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Our global society is affected by, and makes use of, many time-varying processes. Processes related to geothermal energy and CO₂ sequestration can help mitigate climate change and reduce the number of premature deaths (millions annually) due to air pollution from fossil fuels. Processes related to volcanic hazards instead endanger lives and infrastructure in the form of e.g. eruptions, earthquakes, and toxic gases. The related time-varying processes have changing signatures, with specific starting and ending points, and associated time frames, and are investigated in this dissertation using seismicity and time-dependent tomography (TDT).

TDT has been used to, e.g., investigate pre-, syn, and post-eruptive periods in volcanic settings, as well as the stimulation of an enhanced geothermal system. One cannot, however, simply produce results for individual epochs and interpret them. We show how artificial differences between results can arise for such individual inversions, as well as for a joint inversion of asynchronous data, and when using constraints (e.g. inter-model minimization). A pragmatic method is presented to identify whether the differences between results go beyond these artificial differences.

The time-varying processes under investigation relate to the Reykjanes Peninsula, Iceland, which hosts multiple geothermal power plants, and was the location of several striking signals: Multi-year deformation in a volcanic system, followed by 15 months of volcanotectonic unrest, leading to the first eruption on the peninsula in ~780 years.

We show that the multi-year deformation signal is related to a super-critical reservoir that could feed a new geothermal power plant, and identify 14 seismic swarms that cascade along the boundary deformation zone during movements along this zone. We also present the first ever tomographic image of a deep magma reservoir below the Reykjanes Peninsula and follow a propagating dike from the moment it ruptured this reservoir's roof until its arrest, which was followed by a second rupture that lead to the March 2021 eruption in Fagradalsfjall.

We explain three possible mechanisms that can lead to both vertical arrest and lateral deflection of a propagating dike. These mechanisms benefit from contacts between mechanically dissimilar layers. Ample evidence for such contacts is found in the field, in deep wells, in a previous study, and in our tomographic images.

Lastly, we show how the deepening of the seismicity within the magma reservoir during the eruption connects with how the lava samples obtained at the surface evolved from depleted to enriched with time.