Thomas Romary

Unsupervised classification of multivariate geostatistical data

With the increasing development of remote sensing platforms and the evolution of sampling facilities in mining and oil industry, spatial datasets are becoming increasingly large, inform a growing number of variables and cover wider and wider areas. Therefore, it is often necessary to split the domain of study to account for radically different behaviors of the natural phenomenon over the domain and to simplify the subsequent modeling step. The definition of these areas can be seen as a problem of unsupervised classification, or clustering, where we try to divide the domain into homogeneous domains with respect to the values taken by the variables in hand. The application of classical clustering methods, designed for independent observations, does not ensure the spatial coherence of the resulting classes. Image segmentation methods, based on e.g. Markov random fields, are not adapted to irregularly sampled data. Other existing approaches, based on mixtures of Gaussian random functions estimated via the expectation-maximization algorithm, are limited to reasonable sample sizes and a small number of variables. In this work, we propose two algorithms based on adaptations of classical algorithms to multivariate geostatistical data. Both algorithms are model free and can handle large volumes of multivariate, irregularly spaced data. The first one proceeds by agglomerative hierarchical clustering. The spatial coherence is ensured by a proximity condition imposed for two clusters to merge. This proximity condition relies on a graph organizing the data in the coordinates space. The hierarchical algorithm can then be seen as a graph-partitioning algorithm. Following this interpretation, a spatial version of the spectral clustering algorithm is also proposed. The performances of both algorithms are assessed on toy examples and a mining dataset.

Time-dependent global sensitivity analysis of the C-RIVE biogeochemical model in contrasted hydrological and trophic contexts

Dissolved oxygen within water column is a key variable to characterize the water quality. Water quality modeling has been extensively developed for decades. However, complex biogeochemical cycles are described using a high number of parameters. Hence, parameters uncertainty constitutes a major problem in the application of these models. Sensitivity analysis allows the identification of the most influential parameters in a model and a better understanding of the governing processes. This paper presents a time-dependent sensitivity analysis for dissolved oxygen using Morris and Sobol methods combined with a functional principal components analysis for dimension reduction. The aim of this study is to identify the most important parameters of C-RIVE model in different trophic contexts and to understand the biogeochemical functioning of river systems. The results indicate that the maintenance respiration of phytoplankton and the photosynthetic parameters (i.e. photosynthetic capacity, the maximal photosynthesis rate and light extinction coefficients) are the most influential parameters during algal blooms. When the river system becomes heterotrophic, the bacterial activities (moderate and high temperature) and the reaeration coefficients (low temperature) affect the most the dissolved oxygen concentration in the water column. An anthropogenic effect (ship navigation) on variation of dissolved oxygen concentration has been identified and the role of this anthropogenic effect evolves with hydrological and trophic conditions.

First Arrival Travel Time Tomography - Bayesian Approach

First arrival time tomography aims at determining the propagation velocity of seismic waves from experimental measurements of their first arrival time. This problem is usually ill-posed and is classically tackled by considering various iterative linearised approaches. However, these methods can yield wrong seismic velocity for highly nonlinear cases and they fail to estimate the uncertainties associated to the model. In our study, we rely on a Bayesian approach coupled with an interacting Markov chain-Monte Carlo (MCMC) algorithm to estimate the wave velocity and the associated uncertainties. The main difficulty associated to this approach is that traditional MCMC algorithms can be inefficient when multimodal probability distributions or complex velocity models involving a great number of parameters come into play. Therefore, a first step toward an efficient implementation of the Bayesian approach is to properly parametrize the model to reduce its dimension and to select adequate prior distribution for the parameters. In this paper, we present a ten layers probabilistic model for the velocity, that we illustrate on tomography results.