A Perturbative Approach for Modeling Short‐Term Fluid‐Driven Ground Deformation Episodes on Volcanoes: A Case Study in the Campi Flegrei Caldera (Italy)

Ground deformation in volcanic areas is linked to various, often interconnected processes such as magma intrusion, pressurized fluid migration, and thermal expansion effects. The presence of active and extended hydrothermal systems plays a key role and affects the deformation phenomenon in complex ways. In this study, we propose a generalized conceptual and mathematical model, which allows retrieving the flow rate of fluid injection in a volcanic hydrothermal system, assuming a ground deformation data set as input. The basic assumption is that short‐term ground uplift episodes (with characteristic periods of less than 5 years) depend on the injection of volcanic fluids into the hydrothermal system. Then, assuming a deformation field shape independent of time and a linear time‐invariant relation between the amount of injected fluid and the resulting ground deformation, we define a Green's function as the product of spatial and temporal components. The case study is a 3‐D elastic model with permeability and porosity for the Campi Flegrei caldera, Italy. By Green's function, a 2‐km‐long source at 2.4‐km depth, which matches the interferometric synthetic aperture radar deformation, is localized and the amount of injected volcanic fluid in the last 20 years of high‐frequency deformation episodes estimated. In conclusion, we find a good agreement between the measured and estimated temporal deformation patterns and, principally, that fluid injection rates can be retrieved from the deformation field at volcanoes.