces is not a trivial exercise, with the extra time required during data capture and processing negating the advantage in data acquisition rate that lidar platforms offer. A more pragmatic solution may be to use field-based observations of the distribution of fracturing at the outcrop scale to supplement digital discontinuity datasets, with empirically derived statistical models of fracture network scaling (e.g. Odling 1997) potentially able to account for the resolution-dependent censoring of fractures from virtual surveys.
Conclusion
Digital outcrop data capture and analysis techniques provide powerful tools for the characterization of fracture systems developed within naturally fractured reservoir outcrop analogues. In this study, the enhanced data acquisition rate and extended coverage of exposure surfaces that digital-outcrop-based methods allow have been shown to increase the statistical size of fracture orientation datasets, with identified discontinuity sets demonstrating excellent agreement to those from manually obtained fracture populations. However, whilst the greater degree of accessibility to elevated rock surfaces that lidar analysis techniques permit may serve to limit the problems associated with conventional direct surveys (i.e. oversampling of the base of exposures/curtailment of fractures by the exposure edge), an additional suite of biases are introduced into digital discontinuity datasets, with fracture size and density systematically underrepresented. Although both fracture length and density are still broadly comparable between the equivalent datasets, the combined underestimation of both parameters has a significant impact on porosity and permeability estimates, increasing the degree of uncertainty associated with modelled fracture networks populated using virtual fracture attributes. Also, whilst the quantification of the relationship between outcrop model resolution and fracture system scaling in the future may enable these errors to be accounted for prior to the fracture modelling stage, this intrinsic uncertainty currently restricts the usefulness of lidar-based methods to generate inputs for fracture modelling workflows.
Acknowledgments
Initially undertaken as an undergraduate project, this project was completed as part of a PhD study funded by NERC and Total UK, whose financial support is gratefully acknowledged. The authors wish to thank the National Trust and their wardens for granting permission to conduct the research at their Alderley Edge site. Furthermore, the authors extend special thanks to members of the Derbyshire Caving Club (DCC) who provided access to the mines, as well as logistical support and guidance during our visits. More specifically, the vital role of D. Kidd is appreciatively recognized: acting as the liaison officer for the DCC, the work undertaken would not have been possible without his enthusiasm or commitment to the project. David Garcia Selles and Jonathan Imber are thanked for their helpful reviews. Finally, F. Rarity and A. Jonathan are thanked for their technical and logistical assistance.
- © The Geological Society of London 2014
References
Comparison of digital outcrop and conventional data collection approaches for the characterization of naturally fractured reservoir analogues
