Finite Difference Implicit Modeling of Geological Structures

Irakarama, Modeste; Laurent, Gautier; Renaudeau, Julien; Caumon, Guillaume

doi:10.3997/2214-4609.201800794

Cited by 7 publications

(15 citation statements)

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“…This scalar field is obtained by: (1) setting to 0 the value of the samples in contact with the "salt" region and the base of sediments, (2) setting to 1 the value of the samples in contact with the "sediments" region, and (3) interpolating the intermediate values in the remainder of the "uncertain" region. In this paper, we use the finite difference-based interpolation method proposed by Irakarama et al [2018] to generate this scalar field.…”

Section: Generating Salt Boundary Interpretationsmentioning

confidence: 99%

Generating variable shapes of salt geobodies from seismic images and prior geological knowledge

2019

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We have developed an implicit method to automatically generate several possible models of salt top surfaces with varying geometries and topologies. This method can be conditioned to available data such as well markers and seismic picks. Because seismic imaging of salt is prone to velocity uncertainty and Fresnel zone effects, the input of the method is a seismic image that is segmented into three regions: salt, sediments, and uncertain. The uncertain region contains the salt boundary, and all further computations focus within this zone. A monotonic scalar field, ranging from zero on the edge of the certain salt body to one on the maximal possible salt boundary, defines the cumulated probability for a point to be outside the salt body. A random scalar field, also bounded between zero and one, is then used as a threshold for the first scalar field. The salt boundary is implicitly defined by the zero isovalue of the difference between the two fields, and it can be further extracted using marching cubes. The random field parameters have a geometric and topological impact on the simulated salt volumes. They can be adapted to reproduce specific geological features, but their inference remains difficult. The application of the method for the reconstruction of diapir boundaries from a set of partly interpreted sections indicates that it is well-suited to honor numerous constraining data while proposing different possible structural scenarios in the uninterpreted parts.

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Section: Generating Salt Boundary Interpretationsmentioning

confidence: 99%

Generating variable shapes of salt geobodies from seismic images and prior geological knowledge

2019

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“…For the common implicit modeling methods, there is the triangulation with linear interpolation [7], nearest neighbor [8], distance power inverse ratio method [9], linear interpolation [10], local polynomial [11], interpolation of radial basis function [12], spline interpolation [13], ordinary Kriging [14], indicator Kriging [15], universal Kriging [16], etc. Implicit modeling methods have been focused on and studied in the fields of digital terrain modeling [17,18], geological structure modeling [19,20], reservoir modeling [21], hydrogeological modeling [22] and ore body modeling [23][24][25], etc. Among them, three-dimensional implicit modeling of the ore body has become a research hotspot of mining scholars all over the world in recent years.…”

Section: Introductionmentioning

confidence: 99%

Implicit 3D Modeling of Ore Body from Geological Boreholes Data Using Hermite Radial Basis Functions

Wang

Zhao

et al. 2018

Minerals

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Modeling ore body in 3D is the basis of digital intelligent mining. However, most existing three-dimensional mining software uses the contour approach that requires too much man–machine interaction and difficult partial updating. Moreover, accounting for uncertainty and low geometric quality picking is very difficult in the direct contour approach. Therefore, an implicit modeling approach to automatically build the three-dimensional model for ore body by means of spatial interpolation directly based on the geological borehole data with Hermite radial basis function (HRBF) algorithm as the core is proposed. Furthermore, in order to solve the problems of weak continuity of models due to the long-distance original boreholes as well as the boundary-point normal solution error, the densification of original borehole data with the virtual borehole as well as the calculation of point-cloud normal direction based on the adjacent hole-drilling method is proposed. The verification of two mine engineering projects and comparison with the explicit modeling results show that this approach could realize the automatic building of three-dimensional models for the ore body with high geometric quality, timely update and accurate results.

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“…A version of DSI based on the Cartesian grid is introduced in [14]. The roughness factor is designed to minimize second directional derivatives of the implicit function using a finite difference approximation, and the implicit function is interpolated on the grid cells using a piecewise bilinear interpolation.…”

Section: Introductionmentioning

confidence: 99%

“…The roughness factor in DSI is defined as a discrete operator [10]. 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].…”

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. The discontinuities are handled with a ghost-cell technique, resulting in an implicit function defined everywhere in the domain of study.…”

Section: Introductionmentioning

confidence: 99%

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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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Finite Difference Implicit Modeling of Geological Structures

Cited by 7 publications

References 0 publications

Generating variable shapes of salt geobodies from seismic images and prior geological knowledge

Generating variable shapes of salt geobodies from seismic images and prior geological knowledge

Implicit 3D Modeling of Ore Body from Geological Boreholes Data Using Hermite Radial Basis Functions

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

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