  High-angular-resolution observations of asymptotic giant branch (AGB) stars
often reveal non-spherical morphologies for the gas and dust envelopes. We aim
to make a pilot study to quantify the impact of different geometries
(spherically symmetric, spiral-shaped, and disc-shaped) of the dust component
of AGB envelopes on spectral energy distributions (SEDs), mass estimates, and
subsequent mass-loss rate (MLR) estimates. We also estimate the error made on
the MLR if the SED is fitted by an inappropriate geometrical model. We use the
3D Monte-Carlo-based radiative-transfer code RADMC-3D to simulate emission from
dusty envelopes with different geometries (but fixed spatial extension). We
compare these predictions with each other, and with the SED of the AGB star EP
Aqr that we use as a benchmark since its envelope is disc-like and known to
harbour spiral arms, as seen in CO. The SEDs involving the most massive
envelopes are those for which the different geometries have the largest impact,
primarily on the silicate features at 10 and 18 um. These different shapes
originate from large differences in optical depths. Massive spirals and discs
appear akin to black bodies. Optically thick edge-on spirals and discs (with
dust masses of 1e-4 and 1e-5 Msun) exhibit black-body SEDs that appear cooler
than those from face-on structures and spheres of the same mass, while
optically thick face-on distributions appear as warmer emission. We find that
our more realistic models, combined spherical and spiral distributions, are 0.1
to 0.5 times less massive than spheres with similar SEDs. More extreme, less
realistic scenarios give that spirals and discs are 0.01 to 0.05 times less
massive than corresponding spheres. This means that adopting the wrong geometry
for an AGB circumstellar envelope may result in a MLR that is incorrect by as
much as 1 to 2 orders of magnitude when derived from SED fitting.
