  We examine the \alpha-element abundance ratio, [\alpha/Fe], of 5620 stars,
observed by the Sloan Extension for Galactic Understanding and Exploration
survey in the region 6 kpc < R < 16 kpc, 0.15 kpc < |Z| < 1.5 kpc, as a
function of Galactocentric radius R and distance from the Galactic plane |Z|.
Our results show that the high-\alpha\ thick disk population has a short scale
length (L_thick ~ 1.8 kpc) compared to the low-\alpha population, which is
typically associated with the thin disk. We find that the fraction of
high-\alpha\ stars in the inner disk increases at large |Z|, and that
high-\alpha\ stars lag in rotation compared to low-\alpha\ stars. In contrast,
the fraction of high-\alpha\ stars in the outer disk is low at all |Z|, and
high- and low-\alpha\ stars have similar rotational velocities up to 1.5 kpc
from the plane. We interpret these results to indicate that different processes
were responsible for the high-\alpha\ populations in the inner and outer disk.
The high-\alpha\ population in the inner disk has a short scale length and
large scale height, consistent with a scenario in which the thick disk forms
during an early gas-rich accretion phase. Stars far from the plane in the outer
disk may have reached their current locations through heating by minor mergers.
The lack of high-\alpha\ stars at large R and |Z| also places strict
constraints on the strength of radial migration via transient spiral structure.
