The W.K.B. Approximation, Turning Points, and the Measurement of Phase Velocities

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Abstract
The conditions of validity of the W.K.B. approximation in geoacoustic problems are investigated; of particular interest here is the behavior of acoustic-gravity waves in the earth's thermosphere. A conclusion of some general significance is that great care must be exercised in interpreting vertical phase velocity measurements: thus, whereas W.K.B. methods and intuitive arguments suggest an infinite vertical phase velocity at turning points, exact solutions show that this is not necessarily the case. This has obvious practical implications for one's efforts at understanding the structure of a stratified medium by means of phase velocity measurements, particularly where these measurements are made near a turning point.

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