Rayleigh wave data between 20 and 120s period recorded in the western Ross Sea region of Antarctica are inverted using the waveform inversion technique described in Passier and Snieder [1995>. From the data we extract estimates of local S velocity structure beneath the Transantarctic Mountains and the Terror Rift. The shear wave velocities found are up to 6% slower than the PREM model at between 40 and 160 km depth, depending on the propagation path, providing evidence of an anomalously warm upper mantle beneath the Terror Rift and, to a lesser extent, beneath the front of the Transantarctic Mountains. ¿ 2000 American Geophysical Union