  We discuss several physical constraints imposed on elasticity parameters of a
transversely isotropic (TI) tensor. There are three types of restrictions we
investigate; a fundamental one of stability conditions, and two additional
ones, commonly considered in seismology. The first commonly considered
restriction comes from an assumption of a wave with a greater speed in the
horizontal than vertical direction. The second constitute the assumption that
quasi-P wave is faster than quasi-S waves. We show several numerical examples
to examine how these restrictions affect a TI tensor with known values of
certain elasticity constants that could be acquired from the vertical or
horizontal measurements.
