The aim of this paper is to model, by means of the finite element method (FEM), the detection of underground cavities using the "impact echo method" (IEM). The detection of holes by the IEM relies on the analysis of multiple reflections of the compression wave (echoes) between the surface and the hole. The presence of echoes in the recorded signal induces, in the frequency domain, a resonance effect which can be related to the depth of the hole. In order to enhance the performance of IEM, the signal should be analysed in a carefully chosen temporal window (so that the energy of the surface waves does not mask the relevant information). An original time-frequency analysis approach is used. It enhances the resonance frequency determination and helps "choosing an optimum temporal window of observation. The obtained results enabled us to determine the parameters which may influence the resolving power of the method and to define a theoretical thresholds of detection. The experimental verification of these results, performed in real field conditions, is presented in a second part [6].


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