A direct numerical simulation of the three-dimensional unsteady compressible Navier–Stokes equations is performed to investigate the infrasonic field generated in a realistic atmosphere by an explosive source placed at ground level. To this end, a high-order finite-difference method originally developed for aeroacoustic applications is employed. The maximum overpressure and the main frequency of the signal recorded at 4 km distance from the source location are about 4000 Pa and 0.2 Hz, respectively. The atmosphere is parametrized as a vertically stratified medium, constructed by specifying vertical profiles of the temperature and the horizontal wind which reproduce measurements. The computation is carried out up to 140 km altitude and 450 km range. The goal of the present paper is twofold. On the one hand, the feasibility of using a direct numerical simulation of the three-dimensional fluid dynamic equations for the detailed description of long-range propagation in the atmosphere is proven. On the other hand, a physical analysis of the infrasonic field is realized. In particular, great attention is directed towards some important phenomena which are not taken into account or not well predicted by classical propagation models. To begin with, the present study clearly demonstrates that the weakly nonlinear ray theory may lead to an incorrect evaluation of the waveform distortion of high-amplitude waves propagating towards the lower thermosphere. In addition, signals recorded in the shadow zones are investigated. In this regard, the influence on the acoustic field of temperature and wind inhomogeneities of length scale comparable with the acoustic wavelength is analysed. The role of diffraction at the thermospheric caustic is finally examined and it is pointed out that the amplitude of the source may have a strong impact on the length of the shadow zone.