Two-point paraxial traveltimes in an inhomogeneous anisotropic medium

We derive formulae for the approximate computation of two-point paraxial traveltimes (traveltimes between two points) for points arbitrarily chosen in a paraxial vicinity of a reference ray computed in a smoothly varying inhomogeneous anisotropic medium containing structural interfaces. The formulae have a form of the Taylor expansion in Cartesian coordinates of the two-point paraxial traveltime or its square to the quadratic terms. The coefficients of the expansion depend on quantities obtained by ray tracing in Cartesian coordinates and by dynamic ray tracing in ray-centred coordinates. Alternatively, the dynamic ray tracing can be performed in Cartesian coordinates. The advantages of the approach based on dynamic ray tracing in raycentred coordinates are its efficiency and elimination of possible complications that may arise from the redundant fundamental solutions of dynamic ray tracing in Cartesian coordinates (the ray-tangent and non-eikonal solutions).