A geometrical detector model of airborne gamma-ray spectrometry is presented for data acquired using a rectangular detector of arbitrary dimensions. The detector response is modeled by calculating variations in solid angle and detector thickness for sources at different orientations. This gives the total count rate, which is then multiplied by a factor, assumed independent of orientation, to give the peak count rate. The model shows excellent agreement with experimental data collected using a 4.2-liter detector and with Monte Carlo simulations of a 16.8-liter detector. Results for the 4.2-liter crystal showed significant asymmetry. However, for a typical airborne system, with a 16.8-liter crystal, the asymmetry was weak because the detector had about the same solid angle and thickness at any azimuthal angle. The point spread function for the geometrical detector model differed significantly from a uniform detector model, the latter predicting a lower spatial resolution. This implies that surveys designed on the uniform assumption may undersample the signal between flight lines. For example, at 60 m elevation, the area that contributes 90% of the thorium signal is predicted to be 10.9 hectares (ha) for the uniform model and only 7.6 ha for the geometrical model. The model can be extended to incorporate aircraft velocity by convolving the stationary model with a rectangular function. Aircraft velocity can have a substantial influence on the modeled response if long integration times permit significant displacement of sources relative to the height of the aircraft.

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