Insights into the mechanics of en-
echelon sigmoidal vein formation
using ultra-high resolution photogrammetry and computed
Samuel T. Thiele
, Steven Micklethwaite
, Paul Bourke
, Michael Verrall
CET (M006), School of Earth and Environment, The University of Western Australia, 35 Stirling Highway, Crawley, WA 6009, Australia
iVEC@UWA (M024), Faculty of Engineering, Computing and Mathematics, The University of Western Australia, 35 Stirling Highway, Crawley, WA 6009,
Australian Resources Research Centre (ARRC), 26 Dick Perry Avenue, Kensington, WA 6151, Australia
School of Earth, Atmosphere and Environment, Monash University, Clayton, VIC 3800, Australia
Received 16 December 2014
Received in revised form
23 April 2015
Accepted 6 May 2015
Available online 15 May 2015
Two novel techniques, photo based reconstruction (photogrammetry) and computed tomography (CT),
are used to investigate the formation of an exceptional array of sigmoidal veins in a hand sample from
Cape Liptrap, Southern Victoria, and to provide constraint on models for their development. The accu-
racies of the photogrammetric models were tested by comparison with a laser scan generated three
dimensional (3D) model. The photogrammetric model was found to be accurate to at least 0.25 mm and
substantially more detailed than the laser scan. A methodology was developed by which 3D structural
measurements could be extracted from the photogrammetric model. This was augmented with the CT
model which, through its capacity to elucidate internal structure, was used to constrain the geometry
and linkage of structures within the rock volume. The photogrammetric and CT data were then combined
with detailed photomicrographs to evaluate the evolution of the sigmoidal veins in the sample.
The angle between the sigmoidal vein margins and an inferred shear zone, as well as the orientations
of the crystal ﬁbres, were found to imply a rotation of >27
. However coeval pressure solution seams and
older veinlets in the rock bridges between the veins were only found to have rotated by ~10
observation not easily explained using existing models for sigmoidal vein formation.
A new model is proposed in which a signiﬁcant component of sigmoidal vein geometry is due to
localised dilation caused by slip on the pressure solution seams. The process involves strain partitioning
onto pressure solution seams, which leads to exaggeration of sigmoidal vein geometries. If not accounted
for, the apparent vein rotation due to slip partitioning introduces errors into calculations of simple shear
and volume strain based on sigmoidal arrays of this type. Furthermore, the CT data demonstrated that in
3D the veins are continuous and channel-like, implying a far higher degree of connectivity and ﬂuid
transport than is suggested by their 2D form.
©2015 Elsevier Ltd. All rights reserved.
The development of faults and shear zones is a common
response to local and far-ﬁeld stress. Fracturing, ﬂuid ﬂow and vein
formation accompanying these processes are critical for the for-
mation of mineral deposits (Micklethwaite et al., 2010), and present
day manifestations of these processes provide important informa-
tion for interpreting the paleo-environments that have shaped
Sigmoidal veins are a class of en-
echelon vein characterised by
their unusual S or Z shaped geometry, and are common within
deformed sedimentary rocks (Beach, 1975). There has been
considerable uncertainty over the mechanisms controlling the
formation of sigmoidal veins (Beach, 1975; Nicholson and Pollard,
1985; Rickard and Rixon, 1983; Tanner, 1992), and hence how
best to interpret their signiﬁcance in terms of far-ﬁeld palaeostress
E-mail address: firstname.lastname@example.org (S.T. Thiele).
Contents lists available at ScienceDirect
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Journal of Structural Geology 77 (2015) 27e44
orientations, principal strain axes and strain evolution over time
(eg. Belayneh and Cosgrove, 2010; Lisle, 2013). Despite this uncer-
tainty, a simplistic model involving progressive rotation of exten-
sion veins forming within a shear zone (Beach, 1975) has become
established, and is largely accepted uncritically (eg. Davis et al.,
1996; Fossen, 2010; Twiss and Moores, 2007).
This study achieves two objectives. Primarily we examine the
formation of sigmoidal veins using a rock sample collected from
Cape Liptrap, Victoria, which contains a well-preserved sigmoidal
vein array. Secondly we demonstrate application of novel high-
resolution photogrammetric and tomographic methods to struc-
tural geology, examine accuracies of the photogrammetric models
and develop techniques for extraction of structural orientation
data. Photogrammetry and computed tomography (CT) techniques
are non-destructive imaging techniques that allow detailed struc-
tural information to be extracted in three dimensions (3D). In this
study, these techniques were applied to the Cape Liptrap sample
and a workﬂow developed by which uncertainties in the resulting
models could be assessed and 3D structure maps produced,
without damaging the integrity of the specimen. The 3D structure
maps were used to interpret the formation of the vein array,
including an assessment of the sample in the context of published
models for sigmoidal vein formation.
1.1. Geological setting
The study sample was collected from the Early Devonian Liptrap
Formation, exposed at Cape Liptrap in southern Victoria (Fig. 1a).
The Liptrap Formation is a turbidite sequence, comprising
competent carbonate-rich sandstone layers separated by incom-
petent, laterally continuous shale layers (Douglas, 1972; Gray et al.,
1999). The formation has been metamorphosed to lower greens-
chist facies, and is tightly folded and cut by small-displacement
reverse faults associated with the middle Devonian Tabber-
abberan orogeny (Gray et al.,1999; Lennox and Golding, 1989). Gray
et al. (1999) used microstructural and ﬂuid inclusion data to sug-
gest that folding of the Liptrap formation occurred at a depth of
~6e8 km and temperatures of 200e400
The study sample is approximately 45 cm long, 20 cm wide and
15 cm deep and is comprised of homogeneous carbonate-rich
sandstone with an isotropic, equigranular fabric (Fig. 1b). The
veins contained in the sample are ﬁlled with ﬁbrous and blocky
calcite. They occur at a range of scales, and are here classiﬁed into
three different categories, based on their thickness: veins less than
~1 mm thick are classiﬁed as veinlets, veins with thicknesses of
~1e5 mm as minor veins and veins with a thickness >5mmas
major veins. Only the major veins have developed sigmoidal ge-
ometries. These are accompanied by widespread narrow pressure
solution seams up to ~6 cm in length.
The composition of the sample suggests that it is derived from
one of the carbonate-rich sandstone layers in the Liptrap Forma-
tion, and it is reasonable to infer that it is related to the small
reverse faults developed in the folds, which are associated with
localised vein formation. Because the sample was not in situ when
collected, the original orientations of the veins are unknown.
1.2. Models of sigmoidal vein formation
Fractures forming under extension (Mode I) and shear (Mode II)
are expected to form roughly elliptical, planar structures in a ho-
mogeneous rock mass. As such, sigmoidal veins require special
Several models have been proposed for the formation of
sigmoidal vein arrays (Fig. 2). Beach (1975), drawing on prior work
by Shainin (1950) and Riedel (1929), proposed a kinematic model in
which Mode I fractures developing within an existing shear zone
become progressively rotated by simple shear, while their tips
continue to propagate parallel with the maximum compressive
stress axis, and hence develop a sigmoidal geometry (Fig. 2a).
Nicholson and Pollard (1985) presented an alternative me-
chanical model to demonstrate that the mechanical strength of the
rock bridges between adjacent veins can control vein dilation. As a
result, when planar, en-
echelon fracture arrays form and grow the
rock bridges between them can deform as independent beams,
progressively buckling under further stress and creating sigmoidal
vein dilation (Fig. 2b). In contrast to the previous model, this model
suggests that shear offset across the tabular zone occupied by
sigmoidal veins results from the vein growth and rock bridge me-
chanics, rather than the veins developing in a pre-existing shear
Finally, Pollard et al. (1982) and Olson and Pollard (1991) used
Linear Elastic Fracture Mechanics (LEFM) to demonstrate that
closely spaced propagating vein tips will interact with each other.
Olson and Pollard (1991) showed that this interaction alone can
cause sigmoidal fracture geometries (Fig. 2c), while Pollard et al.
(1982) provide a mechanism for generating en-
echelon vein ar-
rays outside of a shear zone, suggesting that they can form on the
margins of a ‘parent fracture’due to small spatial or temporal
changes in local stress ﬁelds.
The different models for sigmoidal vein formation can be
distinguished by predictions they make regarding vein geometry,
ﬁbre orientations and deformation of the rocks surrounding the
veins (Table 1). These predictions were tested against the structures
observed in the Cape Liptrap sample.
Fig. 1. Schematic geology map of the Cape Liptrap region (a), including the location
from where the study sample (b) was collected. Modiﬁed from Janssen et al. (1998).
S.T. Thiele et al. / Journal of Structural Geology 77 (2015) 27e4428
Photogrammetry is a method by which photographs of an ob-
ject, captured from two or more positions, are used to extract 3D
information. Stereophotography, used extensively and for many
years by cartographers and geologists, is a form of photogrammetry
(Bemis et al., 2014).
Recent improvements in digital photography and the develop-
ment of a computational technique called Structure from Motion
(SfM, Sturm and Triggs (1996)) has allowed the generation of fully
3D models from spatially unconstrained imagery (Bemis et al.,
2014). This technique gives geoscientists a much needed method
to objectively and quantitatively capture 3D form and texture in
SfM algorithms identify common points between image pairs in
a set (Lowe, 2004), calculate lens parameters such as focal length
(Pollefeys et al., 1999), and then calculate the relative 3D location
and orientation of each camera and matched feature using an
optimization process known as ‘bundle adjustment’(Triggs et al.,
2000). This produces a 3D point cloud from which a textured
mesh can be built using triangulation techniques (Fabio, 2003) and
projection of the original images onto its surface. Illustrated details
of the method and its application to structural geology are pre-
sented in Bemis et al. (2014).
However for this data to be useful it is necessary to ﬁrst assess
the accuracy and resolution of the photogrammetric model. For this
reason, several independent photogrammetric datasets represent-
ing the 3D form and structure of the Cape Liptrap sample were
compared with each other and with a reference dataset derived by
laser scanning. A computerised tomography (CT) scan was also
generated to help constrain the geometry of structures within the
2.1. Data collection
2.1.1. Sample preparation
Accurate scaling of photogrammetric models requires spatial
reference points with known locations (Bemis et al., 2014; Favalli
et al., 2012). These reference points also help avoid distortions
during photogrammetric processing. For this study, 25 reference
points evenly distributed over the sample surface were used to
spatially reference the photogrammetric models. Distances be-
tween each reference point were measured using a pair of elec-
tronic callipers accurate to ±0.01 mm. A plastic scale plate with
small metal bolts glued to it was also attached to the rock, to allow
alignment of the CT-scan (see below) with the photogrammetric
Four different sets of photographs of the sample were taken in
order to trial different photographic techniques and ensure a highly
accurate model was produced. Photoset 1 was captured using a
Canon EOS 5D Mark III DSLR camera with a 100 mm ﬁxed focal
length lens, and comprised photographs taken in strips 10
the sample was rotated about both its long axis and an orthogonal
axis on a rotating stage ﬁtted with a 10
ratchet. Diffuse lighting
Fig. 2. Models of sigmoidal vein formation. (a) The kinematic model of Beach (1975) with veins, originally parallel to the maximum principal stress axis, rotating under simple shear
within a shear zone. The sigmoidal shape forms as vein tips continue to propagate parallel to the principal stress axis. (b) Mechanical model of Nicholson and Pollard (1985),
showing progressive buckling of rock bridges between veins, which then induces a component of shear to the rock mass. (c) Mechanical model of Olson and Pollard (1991), showing
sigmoidal geometry formed by fracture-tip interactions between fractures in a growing en-
Model predictions for vein formation regarding vein geometry, deformation within rock bridges separating veins and orientation of vein ﬁbres. Note that while the speciﬁc
orientation of vein ﬁbres will depend on the opening mechanisms of the veins, in the criteria listed the ﬁrst-order orientation/misorientation is assumed to be tracking vein
opening and deformation.
Model Vein geometry Deformation of rock bridges Vein ﬁbres
Beach (1975) Central portions of veins misoriented with
respect to far ﬁeld stress.
Rock bridges deformed by shearing; older
structures and fabrics in rock bridges are
rotated by the same amount or more than vein
Vein ﬁbres rotated with veins;
vein ﬁbres oriented
perpendicular to vein walls.
Nicholson and Pollard (1985) Overlapping portions of vein walls misoriented
with respect to far ﬁeld stress.
Rock bridges buckled due to vein dilation; older
structures and fabrics in rock bridges are
rotated by the same amount as vein walls.
Vein ﬁbres oriented obliquely
to vein wall across misoriented
Olson and Pollard (1991) Tips of veins misoriented with respect to far
No rotation of older structures in rock bridges;
vein tips will crosscut older structures and
Vein ﬁbres oriented
perpendicular to vein walls.
S.T. Thiele et al. / Journal of Structural Geology 77 (2015) 27e44 29
was employed to avoid shadows. The camera was mounted on a
tripod so that suitable exposure times (~1 s) could be used and to
avoid motion blur. The extremities of the sample were captured
using an unmounted camera. Each image frame covered a surface
area of approximately 8 10 cm with a ~1/3 overlap with adjacent
images. A total of 516 photographs were captured, concentrated
around the vein set (as this is the area of interest in the sample).
Since the sample has a complex 3D morphology it was not
possible to fully focus some portions of the images. To minimize
this problem, photographs were captured using small apertures (F-
stop 17) to maximise depth of ﬁeld.
Photosets 2e4 were captured by mounting the sample on a
stationary clamp and photographing it from different locations,
maintaining ~30% overlap between images. Photosets 2e3were
generated using the Canon EOS while Photoset 4 was captured
using a Canon PowerShot S95 simple compact digital camera. In all
three cases, because the camera and tripod had to be moved be-
tween each image, the number of photographs that could be taken
was limited due to time constraints, hence limiting the amount of
detail that could be resolved from the photoset. Photosets 2, 3 and 4
contained 307, 52 and 87 photographs respectively.
2.1.3. Laser scanning
3D laser scanning, a technique whereby a laser beam is used to
accurately measure the location of a grid of points on the surface of
an object, was performed at 2000 dpi using a NextEngine 2020I
HD™laser scanner, which has a reported accuracy of 0.127 mm
(Slizewski and Semal, 2009). A total of 15 scans were done, each
from different angles.
A series of high resolution photomicrographs were captured of
the veins in order to properly resolve cross-cutting relationships
between the different vein generations and pressure solution
seams. These were captured using an arm-mounted Leica 6D
stereo-microscope ﬁtted with a Nikon DS-Fi2 camera. Focus
stacking, a technique for enhancing depth of ﬁeld by combining
multiple images (Piper, 2010), was used in many of the photographs
to avoid signiﬁcant focal blur caused by the limited depth of ﬁeld of
A photogrammetric model, generated from a grid of photomi-
crographs of selected veins was also created. In order to avoid
systematic artefacts such as subtle concave distortions (James and
Robson, 2014), the photomicrograph grids were captured with
the camera in both landscape and portrait orientations (Bemis et al.,
2.1.5. CT scanning
The sample was scanned using a Siemens SOMATOM Deﬁnition
AS 64-slice medical CT scanner, in 1275 slices using an X-ray beam
generated at 120 kV and 500 mA. The volumetric resolution of the
resulting model was 512 512 1275 voxels, each 0.5 mm
. Due to
high noise levels in the dataset the CT scan was subsampled by a
factor of two, producing a ﬁnal smoothed tomographic model with
2.2. Data processing
Photogrammetric models were constructed using the commer-
cial software package Agisoft Photoscan™. Processing time was
reduced by running the software on a PC with 256 GB of RAM, 48
Intel Xeon E5-2697 (2.7 GHz) processors, and NVIDIA Quadro
K5000 and Tesla K20c graphics cards.
After loading images, all out-of-focus and background regions
were manually masked out to improve point matching accuracy.
Photographs were then aligned in 3D space, and a sparse point
cloud generated. Models containing reference points were spatially
referenced by manually locating the points in the images and
constraining distances between them using the measured values.
The sparse point cloud was then densiﬁed to produce a signif-
icantly higher resolution dense point cloud, which was used to
construct a triangulated mesh representing the estimated geome-
try of the sample's surface. Meshes with large numbers of elements
were simpliﬁed by decimation to contain 1 million triangles, so that
they could be rendered and manipulated on an ordinary PC.
“Texture mapping”improves the information represented by
triangulated meshes by projecting the original 2D photographs
onto the 3D mesh surface, to produce a surface containing detail
and colour not captured by the geometry alone. Because texture
quality is sensitive to poor-quality and unfocused images, low-
quality photographs were removed from the dataset and
extended masks used to remove unfocused portions of the photo-
graphs before generating the textures.
A photogrammetric model was constructed in this way from
each of the four Photosets. Model A was derived from Photoset 1
(516 images). Initial camera alignment produced a sparse point
cloud of 1,497,646 points in ~5hrs of processing. The dense point
cloud comprised 210, 118, 817 points generated in ~11hrs. The
dense point cloud was used to generate two meshes, one of the
whole sample and one of the area of interest (the vein set) only.
Both meshes were decimated to 1 million triangles.
Models B and C were derived from Photosets 2 and 3 respec-
tively. Model B was derived from 307 photographs with the mesh
decimated to 1 million triangles as in Model A. Model C was derived
from 52 photographs, but only captured the region of the sample
containing the sigmoidal vein set.
Model D was derived from the 87 photographs in Photoset 4.
This model had 98,803 vertices and 197,215 triangles.
Finally, the grid of 45 photomicrographs was used to produce a
model comprising 2,325,997 points. The textured mesh produced
from this point cloud contained 466,970 faces and 234,381 vertices.
2.2.2. Comparison maps
Laser scans were aligned using ScanStudioHD Pro™and then
merged using ArtecStudio9™to produce a complete model of the
rock with 376,875 vertices and 753,746 faces. Photogrammetric
models were compared to the laser scan model using a method
similar to that of Favalli et al. (2012). The composite laser scan was
aligned with each of the photogrammetric models, using the Align
tool in Meshlab (Cignoni et al., 2008) and differences calculated
using the open source tool Metro (Cignoni et al., 1998).
Metro writes the distance between the two meshes being
compared to each vertex, allowing the creation of difference maps.
Conveniently, Meshlab has a ‘Mesh Quality’tool that was used to
map different colour ramps to these vertex values and produce
coloured difference maps.
Histograms describing the area of each mesh with nominated
error values were also generated, and used to calculate mean ab-
solute error (MAE) and a scale invariant percentage error (%Err)
derived by dividing the MAE by the average linear dimensions of
the model. Root mean square error (RMSE) was not used to
compare the models (c.f.Favalli et al., 2012) because RMSE varies
with both average error magnitude and error variance, giving too
S.T. Thiele et al. / Journal of Structural Geology 77 (2015) 27e4430
much weighting to higher error values (Willmott and Matsuura,
2.2.3. CT segmentation
The open-source software package Drishti (Limaye, 2012),
developed for manipulating and rendering 3D tomographic data-
sets, was used to segment the CT scan into veins, pressure solution
seams and background. Due to the low density contrast between
the host rock and calcite vein ﬁlling, segmentation could not be
performed automatically. Instead, each horizontal slice within the
tomographic model was manually interpreted and voxels classiﬁed
as host rock, vein ﬁll or containing substantial pressure solution.
This method of segmentation was sufﬁcient to determine the
general form of the structures in 3D space.
2.3. Structure mapping
A 3D map interpretation of the sigmoidal vein set and associated
veinlets, pressure solution seams and crystal ﬁbres was created
using the most accurate photogrammetric model (Model A).
Because of the 3D nature of the sample, two dimensional (2D) GIS
software such as ArcGIS was not appropriate to perform the map-
ping. Instead, the open source 3D-graphics package Blender (www.
blender.org) was used.
Structures were digitised in Blender using the Grease Pencil tool
to project lines onto the surface of the photogrammetric model,
producing a 3D representation of structures exposed on the surface
of the sample. A Python script (provided in the Supplementary
Materials) was written to export these features to CSV format so
they could be interpreted in other software such as ArcGIS™or
OpenStereo (Grohmann and Campanha, 2010).
2.4. Extraction of planes
Because the surface of the Cape Liptrap sample is not planar, it is
possible to extract 3D orientations from selected points along
structures mapped onto its surface, relative to an arbitrary coor-
dinate system; akin to the classic ‘three-point problem’.AJava
application was developed (provided in the Supplementary
Materials) that estimates a plane of best ﬁt for features in the
structure maps using an implementation of the Random Sample
And Consensus (RANSAC) algorithm (Fischler and Bolles, 1981).
The Java application takes CSV ﬁles containing sets of edges
(deﬁned by two vertices) and builds them into multi-segment lines
based on shared vertices (Fig. 3a). Each line is then divided into
samples (Fig. 2b) of 500 vertices (or less at the tips), a length of
~5 mm. For each of these samples the second and third largest
principal components (C
) are calculated and used to assess
the planarity (P) of the data using:
Samples that perfectly deﬁne a plane have planarity ¼1 (as
¼0), while samples representing either a line or random point
cloud have planarity ¼0asC
either approach zero or are
equal. If planarity is deemed to be sufﬁcient (P>0.75) the sample is
processed using the RANSAC algorithm to produce a plane of best
In this context, the RANSAC algorithm functions by iteratively
calculating the number of points (inliers) that ﬁt within a threshold
distance (0.1 mm) of a plane deﬁned by three randomly selected
points. Random planes are tested until the number of trials (N)
exceeds that required to be statistically conﬁdent the ‘correct’plane
has been tried at least once (Eq. (2)), given the greatest number of
inliers so far achieved (i) and total dataset size (n). The model with
the greatest number of inliers is then returned as the estimate of
the plane of best ﬁt.
Finally, in order to remove some of the random variation
introduced by using a stochastic estimation technique, the model is
further reﬁned by performing least squares regression on the
samples deemed to be inliers by the RANSAC algorithm (Fig. 3f).
Because many of the surfaces of the sample (and hence also the
photogrammetric model) are ﬂat, and some of the veins are not
perfectly planar, this method generates a few false orientations,
sub-parallel with the surface of the sample. These data were not
removed however, as they are relatively few in number and they do
not signiﬁcantly inﬂuence the statistics.
2.5. Measurement of wall-ﬁbre angles
Angles between vein walls and the calcite ﬁbres were measured
manually using the 3D model and a protractor-like tool in Blender.
Angles were all measured clockwise from the vein wall to the ﬁbre,
so that the wall-ﬁbre angle is consistent on either side of the vein. A
Python script was used to export the angles and their locations toa
CSV ﬁle for analysis.
3.1. Photogrammetric model accuracy
Comparisons between photogrammetric models and the laser
scan model (Fig. 4) showed that Model A (Figs. 4e7) was the most
accurate, with MAE ¼0.59 mm and percent error of 0.22%. It is
worth noting that much of this 0.22% error is derived from the two
ends of the sample, which were not a focus of this study and hence
photographed in less detail. The corners of each model generally
have the lowest accuracies (Fig. 4). Likewise, small errors in the
orientation of planar faces appear to cause gradual increases in
error, such as is observed on the front face of Model C (Fig. 4). Errors
are all less than 0.5%, which is equivalent to the results reported by
Favalli et al. (2012).
Mapping the x, y and z components of the normal of each mesh
element to red, green and blue colour values enables visual rep-
resentation of the geometric detail of each model (Figs. 4 and 5).
The geometric detail captured by each model increases with the
number of photographs. Topographic features such as weathered
pressure solution seams are represented much more crisply in
Model A; indeed, the resolution of Model A is sufﬁcient that some of
the vein ﬁbres are discernible in the normal map alone (Fig. 5).
The majority of the face containing the sigmoidal veins in Model
A is accurate to within ~0.25 mm (Fig. 5). Apparent errors around
the margins of the veins and within small pits on the model surface
arise because the photogrammetric model resolves these features
in much ﬁner detail than the laser scan (Fig. 5). This observation
suggests that Model A potentially has greater accuracy than the
laser scan, although there is no quantitative method for verifying
this at the present time.
The texture for Model A is also superior to the other models.
Model B and C have somewhat blurry texture maps, while the
lighting and contrast of the texture maps produced for Model D
make it difﬁcult to resolve features such as vein ﬁbres. The texture
map produced for Model D was also somewhat lower resolution (as
were the images used to produce it).
S.T. Thiele et al. / Journal of Structural Geology 77 (2015) 27e44 31
Fig. 3. Schematic diagram illustrating the process used to extract planes from the 3D structural maps. The intersection of each structural feature and the specimen surface is
represented by a series of linked vertices (a). Note that the roughness of this line has been exaggerated for illustrative purposes. A subset of speciﬁed size (n ¼14) is taken from this
dataset (b) and its principal components (C
) calculated. The principal components are used to evaluate planarity (p, Eq. (1)). When P >0.75, a plane is ﬁtted to the data
using the RANSAC algorithm (Fischler and Bolles, 1981). Individual trials (c), (d) and (e) select three random points and calculate the number of points falling within a threshold
distance of the plane they deﬁne (inliers). The required sample size (N) to be 99% sure the correct plane has been trialled at least once is calculated based on the probability (p) of
choosing three inliers. Once the number of trials is equal to the smallest N, the plane with the greatest number of inliers (d) is used to calculate a ﬁnal plane, by least squares
regression after removing outliers (f).
S.T. Thiele et al. / Journal of Structural Geology 77 (2015) 27e4432
Fig. 4. Accuracy and quality of the photogrammetric models. Error maps show the differences between the photogrammetric and laser scan models. A render of the laser scan is
included as Fig. 5a. Normal maps created by mapping the x, y and z values of each faces normal to red, green and blue colour values show the detail of the underlying mesh, while
the texture maps show the quality of the textures. Note that the close-up of the texture has been rotated. Model A is clearly the most accurate, with lower MAE values than all the
other models and a ‘crisper’normal map. The texture quality of Model A is also superior to the other models, without obvious pixilation or distortion. (For interpretation of the
references to colour in this ﬁgure legend, the reader is referred to the web version of this article.)
S.T. Thiele et al. / Journal of Structural Geology 77 (2015) 27e44 33
Veins, crystal ﬁbres and pressure solution seams are clearly
resolvable in the photogrammetric models (Fig. 6). These structures
were mapped, and measurements of their orientations extracted at
selected points along their surfaces, as well as their relationships
with crystal ﬁbres (Fig. 7). A reference frame was deﬁned such that
the top of the sample represented north (top of Fig. 7) and the
surface containing the sigmoidal veins deﬁned as horizontal. The
orientations of major and minor veins were acquired along both
sides of the veins (e.g. two lines per feature), while veinlets were
measured along a single line. The surface traces of the crystal ﬁbres
and pressure solution seams were also mapped as lines, although
the location of the pressure solution seams is often rather imprecise
due to their irregular geometry and because they are preferentially
eroded. Planar orientations for many of the veins and pressure
solution seams were successfully extracted using the RANSAC
method outlined above.
3.3. Structure orientations
3.3.1. Vein and pressure solution seam orientation
Calculated vein and pressure solution seam orientations are
plotted as poles in Fig. 7. The eigenvectors of these data were used
to estimate population means (Allmendinger et al., 2012), which
are presented in Table 2 and on the stereonets in Fig. 7.
Orientation data collected for the pressure solution seams
contained considerable variation, due to their irregular structure
and difﬁculties mapping their precise location. Notwithstanding
this, the pressure solution seam poles form broad clusters around
. These orientation clusters correspond with
trends evident in the structure map (Fig. 7). The mean orientation
of the pressure solution seams is approximately perpendicular to
the vein orientations. The 95% conﬁdence intervals for the mean
orientation of the major veins, minor veins and veinlets overlap,
and hence they cannot be considered to have signiﬁcantly different
orientations. The average orientation of all the veins in the sample
An envelope was deﬁned around the vein array based on a
systematic coincidence of vein tips, sudden changes in orientation,
shear offsets and zones of increased dilation (Fig. 8a). This envelope
is interpreted to represent the boundaries of a zone of incipient
shear, and is divided into zones of maximum, intermediate and
minor apparent rotation.
The intersection angles between calculated structure orienta-
tions and the interpreted shear zone have been calculated. Because
structure orientations could only be extracted from areas with
topographic relief this data has been complemented with angles
measured in 2D. These angles were measured at 2 mm intervals
Fig. 5. Maps of the laser scan model (a) and photogrammetric Model A (b) created by mapping the x, y and z component of each mesh elements normal to the red, green and blue
channels of the face colour. Subtle features such as calcite ﬁbres within the veins and the thickness of the reference marker are clearly visible in the photogrammetric model,
whereas the laser scan model contains signiﬁcantly less detail. Many of the differences between the laser scan and photogrammetric model (c) could simply result from this
difference in resolution, suggesting that the photogrammetric model is more accurate than the laser scan. (For interpretation of the references to colour in this ﬁgure legend, the
reader is referred to the web version of this article.)
S.T. Thiele et al. / Journal of Structural Geology 77 (2015) 27e4434
from the zone centre (Fig 8a). Because the main face of the sample
approximates a proﬁle section through the array, these angles
approximate the true angle of intersection.
These structure-shear envelope angles, displayed as boxplots in
Fig. 8b, suggest that structure orientations change systematically
across the vein array. Average structure-envelope angles have been
used to calculate the amount of apparent rotation that would be
required to explain the changes in vein orientation across the shear
envelope (Table 3). The orientations of both the non-sigmoidal
veins (minor veins and veinlets) and pressure solution seams
suggest that they have rotated by ~10
on the front face of the
specimen toward the centre of the shear envelope. By contrast, the
sigmoidal veins have substantially greater apparent rotations of
. Many portions of the sigmoidal veins have apparent rotations
3.3.2. Vein ﬁbre orientation
Individual crystal ﬁbres within the sigmoidal veins can be
tracked across the full width of the veins (Figs. 7 and 9), suggesting
that the ﬁbres are roughly oriented within the mapping plane (i.e.
they do not plunge in and out of the surface of the sample). Hence
the mapped orientation approximates the orientation of the long
(c)-axis of the crystals themselves. These ﬁbres generally trend
perpendicular to the veins; however, there is substantial variation
within the population. This variation appears to be spatially
controlled (Fig. 9), with the mean orientation of vein ﬁbres equal to
in vein tips and 070
within vein centres (a difference of ~28
Many individual ﬁbres in the vein centres are oriented at >40
ﬁbres in the vein tips, trending close to 090
The angle between vein ﬁbres and vein walls also varies
spatially. Fibre-wall angles are generally equal to 90
, but there is a
marked divergence from this relationship where the sigmoidal vein
walls bend sharply (Fig. 9).
3.4. Overprinting relationships
Overprinting relationships were examined at millimetre scales
using the photomicrographs and photogrammetric models
Fig. 6. Renders of the front (a) and back (b) of Model A, generated from a set of 516 images with the ﬁnal mesh decimated to 1 million faces. This model has the highest accuracies,
and was the model selected for interpretation. The vein array of interest and the associated pressure solution seams are clearly resolvable. The model was scaled and distortions
minimised through the use of orange markers, where the distances between each marker were accurately constrained using electronic calipers. (For interpretation of the references
to colour in this ﬁgure legend, the reader is referred to the web version of this article.)
S.T. Thiele et al. / Journal of Structural Geology 77 (2015) 27e44 35
constructed from them (included as Supplementary Material).
These relationships were integrated with the macro-scale photo-
grammetric models to interpret the relative timing of structures
observed in the sample.
Representative photomicrographs illustrate systematic cross-
cutting relationships observed between the various vein types and
pressure solution seams (Fig. 10). Most pressure solution seams
crosscut the veinlets and minor veins (Fig. 10beg, i and j), whereas
only a few were observed crosscutting the larger sigmoidal veins.
The sigmoidal veins also crosscut veinlets and minor veins in
several locations (Fig. 10aef and j). Only one location was observed
where a veinlet appears to crosscut one of the sigmoidal veins
(Fig. 10h), though this observation is somewhat ambiguous.
Many of the overprinting relationships observed between the
minor veins and pressure solution seams are mutually crosscutting,
with minor veins often crosscut by several pressure solution seams,
partially crosscut by some, and crosscutting others. The pressure
solution seams often appear to separate zones that have undergone
varying amounts of strain, or that have accommodated strain in
different ways. For example, some domains develop many fractures
with small dilations whereas others develop fewer fractures with
larger dilations (eg. Fig. 10f and i, Fig. 11).
3.5. Vein geometry
Integration of the photogrammetric and CT models provides
detailed constraints on the 3D geometry of the major veins and to a
lesser extent the pressure solution seams within the sample.Blocky
calcite vein ﬁlling is associated with increased x-ray attenuation
while ﬁbrous calcite ﬁlling results in decreased x-ray attenuation
(Fig. 12aec). Pressure solution seams are also expressed in the CT
data, as faint but distinct bands of increased x-ray attenuation
(Fig. 12a). Interpretation of these structures allowed the construc-
tion of a 3D polygonal hull representing the vein set and some of
the associated pressure solution seams (Fig. 12d).
The vein set exposed on the top surface of the sample (Figs. 6a
and 7) is dominated by large, sigmoidal veins. The central sec-
tions of these veins are oriented obliquely to their tips, inclined in a
clockwise direction. These veins also appear to have undergone
substantially more dilation towards the centre of the shear zone
Fig. 7. Structure maps created using the front (a) and back (b) of photogrammetric Model A. Veins are divided into three sets: major (light green), minor (dull green) and veinlets
(dark green). Pressure solution seams are shown in red and vein ﬁbres in grey. 3D structure orientations extracted from these maps are shown in (c) and (d). Pole orientations have
been contoured using the Kamb Method at intervals of 2
and a signiﬁcance of 3
. Note that poles plotting towards the centre of each stereonet are likely artefacts introduced by
the plane-ﬁtting algorithm, and do not represent the true orientation of veins. (For interpretation of the references to colour in this ﬁgure legend, the reader is referred to the web
version of this article.)
Mean structure orientations based on planes extracted from the structure maps using RANSAC. The 95% conﬁdence interval around each mean is also shown, as is the sample
size (n). A 95% conﬁdence interval was not calculated for minor veins as the sample size (14) is not large enough to produce a meaningful result.
Statistic Veinlets Minor veins Major veins Pressure solution seams
Mean orientation 310.1
95% Conﬁdence interval ±6.2
S.T. Thiele et al. / Journal of Structural Geology 77 (2015) 27e4436
hosting the array than at its margins (Figs. 7 and 8). A large number
of pressure solution seams are present around the veins (Fig. 7), and
are more intensely developed towardsthe centre of the shear zone.
These pressure solution seams can extend beyond the bounding
envelope of the vein array. In a few places, seams of different ori-
entations link together and form polygonal networks.
The CT model suggests that about 4.5 cm into the sample the
pressure solution seams disappear and the vein set changes
dramatically. One vein disappears altogether, while the two largest
sigmoidal veins merge (Fig. 12a, c and d). Below this point the veins
appear much more planar. Finally the vein geometry approaches
the relatively planar, non-sigmoidal geometry observed on the
bottom face of the sample (Figs. 6b and 12a and d). Signiﬁcantly, the
geometry of the veins in 3D resemble channel-like structures that
are continuous beyond the dimensions of the sample.
The minor veins and veinlets in the sample are generally planar.
The photomicrographs highlight complex interactions between
these veins and the pressure solution seams on the front face of the
sample. Many of the veins undergo large changes in dilation where
they are crosscut by pressure solution seams (Fig. 11), and many
veins also appear to be truncated by the pressure solution seams
(Figs. 10i and 11d). Fig. 11 also shows that some of the pressure
solution seams have developed shear offset. While these offsets are
not always dextral (eg. Fig. 11a), the offsets are kinematically
consistent with the overall shear zone. Offsets do not appear to
have developed outside of the sigmoidal vein array.
The amount of offset across pressure solution seams appears to
be controlled by orientation; offsets are only observed on seams
that are not perpendicular (>±10
difference) to the sigmoidal vein
tips. These relationships are interpreted to arise from slip parti-
tioning where shear strain resolves along the pressure solution
seams but the microlithons between the pressure solution seams
undergo extension parallel with the movement direction.
Offsets on the pressure solution seams also appear to affect the
sigmoidal veins (Fig. 13). Sections of the sigmoidal veins with
substantially different orientations correlate with intersecting
pressure solution seams and changes in vein aperture.
Fig. 8. Mean intersection angles between structures and the interpreted shear envelope. (a) The intersection angles of each major (sigmoidal) vein wall (bright green dots), minor
vein (dull green dots), veinlet (blue dots) and pressure solution seam (PSS, red dots) were measured in each portion of the shear envelope. Note that for clarity only the three well-
developed sigmoidal veins have been included. (b) Boxplots show that the intersection angle the structures tend to increase towards the centre of the envelope, however not by the
same amount. The orientation of the sigmoidal vein walls increases by an average of 27towards the centre of the shear envelope, whereas the orientations of the veinlets, minor
veins and PSS only increase by 7,11
and 12respectively (Table 3). (For interpretation of the references to colour in this ﬁgure legend, the reader is referred to the web version of
Mean intersection angles between structures and portions of the shear envelope
(Fig. 8). Structures outside or within the outer portion of the shear envelope (outer)
are considered to represent the initial orientation of structures within the centre of
the shear envelope (inner). Hence, the difference between the mean inner inter-
section angle and mean outer intersection angle gives the apparent rotation that the
structure has undergone within the shear zone. The.
Structure Mean intersection angle Apparent rotation
Outer Middle Inner
Minor veins 40
Pressure solution seams 62
Sigmoidal veins 37
S.T. Thiele et al. / Journal of Structural Geology 77 (2015) 27e44 37
4. Discussion eformation, dilation and linkage of sigmoidal
Structural mapping, photomicrographs and computed tomog-
raphy have allowed an interpretation of the processes that led to
the development of the observed vein array. These processes must
explain the geometry of the sigmoidal veins on the top face of the
Cape Liptrap sample, their transition and linkage to form essen-
tially planar veins on the bottom face of the sample and the
inconsistent distribution of pressure solution seams and veinlet
damage in an otherwise apparently homogeneous rock mass.
Furthermore these processes must explain the ~10
non-sigmoidal vein and pressure solution seam orientation across
the array, in contrast to the adjacent >27
change in orientation of
the central portion of the sigmoidal veins and the >40
calcite ﬁbre orientations.
Overprinting relationships allow the relative timing of the last
increment of strain on each structure in the sample to be
established (Fig. 14). The veinlets represent the earliest episodes
of strain, as they are crosscut by all other structures (with a
possible single exception), potentially accompanied by coeval
pressure solution. Progressive deformation led to the develop-
ment of minor veins as strain increased. Dilation of these veins
appears to have been accommodated by partitioning of slip along
pressure solution seams, giving the appearance of extreme
truncation (Figs. 10i and 11d). Finally, the large sigmoidal veins
developed, crosscutting minor veins, veinlets and pressure so-
lution seams in several locations (Fig. 10bed, f, and j). In a few
locations these sigmoidal veins are in turn crosscut by some of
the major pressure solution seams, indicating that activity on
some of the pressure solution seams continued to develop after
vein formation had ceased.
This sequence of events suggests that strain in the array has
progressively localised onto fewer, but larger, structures through
4.2. Constraining models of sigmoidal vein formation
The structural data collected from the photogrammetric and CT
models allow predictions of different models for sigmoidal vein
formation (Table 1) to be tested.
Vein linkages observed in the CT model suggest that in-
teractions between the veins have occurred, however this cannot
explain the geometry of the sigmoidal veins as in the vein-tip
interaction model of Olson and Pollard (1991).Theveintipsof
sigmoidal veins formed by this mechanism will be misoriented
with respect to the far-ﬁeld stress, not vein centres (Table 1). The
similar orientation of the early formed veinlets, the major planar
veins observed on the bottom face of the sample and the tips of
the sigmoidal veins suggest that they were oriented parallel to the
maximum far ﬁeld stress orientation, and it is the sigmoidal vein
centres that became misoriented. Furthermore, vein-tips of
sigmoidal veins formed by a vein-tip interaction mechanism
would be expected to crosscut older structures such as the vein-
lets. This was not observed.
Similarly, the sigmoidal vein geometries could also be attributed
to a counter-clockwise rotation of the far-ﬁeld principal stresses
that occurred during the evolution of the vein array. However if this
were the case, the sigmoidal vein tips would not be sub-parallel to
the older veinlets, as has been observed.
The model of Beach (1975) attributes the geometry of sigmoidal
veins to progressive rotation of propagating veins during shearing,
and requires that any older structures in the shear zone also be
rotated (Table 1). The change in orientation of structures across the
shear zone (Fig. 8) suggests that progressive rotation of this type
may have occurred; however this rotation cannot have exceeded
rotation recorded by the older veinlets, minor veins and
pressure solution seams (Table 3). The orientation of the central
portions of the sigmoidal vein walls and >40
range in orientation
of many of the crystal ﬁbres observed in the central portion of some
of the veins (Fig. 9) requires substantially more than a 10
This suggests that another process is exaggerating the geometry of
the veins while not causing further rotation of older structures in
the rock, and that while rotation may be partially responsible for
Fig. 9. Spatial variation in vein ﬁbre orientation. Vein ﬁbres are coloured by deviations from their average orientation in vein tips. The crystal ﬁbres in the central sections of the
sigmoidal veins deviate by 30e40to this value. Dots along vein margins show the angle between the vein ﬁbres and vein walls as deviations from 90. Most ﬁbre wall angles
approximate 90, although there are exceptions.
S.T. Thiele et al. / Journal of Structural Geology 77 (2015) 27e4438
Fig. 10. Photomicrographs showing crosscutting relationships within the sample. Veinlets are crosscut by larger veins in insets (a), (b), (e), (f), (g) and (j). Inset (h) shows a veinlet that appears to crosscut one of the sigmoidal veins. The
minor veins are also shown to be crosscut by the sigmoidal veins in (c), (d) and (j).
S.T. Thiele et al. / Journal of Structural Geology 77 (2015) 27e44 39
the sigmoidal vein geometries observed in the sample, it cannot
fully explain them.
rotation of the veins and pressure solution seams could
also be attributed to buckling of rock bridges separating the veins,
in accordance with the model of Nicholson and Pollard (1985). The
generally consistent thickness of the rock bridges and lack of
development of shear fabrics suggest that this model may be more
appropriate than the model of Beach (1975) in this case. However,
as with the model of Beach (1975), the rock bridge buckling
mechanism cannot explain the greater rotation of the sigmoidal
vein walls and ﬁbres than older veinlets and minor veins. Fibres
formed due to buckling of the rock bridges would also be expected
to intersect vein walls at an oblique angle (Table 1), whereas most
of the ﬁbre-wall angles observed in the sample were close to 90
4.3. Synthesis: implications for slip partitioning, strain estimates
and ﬂuid communication
In summary, the sigmoidal veins observed in the Cape Liptrap
sample are not easily explained by existing models. Instead we
propose that the pressure solution seams have played a crucial role
in their development. The spatial association between pressure
solution seams and sigmoidal en-
echelon veins was noted by Beach
(1975), however the interaction between the two has never been
Fletcher and Pollard (1981) have suggested that pressure solu-
tion seams can be treated as fractures with negative displacements,
or anticracks. They suggest that these structures often nucleate in
the zone of increased stress around the central portion of dilating
veins, and then propagate outwards to form a structure perpen-
dicular to, and approximately the same length as, the vein.
Pressure solution seams forming in this way within an en-
echelon vein array would quickly breach the rock bridges sepa-
rating the veins, dividing each rock bridge into lithons bounded by
veins and associated pressure solution seams. Consistent with the
predictions of Fletcher and Pollard (1981) the 3D structure mapping
(Fig. 7) shows an association between the pressure solution seams
and the mid-points of many of the sigmoidal veins. In this example,
it should also be noted that the pressure solution seams are
distributed along the full length of the longer veins, particularly on
the left hand side of the sample face (Fig. 7), and that some of the
seams extend well beyond the boundaries of the vein array.
We propose that slight rotation of these pressure solution seams
during continued shear, causes them to become oriented favour-
ably for slip with respect to the far ﬁeld stress. Similar development
of slip on pressure solution seams has been observed extensively in
carbonate rocks (Peacock and Sanderson, 1995; Tondi et al., 2006),
and is thought to play a signiﬁcant role during the nucleation of
faulting (Crider and Peacock, 2004; Graham et al., 2003; Willemse
et al., 1997). Peacock and Sanderson (1995) observed the develop-
ment of pull-apart veins linked by sheared pressure solution seams
in the tips of brittle faults propagating through limestone. Likewise
Fagereng et al. (2010) describe pull-apart veins forming between
sheared pressure solution seams within a sheared mudstone.
A similar process could explain the dramatic changes observed
in vein aperture where they are crosscut by pressure solution seams
(Fig. 11) and could explain the unusual geometry of the sigmoidal
veins in the Cape Liptrap sample. In our interpretation of the Cape
Liptrap sample, slip on rotated pressure solution seams allows
partitioning of strain during ongoing opening increments in the
larger veins, leading to localised dilation within the central portion
of the veins (Fig. 13). Offsets of the vein wall caused by this dilation
explains the extreme rotations of sections of the vein wall observed
Fig. 11. Interactions between veins and pressure solution seams. The pressure solution seams in all plates clearly divide zones that have undergone different amounts of strain, or
have strained in different ways. Veins in (a), (b) and (c) show offset across pressure solution seams. Step changes in vein aperture (highlighted) coincide with intersections between
pressure solution seams displaying offset and vein margins.
S.T. Thiele et al. / Journal of Structural Geology 77 (2015) 27e4440
Fig. 12. Drishti renderings of the CT dataset. (a) Plan view slices of the vein array. (b) Cross-sections of the vein array. (c) Longitudinal sections of the vein array. The plan sections (a)
are perpendicular to the orientation of the vein array and long sections (c) are parallel to it. Veins and pressure solution seams (PSS) interpreted from these data are shown in (d).
S.T. Thiele et al. / Journal of Structural Geology 77 (2015) 27e44 41
in the sample, as well as the observed orientation of crystal ﬁbres in
the vein centres, while the older veinlets in the adjacent rock
bridges are relatively less rotated.
Overall, early increments of strain in the Cape Liptrap sample
have been expressed as widely distributed veinlets, presumably
related to stochastic fracture nucleation within a tabular zone
(Fig. 15a). Further deformation caused progressive strain localiza-
tion (Fig. 15b) and the developmentof the pressure solution seams.
As simple shear caused rotation of these structures, either through
progressive rotation as suggest by Beach (1975), or through buck-
ling (Nicholson and Pollard, 1985), the veins developed a subtle
sigmoidal geometry and the pressure solution seams became ori-
ented favourably for slip. Closely spaced veins also became linked
by cross fractures (Fig. 15c). Finally, slip on pressure solution seams
linking veins in the array caused localized dilation, exaggerating the
geometry of the slightly sigmoidal veins during the later opening
increments and changing the angular relationship between vein
wall and ﬁbres (Fig. 15d). Interestingly, in this later stage of growth
vein lengths are essentially ﬁxed and growth occurs mainly
through slip-related dilation.
Our model of sigmoidal vein formation has implications for both
strain estimates and ﬂuid communication through the crust. Firstly,
sigmoidal veins forming during slip partitioning on pressure solu-
tion seams develop vein-wall geometries that overestimate the
degree of rotation. Thus it becomes critical that the role of pressure
solution is properly assessed prior to quantiﬁcation of simple shear
and volume strain components of shear deformation (c.f.Lisle,
2013). Secondly, the veins have extreme in-plane lengths with
channel-like geometries in 3D, and interlinking pressure solution
seams. In addition, slip movement (and presumably transient
permeability enhancement) has occurred on the linking pressure
solution seams. These observations indicate that a high degree of
hydrological interconnectivity can be achieved through these vein
networks (and interlinked pressure solution seams), over much
larger distances than indicated by their cross-sectional geometry. In
this example, those hydraulic distances exceed the depth of the
sample (>15 cm for veins ~6 cm long), though the actual hydraulic
transport distances are likely much greater.
The key ﬁndings of this study can be summarised as follows:
Photogrammetry is a useful and accurate technique for collect-
ing 3D structural data from hand samples. The model produced
during this study was accurate to within 0.25 mm and sub-
stantially more detailed than the reference laser scan.
Veining and pressure solution initiated during early increments
of strain and became critical components of the resulting shear
deformation and fracture mechanics. After the early veins
formed, strain progressively localised onto fewer but larger
Pressure solution seams and early formation of veinlets pro-
vided markers to assess the deformation that occurred during
the development of a sigmoidal vein array. Rotation of these
markers was not great enough to fully explain the geometry of
the sigmoidal veins. Instead, slip appears to partition onto
pressure solution seams that have undergone small rotations,
causing localized dilation and the exaggeration of sigmoidal
CT models demonstrate that the veins have channel-like ge-
ometries in 3D, penetrating the entire sample, which indicates
that the veins had much greater capacity for linkage and the
communication of crustal ﬂuids than their 2D form suggests.
Volume strain and simple shear calculations from sigmoidal
veins will overestimate angular strain for vein arrays of this
type, when pressure solution is also operative, because the
partitioning of both pure and simple shear onto pressure solu-
tion seams allows the veins to become highly sigmoidal without
requiring substantial rotation or buckling. Thus an assessment
of the role of pressure solution should be made before applying
any techniques that estimate strain from vein geometry.
Fig. 13. Interactions between pressure solution seams (dashed lines) and sigmoidal
veins observed in the photogrammetric micrograph. Unusually oriented sections of the
vein walls correlate with offset on the pressure solution seams and increases in vein
Fig. 14. Sequence diagram showing the interpreted order of formation of the veinlets,
minor veins, major veins and pressure solution seams (PSS) observed within the
sample (see Fig. 10 and Section 3.4).
S.T. Thiele et al. / Journal of Structural Geology 77 (2015) 27e4442
This study derives from an honours thesis by S. Thiele. S.
Micklethwaite acknowledges support from the Hammond-Nisbet
Fellowship. The authors would also like to thank Ake Fagereng
and Betsy Madden for their detailed and constructive reviews.
Appendix A. Supplementary data
Supplementary data related to this article can be found at http://
Allmendinger, R.W., Cardozo, N., Fisher, D.M., 2012. Structural Geology Algorithms:
Vectors and Tensors. Cambridge University Press. http://tinyurl.com/lmo2pxg.
Beach, A., 1975. The geometry of en-echelon vein arrays. Tectonophysics 28,
Belayneh, M., Cosgrove, J.W., 2010. Hybrid veins from the southern margin of the
Bristol Channel Basin, UK. J. Struct. Geol. 32, 192e201.
Bemis, S.P., Micklethwaite, S., James, M.R., Turner, D., Akciz, S., Thiele, S.,
Bangash, H.A., 2014. Ground-based and UAV-based photogrammetry: a multi-
scale, high-resolution mapping tool for structural geology and paleoseismol-
ogy. J. Struct. Geol. 69, 163e178 .
Cignoni, P., Corsini, M., Ranzuglia, G., 2008. Meshlab: an open-source 3d mesh
processing system. Ercim News 73, 45e46.
Cignoni, P., Rocchini, C., Scopigno, R., 1998. Metro: measuring error on simpliﬁed
surfaces. Comput. Graph. Forum 167e174. Wiley Online Library.
Crider, J.G., Peacock, D.C.P., 2004. Initiation of brittle faults in the upper crust: a
review of ﬁeld observations. J. Struct. Geol. 26, 691e707.
Davis, G.H., Reynolds, S.J., Kluth, C., 1996. Structural Geology of Rocks and Regions.
Douglas, J.G., 1972. In: Victoria, G.S.o (Ed.), Explanatory Notes on the Liptrap 1:63
360 Geological Map.
Fabio, R., 2003. From point cloud to surface: the modeling and visualization prob-
lem. Int. Arch. Photogramm. Remote Sens. Spat. Inf. Sci. 34, W10.
Fagereng, Å., Remitti, F., Sibson, R.H., 2010. Shear veins observed within anisotropic
fabric at high angles to the maximum compressive stress. Nat. Geosci. 3,
Favalli, M., Fornaciai, A., Isola, I., Tarquini, S., Nannipieri, L., 2012. Multiview 3D
reconstruction in geosciences. Comput. Geosci. 44, 168e176 .
Fischler, M.A., Bolles, R.C., 1981. Random sample consensus: a paradigm for model
ﬁtting with applications to image analysis and automated cartography. Com-
mun. ACM 24, 381e395.
Fletcher, R.C., Pollard, D.D., 1981. Anticrack model for pressure solution surfaces.
Geology 9, 419e424.
Fossen, H., 2010. Structural Geology. Cambridge University Press, Cambridge.
Graham, B., Antonellini, M., Aydin, A., 2003. Formation and growth of normal faults
in carbonates within a compressive environment. Geology 31, 11e14.
Gray, D.R., Janssen, C., Vapnik, Y.,1999. Deformation character and palaeo-ﬂuid ﬂow
across a wrench fault within a Palaeozoic subductioneaccretion system: War-
atah Fault Zone, southeastern Australia. J. Struct. Geol. 21, 191e214.
Grohmann, C., Campanha, G., 2010. OpenStereo: Open Source, Cross-platform
Software for Structural Geology Analysis. AGU Fall Meeting abstracts, p. 06.
James, M., Robson, S., 2014. Systematic Vertical Error in UAV-derived Topographic
Models: Origins and Solutions.
Janssen, C., Laube, N., Bau, M., Gray, D.R., 1998. Fluid regime in faulting deformation
of the Waratah Fault Zone, Australia, as inferred from major and minor element
analyses and stable isotopic signatures. Tectonophysics 294, 109e130.
Lennox, P.G., Golding, S.D., 1989. Quartz veining in simply folded arenites, Cape
Liptrap, southeast Victoria, Australia. Aust. J. Earth Sci. 36, 243e261.
Limaye, A., 2012. Drishti: a Volume Exploration and Presentation Tool, 85060X-
Lisle, R.J., 2013. Shear zone deformation determined from sigmoidal tension gashes.
J. Struct. Geol. 50, 35e43.
Lowe, D.G., 2004. Distinctive image features from scale-invariant keypoints. Int. J.
Comput. Vis. 60, 91e110.
Micklethwaite, S., Sheldon, H.A., Baker, T.,2010. Active fault and shear processes and
their implications for mineral deposit formation and discovery. J. Struct. Geol.
Nicholson, R., Pollard, D.D., 1985. Dilation and linkage of echelon cracks. J. Struct.
Geol. 7, 583e590.
Olson, J.E., Pollard, D.D., 1991. The initiation and growth of en
J. Struct. Geol. 13, 595e608.
Peacock, D.C.P., Sanderson, D.J., 1995. Pull-aparts, shear fractures and pressure so-
lution. Tectonophysics 241, 1e13.
Piper, J., 2010. Software-based stacking techniques to enhance depth of ﬁeld and
dynamic range in digital photomicrography. In: Hewitson, T.D., Darby, I.A.
(Eds.), Histology Protocols. Humana Press, pp. 193e210.
Pollard, D.D., Segall, P., Delaney, P.T., 1982. Formation and Interpretation of Dilatant
Fig. 15. Conceptual model for the development of a vein array similar to the one observed in the Cape Liptrap sample. (a) Veinlets develop from a broad zone of microfractures
during early increments of shear. Possible early pressure solution. (b) Competition between veinlets and progressive linkage causes strain localization onto fewer, larger veins.
Pressure solution seams initiate and propagate as anticracks, generally originating from the centre of veins (Fletcher and Pollard, 1981). (c) Subtle sigmoidal geometry develops as
veins rotate within the shear zone, either due to the mechanism of Beach (1975) or Nicholson and Pollard (1985). Rotated pressure solution seams become oriented favourably for
slip and begin to partition both pure and simple shear strain. Rock bridges separating closely spaced veins are breached by cross fractures as vein dilation increases. (d) Slip on
pressure solution seams enhances dilation within vein centres, amplifying their sigmoidal geometry.
S.T. Thiele et al. / Journal of Structural Geology 77 (2015) 27e44 43
Pollefeys, M., Koch, R., Van Gool, L., 1999. Self-calibration and metric reconstruction
inspite of varying and unknown intrinsic camera parameters. Int. J. Comput. Vis.
Rickard, M.J., Rixon, L.K., 1983. Stress conﬁgurations in conjugate quartz-vein arrays.
J. Struct. Geol. 5, 573e578.
Riedel, W., 1929. Zur mechanik geologischer brucherscheinungen. Zentralblatt für
Mineralogie. Geol. Pal€
aontol. B 1929, 354e368.
Shainin, V.E., 1950. Conjugate sets of en echelon tension fractures in the Athens
Limestone at Riverton, Virginia. Geol. Soc. Am. Bull. 61, 509e517.
Slizewski, A., Semal, P., 2009. Experiences with low and high cost 3D surface
ar 56, 131e13 8.
Sturm, P., Triggs, B., 1996. A factorization based algorithm for multi-image projec-
tive structure and motion. Comput. VisiondECCV'96 709e720. Springer.
Tanner, P.W.G., 1992. Vein morphology, host rock deformation and the origin of the
fabrics of echelon mineral veins: discussion. J. Struct. Geol. 14, 373e375.
Tondi, E., Antonellini, M., Aydin, A., Marchegiani, L., Cello, G., 2006. The role of
deformation bands, stylolites and sheared stylolites in fault development in
carbonate grainstones of Majella Mountain, Italy. J. Struct. Geol. 28, 376e391.
Triggs, B., McLauchlan, P.F., Hartley, R.I., Fitzgibbon, A.W., 2000. Bundle adjust-
mentda modern synthesis. Vis. Algorithms: Theory Pract. 298e372. Springer.
Twiss, R., Moores, E., 2007.Structural Geology. WH Freeman and Company, New York.
Willemse, E.J.M., Peacock, D.C.P., Aydin, A., 1997. Nucleation and growth of strike-
slip faults in limestones from Somerset, U.K. J. Struct. Geol. 19, 1461e147 7.
Willmott, C.J., Matsuura, K., 2005. Advantages of the mean absolute error (MAE)
over the root mean square error (RMSE) in assessing average model perfor-
mance. Clim. Res. 30, 79.
S.T. Thiele et al. / Journal of Structural Geology 77 (2015) 27e4444