3D form line construction by structural field interpolation (SFI) of geologic strike and dip observations

Hillier, M. J.; Kemp, E A de; Schetselaar, Ernst

doi:10.1016/j.jsg.2013.01.012

Cited by 29 publications

(14 citation statements)

References 19 publications

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“…(19). From that on-contact point, t i is propagated or streamed, in the manner similar to Hillier et al (2013) until it reaches a boundary in the model space. In total, 16 estimated t tangent vectors (not co-located with gradient constraints), as illustrated in Fig.…”

Section: Case Studiesmentioning

confidence: 99%

Three-Dimensional Modelling of Geological Surfaces Using Generalized Interpolation with Radial Basis Functions

et al. 2014

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A generalized interpolation framework using radial basis functions (RBF) is presented that implicitly models three-dimensional continuous geological surfaces from scattered multivariate structural data. Generalized interpolants can use multiple types of independent geological constraints by deriving for each, linearly independent functionals. This framework does not suffer from the limitations of previous RBF approaches developed for geological surface modelling that requires additional offset points to ensure uniqueness of the interpolant. A particularly useful application of generalized interpolants is that they allow augmenting on-contact constraints with gradient constraints as defined by strike-dip data with assigned polarity. This interpolation problem yields a linear system that is analogous in form to the previously developed potential field implicit interpolation method based on co-kriging of contact increments using parametric isotropic covariance functions. The general form of the mathematical framework presented herein allows us to further expand on solutions by: (1) including stratigraphic data from above and below the target surface as inequality constraints (2) modelling anisotropy by data-driven eigen analysis of gradient constraints and (3) incorporating additional constraints by adding linear functionals to the system, such as fold axis constraints. Case studies are presented that demonstrate the advantages and general performance of the surface modelling method in sparse data environments where the contacts that constrain geological surfaces are rarely exposed but structural and off-contact stratigraphic data can be plentiful. Electronic supplementary materialThe online version of this article (

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Section: Case Studiesmentioning

confidence: 99%

Three-Dimensional Modelling of Geological Surfaces Using Generalized Interpolation with Radial Basis Functions

et al. 2014

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“…In recent years, the implicit surface modeling has especially been paid much attention. It has been improved so it can be adjusted to geological data, for example, by the use of Eigen analysis to simulate folds [24,25]. We regret to say, however, that only structural surfaces were constructed without specific geological bodies.…”

Section: Related Workmentioning

confidence: 99%

Towards Automatic and Topologically Consistent 3D Regional Geological Modeling from Boundaries and Attitudes

Guo

Zhou

et al. 2016

IJGI

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Three-dimensional (3D) geological models are important representations of the results of regional geological surveys. However, the process of constructing 3D geological models from two-dimensional (2D) geological elements remains difficult and is not necessarily robust. This paper proposes a method of migrating from 2D elements to 3D models. First, the geological interfaces were constructed using the Hermite Radial Basis Function (HRBF) to interpolate the boundaries and attitude data. Then, the subsurface geological bodies were extracted from the spatial map area using the Boolean method between the HRBF surface and the fundamental body. Finally, the top surfaces of the geological bodies were constructed by coupling the geological boundaries to digital elevation models. Based on this workflow, a prototype system was developed, and typical geological structures (e.g., folds, faults, and strata) were simulated. Geological modes were constructed through this workflow based on realistic regional geological survey data. The model construction process was rapid, and the resulting models accorded with the constraints of the original data. This method could also be used in other fields of study, including mining geology and urban geotechnical investigations.

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“…A.3. To compute this basis, the method described in Hillier et al (2013) is used: using a neighborhood of N neighbors around a given point, the sum of the cross-products of the N normalized normal vectors n i gives the following pole orientation matrix: …”

Section: Translation Of the Fractures Inside The Modelmentioning

confidence: 99%

“…To analyze the field observations, we proceed as follows: the observed fractures are rotated into the local coordinate system (u 0 , v 0 , w 0 ) derived either from the 3D geological model as explained in the paper, or from local analysis of the orientation of the stratigraphy as explained in Hillier et al (2013). This is then done using the inverse of the rotation…”

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confidence: 99%

Stochastic fracture generation accounting for the stratification orientation in a folded environment based on an implicit geological model

Borghi

Renard

Fournier

et al. 2015

Engineering Geology

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a b s t r a c t Keywords:Geological modeling Discrete fracture network (DFN) Stochastic modeling Structural geology This paper presents a new approach in generating stochastic discrete fracture networks. The particularity of the approach is that it allows us to simulate the theoretical families of fractures that are expected in a folded environment. The approach produces fractures that are consistent with the local stratigraphic orientation. The fractures are modeled as simple rectangular planar objects. When they are modeled, they are rotated according to the local stratigraphic orientation. As the stratigraphy is modeled using an implicit approach, we use the gradient of this geological potential field to retrieve the information about the geological orientation. The fracture number and size are following user-defined probability density functions.

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3D form line construction by structural field interpolation (SFI) of geologic strike and dip observations

Cited by 29 publications

References 19 publications

Three-Dimensional Modelling of Geological Surfaces Using Generalized Interpolation with Radial Basis Functions

Three-Dimensional Modelling of Geological Surfaces Using Generalized Interpolation with Radial Basis Functions

Towards Automatic and Topologically Consistent 3D Regional Geological Modeling from Boundaries and Attitudes

Stochastic fracture generation accounting for the stratification orientation in a folded environment based on an implicit geological model

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