Ray perturbation theory, dynamic ray tracing and the determination of Fresnel zones

Ray perturbation theory and dynamic ray tracing both describe the behaviour of seismic rays near a reference ray. The equations of dynamic ray tracing relate changes in position and direction of a ray in the vicinity of a reference ray (paraxial ray) to changes in the reference ray's initial conditions. Ray perturbation theory relates changes in paraxial rays to changes in the slowness field or the reference ray's endpoints. Dynamic ray tracing is performed in ray-centred coordinates, whereas ray perturbation theory may be performed in either ray-centred coordinates or in an external reference frame. Both methods derive from asymptotic ray theory, but their developments have proceeded along largely independent paths. In this paper we explore the relationship between dynamic ray tracing and ray perturbation theory and outline an efficient scheme, based on ray perturbation theory, to compute approximate Fresnel zones in inhomogeneous media.