Velocity structure of the lithosphere-asthenosphere system, to the depth of about 350 km, is obtained for almost 400 cells, sized 1 degree by 1 degree in the Mediterranean region. The models are obtained by the following sequence of methods and tools: surface-wave dispersion measurements and collection; 2D tomography of dispersion relations; non-linear inversion of cellular dispersion relations; smoothing optimization method to select a preferred model for each cell. The 3D velocity model, that satisfies Occam razor principle, is obtained as a juxtaposition of selected cellular models. The reconstructed picture of the lithosphere-asthenosphere system evidences the, globally well known, asymmetry between the W- and E-directed subduction zones, attributed to the westward drift of the lithosphere relative to the mantle. Different relationship between slabs and mantle dynamics cause strong compositional differences in the upper mantle, as shown by large variations of seismic waves velocity, consistent with Polarized Plate Tectonics model.