A method of satellite radar interferometry (SRI) enables the remote measurement of three-dimensional velocities of ice flow over large areas of glaciers. At present, ice-flow velocities are measured primarily *in situ* by use of the Global Positioning System (GPS) in a time-consuming procedure that yields a limited number of data points. In previous efforts to use SRI to determine ice velocities remotely over large areas, measurements were performed along repeat passes. Unfortunately, repeat passes yield data on only the surface displacements associated with the single components of velocity along the radar lines of sight. Moreover, in the absence of additional information, there is no way to separate unambiguously the mixed horizontal and vertical displacement signals acquired via repeat-pass SRI. In contrast, the present method provides three-dimensional velocity data over large areas with horizontal sampling intervals of roughly 100 m.

In the present method, two sets of repeat-pass measurements are acquired along subsequent, nonparallel passes (one ascending, one descending). The repeat-pass measurement geometry is illustrated in the figure, wherein S_{1} and S_{2} denotes a synthetic-aperture radar (SAR) viewing the same surface point from two slightly different (near-repeat) positions at different times, and the vector B denotes the baseline between the two positions. The problem is to find the vertical component and the two horizontal components of the local displacement of the surface between the two measurement times; the local velocity components then equal these components of displacement divided by the time between acquisition of SAR images.

The basic interferometric quantity is the difference between the relative phases of radar signal returned from the same surface point on the two passes. This phase difference is proportional to the range difference (the difference between the distances along the lines of sight), and can be expressed as a term dependent on displacement plus a term dependent on topography. Provided that the measurement geometry (including B) is known, one can estimate the topographical term and thus isolate the displacement-dependent term. For this purpose, B is approximated as a linear function of the along-track coordinate, in a mathematical model with four parameters that are determined by a linear least-squares fit to at least four tie points.

Ordinarily, three measurements of the same surface area from three significantly different directions are necessary to measure three-dimensional velocity. However, it is difficult or impossible to acquire such data in the polar regions, where much of the ice of interest is located. In the present method, it is possible to determine all three components of velocity from measurements from only two directions: This is made possible by the assumption that the ice at the surface flows only along the surface. This assumption is somewhat unrealistic in that ice is known to flow slightly upward from the surface in an ablation zone or slightly downward from the surface in an accumulation zone. Nevertheless, the assumption is useful in that it mathematically constrains one component of velocity. The other two components are mathematically constrained by the measurements from the crossing ascending and descending passes. Thus, all three components of velocity are determined.

*This work was done by Ian Joughin, Ronald Kwok of Caltech and Mark Fahnestock of the University of Maryland for *NASA's Jet Propulsion Laboratory*. For further information,* *access the Technical Support Package (TSP) **free on-line at www.techbriefs.com** under the Physical Sciences category, *or circle no. 147*on the TSP Order Card in this issue to receive a copy by mail ($5 charge).* *NPO-20160*

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This article first appeared in the April, 1998 issue of *NASA Tech Briefs* Magazine.

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