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We develop and then demonstrate a 3-D tomographic ice sounding method applied to very high frequency (VHF) radar data that produces swath measurements of ice sheet surface topography, ice thickness, and radar reflectivity of both the surface and bed of the ice sheet. First, we formulate the ice sheet imaging problem as a problem of estimating signal arrival angles and illustrate how the method resolves ambiguous echoes arriving simultaneously from the left and right sides of the aircraft, as well as from the surface and base of the ice sheet. We then discuss why we chose the time-domain subaperture method for 2-D image formation for ice sounding. We apply the tomographic technique to the data that we collected in May 2006 and again in July 2008 from a multiple-phase-center VHF radar system. We present 3-D images of the upper and lower surfaces of the ice sheet and compare the estimated surface topography with Ice, Cloud, and land Elevation Satellite altimeter nadir track measurements and the measured swath ice thickness with independent nadir depth sounder tracks. We achieved a 5-m surface topography accuracy and a 14-m ice thickness accuracy.