Ground-penetrating radar (GPR) signals are attenuated by both absorption and scattering. We performed low-frequency (<100 MHz) GPR surveys at the Volcanic Tableland of the Bishop (California) Tuff to evaluate the factors that control GPR depth of investigation and to develop insight into the capabilities of such radars for Mars. The subsurface reflection character was very different for two different commercial systems used; together, they revealed both internal welding contacts in the tuff and an abundance of discrete scatterers. Attenuation coefficients were computed from profiles that showed distributed scattering: the semilogarithmic signal decay is directly analogous to seismic coda. The absorption (intrinsic loss) was determined to be ~1 dB/m from low-frequency vertical-electric soundings. The residual attenuation (that is, the attenuation in the absence of absorption) is attributed to scattering. Scattering attenuation of ~1 dB/m at 25--50 MHz corresponds to mean-free paths as short as 4 m, a fraction of the two-way propagation distances of 20--40 m. Therefore the Bishop Tuff is formally a strong scatterer to GPR. The mean-free path is also comparable to the subsurface radar wavelength in this case, maximizing scattering loss. The scatterers themselves likely originate as welding heterogeneities; contrasts in dielectric constant due to density differences may be supplemented by moisture variations. On Mars, scattering is likely to contribute significant losses to GPR signals in all but the most uniform materials, and unfrozen thin films of water in the lower cryosphere could influence both absorption and scattering.