The surface kinematics of reflection wavefronts in such a (not necessarily isotropic) layered earth may be exactly and completely described by two functions of the ray parameter, p. These are the travel-time function, t(p), and the offset function, x(p). The kinematics of a set of such layers is simply and exactly formed because these functions are elements of Abelian groups. That is, the reflection response from the base of n such layers arranged in any order is given by
If we now define v2(p) = x(p)/pt(p) then v2(p)t(p) = x(p)/p. But this latter is addable for constant p and so then must be v2(p)t(p). That is,
where v(p) is some as yet unspecified velocity.