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Phase memory in W.K.B. and phase integral solutions of ionospheric propagation problems

In a slowly varying medium the propagation of waves remote from turning points or coupling points can be expressed in terms of W.K.B. solutions. For an isotropic medium a W.K.B. solution includes a factor that is an exponential of a phase integral or eikonal function. This expresses the cumulative change of phase that has occurred in the medium previously traversed, and has been called the ‘phase memory ’. It depends on the forms of the functions describing the spatial dependence of the medium. The remaining factor of the W.K.B. solution is a function only of the local properties of the medium. For an anisotropic medium such as the ionosphere, however, each W.K.B. solution may contain another factor which is also the exponential of an integral, and which has a memory content because it cannot be absorbed into the local factor. The properties of this new memory term, including its physical explanation, are here examined for radio waves obliquely incident in a horizontally stratified ionosphere.