Implicit Structural Modeling with Local Meshless Functions

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

doi:10.3997/2214-4609.201801235

Cited by 2 publications

(4 citation statements)

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“…Optimization methods have been proposed (Greengard and Rokhlin, 1987, e.g., the fast multipole approach originally introduced by). A recent alternative has also been proposed by Renaudeau et al (2018) using an intermediate set of points which bear local moving least squares basis functions. The overall system becomes sparse, as the basis functions have a local support, but the continuity of the solution is maintained.…”

Section: Full 3-d Modeling Approaches: Implicitmentioning

confidence: 99%

“…(Caumon et al, 2013a;Collon-Drouaillet et al, 2015;Collon et al, 2016). Alternatively, in the case where enough data are available for the problem to be well posed, the increment of the scalar field can be estimated as differences to some reference value (Lajaunie et al, 1997;Chilès et al, 2004;Calcagno et al, 2008;De la Varga et al, 2018;Renaudeau et al, 2018).…”

Section: Full 3-d Modeling Approaches: Implicitmentioning

confidence: 99%

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3-D Structural geological models: Concepts, methods, and uncertainties

Wellmann

Caumon

2018

Advances in Geophysics

168

103

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The Earth below ground is the subject of interest for many geophysical as well as geological investigations. Even though most practitioners would agree that all available information should be used in such an investigation, it is common practice that only a fraction of geological and geophysical information is used. We believe that some reasons for this omission are (a) an incomplete picture of available geological modeling methods, and (b) the problem of the perceived static picture of an inflexible geological representation in an image or geological model. With this work, we aim to contribute to the problem of subsurface interface detection through (a) the review of state-of-the-art geological modeling methods that allow the consideration of multiple aspects of geological realism in the form of observations, information and knowledge, cast in geometric representations of subsurface structures, and (b) concepts and methods to analyze, quantify, and communicate related uncertainties in these models. We introduce a formulation for geological model representation and interpolation and uncertainty analysis methods with the aim to clarify similarities and differences in the diverse set of approaches that developed in recent years. We hope that this chapter provides an entry point to recent developments in geological modeling methods, helps researchers in the field to better consider uncertainties, and supports the integration of geological observations and knowledge in geophysical interpretation, modeling and inverse approaches.

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Section: Full 3-d Modeling Approaches: Implicitmentioning

confidence: 99%

Section: Full 3-d Modeling Approaches: Implicitmentioning

confidence: 99%

3-D Structural geological models: Concepts, methods, and uncertainties

Wellmann

Caumon

2018

Advances in Geophysics

168

103

View full text Add to dashboard Cite

show abstract

“…In practice, this factor may take different forms depending on the chosen domain discretisation scheme [4], [8], [14]. Instead, another approach is to find a continuous operator based on physical arguments, and then discretise it accordingly [13], [15]. An advantage of the latter is that it naturally provides appropriate weights to use during the least square's optimization stage, making the solution less sensitive to the resolution of the discretisation scheme.…”

Section: Introductionmentioning

confidence: 99%

“…In this paper, the proposed implicit method penalizes data constraints by the continuous bending energy, as in [13] and [15]. This problem is discretised on the Cartesian grid, using a piecewise bilinear evaluation on data terms and a finite difference approximation of energy terms, which gives a final linear system to solve close to [14], but with volumetric weights obtained from the discretisation.…”

Section: Introductionmentioning

confidence: 99%

Implicit Modelling of Geological Structures: A Cartesian Grid Method Handling Discontinuities With Ghost Points

Renaudeau

Irakarama

Laurent

et al. 2018

WIT Transactions on Engineering Sciences

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In geology, implicit structural modelling constructs the geometry of geological structures (e.g. layers) by interpolating between sparse field data. A model is represented by a volumetric scalar field which is discontinuous on structural discontinuities such as faults or stratigraphic unconformities. The management of such discontinuities may involve boolean operations on several scalar fields or the creation of conformal meshes. Instead, we propose a ghost cell technique for the cartesian grid together with a set of relations between the ghost points, the regular nodes, and the discontinuities. Consequently, poor quality meshes are avoided and only the resolution of the grid has an impact on the solution. The modelling problem is posed as a least square's minimization of a bending energy penalization on data mismatch functions and approximated by finite difference. As all relationships in the grid are implicitly defined, except close to the discontinuities, this algorithm is computationally efficient. We provide some benchmarks of the method on two-dimensional examples with folds, faults, and erosions.

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Implicit Structural Modeling with Local Meshless Functions

Cited by 2 publications

References 0 publications

3-D Structural geological models: Concepts, methods, and uncertainties

3-D Structural geological models: Concepts, methods, and uncertainties

Implicit Modelling of Geological Structures: A Cartesian Grid Method Handling Discontinuities With Ghost Points

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