The relative motion between the Pacific and Australian plates across the central South Island of New Zealand, as measured by repeated GPS measurements, is distributed over a region more than 80 km wide. The surface distribution of velocity is fit almost equally well by a model in which deformation of the lower lithosphere is concentrated into very narrow slip zones below one or two major faults and by a model in which the lower lithosphere deforms in a broad shear zone. Observations of the splitting of SKS waves permit distinction between the two models on the basis of the finite strain they predict. Deformation in the deep lithosphere that was limited to narrow shear zones would not produce measurable splitting; hence any splitting observed should not correlate with surface tectonics. However, the distribution of fast propagation directions revealed by observations of shear wave splitting do reflect surface tectonics. In particular, the orientations of fast propagation directions are consistent with the finite strain calculated by assuming that the distribution of velocity at depth within the lithosphere resembles the distribution of velocity measured at the surface by GPS. The observed distribution of splitting can be reproduced with an RMS misfit of 15¿, provided that the velocity field is integrated over at least the time interval since significant convergence across the Southern Alps began at about 6.5 Ma.