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In the conventional geometric-optic approximation to wave propagation excited by a source of finite extent, each source point emits rays that transport wave energy along well-defined trajectories, but with transport properties exhibiting singularities in caustic regions where the cross section of ray bundles vanishes. In the first-order quasi-particle approximation the extended source is viewed as a phase space distribution of point quasi-particles whose space-time dependent kinetic properties such as density, average velocity, etc., provide nonsingular measures of the space-time transport of amplitude, wave number, frequency, etc., of the wave train modulation even in caustic regions. The range of ap- plicability of the quasi-particle method is examined in terms of relative space-time scales characteristic of the excitation and medium.