2019
DOI: 10.1007/s11004-019-09789-6
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Implicit Structural Modeling by Minimization of the Bending Energy with Moving Least Squares Functions

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Cited by 33 publications
(22 citation statements)
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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%
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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%
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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%