The study of wave propagation by geometrical optics is applied to a consideration of propagation through a non-uniform, statistically homogenous medium. Following the trajectory of a phase point, two effects are examined; the retardation of the phase point by the variable local wave speed along its trajectory and the further retardation and dispersion resulting from its meandering. Mean and mean-squared displacements are obtained to describe the retardation of the wave front, and the dispersion of the phase point from the incident direction.

The theory has application as a correction to the use of geometrical optics wherever the latter can be employed. In particular, it is shown by an estimate of the magnitude of the pertinent parameters that an application may well be found in the study of the tsunami (a long ‘shallow’ ocean wave).