Potential field theory for ground deformation: a new tool for the space-borne monitoring of volcanoes and fluid reservoirs.

Ground deformation fields are widely recognized as key tools for the study of geological phenomena such as volcanic eruptions, which cause displacements in the Earth’s surface and interior. When ground deformation data are available, modeling approaches enable the characterization of deformation sources, such as overpressurized and migrating volcanic or hydrothermal fluids within the crust. Geodetic data modeling is therefore a powerful approach for monitoring volcanic systems, managing alerts, and mitigating possible disasters.

For the characterization of ground deformation, the satellite-based Interferometric Synthetic Aperture Radar (InSAR) technique now plays a significant role, as it provides high-quality spaceborne data with extensive coverage and varying resolution. Moreover, several technological efforts are currently ongoing within the Earth Observation framework to advance SAR sensors and related satellite missions, as well as to refine data systems in order to automatically provide measurements of the Earth’s surface deformation in near real time. However, these advancements have not yet been matched by comparable progress in geodetic data modeling strategies. Indeed, the most commonly used modeling approaches, based on parametric optimization and tomographic inversion algorithms, are often unable to address the inherent issues of inverse problem solutions. In addition, they rarely guarantee a reliable characterization of the volcanic context, as they rely on several assumptions underlying analytical models. Finite Element (FE) approaches can potentially ensure greater reliability, although the number of variables to be managed and the computational cost increase considerably. As a result, modeling strategies may fail to determine a unique solution for source parameters when adequate model constraints are not available.

This research topic aims to address ambiguities in the modeling of volcanic deformation sources in order to ensure the full exploitation of the large amount of available InSAR data. This task requires methods capable of providing unambiguous constraints on source parameters while being fast, computationally efficient, and easy to implement in automatic modeling tools, making them suitable for monitoring systems. Our proposal is based on imaging and multiscale methods of potential fields, which satisfy these requirements, even though the deformation field itself is not formally defined as a potential field.

Here, we demonstrate that, under certain conditions, potential field theory can be applied to analyze deformation fields, which can be expressed through harmonic and homogeneous functions. During the lecture, we present several tests validating the proposed arguments and discuss the usefulness of potential field theory in addressing different real-world cases (e.g., Campi Flegrei caldera, Yellowstone caldera, Okmok volcano, Uturuncu volcano, and Fernandina and Sierra Negra volcanoes), using Multiridge and ScalFun methods to constrain the geometric parameters of magmatic reservoirs, boundary analysis techniques to image medium heterogeneity, and potential function evaluation to reconstruct the three-dimensional displacement field.

The results highlight that the proposed methodological suite meets all the necessary requirements to improve the geodetic modeling of volcanic systems and can be integrated into monitoring facilities as an automatic and efficient tool.