Refraction Correction for Radio Echo-Sounding of Ice Overlain by Firn

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Abstract
Radio-echo signals travel faster in firn than in ice, which affects the analysis of ice-mass thickness. If this effect is neglected, then the calculated thickness of an ice mass may be in error by an amount of the order of one-tenth of the firn thickness. An exact formulation is derived for the path of the signal through the firn and the ice. Explicit solutions are given for constant, linear, and quadratic profiles of the refractive index in the firn layer.