The pros and cons of the inversion method approach to derive 3D dust
  emission properties of the ISM: the Hi-GAL field centred on
  (l,b)=(30$^{\circ}$,0$^{\circ}$)
  Herschel FIR continuum data obtained as part of the Hi-GAL survey have been
used, together with the GLIMPSE 8 $\mu$m and MIPSGAL 24 $\mu$m data, to attempt
the first 3D-decomposition of dust emission associated with atomic, molecular
and ionized gas at 15 arcmin angular resolution. Our initial test case is a
2$\times$2 square degrees region centred on (l,b)=(30$^{\circ}$,0$^{\circ}$), a
direction that encompasses the origin point of the Scutum-Crux Arm at the tip
of the Galactic Bar. Coupling the IR maps with velocity maps specific for
different gas phases (HI 21cm, $^{12}$CO and $^{13}$CO, and RRLs), we estimate
the properties of dust blended with each of the gas components and at different
Galactocentric distances along the LOS. A statistical Pearson's coefficients
analysis is used to study the correlation between the column densities and the
intensity of the IR emission. This analysis provides evidence that the
2$\times$2 square degree field under consideration is characterized by the
presence of a gas component not accounted for by the standard tracers, possibly
associated with warm H$_{2}$ and cold HI. We demonstrate that the IR radiation
in the range 8 $\mu$m $<$ $\lambda$ $<$ 500 $\mu$m is systematically dominated
by emission originating within the Scutum-Crux Arm. By applying an inversion
method, we recover the dust emissivities associated with atomic, molecular and
ionized gas. Using the DustEM model we obtain an indication for PAHs depletion
in the diffuse ionized gas. However, the main goal of this work is to discuss
the impact of the missing column density associated with the dark gas component
on the accurate evaluation of the dust properties, and to shed light on the
limitations of the inversion method approach when this is applied to a small
section of the Galactic Plane and when the working resolution allows sufficient
de-blending of the gas components along the LOS.
