  Using data from the GALAH pilot survey, we determine properties of the
Galactic thin and thick disks near the solar neighbourhood. The data cover a
small range of Galactocentric radius ($7.9 \leq R_\mathrm{GC} \leq 9.5$ kpc),
but extend up to 4 kpc in height from the Galactic plane, and several kpc in
the direction of Galactic anti-rotation (at longitude $260 ^\circ \leq \ell
\leq 280^\circ$). This allows us to reliably measure the vertical density and
abundance profiles of the chemically and kinematically defined `thick' and
`thin' disks of the Galaxy. The thin disk (low-$\alpha$ population) exhibits a
steep negative vertical metallicity gradient, at d[M/H]/d$z=-0.18 \pm 0.01$ dex
kpc$^{-1}$, which is broadly consistent with previous studies. In contrast, its
vertical $\alpha$-abundance profile is almost flat, with a gradient of
d[$\alpha$/M]/d$z$ = $0.008 \pm 0.002$ dex kpc$^{-1}$. The steep vertical
metallicity gradient of the low-$\alpha$ population is in agreement with models
where radial migration has a major role in the evolution of the thin disk. The
thick disk (high-$\alpha$ population) has a weaker vertical metallicity
gradient d[M/H]/d$z = -0.058 \pm 0.003$ dex kpc$^{-1}$. The $\alpha$-abundance
of the thick disk is nearly constant with height, d[$\alpha$/M]/d$z$ = $0.007
\pm 0.002$ dex kpc$^{-1}$. The negative gradient in metallicity and the small
gradient in [$\alpha$/M] indicate that the high-$\alpha$ population experienced
a settling phase, but also formed prior to the onset of major SNIa enrichment.
We explore the implications of the distinct $\alpha$-enrichments and narrow
[$\alpha$/M] range of the sub-populations in the context of thick disk
formation.
