We determine the 3-D shear wave speed variations in the crust and upper mantle in the southeastern borderland of the Tibetan Plateau, SW China, with data from 25 temporary broad-band stations and one permanent station. Interstation Rayleigh wave (phase velocity) dispersion curves were obtained at periods from 10 to 50 s from empirical Green's function (EGF) derived from (ambient noise) interferometry and from 20 to 150 s from traditional two-station (TS) analysis. Here, we use these measurements to construct phase velocity maps (from 10 to 150 s, using the average interstation dispersion from the EGF and TS methods between 20 and 50 s) and estimate from them (with the Neighbourhood Algorithm) the 3-D wave speed variations and their uncertainty. The crust structure, parametrized in three layers, can be well resolved with a horizontal resolution about of 100 km or less. Because of the possible effect of mechanically weak layers on regional deformation, of particular interest is the existence and geometry of low (shear) velocity layers (LVLs). In some regions prominent LVLs occur in the middle crust, in others they may appear in the lower crust. In some cases the lateral transition of shear wave speed coincides with major fault zones. The spatial variation in strength and depth of crustal LVLs suggests that the 3-D geometry of weak layers is complex and that unhindered crustal flow over large regions may not occur. Consideration of such complexity may be the key to a better understanding of relative block motion and patterns of seismicity. © Journal compilation © 2008 RAS.