On 14 February 2001 the Cluster Ion Spectrometry (CIS) experiment onboard three of the Cluster spacecraft observed velocity-dispersed ion structures (VDIS) as the spacecraft passed from the tail lobes into the plasma sheet boundary layer. These are the first multiple spacecraft observations of the VDIS phenomenon. The Cluster 1 spacecraft (SC1) observed a dispersed ion signature with beamlets and a second structure like that expected to be produced by an echo, while Cluster 3 (SC3) observed much less pronounced structuring a few minutes later. During this same event and over an extended interval the ACE spacecraft observed an interplanetary magnetic field that was directed southward. We have inferred the sources and acceleration mechanisms of the ions in these VDIS observations by following millions of ion trajectories backward and forward in time through time-dependent electric and magnetic fields obtained from a global MHD simulation. ACE data were used as input for the MHD model. We found that almost all of the particles comprising the first (A1) and second (A2) beamlets observed by SC1 had been nonadiabatic earlier in their history, while particles in the A3 beamlet exhibited a combination of adiabatic and nonadiabatic behavior. Beamlet A4 particles were always adiabatic. Moreover, for all of the beamlets the current sheet crossing that took place prior to their detection occurred between x = -13 RE and x = -16 RE in the tail, well earthward of the permanent stochastic "sea" from which all of the beamlets originated. Our model does not favor the multiple source scenario suggested by A. Keiling et al. Instead, it indicates that the source regions of the structures are spatially correlated. We have carried out a similar analysis of the SC3 observations. In general, SC3 beamlets have higher $kappa$ values, partly because of the depolarization of the field lines during these observations. In time forward calculations only a small fraction of ions from SC1 A structures returned to the spacecraft location. "Echoes" were more pronounced on SC3. In addition, in our calculations, some particles from SC1 A structures interacted with the current sheet and returned to the SC3 location, at the time when SC3 observed the A structures. When Cluster observations were organized by latitude instead of time, we found that all three Cluster spacecraft seemed to observe the same primary structure that persisted throughout the interval of observation.