This thesis deals with the nondestructive testing of transmission overhead line structure foundations. A seismic imaging technique is used. The experimental procedure consists of the generation of a seismic wave near the foundation by means of a vibrating source and the measurement of the resulting wave velocity with a set of geophones. The specific goal of the presented work is to provide an inversion scheme in order to determine the shape of foundations from the measured data. This problem corresponds to an inverse scattering problem. Its resolution is particularly difficult because of its ill-posedness and the strong nonlinearity of the direct model. Two inversion methods have been developed. Their common aim is to map the spatial distribution of several physical characteristic of the probed medium. In both cases, a regularized least squares criterion is minimized iteratively. For the first approach, little a priori information is considered. It is based on a Markovian regularization scheme. The differences between neighboring pixels are penalized so that the algorithm converges towards smooth areas separated by sharp boundaries. The second approach takes more relevant priors into consideration. They are related to the particular shape of foundations and to the physical characteristics of earth and concrete. The method is based on a segmentation of the probed area into two regions. Tests were performed on simulated data to evaluate and compare the performance of these two methods.
Regularization and optimization for the seismic imaging of transmission overhead line structure foundations