Speaker: Ayoub Belhachmi
Date: Thursay 09th of January 2025, 1:15pm.
Abstract:
Constructing a geological numerical model is a key step in studying and exploring the subsurface. These models are constructed from seismic or well data, which consist of data points associated with values corresponding to their geological ages. This task involves constructing an implicit function, also known as the stratigraphic function, which interpolates this set of data points. Often, the available data are sparse and noisy, making this task difficult, especially for reservoirs where the geological structures are complex, with distinct discontinuities and unconformities.
In this seminar, we present a novel method for computing the stratigraphic function, which represents geological layers, using piecewise quadratic
đ¶1 splines on triangulations, specifically Powell-Sabin splines. This method enables better handling of geological layers with strong curvatures and reduces mesh resolution while maintaining high smoothness and regularity.
A key focus of our work is regularization, the most challenging component of mesh-based implicit modeling approaches. Classical methods often fail for data with high thickness variations, producing inconsistent models with bubble effects. To address this, we propose two innovative regularization energies inspired by fundamental PDEs: the anisotropic diffusion equation and the bending equation of an anisotropic thin plate. In both approaches, tensors of diffusion or rigidity are iteratively adapted to the data's variations and anisotropy.