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This book presents the theory and results of experimental studies of the propagation of infrasound waves in a real atmosphere with its inherent fine-scale layered structure of wind speed and temperature. It is motivated by the fact that the statistical characteristics of anisotropic (or layered) fluctuations of meteorological fields, the horizontal scales of which significantly exceed their vertical scales, have been very poorly studied compared to those of locally isotropic turbulence in the inertial range of scales. This book addresses this lacuna by developing a theory of the formation of anisotropic inhomogeneities of the atmosphere in a random field of internal gravity waves and vortex structures. Using theory, it explains numerous experimental data depicting the influence of the fine structure of the atmosphere on the propagation of infrasound waves from pulsed sources. The text will appeal to specialists in the fields of acoustics and optics of the atmosphere, remote sensing of the atmosphere, the dynamics of internal waves, nonlinear acoustics, and infrasound monitoring of explosions and natural hazards.