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Surface waves recorded by the nine broad-band stations of the INDEPTH II experiment are analysed to study the crustal structure of southern Tibet. Their frequency range is between approximately 0.015 and 0.050 Hz (i.e. between 20 and 60 s period). Phase velocity dispersion curves are calculated for the regions north and south of the Tsangpo suture, using Wiener filtering of fundamental mode Rayleigh waves incident upon the array with different backazimuths. The two dispersion curves are inverted to obtain the S-wave crustal models north and south of the suture. They show that a low-velocity layer is present in the lower crust north but not south of the Tsangpo suture. To confirm these findings, variations in the amplitudes of the Rayleigh waves across the suture are interpreted by numerical simulation. The strong amplitude variations at a 30 s period are reproduced using a model with a low-velocity layer in the lower crust north of the suture, a normal high-velocity layer to the south, and a sharp transition between these layers.