The Backus <1965> theory of seismic anisotropy is used to obtain expressions for the velocities and polarizations of quasi-P and S waves for rays making small angles to the symmetry axes of an orthorhombic elastic tensor. Expressions are found for P wave polarization and S wave splitting parameters as a function of incidence angle θ and azimuth z. For small θ, splitting and P wave velocity exhibit predominantly a two z variation. P wave velocity squared is given by vp2 = v02 + c1θ2 + c2cos(2z)θ2, where the ci are combinations of coefficients of the elasticity tensor. The eigenvalues corresponding to the fast and slow S waves are given by similar expressions. Variation in P wave horizontal polarization exhibits a 2z variation; δzp = -Δz sin(2z) with little dependence on θ. SKKS and SKS splitting parameters exhibit an azimuthal variation given by φ = φ0 + d1 sin(2z) θ2 and δt = δt0 + e1θ2 + e2 cos(2z)θ2, where φ is the fast direction and δt is the time delay. We report 2z variation in splitting parameters at the Global Seismic Network stations in southern California. We use other estimates of seismic anisotropy to invert for depth-averaged values of the elasticity tensor. The resulting tensor adequately describes azimuthal variation in P wave horizontal polarization <Schulte-Pelkum et al., 2001>, Pn, Rayleigh and Love wave velocities, as well as SKKS and SKS splitting, suggesting they all arise from a common source of anisotropy in the upper 200 km of the mantle.