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.
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