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Weakly interacting massive particles (WIMPs) are one of the leadingcandidates for dark matter. Currently, the most promising method to detect manydifferent WIMP candidates is the direct detection of the recoil energydeposited in a low-background laboratory detector due to elastic WIMP-nucleusscattering. So far the usual procedure has been to predict the event rate ofdirect detection of WIMPs based on some model(s) of the galactic halo. The aimof our work is to invert this process. That is, we study what future directdetection experiment can teach us about the WIMP halo. As the first step weconsider a time-averaged recoil spectrum, assuming that no directionalinformation exists. We develop a method to construct the (time-averaged)one-dimensional velocity distribution function from this spectrum. Moments ofthis function, such as the mean velocity and velocity dispersion of WIMPs, canalso be obtained directly from the recoil spectrum. The only input needed inaddition to a measured recoil spectrum is the mass of the WIMP; no informationabout the scattering cross section or WIMP density is required.Comment: 34 Pages, 9 figure

Reconstructing the velocity distribution of weakly interacting massive particles from direct dark matter detection data