The ambiguity in ray perturbation theory

Ray perturbation theory is concerned with the change in ray paths and travel times due to changes in the slowness model or the end-point conditions of rays. Several different formulations of ray perturbation theory have been developed. In this paper, a formalism is developed where one can specify explicitly the mapping from the reference curve to the perturbed curve by choosing a stretch factor that relates increments in arc length along the reference curve and the perturbed curve. This is incorporated in a theory that is accurate to first order in the ray position and to second order in the travel time. -from Authors