We present a technique for estimating Mars topographic roughness on horizontal scales from about 10 m to 100 m using Shallow Radar (SHARAD) sounding data. Our results offer a view of surface properties complementary to Mars Orbiter Laser Altimeter (MOLA) pulse-width or baseline roughness maps and can be compared to SHARAD peak-echo properties to infer deviations from the average near-surface density. Latitudinal averaging of SHARAD-derived roughness over Arabia and Noachis Terrae shows good agreement with MOLA-derived roughness and provides clear evidence for latitude-dependent mantling deposits previously inferred from image data. In northwestern Gordii Dorsum, we find that bulk density in at least the upper few meters is significantly lower than in other units of the Medusae Fossae Formation. We observe the same behavior indicative of low near-surface density in wind-eroded crater fill in the southern highlands. Combining surface-properties analysis, subsurface sounding, and high-resolution optical images, we show that the Pavonis Mons fan-shaped deposit differs significantly from lobate debris aprons which SHARAD has shown to be ice-cored. There are no internal radar reflections from the smooth-facies portion of the Pavonis Mons fan-shaped deposit, and we suggest that these deposits are either quite thin or have little dielectric (i.e., density) contrast with the underlying terrain. Future application of these techniques can identify other low-density units across Mars, assist in the mapping of regional volatile-rich mantling units, and provide new constraints on the physical properties of the polar layered terrain.