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.

The Etna volcano is renowned worldwide for its extraordinary lava fountains that rise several kilometers above the vent and feed eruptive columns, then drift hundreds of kilometers away from the source. The Italian Istituto Nazionale di Geofisica e Vulcanologia-Osservatorio Etneo (INGV-OE) is responsible for the monitoring of Mt. Etna, and for this reason, has deployed a network of visible and thermal cameras around the volcano. From these cameras, INGV-OE keeps a keen eye, and is able to observe the eruptive activity, promptly advising the civil protection and aviation authorities of any changes, as well as quantifying the spread of lava flows and the extent of pyroclastic and ash plumes by using a careful analysis of the videos recorded by the monitoring cameras. However, most of the work involves analysis carried out by hand, which is necessarily approximate and time-consuming, thus limiting the usefulness of these results for a prompt hazard assessment. In addition, the start of lava fountains is often a gradual process, increasing in strength from Strombolian activity, to intermediate explosive activity, and eventually leading to sustained lava fountains. The thresholds between these different fields (Strombolian, Intermediate, and lava fountains) are not clear cut, and are often very difficult to distinguish by a manual analysis of the images. In this paper, we presented an automated routine that, when applied to thermal images and with good weather conditions, allowed us to detect (1) the starting and ending time of each lava fountain, (2) the area occupied by hot pyroclasts, (3) the elevation reached by the lava fountains over time, and (4) eventually, to calculate in real-time the erupted volume of pyroclasts, giving results close to the manual analysis but more focused on the sustained portion of the lava fountain, which is also the most dangerous. This routine can also be applied to other active volcanoes, allowing a prompt and uniform definition of the timing of the lava fountain eruptive activity, as well as the magnitude and intensity of the event.