FEM-based Surface Displacement Modeling of Magma Intrusions at Kilauea Volcano

Volcanic deformation is the surface expression of the internal dynamics of an inherently complex system resulting from the interaction of magma with the surrounding rocks. Geodetic techniques, as Global Positioning System (GPS) and/or Interferometric Synthetic Aperture Radar (InSAR), are being extensively used to monitor such ground deformation. Nevertheless, it is impossible to directly observe the processes at depth that cause the observed ground deformation. The interpretation of geodetic data requires both, mathematical modeling to simulate the observed signals and inversion approaches to estimate the deformation source parameters. In this study we provide a numerical tool for interpreting geodetic data by solving in an efficient and accurate way the inverse problem to estimate the optimal parameters for magmatic sources (spherical magma chambers and tensile dislocations). In doing so, we propose a Finite Element Method (FEM) for the calculation of Green functions in an heterogeneous medium. The key aspect of the methodology lies in how to incorporate the source into the model and in applying the reciprocity relationship between the station and the source. In our approach, deformation sources are independent of the simulation mesh. The search for the best fit point source(s) is conducted for an array of 3-D locations extending below a predefined volume region. The total number of Green functions is reduced to the number of the observation points by using the reciprocity relationship. We apply this methodology to the recent inflation observed at Kilauea's Southwest Rift Zone in May 2015, observed with the new Sentinel-1 radar interferometry satellite mission, to report the magma transport along the zone.