I work on characterization of buried objects in the narrow or deeper underground within two principal cooperations : one with the BRGM (Orleans, France) which provides measurements and technology; another one with the Division of Applied Mathematics (Patras, Greece). The topic I work on is in-between applied physic and applied mathematic. The main goal is to provide relevant and robust models that take into account the physical behavior of the ground and embedded structures. Different approximations has been used to provide simple analytical expression of the EM fields. The main idea of this work, is to reduce the computational time needed to calculated the scattered direct problem. In fact, the computational time is also reduced for the optimization scheme, used for the localization and the identification of the buried structures. Because it is low-frequency measurements, only simple shaped object is consider as the ellipsoidal one. For these reasons, approximations are also done on integral equations or derivative equations, as asymptotic expansions (LF or for small objects). Some solutions have to be performed on real data, but all of them have been tested with synthetic data, obtained with huge numerical code or given by colleagues within cooperation.
