  An extensive radiative transfer analysis of circumstellar SiO `thermal' radio
line emission from a large sample of M-type AGB stars has been performed. The
sample contains 18 irregulars of type Lb (IRV), 7 and 34 semiregulars of type
SRa and SRb (SRV), respectively, and 12 Miras. New observational material,
which contains data in several SiO rotational lines in the ground vibrational
state, is presented for the IRV/SRVs. The detection rate was about 60%. SiO
fractional abundances have been determined through radiative transfer
modelling. The abundance distribution of the IRV/SRV sample has a median value
of 8E-6. The high mass loss rate Miras have a bimodal abundance distribution, a
low abundance group (on average 4E-7) and a high abundance group (on average
7E-6). The derived SiO abundances are in all cases well below the abundance
expected from stellar atmosphere chemistry, on average by a factor of ten. In
addition, there is a trend of decreasing SiO abundance with increasing mass
loss rate. This is interpreted in terms of depletion of SiO molecules by the
formation of silicate grains in the circumstellar envelopes, with an efficiency
which increases with the mass loss rate. The SiO and CO radio line profiles
differ in shape. In general, the dominating part of the SiO profiles are
narrower than the CO profiles, but they have low-intensity wings which cover
the full velocity range of the CO profile. This is interpreted (as has been
done also by others) as due to the influence of gas acceleration in the region
which produces a significant fraction of the SiO line emission. Finally, a
number of sources which have peculiar CO line profiles are discussed from the
point of view of their SiO line properties.
