An interesting physical meaning is presented for the anisotropy parameter delta , previously introduced by Thomsen to describe weak anisotropy in transversely isotropic media. Roughly, delta is the difference between the P-wave and SV-wave anisotropies of the medium. The observed systematic depth errors in the North Sea are reexamined in view of the new interpretation of the moveout velocity through delta . The changes in delta at an interface adequately describe the effects of transverse isotropy on the P-wave reflection amplitude. The reflection coefficient expression is linearized in terms of changes in elastic parameters. The linearized expression clearly shows that it is the variation of delta at the interface that gives the anisotropic effects at small incidence angles. Thus, delta effectively describes both the moveout velocity and the reflection amplitude variation, two very important pieces of information in reflection seismic prospecting, in the presence of transverse isotropy.