When the velocity distribution in a laterally homogeneous earth is described by dz/du, the derivative of depth with slowness, the earth model thus derived is shown to be linearly related to the delay time function &tgr; (p), the travel time, T(p) and distance X(p), thus allowing the direct application of linear inverse theory to the body wave observations through joint inversion of &tgr; (p), X(p) and T(p) observations. This joint inversion is advantageous in restricting the set of earth models consistent with the data.