Imagerie 2-D/3-D de la teneur en eau en milieu hétérogène par méthode RMP : Biais et incertitudes

摘要

The non-destructive observation of the ground water content’s variability in time and space is a major issue to understand the hydrodynamical functioning of heterogeneous media. Although many geophysical methods derive the water content of the subsurface from intermediate physical parameters, the method of surface nuclear magnetic resonance (SNMR) provide a direct estimate of ground water content. For this method, 2-D or 3-D SNMR tomography applications are only emerging and an in-depth analysis is required to assess their possibilities and limitations. The general resolution of the method is limited because the measurement characterize an important volume and is contaminated by electromagnetic noise. Consequently, the translation of measurement into an image of water content admit many solutions. Among them, several are more desirable than others from a structural/geometrical stand point. Geometrical prior knowledge are used to limit the infinite solution space. The resulting water content estimate is necessarily biased (prior knowledge) and affected by uncertainties (noise). To date, these aspects have never been quantified for 2-D and 3-D SNMR data sets. The processes that are controlling the geometrical rendering and the estimated water volume are analyzed using correlations and linear regressions as they are unbiased tools for the data space analysis. As the MRS inverse problem is non-linear, this thesis proposes a Monte Carlo based methodology (Metropolis-Hastings) to provide water content and uncertainty estimates. As the geometrical prior expectations control the estimates, the resulting bias is explored and discussed for different water content configurations. Finally, the possibilities of MRS imaging are illustrated on two highly heterogeneous environments : karstic and thermo-karstic. The results of the MRS imagery are compared and validated with other sources of knowledge. The first case is a 2-D imaging of the conduit Poumeyssen karst. The latter geometry is precisely known. The second case is the 3-D imaging of a internal cavity inside the French Alp glacier Tete-Rousse, intensively explored by destructive and non-destructive methods.