Following the successive launches of satellites for Earth observation with SAR (Synthetic Aperture Radar) sensor, the volume of available radar data is increasing considerably. In this context, fusion of displacement measurements from SAR imagery is promising both in the community of remote sensing and in geophysics. With this in mind, this Ph.D thesis proposes to extend conventional approaches by combining SAR image processing techniques, information fusion methods and the knowledge on geophysics. First, this Ph.D thesis aims to explore several fusion strategies, joint inversion, pre-fusion and post-fusion, to reduce the uncertainty associated on the one hand to the estimation of the 3-dimensional (3D) displacement at the Earth's surface, on the other hand to physical modeling that describes the source in depth of the displacement observed at the Earth's surface. We evaluate advantages and disadvantages of each fusion strategy in terms of reducing uncertainty and of robustness against noise. Second, we aim to take account of epistemic uncertainty, in addition to the random uncertainty present in the measurements and propose the conventional and fuzzy approaches based on probability theory and possibility theory respectively to model these uncertainties. We analyze and highlight the efficiency of each approach in context of each fusion strategy. The first application consists of estimating the 3D displacement fields at the Earth's surface due to the Kashmir earthquake in October 2005 and the eruption of Piton de la Fournaise in January 2004 on Reunion Island. The second application involves the modeling of the fault rupture in depth related to the Kashmir earthquake. The main achievements and contributions are evaluated from a methodological point of view in information processing and from a geophysical point of view. In the methodological view, in order to address the major difficulties encountered in the application of differential interferometry for measuring the displacement induced by the Kashmir earthquake, a multi-scale strategy based on prior information issued from a deformation model using local frequencies of interferometric phase is adopted successfully. Regarding the measurement uncertainty management, both random and epistemic uncertainties are analyzed and identified in the displacement measurements. The conventional approach and a fuzzy approach based on respectively probability theory and possibility theory are proposed to model uncertainties and manage the uncertainty propagation in the fusion system. In addition, comparisons between possibility distributions enrich the comparisons made simply between displacement values ​​and indicate the relevance of possibility distributions in the considered context. Furthermore, pre-fusion and post-fusion, two fusion strategies different from the commonly used fusion strategy of joint inversion, are proposed to reduce heterogeous uncertainties present in practice in the measurements and to get around the main limitations of joint inversion. Appropriated conditions of the application of each uncertainty management approach are highlighted in the context of these fusion strategies. In the geophysical view, the application of differential interferometry to the Kashmir earthquake is performed successfully for the first time and it completes previous studies based on measurements from the correlation of SAR and optical images, teleseismic measurements and in situ field measurements. Differential interferometry provides accurate displacement information in the far field relative to the fault position. This allows on the one hand reducing uncertainties associated with surface displacement measurements and with model parameters, on the other hand detecting post-seismic movements that exist potentially in the used coseismic measurements covering the post-seismic period. Moreover, taking into consideration of epistemic uncertainty and the proposition of a fuzzy approach for its management, provide a different view of the measurement uncertainty known by most geophysicists and complete the knowledge of the random uncertainty and the application of probability theory in this domain. In particular, the management of uncertainty by possibility theory allows overcoming the problem of under-estimation of uncertainty by probability theory. Finally, comparisons of the displacement measured by SAR images with the displacement measured by optical images and the displacement from in situ field measurements reveal the difficulty to interpret different data sources more or less compatible among them. The tools developed during this Ph.D thesis are included in the MDIFF (Methods of Displacement Information Fuzzy Fusion) package in "EFIDIR Tools" distributed under the GPL lisence.
Fusion of displacement measurements from SAR imagery : application to seismo-volcanic modeling