  Secular gravitational instability (GI) is one promising mechanism for
explaining planetesimal formation. The previous studies on secular GI utilized
a razor-thin disk model and derived the growth condition in terms of the
vertically integrated physical values such as dust-to-gas surface density
ratio. However, in weakly turbulent disks where secular GI can operate, a dust
disk can be orders of magnitude thinner than a gas disk, and analyses treating
the vertical structures are necessary to clarify the interplay of the midplane
dust motion and the upper gas motion. In this work, we perform vertically
global linear analyses of secular GI with the vertical domain size of a few gas
scale heights. We find that dust grains accumulate radially around the midplane
while gas circulates over the whole vertical region. We obtain well-converged
growth rates when the outer gas boundary is above two gas scale heights. The
growth rates are underestimated if we assume the upper gas to be steady and
regard it just as the source of external pressure to the dusty lower layer.
Therefore, treating the upper gas motion is important even when the dust disk
is much thinner than the gas disk. Conducting a parameter survey, we represent
the growth condition in terms of the Toomre's $Q$ value for dust and
dust-to-gas surface density ratio. The critical dust disk mass for secular GI
is $\sim10^{-4}$ stellar mass for the dust-to-gas surface density ratio of
0.01, the Stokes number of 0.1, and the radial dust diffusivity of
$10^{-4}c_{\mathrm{s}} H$, where $c_{\mathrm{s}}$ is the gas sound speed and
$H$ is the gas scale height.
