  Atomic clock technology is advancing rapidly, now reaching stabilities of
$\Delta f/f \sim 10^{-18}$, which corresponds to resolving $1$ cm in equivalent
geoid height over an integration timescale of about 7 hours. At this level of
performance, ground-based atomic clock networks emerge as a tool for monitoring
a variety of geophysical processes by directly measuring changes in the
gravitational potential. Vertical changes of the clock's position due to
magmatic, volcanic, post-seismic or tidal deformations can result in measurable
variations in the clock tick rate. As an example, we discuss the geopotential
change arising due to an inflating point source (Mogi model), and apply it to
the Etna volcano. Its effect on an observer on the Earth's surface can be
divided into two different terms: one purely due to uplift and one due to the
redistribution of matter. Thus, with the centimetre-level precision of current
clocks it is already possible to monitor volcanoes. The matter redistribution
term is estimated to be 2-3 orders of magnitude smaller than the uplift term,
and should be resolvable when clocks improve their stability to the
sub-millimetre level. Additionally, clocks can be compared over distances of
thousands of kilometres on a short-term basis (e.g. hourly). These clock
networks will improve our ability to monitor periodic effects with
long-wavelength like the solid Earth tide.
