Inferring 3D displacement time series through InSAR measurements and potential field theory in volcanic areas.

Interferometric SAR (InSAR) techniques allow the detection of ground displacements along the satellite line-of-sight (LOS) directions. Moreover, InSAR can discriminate the ground deformations along the Up-Down and East-West by combining information gathered through ascending and descending paths. Conversely, the LOS-projected ground displacements remain less sensitive to the North-South components because almost all modern satellites fly along near-polar orbits. Our research aims to circumvent this limitation by developing a new method for reconstructing the 3-D ground displacement field in volcanic regions based on potential field theory and using InSAR measurements. We present the theoretical argumentations related to the developed method, demonstrating its efficacy through synthetic tests reconstructing the 3-D ground displacement field in elastic conditions. Then, we provide a 3-D ground displacement time series of the pre-eruptive displacement patterns related to the 2018 eruption at Sierra Negra volcano (Galapagos Archipelago, Ecuador). Our analysis revealed a maximum North-South displacement rate that increased from 40 cm/yr in the early pre-eruptive stage to 70 cm/yr before the eruption. The reliability of our results has been tested through comparison with Global Navigation Satellite System measurements. Our approach is innovative and represents a helpful tool for the investigation and modelling of volcanic sources.