Retrieval of the three-dimensional wave structure of gravity waves from multi-position airglow measurements

The aim of this work is to develop mathematical foundation of a method which can be used to infer the three-dimensional gravity wave characteristics from multi position airglow observations from space. This work derives a one-dimensional Fredholm integral equation of the first kind, which describes the relations between the gravity wave spectrum and spatial structure of wave perturbations registered by a space-based airglow imager. It is shown that the solution of this equation belongs to the central slice through a three-dimensional gravity wave spectrum, whose plane is perpendicular to the optical axis of the airglow imager. Thus, in order to retrieve the three-dimensional gravity wave characteristics from the airglow observations performed from space, it is needed to obtain the set of images of a local emission layer area from different imager positions. Then this data must be processed using the developed mathematical techniques to obtain a set of the central slices of the three-dimensional gravity wave spectrum. Applying the technique, for a superposition of three individual waves, amplitude and wave vector can be determined. (C) 2013 Elsevier Ltd. All rights reserved.