We propose a new technique, named SISTEM, based on the elastic theory, to efficiently estimate 3-D displacements for producing deformation maps by integrating sparse Global Positioning System (GPS) measurements of deformations and differential interferometric synthetic aperture radar (DInSAR) maps of movements of the Earth's surface. Previous approaches in the literature to combine GPS and DInSAR data require two steps: a first step in which sparse GPS measurements are interpolated in order to fill in GPS displacements in the DInSAR grid and a second step to estimate the 3-D surface displacement maps by using a suitable optimization technique. One of the advantages of the proposed approach, compared to previous ones, is that it does not require the preliminary interpolation of the observed deformation pattern. Indeed, we propose a linear matrix equation which accounts for both the GPS and DInSAR data whose solution simultaneously provides the strain tensor, the displacement field, and the rigid body rotation tensor. The mentioned linear matrix equation is solved by using the weighted least square (WLS), thus assuring both numerical robustness and high computation efficiency. The methodology was tested on both synthetic and experimental data, these last from GPS and DInSAR measurements carried out on Mount Etna during the 2003-2004 period. In order to appreciate the accuracy of the results, the estimated standard errors computed by the WLS are provided. These tests also allow optimizing the choice of specific parameters of this algorithm. This method can be further exploited to account for other available data sets, such as additional interferograms or other geodetic data (e.g., leveling, tilt, etc.), in order to achieve higher accuracy.

On December 24th, Mt. Etna volcano underwent a seismic crisis beneath the summit and upper southern flank of the volcano, accompanied by significant ash emission. Eruptive fissures opened at the base of summit craters, propagating SE‐wards. This lateral eruption lasted until December 27th. Despite the small eruption, seismic swarm and ground deformation were very strong. Sentinel‐1 interferograms show a wide and intense ground deformation with some additional features related to volcano‐tectonic structures. We inverted DInSAR data to characterise the magma intrusion. The resulting model indicates that a large dyke intruded but aborted its upraise at about the sea level; however, this big intrusion stretched the edifice, promoting the opening of the eruptive fissures fed by a shallower small dyke, and activating also several faults. This model highlights that a big intrusion beneath a structurally complex volcano represents a main issue even if the eruption is aborted.

Gravitational collapse of Mount Etna’s SE flank: New seafloor geodetic data capture active displacement of underwater volcanic flank.