Implicit modeling of folds and overprinting deformation

Abstract

International audienceThree-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

Inversion of Structural Geology Data for Fold Geometry

“…The geological map (Figure ) is inverted to find the joint posterior distribution for the fold geometry. Each sample of the posterior distribution defines interpolation constraints for the implicit folding algorithm (Grose et al, ; Laurent et al, ). Two hundred model realizations (Figures e and f) are generated by sampling parameter values from the joint posterior distribution to inform the fold interpolation constraints.…”

“…Three‐dimensional models are usually more difficult to create than a geological map because they require the prediction of geological structures away from observations, usually at depth, which are difficult to constrain from surface observations and sparse drill hole data sets. There are a range of different approaches where modeling methods either: (1) almost exclusively use prior geological knowledge (Jessell & Valenta, ), (2) a hybrid approach where geological knowledge is incorporated by adding some kinematic information and combined with direct observations (Bigi et al, ; Laurent et al, , ; Moretti, ), and (3) other systems only using observations in 3‐D space. A common method for building 3‐D models is to only consider observations to create an explicit representation of the surface by either interpolating between data points or triangulating a surface directly from the data (Caumon et al, ; Mallet, , ).…”

“…(1) almost exclusively use prior geological knowledge (Jessell & Valenta, 1996), (2) a hybrid approach where geological knowledge is incorporated by adding some kinematic information and combined with direct observations (Bigi et al, 2013;Laurent et al, 2013Laurent et al, , 2016Moretti, 2008), and (3) other systems only using observations in 3-D space. A common method for building 3-D models is to only consider observations to create an explicit representation of the surface by either interpolating between data points or triangulating a surface directly from the data (Caumon et al, 2009;Mallet, 1992Mallet, , 2002.…”

“…We demonstrate the inversion of structural geology data for characterizing fold geometries using a Fourier series to represent the fold geometry (Grose et al, 2017), first on a range of simple fold shapes in one dimension and then on a more complicated synthetic 3-D model representing doubly plunging parasitic folding. Laurent et al (2016) introduce a global fold frame with three coordinates (x, y, and z) representing the structural elements of the fold. The z coordinate of the fold frame is constrained so that direction vector e z is perpendicular to the observations of the axial foliation associated with the folding event and observations of the axial surface of the fold (Laurent et al, 2016).…”

Inversion of geological knowledge for fold geometry

“…Building three-dimensional (3D) geological models is a complicated task requiring an assimilation of available datasets, prior geological interpretation, and geological knowledge. Recent developments in 3D modeling algorithms and techniques Massiot and Caumon, 2010;Hillier et al, 2013Laurent et al, 2016;Grose et al, 2017Grose et al, , 2018Cowan et al, 2003] have significantly improved how direct observations can be used to constrain surface geometries. The process of creating 3D geological models to represent subsurface geometries can be framed as an inverse problem where the aim is to infer parameter values for the interpolation algorithm given geological observations [Grose et al, 2018].…”