A technique to probe the interior of three-dimensional dynamic granular sys
tems is presented. Positron emission particle tracking (PEPT) allows a sing
le tracer particle to be followed around a three dimensional vibrofluidized
granular bed for periods up to six hours. At present the technique is able
to resolve the position of the grains to +/-4 mm, with an average temporal
resolution of about 7 ms. Packing fraction profiles are calculated by maki
ng use of the ergodicity of the system, and granular temperature profiles a
re obtained, in the dilute case, from the short time behavior of the mean s
quared displacement. At longer times, the mean squared displacement shows a
range of behavior which can be explained by the presence of strong gradien
ts in the packing fraction. Convection currents were observed, but were suf
ficiently small in magnitude to be ignored during the analysis of grain mot
ion. The system was modeled using the Smoluchowski equation, which was solv
ed numerically, and the results compared with the experimentally determined
displacement probability density functions. Good agreement between experim
ent and numerical results was achieved using Brownian motion relationships
modified to accommodate differences between granular systems and thermal sy
stems.