Ray tracing for sonic wave propagation in a two-dimensional atmosphere structure is performed in the presence of spatially variable wind by using an Hamiltonian approach. Paraxial ray tracing is deduced by first-order perturbations. Using standard atmospheric data or illustrative models, we test numerically the Hamiltonian approach. The ray tracing allows accurate estimation of trajectories and associated travel-times as well as stable and accurate amplitude variations along a ray. Lateral variations of both sonic and wind velocity are important for quantitative evaluation of acoustic waves. Gradients of the wind field must be taken into account for precise quantification of ray trajectories and, consequently, for the localization of ground impacts, a key element for any micro-barometric recording station.