Abstract. Joint inversion of Rayleigh wave phase velocity dispersion and P receiver function has been applied to study the structure of the upper mantle beneath the south-western margin of the East European Craton. The data were gathered in the passive seismic experiment 13 BB Star (2013–2016) in the area of the crust recognized from previous borehole and refraction surveys. Several fundamental issues inherent in the linearised inversion were addressed in this work, including exploitation of a priori knowledge, choice of model's depth, trapping by local minima associated with non-uniqueness of the misfit-function optimization problem, proper weighting of data sets characterized by different uncertainties, and credibility of the final models. The last was investigated with novel 1D checkerboard tests juxtaposed with resolution matrix analysis. We advocate the usefulness of linearised approach when handled with proper care, and show that the resolution analysis is an indispensable step when choosing the inversion parameters. It allowed us to obtain reliable S-wave velocity models down to 200 km depth beneath the 13 BB Star array, indicating the presence of a Paleozoic asthenosphere and the ceiling of the deeper, Precambrian, lithosphere-asthenosphere transition zone.