Ray tracing has recently been expressed for anisotropy specified in a local Cartesian coordinate system, which may continuously vary in a model. It takes advantage of the fact that anisotropy has often a simpler nature locally (and is thus specified by a less number of elastic parameters) and the orientation of its symmetry elements may vary. Here we extend this approach by replacing the local Cartesian coordinate system with a curvilinear one of a global extent and by applying the approach to ray tracing and inhomogeneous dynamic ray tracing. Our formulation has several advantages compared to standard ray tracing and inhomogeneous dynamic ray tracing for anisotropy specified in global Cartesian coordinates. Among these are improved efficiency, lower consumption of computer memory, and conservation of anisotropic symmetry throughout the model.