Methods are developed to calculate acoustic propagation paths through an atmospheric layer surrounding a spherical globe in order to more accurately model the propagation of infrasonic signals, which are often observed after propagating hundreds or thousands of kilometers. A generalized curvilinear coordinate system is used to define the ray tracing equations from the eikonal equation for a moving, inhomogeneous atmosphere, and the specific case of spherical coordinates is applied to obtain a system of coupled equations describing geometric propagation paths in an atmospheric layer surrounding a globe. Comparison with propagation predictions using a Cartesian geometry shows that even for relatively short infrasonic propagation distances of a few hundred kilometers, differences introduced by the change in geometry are significant. Characteristics of the stratospheric pair are considered, and it is found that differences in the upward and downward legs of the propagation paths corresponding to the fast and slow stratospheric arrivals are changed such that spherical coordinate geometry predicts a decrease in the relative arrival time between the two. Analysis of regional infrasonic signals produced by a series of surface explosions shows that predictions obtained using spherical geometry are more accurate in cases where the tropospheric and stratospheric waveguides are accurately characterized.