In the past few years, seismic tomography has begun to provide detaile
d images of seismic velocity in the Earth's interior which, for the fi
rst time, give direct observational constraints on the mechanisms of h
eat and mass transfer. The study of surface waves has led to quite det
ailed maps of upper-mantle structure, and the current global models ag
ree reasonably well down to wavelengths of approximately 2000 km. Usua
lly, the models contain only elastic isotropic structure, which provid
es an excellent ht to the data in most cases, For example, the varianc
e reduction for minor and major are phase data in the frequency range
7-15 mHz is typically 65-92 per cent and the data are ht to within 1-2
standard deviations. The fit to great-circle phase data, which are no
t subject to bias from unknown source or instrument effects, is even b
etter. However, there is clear evidence for seismic anisotropy in vari
ous places on the globe. This study demonstrates how much (or little)
the fit to the data is improved by including anisotropy in the modelli
ng process. It also illuminates some of the trade-offs between isotrop
ic and anisotropic structure and gives an estimate of how much bias is
introduced by neglecting anisotropy. Finally, ave show that the addit
ion of polarization data has the potential for improving recovery of a
nisotropic structure by diminishing the trade-offs between isotropic a
nd anisotropic effects.