Surface Impedance Time Domain Reflectometry for the Determination of Ice Depth

Abstract

The analysis of the surface impedance of a horizontally stratified earth is similar to the impedance of a step‐wise discontinuous lossy transmission line. Time Domain Reflectometry (TDR) is commonly used in transmission line assessment to determine the location of faults. There are electrical conditions where TDR can be applied to a two layered subsurface to determine the time of flight of the EM wave and hence the thickness of the top layer. When the upper layer resistivity is sufficiently contrasted over a conductive second layer, then transforming surface impedance data measured across a broad band of frequencies into the time domain allows one to determine the time of flight to the subsurface boundary.

If the maximum frequency, frequency step size and number of steps are optimised for the two layers a periodicity appears in the surface impedance profile. It is demonstrated through computer modelling that a layer of ice on rock or sea water gives a return time of flight equal to the separation time of peaks in the time domain surface impedance profile. The technique requires a vertically polarised transmitter which steps up to the high frequency (HF) range. For example an ice layer of 30 to 400 meters thickness requires frequencies up to 5MHz.

In this paper, the basic theory for the use of TDR techniques in the interpretation of the surface impedance data is explained, and computer modelling results are presented