Gautier Laurent

3D geomodelling combining implicit surfaces and Voronoi-based remeshing

In this paper we demonstrate how recent geomodelling techniques can be combined and used to build a 3D geological model on a real case study: the former coal mine of Merlebach (France), that is targeted to be exploited for low-temperature geothermal energy production. From geological maps, cross-sections, borehole and mine exploitation data, we build a 3D model in which are identified the rocks and infrastructures having significantly different permeabilities. First, a structural model of the main geological interfaces in our area of interest (2 horizons and 13 faults) is built with classical geomodelling techniques. Then, we propose to model by surfaces the 71 irregularly stacked, very close and very thin, sub-vertical coal beds. To ease their construction, we use an implicit method which represents 3D surfaces as isovalues of a scalar field defined in a 3D tetrahedral grid of the area. The corresponding triangulated surfaces are remeshed with a recently proposed method based on Voronoi diagrams so that the exploited parts of the coal beds, now filled by sand, can be computed. The 3D surface-based geological model, in which infrastructures can be inserted as piecewise lines, can be volumetrically meshed. It is available for download as supplemental material, as well as a volumetric grid.

Iterative Thickness Regularization of Stratigraphic Layers in Discrete Implicit Modeling

Discrete implicit modeling consists in representing structural surfaces as isovalues of three-dimensional piecewise linear scalar fields, which are interpolated from available data points. Data are expressed as local constraints that can enforce the value of the scalar fields as well as their gradients. This paper illustrates some limitations of published discrete implicit methods, related to the difficulty of controlling the norm of scalar field gradient and its evolution over the interpolated domain. It is shown that important artifacts may arise due to the intrinsic dependence between variations in the norm and the direction of the scalar field gradient, from one element to its neighbors. Evidence that these artifacts are related to mesh facet direction with respect to gradient direction are given. The artifacts lead to rapid and uncontrolled variations of thickness that may induce erroneous interpolations. This paper proposes two original approaches to overcome these problems. The first one consists in iteratively adjusting the norm of scalar field gradients in the direction obtained after previous iterations. The second solution consists in optimizing the mesh used by the interpolation. This requires finding appropriate mesh facet orientation with respect to scalar field gradient. These methods demonstrate that the results of discrete implicit surface interpolation can be improved and call for further development of available interpolation schemes.

A Parametric Unfault-and-refault Method for Chronological Structural Modeling

We present a structural modeling method that uses an object model of fault to produce consistent fault-related deformations. Our numerical fault operator relies on geometric and kinematic parameters that are determined by numerical optimization to fitting interpretations points in the fault neighborhood. We use our operator sequentially to model faults that have been affected by more recent faulting events. The method can be used to explore uncertainties about the chronology of the different faulting events. We illustrate our workflow to model the top of a faulted basement located offshore Morocco. This basement reservoir analogue is imaged by 2D seismic lines and the relative ages of the two fault families are uncertain. We applied our method to build three different scenarios. In one of the scenarios, removing the displacement of the younger strike-slip fault enables us to correlate fault sticks that seem isolated in the present day geometry. The modeled faults have larger lateral extensions, leading to a more compartmentalized reservoir.