A numerical investigation of the effects of shear wave splitting for vertical propagation in a smoothly varying anisotropic medium is presented. Through forward modeling, we predict the olivine lattice preferred orientation (LPO) developed in the oceanic upper mantle in response to the absolute plate motion (APM). We consider the effect of a change in APM similar to the one that presumably caused the kink in the Emperor-Hawaii seamount island chain in the north Pacific. This results in an oblique orientation between lithospheric and asthenospheric anisotropy. Numerical simulations of shear wave propagation are used to estimate the characteristics of shear-wave splitting. Ray theory does not account for coupling between shear waves in the depth-dependent anisotropic medium due to the implicit assumption of high frequency. A forward propagator technique for calculating waveforms and splitting parameters is used to assess frequency-dependent effects. The results show that ray theory is valid for estimating the splitting only for frequencies above 1 Hz. At frequencies more realistic for SKS propagation, apparent splitting parameters exhibit a &pgr;/2 dependence on the incoming shear wave polarization (back azimuth). For certain back azimuth ranges, shear wave splitting is very frequency dependent with apparent delay times ranging from 1 to 4 s and apparent fast polarization directions changing rapidly by up to 80¿. Thus stacking of shear wave splitting measurements for largely different initial polarizations and frequencies should be avoided. Depth-dependent anisotropy implies that shear wave splitting analyses will be sensitive to filtering. Anisotropic depth variations cannot be resolved unambiguously from splitting observations at relatively long periods (>5 s). It is not possible, for instance, to discriminate between smooth and abrupt transitions separating the anisotropic regions. Shorter-period waveforms provide further information on the fine structure of anisotropic depth variations. A comparison between splitting calculations and observations from Hawaii suggests a divergent past APM direction or may indicate an alternative mechanism responsible for the lithospheric anisotropy. ¿ 1999 American Geophysical Union