In order to illustrate wave propagation concepts of ray theory, breakdown of ray theory at caustics, the formation of caustics, free oscillations, and the mode-ray duality, elastic wave propagation in a homogeneous, isotropic fluid sphere is considered. The analytical solution is simply expressed in terms of spherical Bessel functions, but their correct evaluation is an interesting numerical exercise. The solution shows some very interesting features, including near-field terms at short distances, and apparent polarity reversals due to the effect of double caustics.

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