Implicit Structural Modeling by Minimization of the Bending Energy with Moving Least Squares Functions

Renaudeau, Julien; Malvesin, E.; Maerten, Frantz; Caumon, Guillaume

doi:10.1007/s11004-019-09789-6

Cited by 33 publications

(22 citation statements)

References 37 publications

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“…In LoopStructural surfaces are implicitly represented by an isovalue of one or more volumetric scalar fields (Calcagno et al, 2008a;Caumon et al, 2013;Cowan et al, 2003;Frank et al, 2007;Gonçalves et al, 2017;Hillier et al, 2014;Jessell, 1981;de la Varga et al, 2019;Lajaunie et al, 1997;Mallet, 2002Mallet, , 2014Manchuk and Deutsch, 2019;Maxelon et al, 2009;Moyen et al, 2004;Renaudeau et al, 2019;Yang et al, 2019). The geological rules are managed by adding the geological event (folding event, one fault, another fault, an unconformity) structural parameters in a time-aware approach, where the most recent event is added first and the constraints are added backwards in time.…”

Section: Methodsmentioning

confidence: 99%

“…All implicit surface modelling techniques involve finding a combination of weighted basis functions that fit the geological observations. There are two main approaches used for implicit surface modelling: (1) data-supported approaches where the basis functions are estimated at the data points (Calcagno et al, 2008a;Cowan et al, 2003;Gonçalves et al, 2017;Hillier et al, 2014;Lajaunie et al, 1997) and (2) discrete interpolation where the basis functions are located on a predefined support (Caumon et al, 2013;Frank et al, 2007;Irakarama et al, 2018;Renaudeau et al, 2019). The algorithms are often linked to commercial software, e.g.…”

Section: Introductionmentioning

confidence: 99%

“…LoopStructural is a new geological modelling engine developed within the Loop 4 consortium (Ailleres et al, 2018). The core modelling library within LoopStructural depends on scipy (Virtanen et al, 2020), numpy (Van Der Walt et al, 2011) and pandas (pandas development team, 2020), the core scientific Python libraries. A visualisation module uses LavaVu (Kaluza et al, 2020), a minimal OpenGL visualisation package allowing for models to be visualised within a Jupyter notebook environment.…”

Section: Introductionmentioning

confidence: 99%

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LoopStructural 1.0: time-aware geological modelling

et al. 2021

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Abstract. In this contribution we introduce LoopStructural, a new open-source 3D geological modelling Python package (http://www.github.com/Loop3d/LoopStructural, last access: 15 June 2021). 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 three 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 and 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 km × 52 km model of the Flinders Ranges in South Australia using map2loop.

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Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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LoopStructural 1.0: time-aware geological modelling

et al. 2021

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“…where the first term is the bending energy of Enriquez et al (1983); Turk and O'Brien (2002); Renaudeau et al (2019), and the second term is half the squared (mean) curvature of Briggs (1974), also known as the squared Laplacian (Levy, 1999). Figure 5b shows an example using the roughness operator ( 26)/( 27) to a modified version of a two-dimensional benchmark model proposed by Renaudeau et al (2017a).…”

Section: Directional Second Derivativesmentioning

confidence: 99%

“…Computation times that used to be acceptable for building a single "best model" are becoming far too long when considering stochastic approaches for sampling uncertainty. Other recent research and advances in implicit modeling include better modeling of folds Grose et al, 2017), automated building of models that conform to seismic data (Wu, 2017), more numerically efficient discretization schemes (Renaudeau et al, 2018), and many more (Mallet, 2014;Gonçalves et al, 2017;Martin and Boisvert, 2017;Renaudeau et al, 2019). As we move towards an era of multi-realization structural modeling (Caumon, 2010), new challenges continuously emerge and motivate the quest for more robust and more efficient structural implicit modeling schemes.…”

Section: Introductionmentioning

confidence: 99%

Finite Difference Implicit Structural Modeling of Geological Structures

et al. 2020

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We introduce a new method for implicit structural modeling. The main developments in this paper are the new regularization operators we propose by extending inherent properties of the classic one-dimensional discrete second derivative operator to higher dimensions. The proposed regularization operators discretize naturally on the Cartesian grid using finite differences, owing to the highly symmetric nature of the Cartesian grid. Furthermore, the proposed regularization operators do not require any special treatment on boundary nodes, and their generalization to higher dimensions is straightforward. As a result, the proposed method has the advantage of being simple to implement. Numerical examples show that the proposed method is robust and numerically efficient.

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Taking Better Advantage of Fold Axis Data to Characterize Anisotropy of Complex Folded Structures in the Implicit Modeling Framework

et al. 2021

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When too few field measurements are available for the geological modeling of complex folded structures, results of implicit methods typically exhibit an unsatisfactory bubbly aspect. However, in such cases, anisotropy data are often readily available but not fully exploited. Among them, fold axis data are a straightforward indicator of this local anisotropy direction. Focusing on the so-called potential field method, this work aims to evaluate the effect of the incorporation of such data into the modeling process. Given locally sampled fold axis data, this paper proposes to use the second-order derivatives of the scalar field in addition to the existing first-order ones. The mathematical foundation of the approach is developed and the respective efficiencies of both kinds of constraints are tested. Their integration and impact are discussed based on a synthetic case study, thereby providing practical guidelines to geomodeling tool users on the parsimonious use of data for the geological modeling of complex folded structures.

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Implicit Structural Modeling by Minimization of the Bending Energy with Moving Least Squares Functions

Cited by 33 publications

References 37 publications

LoopStructural 1.0: time-aware geological modelling

LoopStructural 1.0: time-aware geological modelling

Finite Difference Implicit Structural Modeling of Geological Structures

Taking Better Advantage of Fold Axis Data to Characterize Anisotropy of Complex Folded Structures in the Implicit Modeling Framework

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