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Extraction of high-resolution structural orientations from digital data: A Bayesian approach


Abstract and Figures

Measurement of structure orientations is a key part of structural geology. Digital outcrop methods provide a unique opportunity to collect such measurements in unprecedented numbers, and are becoming widely applied. However, orientation estimates produced by plane fitting can be highly uncertain, especially when observed data are approximately collinear or the structures of interest comprise differently oriented segments. Here we present a Bayesian approach to plane fittingthat can use data extracted from digital outcrop models to constrain the orientation of structures and their associated uncertainty. We also describe a moving-window search algorithm that exploits this Bayesian formulation to estimate local structure orientations for segmented structures. These methods are validated on synthetic datasets for which both the structure orientation and associated uncertainty is known. Finally, we implement the method in the point cloud analysis package CloudCompare and use it to estimate the orientation and thickness of dykes exposed in cliffs on the island of La Palma (Spain).The results highlight the potential of this method to generate structural data at unprecedented spatial resolution, while simultaneously characterising the associated uncertainties.
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Accepted Manuscript
Extraction of high-resolution structural orientations from
digital data: A Bayesian approach
Samuel T. Thiele1, Lachlan Grose1, Tiangang Cui2, Alexander R. Cruden1, Steven
1School of Earth, Atmosphere and Environment, Monash University, Melbourne, 3800,
2School of Mathematical Sciences, Monash University, Melbourne, 3800, Australia
Correspondence to: Samuel T. Thiele (
Keywords: Digital outcrop geology, plane-fitting, orientation measurement, structure normal
estimate, uncertainty
Measurement of structure orientations is a key part of structural geology. Digital outcrop
methods provide a unique opportunity to collect such measurements in unprecedented
numbers, and are becoming widely applied. However, orientation estimates produced by plane
fitting can be highly uncertain, especially when observed data are approximately collinear or
the structures of interest comprise differently oriented segments. Here we present a Bayesian
approach to plane fitting that can use data extracted from digital outcrop models to constrain
the orientation of structures and their associated uncertainty. We also describe a moving-
window search algorithm that exploits this Bayesian formulation to estimate local structure
orientations for segmented structures. These methods are validated on synthetic datasets for
which both the structure orientation and associated uncertainty is known. Finally, we
implement the method in the point cloud analysis package CloudCompare and use it to estimate
the orientation and thickness of dykes exposed in cliffs on the island of La Palma (Spain). The
results highlight the potential of this method to generate structural data at unprecedented spatial
resolution, while simultaneously characterising the associated uncertainties.
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1. Introduction
Understanding and quantifying the orientation of geological structures is a key component of
many geological studies, from resource exploration, tectonic reconstructions and three-
dimensional (3D) modelling to geotechnical analyses. One challenge is quantifying the
uncertainties associated with primary structural observations, which is often further
complicated by limited access to outcrops and the multiscale nature of geological observations.
It is now practical to create accurate, sub-cm resolution 3D digital reconstructions of outcrops,
over areas as large as 1 km2, with the advent of Structure-from-Motion (SfM) photogrammetry
and terrestrial laser scanners (McCaffrey et al., 2005; Vollgger and Cruden, 2016; Dering et
al., 2019a). These digital outcrops form the basis for an objective, reproducible and quantitative
approach for collecting basic field information and orientation measurements at unprecedented
spatial intensity.
Analyses of these high resolution datasets allow detailed structural and stratigraphic mapping
(Pringle et al., 2006; Jones et al., 2009; Nesbit et al., 2018), and have provided new insight into
geological processes such as faulting (Bemis et al., 2014; Bond et al., 2017; Corradetti et al.,
2017; Kirsch et al., 2018), folding (Schober and Exner, 2011; Vollgger and Cruden, 2016;
Menegoni et al., 2018), dyke intrusion (Healy et al., 2018; Magee et al., 2018; Dering et al.,
2019b) and vein formation (Thiele et al., 2015). Descriptions of fracture populations derived
from digital outcrops are also widely used in the engineering community for rock stability
analyses (Haneberg, 2008; Ferrero et al., 2009; Salvini et al., 2013; Bonilla-Sierra et al., 2015;
Mancini et al., 2017; Thoeni et al., 2018). Regardless of the application, the orientations of
specific structures (e.g., bedding, veins and fractures) are of interest, and are typically
represented locally as a plane described by dip and dip-direction or strike angles.
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Structures that exert a control on outcrop morphology, such as joints, can be measured directly
where they form a sub-planar region on the outcrop surface. This is achieved by fitting planes
to regions of co-planar points (“facets”) on the reconstructed outcrop surface, which is typically
combined with some form of clustering algorithm to allow automatic detection (e.g., García-
Sellés et al., 2011; Lato and Vöge, 2012; Dewez et al., 2016). Assuming an accurate digital
outcrop model, the results of these estimates tend to be robust because the area of exposed
structure will be far from co-linear, and uncertainty around the orientation estimate, although
rarely quantified, will typically be quite small (Gallo et al., 2018).
In contrast, many structures intersect the outcrop surface at a large angle to form an intersection
trace (Fig. 1). These traces can also be used to estimate the orientation of a structure using
plane-fitting routines; however, the accuracy of the result is highly dependent on the relief of
the outcrop. As Fernández (2005) and Jones et al. (2016) show, the best-fit plane through a
trace becomes progressively less constrained as the co-linearity of the trace increases; an
infinite number of equally valid planes will fit a co-linear trace. Both Fernández (2005) and
Jones et al. (2016) suggests that traces above a conservative linearity threshold should be
excluded from orientation analyses because they will not produce robust orientation estimates.
Seers and Hodgetts (2016b) build on this work, pointing out that even perfectly co-linear traces
constrain the orientation of a structure to a single axis of rotation, and they quantify the
relationship between co-linearity and uncertainty by stochastically generating synthetic traces
and characterising the spread of the resulting orientation estimates. Their method, however,
cannot be applied in practice because it relies on the stochastic sampling of many hundreds of
intersection traces for each structure, while in reality only a single trace is observed.
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Figure 1. Synthetic examples of intersections between a simple planar structure (a) and more
complex composite structure (b) with a randomly generated fractal outcrop surface. The
intersection trace (heavy black line) between the structure and the outcrop surface is commonly
observed and, for non-planar outcrops, can be used to constrain the geometry of the structure.
The structure normal n, represented in spherical coordinates by θ→ϕ, and outcrop normal u is
also shown, as well as the angle γ between the structure and the outcrop.
Plane-fitting algorithms applied to digital outcrop models produce the best results if they can
average the orientation of a structure over a large area, as doing so exploits often subtle
topographic variation to reduce the co-linearity of the trace. This is advantageous for structures
that are truly sub-planar at the large-scale, as it removes local variation that would add error to
compass-clinometer measurements. However, many real structures have more complex
geometries. For example, faults often contain jogs, step-overs and restraining bends at larger
scales while dykes and veins often change orientation in broken bridges or near fracture tips.
These variations in structure geometry, and errors incurred during trace digitisation, will result
in variance along the trace that is co-planar with the outcrop surface. This variance, especially
if combined with large-scale non-planarity of the structure, will bias structure orientation
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estimates towards parallelism with the outcrop surface (e.g., Fig. 7 in Thiele et al., 2015).
Overcoming this “outcrop-normal bias” is essential for producing reasonable estimates of the
orientation of a structure.
Bayesian statistics provides a rigorous framework for integrating expert knowledge with
observed data to provide either single (maximum a postiori) or multiple estimates of
parameters of interest, by deriving and then sampling from a posterior distribution (Tarantola,
2006). Bayesian methods are commonly applied to fit multivariate linear models (planes in 3D)
to point data (Tiao and Zellner, 1964) and reconstruct surfaces from point-clouds (e.g., Torr,
2002; Erdogan et al., 2012). Here we develop a Bayesian method for the specific purpose of
estimating a geological structure’s orientation from its intersection with the surface in a way
that: (1) probabilistically describes the increase in uncertainty as traces become co-linear; (2)
accounts for outcrop-normal bias, and; (3) provides orientation estimates at each point, and so
can be applied to structures that are non-planar at the large scale. We validate this approach,
which we term “structure-normal estimation”, by applying it to a series of synthetic datasets
and present a case study in which we estimate the orientation and thickness of dykes exposed
in cliffs on the island of La Palma (Canary Islands, Spain).
2. Bayesian plane fitting
The orientation of a planar structure can be described in spherical coordinates by the
geographical bearing or trend ϕ and inclination or plunge θ of its normal vector n, also known
as the pole to the plane and written here as θ→ϕ (Fig. 1a). It is also useful to express n in
Cartesian coordinates by computing its direction cosines:
 Eq. 1.
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A set of N position vectors (u0, u1 uN) can readily be sampled from the intersection trace
using, for example, digital outcrop methods (e.g., Seers and Hodgetts, 2016a; Thiele et al.,
2017; Guo et al., 2018), providing the raw data with which we wish to constrain ϕ and θ. The
spatial distribution of these points is summarised by their covariance, or specifically for our
purposes, by constructing an unscaled covariance matrix X, hereafter referred to as a scale
matrix (Eq. 2).
 Eq. 2.
The average normal vector to the outcrop in which a trace is observed, o, is also easily measured
using field or digital outcrop methods. It is well established that traces formed by structures
with orientations similar to the outcrop (n o) are less likely to be observed (Terzaghi, 1965),
and hence we can define a priori that an observed trace is more likely to originate from a
structure intersecting the outcrop at a higher angle.
Bayes theorem (Eq. 3) provides a robust framework for combining this prior knowledge, or
P(ϕ, θ; o), with the observed data X by using a likelihood function P(X | ϕ, θ) to derive a
posterior distribution P(ϕ, θ | X) that constrains the orientation of the planar structure:
Eq. 3.
In practice, Equation 3 can be simplified because P(X) is constant for an observed trace,
allowing the calculation of an unnormalised posterior distribution (Eq. 4). Note that numerical
techniques such as the Metropolis-Hastings Monte-Carlo Markov chain method (Metropolis et
al., 1953; Hastings, 1970) can be used to sample directly from the unnormalised posterior
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 Eq. 4.
In the following sections we derive the prior distribution P(ϕ, θ; o) based on the commonly
used Terzaghi correction factor (Terzaghi, 1965), and likelihood function P(X | ϕ, θ) that uses
the Wishart distribution (Wishart, 1928) to quantify how well an observed scale matrix X fits
structures of different orientations.
2.1. Terzaghi Prior
The Terzaghi correction provides a scaling factor that accounts for biases caused by the low
probability of observing structures with a similar orientation to the outcrop or scan-line on
which data are collected (Terzaghi, 1965). We adapt this correction factor and use it to describe
the prior-probability of observing a structure given its angle of intersection with the outcrop in
which it is exposed. Assuming an arbitrary set of planar structures with true-spacing S0, and a
single planar outcrop surface, the projected spacing (S) of intersection traces observed on the
outcrop surfaces is a function of the acute angle γ between the structure and outcrop normals n
and o (Eq. 5, 6):
 Eq. 5
 Eq. 6.
Structures from this set will be observed with a frequency f in traverses along the outcrop that
are perpendicular to the projected structure orientation, where:
Eq. 7.
Therefore, for a structure belonging to a hypothetical set of similarly oriented structures, the a
priori probability of observing a structure trace intersecting a sub-planar outcrop of known
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orientation and limited extent will be proportional to sin(γ). Hence, noting that n can be
explicitly calculated from ϕ and θ as per Equation 1, the prior probability distribution P(ϕ, θ;
o) becomes:
 Eq. 8.
2.2. Wishart likelihood function
The Wishart distribution (Eq. 9; Wishart, 1928) expresses the probability of observing scale
matrix X from d + 1 independent observations drawn from a multivariate normal distribution
with an underlying population covariance matrix V, expressed here for 3D data as:
Eq. 9,
where Γ3 is the 3D gamma function, and tr and det are the trace and determinant functions
respectively. An arbitrary postulated covariance matrix V can be decomposed into a matrix of
eigenvectors ε1, ε2 and ε3 and eigenvalues λ1, λ2 and λ3 such that:
 
  
  Eq. 10.
If we assume fixed eigenvalues, estimated from the observed covariance of the structures
intersection-trace, then V can be derived from three angles representing the rotation of the
eigenvectors: ϕ, θ and a third angle, α, which we introduce below. The third eigenvector (ε3)
of a 3D covariance matrix gives the direction of lowest variance, and hence the normal to the
best-fit plane, and so will be equal to the direction cosines of a structure with orientation θ→ϕ:
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 Eq. 11.
By defining the third rotation, α, as the angle between ε2 and the projection of ε3 onto the
horizontal plane (assuming ε3 is not vertical), we can describe ε2 as:
rotated by angle α around ε3, which simplifies to:
rotated by angle α around ε3.
This can be expanded using Rodrigues’ rotation formula (Rodrigues, 1840; Koks, 2006) to
 Eq. 12.
Finally, ε1 can be calculated from ε2 and ε3 using the vector product:
Eq. 13.
Hence, a postulated population covariance matrix Vϕ,θ,α can be constructed for any
hypothesised structure orientation (ϕ, θ) and additional rotational term α using Equation 10.
Substituting Vϕ,θ,α into the Wishart distribution, it follows that the likelihood an observed trace
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and associated scale matrix X result from a structure oriented at θ→ ϕ (and with an eigensystem
rotated by angle α to give a proposed population covariance matrix Vϕ,θ,α) is:
Eq. 14.
Using the Terzaghi prior described in Section 2.1, and a uniform prior P(α) for α, the
unnormalised posterior distribution P(ϕ, θ, α | X ) becomes:
 Eq. 15.
If necessary, α can be marginalised by integration to give a posterior distribution for ϕ and θ
 Eq. 16.
Examples of the Terzaghi prior, Wishart likelihood and resulting posterior distributions are
shown in Fig. 2, visualised on equal area, lower hemisphere stereographic projections. These
highlight the anisotropic distribution of uncertainty that results from the often high degree of
co-linearity in observed structure trace data (Seers and Hodgetts, 2016b).
It is important to note at this point that the confidence given to the observed scale matrix X,
and hence the tightness of the resulting posterior (Fig. 3), depends on the number of
independent observations used to estimate it (i.e., the degrees of freedom d in Eq. 14). In real-
world applications, and the synthetic examples we present in Section 5, points defining the
trace of a structure will show local autocorrelation and systematically distributed errors (i.e.,
not be statistically independent), meaning that d needs to be chosen based on the quality of the
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Figure 2. Lower hemisphere stereographic projections of the unnormalised prior (a), likelihood
(b) and posterior (c) distributions for a poorly constrained (largely co-linear) structural trace
observed on an outcrop with a normal vector (o) oriented 25˚→330˚. Areas of high probability
density are shown in red.
Figure 3. Wishart distributions showing the reduction in variance as the degrees of freedom d
3. Structure-normal estimation
The Bayesian plane-fitting approach assumes that structure traces result from truly planar
structures. In reality this is often not the case as structures, especially dykes, faults and veins,
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often comprise differently oriented segments (Fig. 4a). In such instances, a single orientation
estimate is inappropriate. Instead, we treat the problem as a surface-normal estimation problem
where we create “structure normal estimates” (SNEs) at every point along the trace.
The creation of SNEs is achieved by the application of a moving-window search algorithm,
which, for windows defined by start point ui and end point uj in the ordered list of points (u0,
u1 uN):
1. Calculates and stores the scale (X) matrices of points (ui, ui+1, uj) inside each window
(Fig. 4b).
2. Evaluates the unnormalised posterior probability density P(ϕ, θ, α | X) for each window
at the maximum likelihood estimate for ϕ, θ and α. These are easily calculated from the
eigenvectors of X, and will in almost all cases represent the maxima of P(ϕ, θ, α | X),
the only exception being where the plane falls almost sub-parallel to the outcrop
orientation and the posterior becomes bimodal. Once computed, P(ϕ, θ, α | X) is stored
in a symmetric two-dimensional (2D) matrix such that Mij contains the posterior density
of a window starting at point i and ending at point j (Fig. 4c). Higher values of Mij result
from windows with tighter posterior distributions, and hence represent better
constrained orientation estimates.
3. Finds the window with the largest unnormalised posterior probability density at each
point (u0, u1 uN), and hence the best-constrained orientation estimate at that location
(i.e. finds the maximum value in Mij where i < p < j for each point up; Fig. 4d).
4. Draws orientation samples (ϕ, θ) from the posterior distribution defined by the best-
constrained window for each point, as identified in the previous step, using the
Metropolis-Hastings Monte-Carlo Markov-Chain method.
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Figure 4. Example of a dyke comprising sub-planar segments with different orientations
(a). A moving window is applied (b) to create a matrix where each element Mij contains the
unscaled posterior probability density of the best-fit plane through data within a window
starting at i and ending at j (c). This matrix is searched to find the most constrained best-fit
plane for each point p (d) and hence derive the structure normal estimates (SNEs).
The results of this are distinct orientation estimates for every point, allowing different sections
of the trace to have different orientations. The size of acceptable search windows is also
constrained to define the scale at which the orientation estimates are expected to be averaged
over and avoid spurious small or large search windows.
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4. Implementation.
The methods described above have been implemented in the Compass plugin (Thiele et al.,
2017), which comes bundled with the standard version of CloudCompare
( Source code for the entire program, including the Compass plugin,
is available at A python library that implements the SNE
algorithm is also available at This python library also
includes a variety of utility functions for loading and visualising xml files exported from the
Compass plugin. Code for the following synthetic tests of the SNE method can also be found
as part of this library (
5. Results and validation
5.1. Synthetic examples
In the following section, we generate synthetic structural traces by intersecting a fractal surface
representing topography with a second, differently oriented fractal surface representing a sub-
planar structure. Monte Carlo sampling of the best-fit plane through these intersection traces
then provides an independent estimate of uncertainty, as described by Seers and Hodgetts
(2016b), that can be compared with results from our Bayesian model.
First, we generate a two-dimensional elevation grid representing the surface of a structure
dipping 55˚ to the south and add a small amount (1% of the length) of fractal variation using
the spectral synthesis method (Fisher et al., 2012). This synthetic structure is then intersected
with 1000 randomly generated, sub-horizontal outcrop topographies (also generated with the
spectral synthesis method) to create a set of synthetic intersection traces (Fig. 1a). The 3rd
eigenvector of each of these traces are then computed, resulting in a sample of 1000 plausible
orientation estimates as per Seers and Hodgetts (2016b). The amplitude of topographic relief
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is varied in different experimental groups to explore the associated change in orientation
Our Bayesian method is then applied to the last-generated (1000th) structural trace, and the
resulting posterior distribution explicitly evaluated for comparison with the Monte-Carlo
sampled population. As our synthetic trace has a long axis parallel to the strike of the structure,
orientation uncertainty will almost entirely cause variation of the estimated dip, and so for easy
comparison we only compare variations in dip. These results suggest a close fit (overlaps of
73-88%; Fig. 5) between the “true-uncertainty” sampled using the Monte Carlo method and
our Bayesian posterior distribution.
Figure 5. Kernel density estimates of structure orientations observed by stochastically
generating random topographies (blue line) and the posterior distribution generated by applying
our Bayesian method to a single structural trace (red line). Traces were generated by
intersecting a sub-planar fractal surface with fractal topographies with amplitudes of 4% (a),
8% (b) and 20% (c) of the trace length, and a degrees of freedom d = 10 was used when
evaluating the posterior distribution. The dashed black line shows the actual orientation of the
structure, and the green area the overlap between the two kernel density estimates.
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We also tested a more complex example where the synthetic structure changes in orientation
along strike (Fig. 1b). Similar to the example above, the best-fit plane to each differently
oriented subsection of the Monte-Carlo sampled traces were computed to give an independent
estimate of orientation uncertainty. Unlike the previous example, we do not explicitly evaluate
the posterior, as doing so on every point in the trace (each of which has a potentially different
orientation estimate) is computationally expensive. Instead, a Metropolis-Hastings sampler
was used to generate 100 samples from the posterior of each point. These were then aggregated
to provide a sample describing the plausible variation of structure orientations that could be
derived from the trace. The sampler was initialised at the maximum-likelihood position
because, in our case, this generally coincides with the maxima of the posterior distribution,
avoiding the need for an initialisation period (burn-in; Kass et al., 1998). Proposed samples
were generated by sampling perturbations from a normal distribution with a standard deviation
of 0.075 radians and accepted or rejected using the Metropolis-Hastings method.
As with the previous example, the Bayesian and Monte-Carlo uncertainty estimates are similar,
although the Bayesian results clearly show a larger spread, suggesting higher uncertainty (Fig.
6). This is reasonable given the Bayesian results are estimated from a single trace, and suggest
that the method is capable of identifying subdomains within complex, multi-planar structures
and quantifying the range of credible orientations that could be attributed to them. As in the
previous example, a d ≈ 10 degrees of freedom was found to produce the best match.
5.2. Application to the Taburiente dyke swarm
We now present an application to real field data from the island of La Palma (Canary Islands,
Spain). Dykes within the Taburiente volcano are spectacularly exposed here along a series of
cliffs that resulted from erosion of a collapse-scarp formed by catastrophic volcano edifice
failure at ca. 550 Ma (Carracedo, 1994). The cliffs are accessible at a location known locally
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as Hoyo Verde (Fig. 7a), where a swarm of ~550 m spaced, ~0.54 m thick mafic dykes and
sills can be observed (Fig. 7b). These intrusions exhibit geometries ranging from tabular dykes
to complex, anastomosing dyke networks and small saucer-shaped sills. They are also exposed
across much of their section as they intersect the cliff face, which dips broadly at ~50-60° but
locally contains significant topographic variation, allowing the estimation of the dyke
orientations from their intersection traces.
An Unmanned Aerial Vehicle (UAV) survey was completed using a DJI Phantom 4 Pro and
integrated camera (20-megapixel CMOS sensor). Flight lines were manually controlled and
flown horizontally at a distance of ~35 m from the cliff. The images were acquired frequently
enough to maintain ~80% overlap both laterally and vertically. The camera was alternated
between pointing forwards and angled at ~30˚ downwards to (1) ensure sufficient vertical
overlap between images and (2) avoid the systematic distortions that can occur when camera
orientation is fixed (James and Robson, 2014). This resulted in an approximate ground-
sampling distance of ~1 cm/pixel over the surveyed area. Significant topography resulting in
poor GPS reception precluded the deployment of accurately surveyed ground control points.
We also measured dyke orientations and thicknesses along a traverse bisecting the model using
a compass and tape measure, providing a reference with which to validate orientation estimates.
A Structure-from-Motion Multi-View-Stereo workflow, as implemented in Agisoft Photoscan
1.4.3, was then used to reconstruct the geometry of the outcrop in 3D. This reconstruction
comprised ~100 million points covering an area of ~38,000 m2 (~2600 points/m2) and was
georeferenced using approximate camera locations stored by the UAV using its on-board GPS.
This georeferencing was then refined by comparison with the publicly available 2014 Spanish
LiDAR survey series (which has a resolution of ~0.75 points/m2 at this location) and optimised
using the iterative closest point algorithm in CloudCompare.
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Fig. 6. Lower hemisphere stereographic projection of orientation estimates of normals to a
planar structure consisting of two differently oriented planar segments. As with Figure 5,
Monte Carlo sampled orientation estimates (a) indicate the amount of uncertainty present in
the orientation estimates for different degrees of topographic relief. Orientation estimates
produced from a single structural trace by Monte Carlo Markov Chain sampling the posterior
distributions of each structure-normal (b) estimated using the moving window method
described in section 4 match these closely, although the moving-window method results in a
noticeably wider spread of SNEs.
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Figure 7. Dyke swarms from Hoyo Verde on the island of La Palma, Spain (a) recorded using
a UAV to capture 203 images in a regular survey pattern, an example of which is shown in (b).
Dykes mapped using a digital outcrop model constructed from these images (c) have been used
to test the structure normal estimation method and measure dyke thickness (d), visualised here
using the colour table. Field measurements of dyke orientation and thickness have been
included on (c) for reference.
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The upper and lower contacts of dykes visible in the model were then extracted using the semi-
automatic “trace tool” of the Compass plugin in CloudCompare (Thiele et al., 2017), which
uses the colour (RGB) gradient and a least-cost-path algorithm to “follow” contacts between
user-defined waypoints (Fig. 7c). We then used the CloudCompare implementation of the
method presented in this study to estimate the orientation and thickness of the dykes at each
point along these traces.
The resulting SNEs were then carefully censored using the segment tool in CloudCompare.
This was necessary as the method described in Section 3 assumes a locally planar structure,
while the dykes sometimes have a curved otherwise non-planar geometry. This complexity can
result in well-constrained but incorrect best-fit planes, which are generally sub-parallel to the
outcrop surface. The large angle between the outcrop surface and incorrect SNEs, and typically
anomalous orientations compared to other SNEs from the same structure meant that, in most
cases, spurious results could be manually identified and removed without significant
After vetting, SNEs remained for 68% of the original ~5.2 km of digitised dyke margins, spaced
every ~7 cm (Fig. 7d). The orientation of these remaining SNEs (Fig. 8a) hint at several
differently oriented dyke sets, one shallow dipping and striking roughly west, and two (possibly
three) steeper sets striking north and north-north-west.
In many studies, the true-thicknesses of sedimentary units, dykes or other structures is of
interest (e.g., Krumbholz et al. 2014; Nesbit et al., 2018; Dering et al., 2019a). True-thickness,
as opposed to the apparent thickness observed on the outcrop, requires knowledge of the
structures orientation (see Fig. 9 in Dering et al., 2019a), providing a relevant application of
the SNE algorithm. We use SNEs on opposite sides of dykes extracted from the Hoyo Verde
model to calculate the true thickness of each intrusion and the associated uncertainty (Fig. 8b).
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These measurements suggest that the dykes have a median true thickness of 50 cm and
generally follow a lognormal distribution, similar to thickness data for other dykes in Caldera
Taburiente (Krumbholz et al., 2014).
Hand-measured dyke orientation and thickness measurements were also acquired at 26 sites
and subsequently located on the digital outcrop model using recorded GPS location and field-
notes. Of these, 15 corresponded to dyke sections with SNEs and so have been directly
compared (Fig. 9). These comparisons show broadly consistent results, but also highlight some
differences in orientation (>30°) and thickness (>20 cm). Of the 15 comparisons (Fig. 9b), 10
are within 15°, which we suggest is reasonable given some of the dykes contain a significant
amount of magnetite, meaning the compass measurements are probably only accurate to ± 15°.
Figure 8. Equal-area lower hemisphere stereographic projection (a) overlying hand-measured
orientations (red and black squares) on the contoured log-density of SNE samples and
histogram (b) of associated thickness estimates. Orientation measurements with corresponding
SNEs (and hence included in Fig. 9) are shown in red, while the black triangle shows the
average orientation of the normal to the outcrop. Several statistical distributions fitted to the
thickness data are also provided for reference.
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Figure 9. Differences between the SNEs and directly measured field data. Angular differences
are shown both in aggregate (a) and at an individual measurement level (b). Differences
between thicknesses estimated using the SNEs and corresponding hand-measured values are
shown (c), excluding multiple-intrusions.
6. Discussion
The Hoyo Verde case study highlights the ability of our method to provide quantitative
measurements of structure orientations and thicknesses from intersection-traces captured in a
digital outcrop model. The unprecedented number of these orientation and thickness
measurements, and associated characterisation of orientation uncertainty, provide a far more
robust description of dyke geometry than the spot orientations or thickness measurements
traditionally employed in the field. Most measurements extracted from the Hoyo Verde model
are also within entirely inaccessible terrain, illustrating the potential of digital outcrop methods
for analyses of inaccessible areas and features.
The degrees of freedom used in the Wishart distribution (d) change the confidence placed in
the observed structural trace, and hence the uncertainty surrounding the SNEs. It is likely that
an analysis of autocorrelation within the structural traces could provide guidance as to a
Accepted Manuscript
reasonable value for d, although this is beyond the scope of this contribution. In the absence of
further information, and in light of the synthetic tests presented in Section 4, we suggest using
a lower value (~10). As planes become well constrained, the importance of d decreases,
meaning the choice of value will mostly affect SNEs with high uncertainty.
Despite both careful vetting and the use of a low value for d, direct comparisons between
structures measured in the field and corresponding SNEs revealed some discrepancies of >20-
40°. Visualisations of the digital outcrop model suggests that the SNEs are a more reasonable
estimation of the dyke orientation than the compass measurements in these cases. We suggest
that it is likely they occur because point-orientation estimates acquired with a compass are not
representative of large-scale orientation, especially because dyke contacts at Hoyo Verde are
irregular at the 1-5 m scale. This highlights the importance of averaging structure orientation
over large areas, at least for these dykes, which is difficult to achieve using traditional methods.
The ability outlined here to represent orientation estimates as posterior probability density
functions (rather than individual measurements with unknown uncertainty) also provide
opportunities for probabilistic discrimination between structure sets and therefore estimation
of the probability that an observed structure belongs to a predefined set. As such, the method
may allow a distinction between intra-set variance and measurement uncertainty, improving
our ability to characterise structure sets during, for example, fracture-network modelling or
geotechnical analysis. The development of such methods would further improve the rigour of
classic and widely applied structural geology techniques.
Finally, in terms of future work, our case study demonstrates the importance of careful vetting
to remove misleading orientation estimates caused by local geometric complexities. It is
possible that this vetting process could be automated or semi-automated by identifying and
removing statistical outliers and, in the case of structures such as dykes or sedimentary units,
Accepted Manuscript
checking the consistency of independent SNEs from the upper and lower surfaces. Regardless,
we recommend that all SNEs are carefully checked before use, especially since this is
straightforward in an interactive 3D environment such as CloudCompare.
The authors would like to gratefully acknowledge the staff at Parque Nacional Caldera de
Taburiente for their generous support and hospitality during collection of the field data
presented in this study. ST was supported by a Westpac Future Leaders Scholarship and
Australian Postgraduate Award. LG was supported by ARC grant LP170100985. Finally, we
would like to acknowledge Clare Bond and Florian Wellmann for their thoughtful and
constructive reviews.
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... One such limitation that affects DOM efficacy are errors and uncertainties associated with orientation estimation of geological features (Lato et al., 2009;Jones et al., 2016;Cawood et al., 2017;Thiele et al., 2019). Cawood et al. (2017) demonstrate that orientation measurement accuracy derived from DOMs is dependent on the quality and precision of the reconstructed surface (Cawood et al., 2017;Fleming and Pavlis, 2018). ...
... Methods to statistically constrain orientation measurement inconsistencies from outcrop have been investigated (Fernández, 2005;Seers and Hodgetts, 2016;Gallo et al., 2018;Fleming and Pavlis, 2018;Thiele et al., 2019). These studies demonstrate that the reliability of an orientation estimate from remotely sensed data relies considerably on the collinearity of the set of points used to derive the estimation. ...
... The results from our experiments collaborate those from previous studies (Fernández, 2005;Seers and Hodgetts, 2016;Thiele et al., 2019), maintaining that collinearity serves as a substantial medium for assessing the quality of orientation estimates from georeferenced data. As such, we implemented a simple procedure in VRGS that computes collinearity alongside the orientation estimate once a structure is measured. ...
In this study, we examine the errors and uncertainties associated with orientation measurements collected from digital outcrop models using the geometrical property, collinearity. Collinearity is expressed as the characteristics of a set of points lying on a single straight line, and is beneficial because a trace far from collinear is required for obtaining accurate orientation measurements of planar geological bodies from digital outcrop models. We, thus, demonstrate this relationship, as well as assess the impact any associated errors have on orientation distribution forms using orientation measurement traces collected from sandstone intrusions with a digital outcrop model of the Panoche Giant Injection Complex acquired through light detection and ranging and photogrammetry techniques. Our experiments highlight how in addition to sampling bias and sample size, unreliable orientation estimates can negatively affect interpretation. We show that the distribution of orientation for a network of geological structures (e.g., fractures, sandstone intrusions) in a particular region can be altered with the inclusion of erroneous measurements. From our case study, it was noted that the high proportion of unreliable orientation measurements obtained when using a digital outcrop model of the study area resulted in inconsistencies in the structural analysis that could have been attributed to other factors. Thus, without putting into consideration the reliability of the samples, a sampling issue will still be faced, regardless of using the appropriate sample size and technique.
... Bemis et al., 2014;Dering et al., 2019). These digital outcrop models and details of the methods used to construct them are described in (Thiele et al., 2019a;Thiele et al., 2020). For this study, we focus on three surveys from a site known locally as Hoyo Verde (Fig. 1a), where dykes of different orientations intersect to form multi-dykes (Fig. 1b). ...
... A lower hemisphere stereographic projection (stereonet) with density contours of poles to the older, shallower dipping dykes (blue) and steeper cross cutting dykes (red) is provided in (b) for reference, along with a stratigraphic log interpreted from UAV images. A total of 46715 dyke orientation estimates were extracted from the UAV data using the method of Thiele et al. (2019a). The average orientation of the cliff is given by the black triangle. ...
... Mapping of these using the digital outcrop model (a) shows a set of shallow-dipping (~45° NW) dykes capturing and re-orienting a later generation of steeply-dipping dykes (b, c), The acute intersection angles between the older intrusions and captured dykes have been measured using structure-normal estimates (cf. Thiele et al., 2019a) created during the digital outcrop mapping and are shown in (a). Figure 3. A selection of different margin-parallel joint styles observed in dykes throughout La Palma, ranging from shalelike fracture cleavages (a) to persistent (b) and sometimes imbricated joints (c) and more widely spaced but highly persistent (10s of metres) "tram-track" joints (d). ...
Full-text available
Field observations and unmanned aerial vehicle surveys from Caldera Taburiente (La Palma, Canary Islands, Spain) show that pre-existing dykes can capture and re-direct younger ones to form multiple dyke composites. Chill margins suggest that the older dykes were solidified and cooled when this occurred. In one multiple dyke example, an 40Ar/39Ar age difference of 200 kyr was determined between co-located dykes. Petrography and geomechanical measurements (ultrasonic pulse and Brazilian disc tests) show that a microscopic preferred alignment of plagioclase laths and sheet-like structures formed by non-randomly distributed vesicles give the solidified dykes anisotropic elastic moduli and fracture toughness. We hypothesise that this anisotropy led to the development of margin-parallel joints within the dykes, during subsequent volcanic loading. Finite element models also suggest that the elastic contrast between solidified dykes and their host rock elevated and re-oriented the stresses that governed subsequent dyke propagation. Thus, the margin- parallel joints, combined with local concentration and rotation of stresses, favoured the deflection of subsequent magma- filled fractures by up to 60° to form the multiple dykes. At the edifice scale, the capture and deflection of active intrusions by older ones could change the organisation of volcanic magma plumbing systems and cause unexpected propagation paths relative to the regional stress. We suggest that reactivation of older dykes by this mechanism gives the volcanic edifice a structural memory of past stress states, potentially encouraging the re-use of older vents and deflecting intrusions along volcanic rift zones or towards shallow magma reservoirs.
... A lower hemisphere stereographic projection (stereonet) with density contours of poles to the older, shallower dipping dykes (blue) and steeper cross cutting dykes (red) is provided in (b) for reference, along with a stratigraphic log interpreted from UAV images. A total of 46,715 dyke orientation estimates were extracted from the UAV data using the method of Thiele, Grose, et al. (2019). The average orientation of the cliff is given by the black triangle. ...
... Mapping of these using the digital outcrop model (a) shows a set of shallow-dipping (∼45° NW) dykes capturing and re-orienting a later generation of steeply dipping dykes (b, c), The acute intersection angles between the older intrusions and captured dykes have been measured using structure-normal estimates (cf. Thiele, Grose, et al., 2019) created during the digital outcrop mapping and are shown in (a). degassing pathways that form along straight bands parallel to the dyke margins, although we speculate that such sheets could form when vesicles adhere to solidifying dyke margins during periods of lower magma pressure or flux, and in the case of sheets within dyke cores, during the final stages of dyke activity. ...
Full-text available
Field observations and unmanned aerial vehicle surveys from Caldera Taburiente (La Palma, Canary Islands, Spain) show that pre-existing dykes can capture and re-direct younger ones to form multiple dyke composites. Chill margins suggest that the older dykes were solidified and cooled when this occurred. In one multiple dyke example, an 40Ar/39Ar age difference of 200 kyr was determined between co-located dykes. Petrography and geomechanical measurements (ultrasonic pulse and Brazilian disc tests) show that a microscopic preferred alignment of plagioclase laths and sheet-like structures formed by non-randomly distributed vesicles give the solidified dykes anisotropic elastic moduli and fracture toughness. We hypothesize that this anisotropy led to the development of margin-parallel joints within the dykes, during subsequent volcanic loading. Finite element models also suggest that the elastic contrast between solidified dykes and their host rock elevated and re-oriented the stresses that governed subsequent dyke propagation. Thus, the margin-parallel joints, combined with local concentration and rotation of stresses, favored the deflection of subsequent magma-filled fractures by up to 60° to form the multiple dykes. At the edifice scale, the capture and deflection of active intrusions by older ones could change the organization of volcanic magma plumbing systems and cause unexpected propagation paths relative to the regional stress. We suggest that reactivation of older dykes by this mechanism gives the volcanic edifice a structural memory of past stress states, potentially encouraging the re-use of older vents and deflecting intrusions along volcanic rift zones or toward shallow magma reservoirs.
... This profound theorem is based on conditional probability, which many geotechnical engineers are not familiar with, but can be represented graphically as shown in figure 19. Figure 20. Bayesian approach to analysis of structural orientations (after Thiele et al. [14]). Figure 19 shows how the data, in the form of a distribution known as the likelihood, is augmented by existing knowledge in the form of a prior distribution to give an improved estimate of the data in the form of the posterior distribution. ...
... Whereas automated processing of captures is more advantageous when considering that 3D reconstructions can be used in downstream semi-automated and automated processes (e.g. Riquelme et al., 2014Riquelme et al., , 2018Guo et al., 2017;García-Luna et al., 2019;Thiele et al., 2019;Kong et al., 2020). Although the use of laser pointers for GCPs in underground mining is unsuitable, they can be used in other inaccessible areas such as open pit highwalls and cliffs. ...
The use of structure-from-motion, multi-view stereo (SfM-MVS) in the mining industry is well-established for capturing digital data on surface. However, the application of SfM-MVS in active underground mining has received less attention as there are unique challenges that need to be overcome, especially if a procedure is to be applied daily in active mining. Unique challenges include preparation time, camera positioning, illumination and useability. The faces of active development drives are generally only available for a short period before prepared and blasted, thus information is lost if not mapped immediately. Furthermore, due to safety concerns, unsupported faces cannot be approached for physical mapping. SfM-MVS allows these faces to be viewed and mapped in the form of a virtual outcrop, thus, allowing for remote mapping of underground development, which at the Dugald River mine, located in Queensland, Australia, allowed for mapping continuity as staff worked remotely during COVID-19. This contribution describes how to set-up a capture in an underground mine to produce high-quality SfM-MVS 3D reconstructions of development faces. The methodology can be readily incorporated into a standard operating procedure. While the procedure can be used with most photogrammetry software packages that utilise SfM-MVS algorithms, it is best utilised using the provided Python script and Agisoft Metashape Professional v1.6. The script allows for automation of capture processing, which can free up several hours per day compared to user-interacted processing.
... These developments are also closely tied to major methodological improvements for virtual outcrop model (VOM) interpretation. All these advancements have accelerated the use of digital outcrop data capture and analysis in field geology, transforming what was principally a visualization medium into fully interrogatable quantitative geo-data objects (Jones et al., 2004;Bemis et al., 2014;Howell et al., 2014;Hodgetts et al., 2015;Biber et al., 2018;Bruna et al., 2019;Caravaca et al., 2019;Thiele et al., 2019;Triantafyllou et al., 2019). Initially, close-range remote-sensing studies seeking to reconstruct and analyze rock outcrops were dominantly built around terrestrial laser scanning systems (terrestrial lidar), which became commercially available around two decades ago (e.g., Bellian et al., 2002). ...
Full-text available
Since the advent of affordable consumer-grade cameras over a century ago, photographic images have been the standard medium for capturing and visualizing outcrop-scale geological features. Despite the ubiquity of raster image data capture in routine fieldwork, the development of close-range 3D remote-sensing techniques has led to a paradigm shift in the representation and analysis of rock exposures from two- to three-dimensional forms. The use of geological 3D surface reconstructions in routine fieldwork has, however, been limited by the portability, associated learning curve, and/or expense of tools required for data capture, visualization, and analysis. Smartphones are rapidly becoming a viable alternative to conventional 3D close-range remote-sensing data capture and visualization platforms, providing a catalyst for the general uptake of 3D outcrop technologies by the geological community, which were up until relatively recently the purview of a relatively small number of geospatial specialists. Indeed, the continuous improvement of smartphone cameras, coupled with their integration with global navigation satellite system (GNSS) and inertial sensors provides 3D reconstructions with comparable accuracy to survey-grade systems. These developments have already led many field geologists to replace reflex cameras, as well as dedicated handheld GNSS receivers and compass clinometers, with smartphones, which offer the equivalent functionality within a single compact platform. Here we demonstrate that through the use of a smartphone and a portable gimbal stabilizer, we can readily generate and register high-quality 3D scans of outcropping geological structures, with the workflow exemplified using a mirror of a seismically active fault. The scan is conducted with minimal effort over the course of a few minutes with limited equipment, thus being representative of a routine situation for a field geologist.
... ). In der für die vorliegende Arbeit häufig verwendeten Software CloudCompare ist eine semiautomatisierte Methode implementiert: Das Plug-in vonThiele et al. (2017Thiele et al. ( , 2019 ermittelt in 3D-Punktwolken automatisiert Spuren zwischen zwei manuell gepickten Punkten. In jüngerer Zeit erschienen diverse weitere Arbeiten, die sich mit einer automatisierten Erfassung von (Kluft)Spuren befassen (u.a.Umili et al. 2013, Li et al. 2016, Bolkas et al. 2018, Guo et al. 2018). ...
Full-text available
Für viele Tiefengeothermie- und manche Kohlenwasserstofflagerstätten sind natürliche Bruchnetzwerke von sehr großer Bedeutung, da wirtschaftlich nutzbare Fließraten und Porositäten von ihnen abhängen. Aufschlussanalogstudien sind ein wichtiges und ver-gleichsweise kosteneffektives Werkzeug, um Vorhersagen über potenzielle geklüftete Reservoire im Untergrund zu treffen. Auch zur Beurteilung der geomechanischen Eigenschaften von Gesteinskörpern müssen Bruchnetzwerke anhand von Aufschlüssen charakterisiert werden. Im Rahmen von Aufschlussanalogstudien kommen vermehrt Fernerkundungstechniken wie TLS (Terrestrisches Laserscanning) zum Einsatz. Damit gewonnene 3D-Punktwolken sind die Grundlage für hochauflösende digitale Aufschluss-modelle („Digital Outcrop Models“, kurz DOMs). Mit DOMs lassen sich (i) Orientie-rungen, Positionen und Geometrien von Trennflächen extrahieren, (ii) Felddaten präzise räumlich integrieren, (iii) verschiedene Abbaustände in Steinbrüchen erfassen und vergleichen, (iv) sedimentärer Strukturen räumlich interpretieren sowie (v) strukturelle Rahmen für Reservoirmodelle gewinnen. Im Rahmen der vorliegenden Dissertation wurden fotorealistische DOMs von Stein-brüchen im Buntsandstein (Oberes Perm bis Untere Trias), im Muschelkalk (Mittlere Trias) und einem natürlichen Granitaufschluss (Karbon) als Analoga potenzieller geo-thermischer Reservoire im Untergrund des Oberrheingrabens (SW-Deutschland, E-Frankreich) erstellt. Der Hauptteil der Arbeit widmet sich der Entwicklung von Techni-ken zur automatisierten Extraktion von Flächeninformationen aus DOMs, insbesondere von Kluftinformationen, die sich zur Modellierung von diskreten Bruchnetzwerken verwenden lassen. In Kooperation mit der Abteilung Geoinformatik des Geographischen Instituts, Universi-tät Heidelberg, wurde ein robuster Algorithmus zur automatisierten Berechnung von Flächeninformationen in 3D-Punktwolken entwickelt. Die daraus hervorgegangene automatisierte Flächenanalyse wird in der vorliegenden Dissertation vorgestellt. Sie basiert auf Segmentierung mittels Bereichswachstumsverfahren und lässt sich über eine Reihe von Homogenitätskriterien aktiv an unterschiedliche Oberflächen, Datenqualitäten und Fragestellungen adaptieren. Die Möglichkeiten dieser sehr flexiblen Methode werden ausführlich beleuchtet und die Plausibilität automatisiert erstellter Flächensegmente überprüft. Der bearbeitete Granitaufschluss besitzt komplexe Flächenformen, die genutzt wurden, um die Flächenerfassung mit der automatisierten Flächenanalyse anhand verschiedener statistischer Verfahren zu validieren. Zu diesem Zweck wurden auch mehr als 1000 Flächen konventionellen mit einem Gefügekompass aufgenommen und die Orientierungen von 122 Flächen mit einer händischen digitalen Referenzmethode im DOM eingemessen. Die Segmentgröße ist eines der wichtigsten Kriterien der automatisierten Flächenanalyse zum Verwerfen irrelevanter Segmente. Sie ist durch die Anzahl der Punkte eines Seg-ments definiert. Die Punktmenge pro Flächeneinheit ist in TLS-Punktwolken jedoch abhängig von der Perspektive des Scanners zur gemessenen Oberfläche. Es wurde ein trigonometrisches Verfahren zur Korrektur dieses perspektivischen Einflusses hergeleitet und in den Algorithmus der automatisierten Flächenanalyse integriert. Damit berechnete Punktanzahlen sind proportional zum Flächeninhalt des Segments, der daraus auto-matisiert berechnet werden kann. Diese Segmentgrößenkorrektur wurde durch Messun-gen an einer künstlichen Standardfläche und in zwei DOMs mittels an den Punktwolken angelegte 2D-Polygonen detailliert validiert. Für einen Aufschlusses im Buntsandstein wurde exemplarisch ein diskretes Bruchnetz-werk modelliert, das auf digital extrahierten Kluftparametern basiert. Der präsentierte Workflow bietet neue Einsichten in detaillierte virtuelle Messungen von Kluftintensitäten (P10-Kennzahl) und zeigt Möglichkeiten und Grenzen digitaler Charakterisierung von Bruchnetzwerken auf. Die Validierung der digitalen Orientierungsmessungen am Granitaufschluss ergab eine durchschnittliche Abweichung zu den Kompassmessungen von 5,0° für Vergleiche an einzelnen Flächen und Abweichungen zwischen 1,0° und 1,6° für die mittlere Orientierung von drei erkannten Kluftscharen. Der Vergleich mit einer digitalen Refe-renzmethode und weitere Qualitätskontrollen weisen deutlich darauf hin, dass die mit der automatisierten Flächenanalyse gemessenen Orientierungen eine signifikant höhere Ge-nauigkeit als die Werte der Kompassmessungen haben. Die Überprüfung der Segmentgrößenkorrektur mit der künstlichen Standardfläche ergab für Sichtwinkel unter 80° eine systematische Abweichung der berechneten Flächeninhalte von +3 %. Die zufällige Abweichung ist geringer: die Messwerte liegen im Bereich ±1 % um ihren Mittelwert, der Variationskoeffizient beträgt 0,45 %. Die systematische Abwei-chung konnte durch die Eigenschaften des verwendeten TLS erklärt und mit zwei entwickelten Verfahren fast vollständig korrigiert werden. Die Abweichungen zu Flächeninhalten von automatisiert an die segmentierten Punktwolken zweier DOMs angelegter 2D-Polygone haben einen Median von 6,4 % sowie 4,3 % für Sichtwinkel unter 70° und 4,9 % und 3,9 % für Sichtwinkel unter 60°. Allerdings hängt die Überein-stimmung der Ergebnisse aus den Methoden stark von der gewählten maximalen Kantenlänge des Polygonzugs ab. Einzelne Trennflächen oder gesamte Bruchnetzwerke können mit den in dieser Disser-tation präsentierten TLS-basierten Methoden risikoarm, automatisiert und dadurch effi-zient charakterisiert werden. Unzugängliche Aufschlussareale werden dadurch messtech-nisch erschlossen. Etablierte händische Messtechniken lassen sich virtuell in DOMs adaptieren. Ermittelte Positionen, Orientierungen und Geometrien von Flächen und anderer Strukturen sind von sehr hoher Genauigkeit und eignen sich als Datenbasis für Kluftmodellierungen, die Abschätzungen der hydraulischen und geomechanischen Eigenschaften von Kluftnetzwerken ermöglichen.
... The term "orientation" has been employed in the fields of humanities, social sciences, natural sciences, and technology in various ways, including, among others, value orientation, 1 new member orientation (or "training"), fiber-reinforced composites, 2,3 non-woven or electro-spun nanofibers 4 and membranes, 5 fiber orientation in extruded dried meat, 6 and structural orientation in geology. 7 These "orientations" each have corresponding testing methods and modes of expression. ...
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Using a fiber orientation degree measurement instrument (i.e., a dynamic modulus tester), 28 groups of averaged sonic pulse travel times in a polypropylene monofilament were measured and recorded under five pre-tensions across eight separation distances. The zero-time (or delay time) T0, sonic velocity C, sonic modulus E, Hermans orientation factor F, and orientation angle θ were calculated via two- and multi-point methods. The good agreement observed between the scatter plots of calculated data and the regression lines shows that the multi-point method provides reliable, accurate determination of the sonic modulus (or the dynamic elastic modulus) and the orientation parameters. Surprisingly, the zero-time for sonic pulse propagation depends significantly on the separation distance in practice, although it does not in theory. For easy and rapid measurement or relative comparisons using the two-point method, the optimal range of pre-tension is 0.1 gf/den–0.2 gf/den, and the optimal separation distances are 200 mm and 400 mm. The two-point method is appropriate for industrial applications, while because of its greater accuracy, the multi-point method is preferred for scientific research.
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Strike and dip are essential to the description of geological features and therefore play important roles in 3D geological modeling. Unevenly and sparsely measured orientations from geological field mapping pose problems for the geological modeling, especially for covered and deep areas. This study developed a new method for estimating strike and dip based on structural expansion orientation, which can be automatically extracted from both geological and geophysical maps or profiles. Specifically, strike and dip can be estimated by minimizing an objective function composed of the included angle between the strike and dip and the leave-one-out cross-validation strike and dip. We used angle parameterization to reduce dimensionality and proposed a quasi-gradient descent (QGD) method to rapidly obtain a near-optimal solution, improving the time-efficiency and accuracy of objective function optimization with the particle swarm method. A synthetic basin fold model was subsequently used to test the proposed method, and the results showed that the strike and dip estimates were close to the true values. Finally, the proposed method was applied to a real fold structure largely covered by Cainozoic sediments in Australia. The strikes and dips estimated by the proposed method conformed to the actual geological structures more than those of the vector interpolation method did. As expected, the results of 3D geological implicit interface modeling and the strike and dip vector field were much improved by the addition of estimated strikes and dips.
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The fitting of a plane to data points is essential to the geosciences. However, it is recognized that the reliability of these best‐fit planes depends upon the point set distribution and geometry, evaluated in terms of the eigen based parameters derived from the moment of inertia analysis. Despite its significance, few studies have addressed the uncertainties of the analysis, which can adversely affect the reproduction of results one of the cornerstones of scientific endeavour. Aiming to contribute towards the neglected issue of the moment of inertia precision, we have developed a bootstrap resampling scheme to empirically discover the distribution of uncertainties in the orientation of best‐fit planes. Dispersion of the bootstrapped normal vectors to the best‐fit plane is regarded as a measure of precision, evaluated with the maximum angular distance from the optimal solution. This rationale was tested using Monte Carlo generated samples covering a comprehensive range of shape parameters to assess the dependence between eigen parameters and their inherent bias. Our results show that the oblateness of the point‐cloud is a robust parameter to assess the reliability of the best‐fit plane. Given this, the method was then applied to a publicly available lidar‐dataset. We argue that georeferenced point‐clouds with an oblateness parameter greater than 3 and 1.5 may be placed at 95% confidence levels of 5 and 10 degrees respectively. We propose using these values as thresholds to obtain robust best‐fit planes, guaranteeing reproducible results for scientific research.
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Recent advances in photogrammetry and computer vision have seen a growing interest in 3D image-based modelling. Semi-automatic workflows for processing large image sets are now available as commercial and open-source solutions, and coupled with low cost photo-imaging sensors, a new era of slope visualisation opportunities has begun. This paper investigates the application of low-cost image sensors, including a smartphone, two off-the-shelf compact digital cameras and a Raspberry Pi camera module, and low-cost aerial platforms, including one quadcopter with an action camera and another quadcopter with a built-in camera, to geotechnical problems. The study showed that reliable rock surface models can be created from images acquired by any of the different sensors tested, with the photogrammetric models able to match a laser scanner model to within 5 to 11 mm for the majority of areas on the slope. Reliability decreased for areas that were in heavy shade at the time of image acquisition, with errors of as much as 28 mm in extreme cases, although these were unusual. Models derived from terrestrial and aerially-mounted sensors performed similarly well, except for images acquired by a low-cost UAV for which the only positional control was an on-board GPS, which could only achieve an accuracy of 80-150 mm for the majority of points. Dips inferred from features in the virtual model were generally accurate to within 1 to 2 degrees. The variation in the dip direction is bigger, and in some cases even more than 12 degrees. Several of the steeper virtual measurements also have reversed dip directions. The reversed virtual dip measurements were a numerical anomaly, associated with the interpretation of very steep dip angle values from the model.
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Mapping lithology and geological structures accurately remains a challenge in difficult terrain or in active mining areas. We demonstrate that the integration of terrestrial and drone-borne multi-sensor remote sensing techniques significantly improves the reliability, safety, and efficiency of geological activities during exploration and mining monitoring. We describe an integrated workflow to produce a geometrically and spectrally accurate combination of a Structure-from-Motion Multi-View Stereo point cloud and hyperspectral data cubes in the visible to near-infrared (VNIR) and short-wave infrared (SWIR), as well as long-wave infrared (LWIR) ranges acquired by terrestrial and drone-borne imaging sensors. Vertical outcrops in a quarry in the Freiberg mining district, Saxony (Germany), featuring sulfide-rich hydrothermal zones in a granitoid host, are used to showcase the versatility of our approach. The image data are processed using spectroscopic and machine learning algorithms to generate meaningful 2.5D (i.e., surface) maps that are available to geologists on the ground just shortly after data acquisition. We validate the remote sensing data with thin section analysis and laboratory X-ray diffraction, as well as point spectroscopic data. The combination of ground- and drone-based photogrammetric and hyperspectral VNIR, SWIR, and LWIR imaging allows for safer and more efficient ground surveys, as well as a better, statistically sound sampling strategy for further structural, geochemical, and petrological investigations.
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Seismological and geodetic data from modern volcanic systems strongly suggest that magma is transported significant distance (tens of kilometres) in the subsurface away from central volcanic vents. Geological evidence for lateral emplacement preserved within exposed dykes includes aligned fabrics of vesicles and phenocrysts, striations on wall rocks and the anisotropy of magnetic susceptibility. In this paper, we present geometrical evidence for the lateral emplacement of segmented dykes restricted to a narrow depth range in the crust. Near-total exposure of three dykes on wave cut platforms around Birsay (Orkney, UK) are used to map out floor and roof contacts of neighbouring dyke segments in relay zones. The field evidence suggests emplacement from the WSW towards the ENE, and that the dykes are segmented over their entire vertical extent. Geometrical evidence for the lateral emplacement of segmented dykes is likely more robust than inferences drawn from flow-related fabrics, due to the prevalence of ubiquitous ‘drainback’ events (i.e. magmatic flow reversals) observed in modern systems.
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The deformation structures (folds and fractures) affecting Monte Antola flysch formation in the area of Ponte Organasco (Northern Apennines-Italy) were analyzed by Unmanned Aerial Vehicle Digital Photogrammetry (UAVDP). This technique allowed the realization of Digital Outcrop Models (DOMs) interpreted in a stereoscopic environment by collecting a large number of digital structural measures (strata, fractures and successively fold axes and axial planes). In particular, by UAVDP was possible to analyze the relationships between folds and fractures all along the study structures. The structural analysis revealed the presence of a series of NE-vergent folds characterized by a typical Apenninic trend and affected by four main sets of fractures. Fractures are always sub-orthogonal to the bedding, maintains constant angular relationships with the bedding and seems linked to the folding deformation. The study shows that the UAVDP technique can overcome the main limitations of field structural analysis such as the scarce presence and the inaccessibility (total or partial) of rock outcrops and allows for acquiring images of rock outcrops at a detailed scale from user-inaccessible positions and different points of view and analyze inaccessible parts of outcrops.
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The present paper explores the combination of unmanned aerial vehicle (UAV) photogrammetry and three-dimensional geomechanical modeling in the investigation of instability processes of long sectors of coastal rocky cliffs. The need of a reliable and detailed reconstruction of the geometry of the cliff surfaces, beside the geomechanical characterization of the rock materials, could represent a very challenging requirement for sub-vertical coastal cliffs overlooking the sea. Very often, no information could be acquired by alternative surveying methodologies, due to the absence of vantage points, and the fieldwork could pose a risk for personnel. The case study is represented by a 600 m long sea cliff located at Sant'Andrea (Melendugno, Apulia, Italy). The cliff is characterized by a very complex geometrical setting, with a suggestive alternation of 10 to 20 m high vertical walls, with frequent caves, arches and rock-stacks. Initially, the rocky cliff surface was reconstructed at very fine spatial resolution from the combination of nadir and oblique images acquired by unmanned aerial vehicles. Successively, a limited area has been selected for further investigation. In particular, data refinement/decimation procedure has been assessed to find a convenient three-dimensional model to be used in the finite element geomechanical modeling without loss of information on the surface complexity. Finally, to test integrated procedure, the potential modes of failure of such sector of the investigated cliff were achieved. Results indicate that the most likely failure mechanism along the sea cliff examined is represented by the possible propagation of shear fractures or tensile failures along concave cliff portions or over-hanging due to previous collapses or erosion of the underlying rock volumes. The proposed approach to the investigation of coastal cliff stability has proven to be a possible and flexible tool in the rapid and highly-automated investigation of hazards to slope failure in coastal areas.
We propose a new automatic methodology for identifying discontinuity traces directly from 3D point clouds of natural rocky slopes. The potential feature points of the discontinuity traces were detected based on a 1D truncated Fourier series. To extract trace points from the potential feature points, a curvature-weighted Laplacian-like smoothing technique was used to thin these points. Finally, the trace lines were constructed through a feature-parameter-weighted line growing algorithm. The effectiveness of the method was tested with four data sets. Additionally, the results of two of the data sets were compared with the results of CloudCompare and an existing method. Finally, the area density was calculated based on the extracted trace lines. The results show that the proposed discontinuity trace extraction method is fast, effective and automatic and has the potential for use as a supplement to traditional direct measurements of discontinuity traces, thereby providing important supplemental data for fracture related research.
Over the last few decades, significant advances in using geophysical techniques to image the structure of magma plumbing systems have enabled the identification of zones of melt accumulation, crystal mush development, and magma migration. Combining advanced geophysical observations with petrological and geochemical data has arguably revolutionised our understanding of, and afforded exciting new insights into, the development of entire magma plumbing systems. However, divisions between the scales and physical settings over which these geophysical, petrological, and geochemical methods are applied still remain. To characterise some of these differences and promote the benefits of further integration between these methodologies, we provide a review of geophysical techniques and discuss how they can be utilised to provide a structural context for and place physical limits on the chemical evolution of magma plumbing systems. For example, we examine how Interferometric Synthetic Aperture Radar (InSAR), coupled with Global Positioning System (GPS) and Global Navigation Satellite System (GNSS) data, and seismicity may be used to track magma migration in near real-time. We also discuss how seismic imaging, gravimetry and electromagnetic data can identify contemporary melt zones, magma reservoirs and/or crystal mushes. These techniques complement seismic reflection data and rock magnetic analyses that delimit the structure and emplacement of ancient magma plumbing systems. For each of these techniques, with the addition of full-waveform inversion (FWI), the use of Unmanned Aerial Vehicles (UAVs) and the integration of geophysics with numerical modelling, we discuss potential future directions. We show that approaching problems concerning magma plumbing systems from an integrated petrological, geochemical, and geophysical perspective will undoubtedly yield important scientific advances, providing exciting future opportunities for the volcanological community.
Fault roughness is a measure of the dimensions and distribution of fault asperities, which can act as stress concentrators affecting fault frictional behaviour and the dynamics of rupture propagation. Studies aimed at describing fault roughness require the acquisition of extremely detailed and accurate datasets of fault surface topography. Fault surface data have been acquired by methods such as LiDAR, laser profilometers and white light interferometers, each covering different length scales and with only LiDAR available in the field. Here we explore the potential use of multi-view photogrammetric methods in fault roughness studies, which are presently underexplored and offer the advantage of detailed data acquisition directly in the field. We applied the photogrammetric method to reproduce fault topography, by using seven dm-sized fault rock samples photographed in the lab, three fault surfaces photographed in the field, and one control object used to estimate the model error. We studied these topographies estimating their roughness scaling coefficients through a Fourier power spectrum method. Our results show scaling coefficients of 0.84 ± 0.17 along the slip direction and 0.91 ± 0.17 perpendicularly to it, and are thus comparable to those results obtained by previous authors. This provides encouragement for the use of photogrammetric methods for future studies, particularly those involving field-based acquisition, where other techniques have limitations.
To ensure the effective long-term storage of CO2 in candidate geological storage sites, evaluation of potential leakage pathways to the surface should be undertaken. Here we use a series of natural CO2 seeps along a fault in South Africa to assess the controls on CO2 leakage to the surface. Geological mapping and detailed photogrammetry reveals extensive fracturing along the mapped fault trace. Measurements of gas flux and CO2 concentration across the fracture corridor give maximum soil gas measurements of 27% CO2 concentration and a flux of 191 g m⁻² d⁻¹. These measurements along with observations of gas bubbles in streams and travertine cones attest to CO2 migration to the surface. Permeability measurements on the host rock units show that the tillite should act as an impermeable seal to upward CO2 migration. The combined permeability and fracture mapping data indicate that fracture permeability creates the likely pathway for CO2 migration through the low permeability tillite to the surface. Heterogeneity in fracture connectivity and intensity at a range of scales will create local higher permeability pathways along the fracture corridor, although these may seal with time due to fluid-rock interaction. The results have implications for the assessment and choice of geological CO2 storage sites, particularly in the assessment of sub-seismic fracture networks.