Développement d'algorithmes pour le calage de modèles géologiques par méthodes géostatistiques discrètes et spectrales

Incorporating uncertain, auxiliary, and dynamic data into a stochastic process can significantly improve the prediction of risk assessment for complex geological phenomena in petroleum and mining engineering, or hydrogeology. In practice, calibration of indirect data (i.e., uncertain, auxiliary, and dynamic data) is one of the commonly used approaches to obtain realist geological simulations. However, calibration algorithms suffer from computational limitations. To name only these, problems about the convergence of the objective function, preservation of the spatial distribution, integration of irregularly spaced data, computational memory issues, local integration of indirect data, and unfavourable initial state may be met. This thesis aims to produce two distinct algorithms for the calibration of property fields to indirect data. The first algorithm aims to improve the objective function convergence and allows local calibration of the field. The calibration process uses a cooling schedule that transforms over time the global optimization through quasi-local ones. The second algorithm seeks to limit memory space problems and allows the calibration of indirect data on irregular grids by the sequential building of the field. The idea of the two algorithms is to combine geostatistical simulation methods with robust optimization mechanisms to overcome the problems listed above. A comparison study is carried out to assess the pros and cons of the two algorithms over one recent algorithm and two algorithms mainly used in reservoir simulations. The first algorithm, namely FFTMA-SA, combines the simulated annealing algorithm to the random term of the FFTMA generator. The innovative aspect of this method concerns the integration of annealing on the perturbation mechanism (i.e. use of annealing on the number of perturbed points). The objective is to ensure initially a global calibration through perturbations of numerous points. Subsequently, the annealing reduces over time the number of perturbed points making it possible to migrate to a local calibration. The perturbed points may be restricted to a sub-region of the geological phenomenon to generate a purely local calibration. FFTMA-SA obtained a better convergence than the simulated annealing algorithm and the FFTMA method combined with the gradual deformation. The second algorithm entitled S-STBM proposes to use the spectral turning band simulator to calibrate property fields to indirect data by phase optimization. Consequently, this results in the first purely constructive calibration method, making it possible to obtain calibrated simulations to indirect data. The advantage of this method is that it allows the integration of irregularly spaced data and solves memory space issues. The results demonstrated a convergence rate equivalent to FFTMA-SA when thousands of iterations are performed. Despite phases optimization, the examples illustrated that the variogram of the simulated fields differs slightly from the desired one, partly due to the integration of a post-conditioning by kriging before the calculation of the objective function. Using the purely constructive nature of the S-STBM method, the algorithm can address the facies conditioning problem in large truncated Gaussian or plurigaussian simulations. The approach traditionally applied is the Gibbs sampler. The idea is to first ensure the constraints on the latent Gaussian values to the conditioning data. Then, iterative perturbation introduces slowly the spatial correlation between these points. However, the presence of numerous data may render the algorithm inefficient. The idea brought is to reverse the problem by ensuring spatial distribution by construction and by using the constructive nature of S-STBM to quickly constraints Gaussian latent values through a calibration process. The proposed approach is shown to be one to three orders of magnitude faster than the Gibbs sampler. Moreover, the calibration process has no computer memory issues and has a computational complexity of only O(n) compared to the Gibbs sampler, which is O(n2). To reduce the computation time, one may stop the calibration process when the latent Gaussian values are relatively close to the constraints and switch to a truncated version of the sequential Gaussian simulation algorithm to finish the calibration. To conclude the thesis, an exhaustive study compared the performance of five variogrambased calibration approaches on five geological problems. The five algorithms studied are the two algorithms proposed in this thesis (namely FFTMA-SA and S-STBM) followed by the traditional version of gradual deformation, the iterative spatial resampling method, and phase annealing. S-STBM and FFTMA-SA obtained good calibration results for the five scenarios compared to the three others. The constructive nature of the S-STBM method resulted in a rapid reduction of the objective function by one to two orders of magnitude after only two hundred iterations. Moreover, S-STBM avoids the difficulty encountered by other calibration algorithms that starts from an initial state that may exhibit characteristics incompatible with the indirect data. The cooling strategy of FFTMA-SA on the number of perturbed points quickly contained the negative impact of the initial state resulting in an efficient calibration in the majority of the scenarios studied. Note that the study indicates that the nature of the indirect data must be compatible with the calibration algorithm to obtain efficient calibration. This study also found that some common inversion problems can be properly calibrated using all tested methods, calling into question their use for evaluating the performance of calibration algorithms. The two calibration algorithms presented in this dissertation improved the conditioning to indirect data by solving the problems of local optimum, local calibration, convergence issues, memory limitations, and irregular grid data. FFTMA-SA and S-STBM form a pair of algorithms that generated geostatistical simulations calibrated to uncertain, auxiliary, and dynamic data to improve the estimation and risk assessment of complex geological models in mining and petroleum engineering and hydrogeology. The dissertation ends with a discussion of the future applications of the FFTMA-SA and S-STBM algorithms for the estimation of uncertainties for multivariate geological models.