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Time-dependent gravimetric measurements can detect subsurface processes long before magma flow leads to earthquakes or other eruption precursors. The ability of gravity measurements to detect subsurface mass flow is greatly enhanced if gravity measurements are analyzed and modeled with ground-deformation data. Obtaining the maximum information from microgravity studies requires careful evaluation of the layout of network benchmarks, the gravity environmental signal, and the coupling between gravity changes and crustal deformation. When changes in the system under study are fast ͑hours to weeks͒, as in hydrothermal systems and restless volcanoes, continuous gravity observations at selected sites can help to capture many details of the dynamics of the intrusive sources. Despite the instrumental effects, mainly caused by atmospheric temperature, results from monitoring at Mt. Etna volcano show that continuous measurements are a powerful tool for monitoring and studying volcanoes.Several analytical and numerical mathematical models can beused to fit gravity and deformation data. Analytical models offer a closed-form description of the volcanic source. In principle, this allows one to readily infer the relative importance of the source parameters. In active volcanic sites such as Long Valley caldera ͑California, U.S.A.͒ and Campi Flegrei ͑Italy͒, careful use of analytical models and high-quality data sets has produced good results. However, the simplifications that make analytical models tractable might result in misleading volcanological interpretations, particularly when the real crust surrounding the source is far from the homogeneous/isotropic assumption. Using numerical models allows consideration of more realistic descriptions of the sources and of the crust where they are located ͑e.g., vertical and lateral mechanical discontinuities, complex source geometries, and topography͒. Applications at Teide volcano ͑Tenerife͒ and Campi Flegrei demonstrate the importance of this more realistic description in gravity calculations.

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La Palma island is one of the highest potential risks in the volcanic archipelago of the Canaries and therefore it is important to carry out an in-depth study to define its state of unrest. This has been accomplished through the use of satellite radar observations and an original state-of-the-art interpretation technique. Here we show the detection of the onset of volcanic unrest on La Palma island, most likely decades before a potential eruption. We study its current evolution seeing the spatial and temporal changing nature of activity at this potentially dangerous volcano at unprecedented spatial resolutions and long time scales, providing insights into the dynamic nature of the associated volcanic hazard. The geodetic techniques employed here allow tracking of the fluid migration induced by magma injection at depth and identifying the existence of dislocation sources below Cumbre Vieja volcano which could be associated with a future flank failure. Therefore they should continue being monitored using these and other techniques. The results have implications for the monitoring of steep-sided volcanoes at oceanic islands.