Abstract. In this paper, a comprehensive explanation of the analysis (filtering and inversion) of the Rayleigh-wave ellipticity will be performed, as well as, how it can be used to determine the local crustal structure beneath the recording station. This inversion problem and the necessary assumptions to solve it will be described in this paper, jointly to the methodology used to invert the Rayleigh-wave ellipticity. The results presented in this paper will show that the analysis (filtering and inversion) of the Rayleigh-wave ellipticity is a powerful tool, to study the local structure of the crust beneath the recording station, being this kind of analysis very useful for seismic risk and/or seismic design studies, because provides local earth models in the range of crustal depths.