Ray-Tracing Evaluation of the Field at and near Caustics

A fundamental limitation of geometrical acoustics is its inability to describe the field near caustics. evaluation of the wave solution near the caustic due to Brekhovskikh [Waves in Layered Media, Academic Press, New York, 1960), pp. 484–485]. For most applications this approach is too restrictive in that it applies only to layered media and only within a thin boundary layer about the caustic. Uniform asymptoti c expansions due to Ludwig [Comm. Pure Appl. Math. 19, 215–250 (1966)] and Kravtsov [Radiofiziko 7, 664–673 (1964)] are valid for arbitrary refracting media and provide the connection between the field at the caustic and coherent ray theory which is valid far from the caustic. Implementation of these results in standard ray-tracing programs is readily achieved since only the travel times and geometrical amplitudes of ordinary ray theory are required. An example is presented to illustrate both the utility of the Ludwlg-Kravtsov theory and its advantage over the older method. [Work supported by Office of Naval Research.]