Propagation of internal acoustic-gravity waves around a spherical Earth

The refraction of internal acoustic-gravity waves by the earth's spherically symmetric gravitational field is investigated by using the approximation of geometrical acoustics in an isothermal atmosphere. Instead of following straight lines the ray paths of internal acoustic waves bend away from the earth, whereas the ray paths of internal gravity waves bend toward the earth so as to nearly match the earth's curvature. Consequently, the use of a flat-earth approximation for describing long-distance propagation around a spherical earth is well justified for internal gravity waves, although not for internal acoustic waves.