Foliation fields and 3D cartography in geology: Principles of a method based on potential interpolation

Lajaunie, Christian; Courrioux, Gabriel; Manuel, Laurent

doi:10.1007/bf02775087

Cited by 260 publications

(217 citation statements)

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“…More specifically, explicit geometric engines require full expert knowledge while implicit ones are based on observed field data, variographic analysis and topological constraints (Jessell et al, 2014a). Geometric modeling engines interpolate features from sparse structural data and topological assumptions (Aug et al, 2005;Jessell et al, 2014a); they require prior knowledge of topology and are computationally affordable (Lajaunie et al, 1997;. Dynamic modeling engines require knowledge of initial geometry, physical properties and boundary conditions; the modeling process is computationally expensive.…”

Section: Mcue Methodsmentioning

confidence: 99%

“…That is, values for the dispersion of the spherical disturbance distributions used for the foliations were estimated on the basis of the variability in plane measurements observed by other authors (Nelson et al, 1987;Stigsson, 2016;Allmendiger et al, 2017;Cawood et al, 2017;Novakova and Pavlis, 2017) in a variety of settings and for different types of devices. Perturbation parameters for interfaces were designed to meet observed GPS uncertainty (Jennings et al, 2010) and observed experimental interface variability in previous authors' works (Courrioux et al, 2015;Lark et al, 2014Lark et al, , 2013. More specifically it was assumed that the observed end variability in the interfaces' locations in their models can be transposed to the presented cases.…”

Section: Impact Of Pole Vector Sampling Versus Dip Vector Samplingmentioning

confidence: 99%

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Monte Carlo simulation for uncertainty estimation on structural data in implicit 3-D geological modeling, a guide for disturbance distribution selection and parameterization

et al. 2018

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Abstract. Three-dimensional (3-D) geological structural modeling aims to determine geological information in a 3-D space using structural data (foliations and interfaces) and topological rules as inputs. This is necessary in any project in which the properties of the subsurface matters; they express our understanding of geometries in depth. For that reason, 3-D geological models have a wide range of practical applications including but not restricted to civil engineering, the oil and gas industry, the mining industry, and water management. These models, however, are fraught with uncertainties originating from the inherent flaws of the modeling engines (working hypotheses, interpolator's parameterization) and the inherent lack of knowledge in areas where there are no observations combined with input uncertainty (observational, conceptual and technical errors). Because 3-D geological models are often used for impactful decision-making it is critical that all 3-D geological models provide accurate estimates of uncertainty. This paper's focus is set on the effect of structural input data measurement uncertainty propagation in implicit 3-D geological modeling. This aim is achieved using Monte Carlo simulation for uncertainty estimation (MCUE), a stochastic method which samples from predefined disturbance probability distributions that represent the uncertainty of the original input data set. MCUE is used to produce hundreds to thousands of altered unique data sets. The altered data sets are used as inputs to produce a range of plausible 3-D models. The plausible models are then combined into a single probabilistic model as a means to propagate uncertainty from the input data to the final model. In this paper, several improved methods for MCUE are proposed.The methods pertain to distribution selection for input uncertainty, sample analysis and statistical consistency of the sampled distribution. Pole vector sampling is proposed as a more rigorous alternative than dip vector sampling for planar features and the use of a Bayesian approach to disturbance distribution parameterization is suggested. The influence of incorrect disturbance distributions is discussed and propositions are made and evaluated on synthetic and realistic cases to address the sighted issues. The distribution of the errors of the observed data (i.e., scedasticity) is shown to affect the quality of prior distributions for MCUE. Results demonstrate that the proposed workflows improve the reliability of uncertainty estimation and diminish the occurrence of artifacts.

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Section: Mcue Methodsmentioning

confidence: 99%

Section: Impact Of Pole Vector Sampling Versus Dip Vector Samplingmentioning

confidence: 99%

Monte Carlo simulation for uncertainty estimation on structural data in implicit 3-D geological modeling, a guide for disturbance distribution selection and parameterization

et al. 2018

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“…The 3D preliminary model of the study area has been achieved using the geological map, including lithological boundaries, and field structural data, as well as the AMS foliation in granitic rocks. For this purpose, we used the "3D Geomodeller" software (Aug 2004;, which reproduces 3D geological geometries based on interpolation of a scalar field in space (Lajaunie et al 1997;Chilès et al 2004), where a lithological contact corresponds to an isovalue of this field and the dipping of the structures corresponds to the gradient of this field. The topological relationships between the different lithological units and the geometrical relationships, like superposition, intrusion or cross-cutting relations, are taken into account through a "lithological pile", in order to reproduce complex geological systems as realistically as possible.…”

Section: Preliminary 3d Geological Modelmentioning

confidence: 99%

Gravity inversion, AMS and geochronological investigations of syntectonic granitic plutons in the southern part of the Variscan French Massif Central

Joly

Faure

Martelet

et al. 2009

Journal of Structural Geology

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“…Orientation data represent normal vectors (dip direction, dip, younging direction/polarity) to these equipotential lines/planes and are thus regarded as the gradient of the corresponding scalar field. Again, the scalar field is obtained by threedimensional interpolation, but one advantage of this approach is that it allows a set of surfaces accounting for all orientation data to be modelled simultaneously (e.g., Cowan et al, 2003;Lajaunie et al, 1997;Turk and O'Brien, 2002).…”

Section: Introductionmentioning

confidence: 99%

“…The workflow is focused on implicit modelling with GeoModeller, since this program is the most convenient for handling the type of data that is collected and used in such complexly deformed terrains (e.g., Martelet et al, 2004;Talbot et al, 2004;Maxelon and Mancktelow, 2005;Joly et al, 2008). The main advantage of 3D Geomodeller is its interpolation method, which uses a potential-field approach (Lajaunie et al, 1997;Chilè s et al, 2006;Calcagno et al, in press). The method defines a function T(x, y, z) interpolated by co-kriging from points located on interfaces, considered as having a common (unknown) potential value for each interface, and directional data representing the gradient of T. Thanks to the dual form of the co-kriging, it is possible to solve the system just once, and then use it as an interpolator to estimate T at any point p in space.…”

Section: Introductionmentioning

confidence: 99%

A workflow to facilitate three-dimensional geometrical modelling of complex poly-deformed geological units

Maxelon

Renard

Courrioux

et al. 2009

Computers & Geosciences

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a b s t r a c tThe three-dimensional (3D) geometry of complexly deformed regions is often beyond the scope of simple 2D and 2.5D representation in cross-sections and block diagrams. Methods must be developed for fully three-dimensional representation. A workflow for such three-dimensional modelling of structurally complex areas is presented. Data requirements are tailored to typical results of structural field work in strongly deformed rocks from mid-crustal levels. The workflow is based on data evaluation and data export using standard geographical information system and database management systems. Three-dimensional modelling in polyphase deformed areas is highly dependent on the correct interpretation of variations in the orientation of the dominant planar fabrics. The computer-aided earth-modelling software 3D GeoModeller is well adapted for managing this problem. It calculates the geometry of geological interfaces taking into account simultaneously the foliation data and location of lithological contacts. The workflow is based on iterative model refinement based on interactive editing of the geometry in section and map views with data assessment and pre-processing using GIS software. This approach assures internal consistency of the resulting three-dimensional models. Modelling of the Lower Lepontine Nappes in the Central Alps is used as an illustrative example from a complexly deformed terrain.

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Foliation fields and 3D cartography in geology: Principles of a method based on potential interpolation

Cited by 260 publications

References 8 publications

Monte Carlo simulation for uncertainty estimation on structural data in implicit 3-D geological modeling, a guide for disturbance distribution selection and parameterization

Monte Carlo simulation for uncertainty estimation on structural data in implicit 3-D geological modeling, a guide for disturbance distribution selection and parameterization

Gravity inversion, AMS and geochronological investigations of syntectonic granitic plutons in the southern part of the Variscan French Massif Central

A workflow to facilitate three-dimensional geometrical modelling of complex poly-deformed geological units

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