Numerical simulations of depth-dependent anisotropy and frequency-dependent wave propagation effects

A numerical investigation of the effects of shear wave splitting for vertic al propagation in a smoothly varying anisotropic medium is presented. Throu gh forward modeling, we predict the olivine lattice preferred orientation ( LPO) developed in the oceanic upper mantle in response to the absolute plat e motion (APM). We consider the effect of a change in APM similar to the on e that presumably caused the kink in the Emperor-Hawaii seamount island cha in in the north Pacific. This results in an oblique orientation between lit hospheric and asthenospheric anisotropy. Numerical simulations of shear wav e propagation are used to estimate the characteristics of shear-wave splitt ing. Ray theory does not account for coupling between shear waves in the de pth-dependent anisotropic medium due to the implicit assumption of high fre quency. A forward propagator technique for calculating waveforms and splitt ing parameters is used to assess frequency-dependent effects. The results s how that ray theory is valid for estimating the splitting only for frequenc ies above 1 Hz. At frequencies more realistic for SKS propagation, apparent splitting parameters exhibit a pi/2 dependence on the incoming shear wave polarization (back azimuth). For certain back azimuth ranges, shear wave sp litting is very frequency dependent with apparent delay times ranging from 1 to 4 s and apparent fast polarization directions changing rapidly by up t o 80 degrees. Thus stacking of shear wave splitting measurements for largel y different initial polarizations and frequencies should be avoided. Depth- dependent anisotropy implies that shear wave splitting analyses will be sen sitive to filtering. Anisotropic depth variations cannot be resolved unambi guously from splitting observations at relatively long periods (>5 s). It i s not possible, for instance, to discriminate between smooth and abrupt tra nsitions separating the anisotropic regions. Shorter-period waveforms provi de further information on the fine structure of anisotropic depth variation s. A comparison between splitting calculations and observations from Hawaii suggests a divergent past APM direction or may indicate an alternative mec hanism responsible for the lithospheric anisotropy.