Reconstructing the Shape of Magma Domains from Observations of Ground Deformation in Volcanic Regions

Volcano geodesy provides information about shallow magma domains (locations of magma) in volcanic areas, usually inferred through inversion of geodetic data giving a set of parameters, such as position and internal magma pressure change. These inversions require a model of the crust and the embedded magma domain, typically with an assumed specific shape for the magma domain. This shape is constrained to be parametrizable to be inverted for, thus is limited to classical regular shapes among spheres, ellipsoids and sills, which are unlikely to capture the morphological complexity of actual magma domains. Here, we present an alternate approach to invert for the shape of the magma domain without requiring any prior assumptions about it, based on recent techniques from the field of shape optimization. Instead of optimizing a finite vector of parameters, the entire shape of the magma domain is optimized to minimize the discrepancy between observed ground displacements and those predicted by the model, under the assumption of an elastic crust. More precisely, our strategy relies on a “shape gradient'' descent based on the concept of shape derivative and on the level set method to track changes in the magma domain boundary. We provide magmaOpt, a Python and FreeFEM based code that iteratively performs the shape gradient search and solves successive partial differential equations that govern the problem on an evolving mesh of the area of interest. First, we demonstrate the potential of the method using a test case with synthetic data. Then, we apply the method to data from interferometric analysis of synthetic aperture radar satellite images (InSAR) observations of the 2022 inflation episode in Svartsengi, Iceland, to explore possible shapes of the magma domain responsible for the inflation. This work paves the way for a new class of methods that provide more information on magma domains and ultimately lead to better volcanic hazard monitoring.