A recent method for modeling folds uses a fold frame with coordinates based on the structural geology of folds: fold axis direction, fold axial surface and extension direction. The fold geometry can be characterised by rotating the fold frame by the pitch of the fold axis in the axial surface and the angle between the folded foliation and the axial surface. These rotation angles can be expressed as 1D functions of the fold frame coordinates. In this contribution we present methods for extracting and automatically modeling the fold geometries from structural data. The fold rotation angles used for characterising the fold geometry can be calculated locally from structural observations. The fold rotation angles incorporate the structural geology of the fold and allow for individual structural measurements to be viewed in the context of the folded structure. To filter out the effects of later folding the fold rotation angles are plotted against the coordinates of the fold frame. Using these plots the geometry of the folds can be interpolated directly from structural data where we use a combination of radial basis function and harmonic analysis to interpolate and extrapolate the fold geometry. This contribution addresses a major limitation in existing methods where the fold geometry was not constrained from structural data. We present two case studies: a proof of concept synthetic model of a non-cylindrical fold and an outcrop of an asymmetrical fold within the Lachlan Fold belt at Cape Conran, Victoria, Australia.
Papers
Recent developments in structural modeling techniques have dramatically increased the capability to incorporate fold-related data into the modeling workflow. However, these techniques are lacking a mathematical framework for properly addressing structural uncertainties. Previous studies investigating structural uncertainties have focused on the sensitivity of the interpolator to perturbing the input data. These approaches do not incorporate conceptual uncertainty about the geological structures and interpolation process to the overall uncertainty estimate. In this work, we frame structural modeling as an inverse problem and use a Bayesian framework to reconcile structural parameters and data uncertainties. Bayesian inference is applied for determining the posterior probability distribution of fold parameters given a set of structural observations and prior distributions based on general geological knowledge and regional observations. This approach allows for an inversion of structural geology data, where each realization can differ in the structural description of the fold geometries, instead of finding only a single best fit solution. We show that analyzing the variability between the resulting models highlights uncertainties associated with the geometry of regional structures. These areas can be used to target where additional data would be most beneficial for improving the model quality and efficiently reducing structural uncertainty.
The process of building three-dimensional (3D) geological models can be framed as an inverse problem where a model describing the 3D distribution of rock units is non-uniquely derived from geological observations. The inverse problem theory provides a powerful framework for inferring these parameters from all geological observations, in a similar way to how a geologist can iteratively update their structural interpretation while mapping. Existing geological knowledge is usually indirectly incorporated into 3D models using the geologist’s non-unique interpretation as form lines, cross sections and level maps. These approaches treat constraints derived from geological knowledge in the same way as direct observations, diluting and confusing both information provided by geological knowledge and hard data resulting in significant subjectivity. We present a geological inversion using Bayesian inference where geological knowledge can be incorporated directly into the interpolation scheme with likelihood functions and informative prior distributions. We demonstrate these approaches on a series of synthetic fold shapes as a proof of concept and a case study from the Proterozoic Davenport Province in the Northern Territory, Australia. The combined inversion of geological data and knowledge significantly reduces the uncertainty in possible fold geometries where data is sparse or highly ambiguous. This could be used by geologists while mapping to propagate information about uncertainties throughout the mapping/model building process and would allow for different structural interpretations to be rapidly tested for targeted data collection.
In this contribution we introduce LoopStructural, a new open source 3D geological modelling python package ( https://www.github.com/Loop3d/LoopStructural). LoopStructural provides a generic API for 3D geological modelling applications harnessing the core python scientific libraries pandas, numpy and scipy. Six different interpolation algorithms, including 3 discrete interpolators and 3 polynomial trend interpolators, can be used from the same model design. This means that different interpolation algorithms can be mixed and matched within a geological model allowing for different geological objects e.g. different conformable foliations, fault surfaces, unconformities to be modelled using different algorithms. Geological features are incorporated into the model using a time-aware approach, where the most recent features are modelled first and used to constrain the geometries of the older features. For example, we use a fault frame for characterising the geometry of the fault surface and apply each fault sequentially to the faulted surfaces. In this contribution we use LoopStructural to produce synthetic proof of concepts models and a 86 x 52 km model of the Flinders ranges in South Australia using map2loop.
Without properly accounting for both fault kinematics and faulted surface observations, it is challenging to create 3D geological models of faulted geological units that are seen in all tectonic settings. Geometries where multiple faults interact, where the faulted surface geometry significantly deviate from a flat plane and where the geological interfaces are poorly characterised by sparse data sets are particular challenges. There are two existing approaches for incorporating faults into geological surface modelling: one approach incorporates the fault displacement into the surface description but does not incorporate fault kinematics and in most cases will produce geologically unexpected results such as shrinking intrusions, fold hinges without offset and layer thickness growth in flat oblique faults. Another approach builds a continuous surface without faulting and then applies a kinematic fault operator to the continuous surface to create the displacement. Both approaches have their strengths, however neither approach can capture the interaction of faults within complicated fault networks e.g fault duplexes, flower structures and listric faults because they either (1) impose an incorrect (not defined by data) fault slip direction; or (2) require an over sampled data set that describes the faulted surface location. In this study we integrate the fault kinematics into the implicit surface by using the fault kinematic model to restore observations and the model domain prior to interpolating the faulted surface. This approach can build models that are consistent with observations of the faulted surface and fault kinematics. Integrating fault kinematics directly into the implicit surface description allows for complex fault stratigraphy and fault-fault interactions to be modelled. Our approaches show significant improvement in capturing faulted surface geometries especially where the intersection angle between the faulted surface geometry and the fault surface varies (e.g. intrusions, fold series) and when modelling interacting faults (fault duplex).
We present two Python libraries (map2loop and map2model) which combine the observations available in digital geological maps with conceptual information, including assumptions regarding the subsurface extent of faults and plutons to provide sufficient constraints to build a reasonable 3D geological model. At a regional scale, the best predictor for the 3D geology of the near-subsurface is often the information contained in a geological map. This remains true even after recognising that a map is also a model, with all the potential for hidden biases that this model status implies. One challenge we face is the difficulty in reproducibly preparing input data for 3D geological models. The information stored in a map falls into three categories of geometric data: positional data such as the position of faults, intrusive and stratigraphic contacts; gradient data, such as the dips of contacts or faults and topological data, such as the age relationships of faults and stratigraphic units, or their adjacency relationships. This work is being conducted within the Loop Consortium, in which algorithms are being developed that allow automatic deconstruction of a geological map to recover the necessary positional, gradient and topological data as inputs to different 3D geological modelling codes. This automation provides significant advantages: it reduces the time to first prototype models; it clearly separates the primary data from subsets produced from filtering via data reduction and conceptual constraints; and provides a homogenous pathway to sensitivity analysis, uncertainty quantification and Value of Information studies. We use the example of the re-folded and faulted Hamersley Basin in Western Australia to demonstrate a complete workflow from data extraction to 3D modelling using two different Open Source 3D modelling engines: GemPy and LoopStructural.
Three-dimensional structural modeling is gaining importance for a broad range of quantitative geoscientific applications. However, existing approaches are still limited by the type of structural data they are able to use and by their lack of structural meaning. Most techniques heavily rely on spatial data for modeling folded layers, but are unable to completely use cleavage and lineation information for constraining the shape of modeled folds. This lack of structural control is generally compensated by expert knowledge introduced in the form of additional interpretive data such as cross-sections and maps. With this approach, folds are explicitly designed by the user instead of being derived from data. This makes the resulting structures subjective and deterministic. This paper introduces a numerical framework for modeling folds and associated foliations from typical field data. In this framework, a parametric description of fold geometry is incorporated into the interpolation algorithm. This way the folded geometry is implicitly derived from observed data, while being controlled through structural parameters such as fold wavelength, amplitude and tightness. A fold coordinate system is used to support the numerical description of fold geometry and to modify the behavior of classical structural interpolators. This fold frame is constructed from fold-related structural elements such as axial foliations, intersection lineations, and vergence. Poly-deformed terranes are progressively modeled by successively modeling each folding event going backward through time. The proposed framework introduces a new modeling paradigm, which enables the building of three- dimensional geological models of complex poly-deformed terranes. It follows a process based on the structural geologist approach and is able to produce geomodels that honor both structural data and geological knowledge. ©
Fracture systems are often geometrically invariant across a range of scales, but the impact of structural inheritance on this relationship is poorly understood. This paper shows how fracture orientations in sedimentary rocks vary at different scales when influenced by pre-rift basement structures. We use high-resolution unmanned aerial vehicle (UAV) orthophotos to map folds and fractures in the basement and cover rocks of the Gippsland Basin, southeast Australia. Outcrop-scale observations are compared with >1 km long faults previously interpreted from potential field data. We use length-coloured rose diagrams of fracture traces to compare trends in fracture orientations. Early Cretaceous syn-rift normal faults exhibit the same ENE-WSW trend at basin (>1 km) and outcrop (meters) scales. Pervasive outcrop-scale, subvertical, NNW-SSE striking joints record a subsequent regional shortening event, but at the basin scale this is only expressed as reverse reactivated ENE-WSW striking faults. Thus, fabrics and/or faults in the underlying basement exert significant control on the orientation of basin-scale fractures in the cover but appear to have limited influence on outcrop-scale fracture orientations. Our observations show that fracture systems influenced by structural inheritance are not scale-invariant, and that a proper understanding of structural architecture can only be achieved by analysing data that span multiple scales.
The advent of large digital datasets from un- manned aerial vehicle (UAV) and satellite platforms now challenges our ability to extract information across multiple scales in a timely manner, often meaning that the full value of the data is not realised. Here we adapt a least-cost-path solver and specially tailored cost functions to rapidly inter- polate structural features between manually defined control points in point cloud and raster datasets. We implement the method in the geographic information system QGIS and the point cloud and mesh processing software CloudCompare. Using these implementations, the method can be applied to a variety of three-dimensional (3-D) and two-dimensional (2-D) datasets, including high-resolution aerial imagery, dig- ital outcrop models, digital elevation models (DEMs) and geophysical grids. We demonstrate the algorithm with four diverse applications in which we extract (1) joint and contact patterns in high-resolution orthophotographs, (2) fracture patterns in a dense 3-D point cloud, (3) earthquake surface ruptures of the Greendale Fault associated with the Mw7.1 Darfield earth- quake (New Zealand) from high-resolution light detection and ranging (lidar) data, and (4) oceanic fracture zones from bathymetric data of the North Atlantic. The approach im- proves the consistency of the interpretation process while retaining expert guidance and achieves significant improve- ments (35–65 %) in digitisation time compared to traditional methods. Furthermore, it opens up new possibilities for data synthesis and can quantify the agreement between datasets and an interpretation.
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 ap- proximately 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 the 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.
Fracture systems are often geometrically invariant across a range of scales, but the impact of structural inheritance on this relationship is poorly understood. This paper shows how fracture orientations in sedimentary rocks vary at different scales when influenced by pre-rift basement structures. We use high-resolution unmanned aerial vehicle (UAV) orthophotos to map folds and fractures in the basement and cover rocks of the Gippsland Basin, southeast Australia. Outcrop-scale observations are compared with >1 km long faults previously interpreted from potential field data. We use length-coloured rose diagrams of fracture traces to compare trends in fracture orientations. Early Cretaceous syn-rift normal faults exhibit the same ENE-WSW trend at basin (>1 km) and outcrop (meters) scales. Pervasive outcrop-scale, subvertical, NNW-SSE striking joints record a subsequent regional shortening event, but at the basin scale this is only expressed as reverse reactivated ENE-WSW striking faults. Thus, fabrics and/or faults in the underlying basement exert significant control on the orientation of basin-scale fractures in the cover but appear to have limited influence on outcrop-scale fracture orientations. Our observations show that fracture systems influenced by structural inheritance are not scale-invariant, and that a proper understanding of structural architecture can only be achieved by analysing data that span multiple scales.