A linear relationship between Earth models and seismic body wave data

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 τ(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, τ(p), X(p) and T(p) observations. This joint inversion is advantageous in restricting the set of earth models consistent with the data.