We describe a technique for measuring shear wave splitting in the mantle of the oceans and poorly instrumented continental regions. The idea of the method is to analyze evolution of the form of the particle motion in the long-period multiple ScS and sScS phases as a function of the order of reflection. The differential motion is inverted into the parameters of azimuthal anisotropy. The technique is applied to the digital recordings of events from the Tonga-Kermadek seismic zone at station AFI. It is found that the fast direction of anisotropy in the mantle beneath the Pacific plate is close to the present day absolute-velocity direction of the plate. ¿ American Geophysical Union 1992