Theory of Radio Echoes From Glacier Beds

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Abstract
We review the theory of interpreting the echoes received back at the source from a glacier bed illuminated with a wide-angle beam of quasimonochromatic radio waves. It is convenient wherever possible to separate bed relief into “geography” and “roughness”. “Geography” is the surface that results from horizontally smoothing the bed over distances comparable with the mean heighthof the source above the bed. The geography can be deduced from the lime delays of specular reflections, provided these can be identified, “Roughness” is the statistics of the departures of the actual bed from the geography on scales down to about one-tenth of the predominant wavelength in the travelling pulse. The average heightSand horizontal dimensionL(where these quantities can be defined) of the irregularities can be deduced from measurements of the average value of the echo envelopepas a function of time delay. It is also possible to distinguish qualitatively different beds with the sameSandL. If the source-receiver unit moves keepinghconstant, thenpfluctuates about its mean value. This “spatial fading” can be used to detect horizontal ice displacements of less than one hundredth of a wavelength. To detect vertical ice motion it is necessary to observe the phase of the echo.

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