The propagation of Lg waves in complex media can be described either by means of a modal superposition scheme with numerical integration through the heterogeneity or by using ray diagrams. Rays are set off at equal horizontal intervals in a stratified zone adjacent to the heterogeneity, with phase velocities appropriate to particular modes. The constructive interference pattern in the stratified medium is modified in the horizontally varying region to give a graphic illustration of the propagation effects. The ray method agrees well with the modal calculations but may be conveniently applied in more general circumstances, e.g., to include surface topography or permanent changes in crustal structure.

Structural boundaries which involve sudden thinning of the crustal wave guide are particularly disruptive to the Lg train, as at a pinch in crustal thickness or the continent-ocean transition. The effects of localized thickening are more subtle. The relatively sharp cutoff for Lg waves in some structures, e.g. in the Tibetan Plateau, can be explained by the source being no longer able to couple into the crustal wave guide at the receiver.

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