The inverse problem of radio-echo sounding consists in the reconstruction of subglacial relief from the known radio-echo profile, and the path, and speed of the aircraft. The present work shows that in the geometrical optical approach the solution of the inverse problem for a homogeneous, two-dimensional object (valley glacier) exists, and there is a unique solution. An algorithm for interpretation of the experimental data is suggested. It may be considered as the generalization of Harrison’s transformations for any surfaces. paths, and speed.

The direct problem of radio-echo sounding consists in the reconstruction of radio-echo profile from the known surface and subsurface relief, path, and aircraft speed. The analysis of traces in the standard radio-echo sounding mode of operation reveals the possibility of introducing a three-index trace classification {K, sign S’(o), K+} where K is the number of real roots characteristic of the equations, K+ the number of positive roots, and S’(o) the position derivative, the argument being equal to zero. The form {o, — o} is optimal for the precision of the calculation of the reflected surface coordinates, as well as for the simplicity of the interpreted picture. By a special choice of the altitude of flight, any form of any surface can be brought to {o, —o}. The decrease in beam width is equivalent to the diminution of roots of the characteristic equations. For a pencil beam the trace degenerates into a point.

The attenuation of the reflected signal depends on the glacier geometry, the dielectric parameters of the medium, the altitude and the course of the aircraft, as well as statistical characteristics of the mutual orientation of the interfaces and aerials. For the description of the energetics of radio-echo sounding, equivalent reflecting surfaces are suggested. These surfaces correspond to the Harrison’s equivalent reflecting surface. Exact formulae for the power of coherent and incoherent components of the reflected signal are obtained. Components of the full attenuation such as absorption, depolarization, and spherical divergence, are investigated with respect to refraction and focusing effects.