The formation of caustics in two- and three-dimensional media

In terms of ray theory, the focus point (also related to caustics and tripl ications) is the point in space where the ray position is stationary for pe rturbations in the initial condition. Criteria for the formation of caustic s are presented. With ray perturbation theory, a condition for the developm ent of triplications is defined for plane wave sources and for point source s. This theory is then applied to two cases of slowness media: 1-D slowness perturbation models and 2-D Gaussian random media. The focus position in 1 -D slowness models is proportional to the inverse of the square root of rel ative slowness fluctuations. For Gaussian random media, the distance at whi ch caustics generate is dependent on the relative slowness perturbation to the power of -2/3. We use snapshots of propagating plane wavefields to show that caustics develop as predicted by theory. The theory for caustic forma tion can be generalized to three dimensions.