  Weakly interacting massive particles (WIMPs) are one of the leading
candidates for dark matter. Currently, the most promising method to detect many
different WIMP candidates is the direct detection of the recoil energy
deposited in a low-background laboratory detector due to elastic WIMP-nucleus
scattering. So far the usual procedure has been to predict the event rate of
direct detection of WIMPs based on some model(s) of the galactic halo. The aim
of our work is to invert this process. That is, we study what future direct
detection experiment can teach us about the WIMP halo. As the first step we
consider a time-averaged recoil spectrum, assuming that no directional
information exists. We develop a method to construct the (time-averaged)
one-dimensional velocity distribution function from this spectrum. Moments of
this function, such as the mean velocity and velocity dispersion of WIMPs, can
also be obtained directly from the recoil spectrum. The only input needed in
addition to a measured recoil spectrum is the mass of the WIMP; no information
about the scattering cross section or WIMP density is required.
