Characterizing the Glacier Bed Using a Radio-Echo Technique

Abstract

If glacier ice is assumed to be a uniaxial birefringent material then two parameters are needed for describing the orientation behaviour of the polarization ellipse of a radio signal returned from the glacier bed. These are δ, the relative phase between the ordinary and extraordinary wave, and r, the ratio of their attenuation coefficients (Woodruff and Doake, 1979). If it is assumed that the attenuation in ice is isotropic, then a value of r other than unity will be due to anisotropic reflection coefficients at the glacier bed. A simple way of measuring r separately from δ could then be used to characterize the reflecting surface.

Defining a rectangular coordinate system in which the wave propagates in the z direction, the effective optic axis lies in the zy plane, a linear transmitted wave of strength E ₀ is at an angle α to the x axis then the powers received in linear aerials aligned along the x′y′ axes of a rectangular coordinate system at an angle θ to the xy system are given by

where A_x and A_y are the attenuation coefficients in the x and y directions and r = A_y/A_x .

By adding the powers in the two aerials the total received power is

which is independent of θ, the azimuth of the receiving aerials. This is a well-known result in radar theory and practice. However, because of the dependence on α, by rotating the transmitting aerial a value for r can be found from the amplitude of the variation in the total power

The choice of the value for r arises because of a 90° ambiguity in the direction of the optic axis which can only be resolved by the full procedure of rotating both aerials.