The altitude dependence of terrestrial gamma-ray spectra; a simple model

Accurate airborne multichannel gamma-ray surveys require accurate knowledge of the spectral shapes of the natural radioelements and their variation with height. Simple physical considerations suggest a model with two spectral components for each radioelement, in which the first component decays into the second with increasing height. The two spectral components are approximately identified with gamma rays that have been scattered and those that have not been scattered since entering the atmosphere, although this interpretation is irrelevant to the applications of the model. The model's analytic representation of spectral dependence on height yields an explicit formula for the effective height of the detector as deduced from spectral shape. Atmospheric radon is shown to produce a negative effective height, which implies a possible method for estimating atmospheric radon directly rather than from spectral shape. An extension of this approach gives an approximate formula for estimating the spectral contribution of an arbitrarily stratified distribution of radon.