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 clocks 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 Earths 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.
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