We propose a fast ray tracing method on a laterally heterogeneous Earth. When the square of slowness is expanded into spherical harmonics, an approximate analytical ray tracing can be performed. Using a Hamiltonian formulation, we introduce new coordinates, that have the specific adiabatic invariance of action/angle coordinates. A first-order solution is constructed in this new coordinate system. Excellent agreement is obtained between numerical and approximate analytical ray tracings, for the global model of Nakanishi and Anderson [1984> with an azimuthal order 6. ¿ American Geophysical Union 1989