In geophysics the anisotropy in elastic properties is usually weak, in which case .  When the exact expressions for the wave velocities above are linearized in these small quantities, they simplify to
where 
are the P and S wave velocities in the direction of the axis of symmetry () (in geophysics, this is usually, but not always, the vertical direction).  Note that  may be further linearized, but this does not lead to further simplification.
The approximate expressions for the wave velocities are simple enough to be physically interpreted, and sufficiently accurate for most geophysical applications.  These expressions are also useful in some contexts where the anisotropy is not weak.