Speaker: Christophe Reype

Date: Thursday 9th of February 2023, 1:15pm.

Abstract:

The analysis of hydrogeochemical data aims to improve the understanding of mass transfer in the sub-surface and the Earth's crust. This work focuses on the study of fluid-fluid interactions through fluid mixing systems, and more particularly on the detection of the compositions of the mixing sources. The detection is done by means of a point process: the proposed model is unsupervised and applicable to multidimensional data.

    Physical knowledge of the mixtures and geological knowledge of the data are directly integrated into the probability density of a Gibbs point process, which distributes point patterns in the data space, called the Hug model. The detected sources form the point pattern that maximises the probability density of the Hug model. This probability density is known up to the normalisation constant. The knowledge related to the parameters of the model, either acquired experimentally or by using inference methods, is integrated in the method under the form of prior distributions. The configuration of the sources is obtained by a simulated annealing algorithm and Markov Chain Monte Carlo (MCMC) methods. The parameters of the model are estimated by an approximate Bayesian computation method (ABC).
    
    First, the model is applied to synthetic data, and then to real data. The parameters of the model are then estimated for a synthetic data set with known sources. Finally, the sensitivity of the model to data uncertainties,  to parameters choices and to algorithms set-up is studied.