The acoustic ray tracing relations are extended by the inclusion of auxiliary parameters describing variations in the spatial ray coordinates and eikonal vector due to changes in the initial conditions. Computation of these parameters allows one to define the geometric spreading factor along individual ray paths and assists in identification of caustic surfaces so that phase shifts can be easily identified. A method is developed leveraging the auxiliary parameters to identify propagation paths connecting specific source-receiver geometries, termed eigenrays. The newly introduced method is found to be highly efficient in cases where propagation is non-planar due to horizontal variations in the propagation medium or the presence of cross winds. The eigenray method is utilized in analysis of infrasonic signals produced by a multi-stage sounding rocket launch with promising results for applications of tracking aeroacoustic sources in the atmosphere and specifically to analysis of motor performance during dynamic tests.