  Most of the quantitative information about the magnetic field vector in solar
prominences comes from the analysis of the Hanle effect acting on lines formed
by scattering. As these lines can be of non-negligible optical thickness, it is
of interest to study the line formation process further. We investigate the
multidimensional effects on the interpretation of spectropolarimetric
observations, particularly on the inference of the magnetic field vector. We do
this by analyzing the differences between multidimensional models, which
involve fully self-consistent radiative transfer computations in the presence
of spatial inhomogeneities and velocity fields, and those which rely on simple
one-dimensional geometry. We study the formation of a prototype line in ad hoc
inhomogeneous, isothermal 2D prominence models. We solve the NLTE polarized
line formation problem in the presence of a large-scale oriented magnetic
field. The resulting polarized line profiles are then interpreted (i.e.
inverted) assuming a simple 1D slab model. We find that differences between
input and the inferred magnetic field vector are non-negligible. Namely, we
almost universally find that the inferred field is weaker and more horizontal
than the input field. Spatial inhomogeneities and radiative transfer have a
strong effect on scattering line polarization in the optically thick lines. In
real-life situations, ignoring these effects could lead to a serious
misinterpretation of spectropolarimetric observations of chromospheric objects
such as prominences.
