  We analyze the origin of the three dimensional (3D) magnetism observed in
nonhydrated Na-rich Na$_x$CoO$_2$ within an itinerant spin picture using a 3D
Hubbard model. The origin is identified as the 3D nesting between the inner and
outer portions of the Fermi surface, which arise due to the local minimum
structure of the $a_{1g}$ band at the $\Gamma$-A line. The calculated spin wave
dispersion strikingly resembles the neutron scattering result. We argue that
this 3D magnetism and the spin fluctuations responsible for superconductivity
in the hydrated systems share essentially the same origin.
