  H$_2$O maser emission at 22 GHz in the circumstellar envelope is one of the
good tracers of detailed physics and kinematics in the mass loss process of
asymptotic giant branch stars. Long-term monitoring of an H$_2$O maser spectrum
with high time resolution enables us to clarify acceleration processes of the
expanding shell in the stellar atmosphere. We monitored the H$_2$O maser
emission of the semi-regular variable R Crt with the Kagoshima 6-m telescope,
and obtained a large data set of over 180 maser spectra during 1.3 years with
an observational span of a few days. Based on an automatic peak detection
method based on a least-squares fitting with a Gaussian basis function model,
we exhaustively detected peaks as significant velocity components with the
radial velocity on a 0.1 km/s scale. This analysis result shows that the radial
velocity of red-shifted and blue-shifted components exhibits a change between
acceleration and deceleration on the time scale of a few hundred days. These
velocity variations are likely to correlate with the intensity variations, in
particular during flaring state of H$_2$O masers. It seems reasonable to
consider that the velocity variation of the maser source is caused by the shock
propagation in the envelope due to stellar pulsation. However, it is difficult
to explain the relationship between the velocity variation and the intensity
variation only from shock propagation effects. We found that a time delay of
the integrated maser intensity with respect to the optical light curve is about
150 days.
