SISTEM PLUS: a second order Strain Model based method to integrate DInSAR and terrestrial geodetic data.

In recent years, great efforts have been made by the research community to define and improve computational methods aimed at integrating DInSAR and GNSS data to estimate three-dimensional (3D) ground displacements maps. In particular, the SISTEM method (Guglielmino et al., 2011), which was the first that used the Strain Model (SM) to solve 3D deformations by combining GNSS and DInSAR data, has been both widely utilized and continuously improved since its proposal.

In this work, we propose the SISTEM PLUS method, an evolution of the original SISTEM method achieved through the adoption of a second order Strain Model.

The SISTEM PLUS method, like the original SISTEM one, is a linear in the parameters model solved by using the weighted least square (WLS). The usage of a second order Strain Model has yielded the following main advantages: a notable improvement in results accuracy and the provision of a mathematical framework for the effective integration of tilt measurements, in addition to DInSAR and GNSS data.

On the other hand, the usage of a second order Strain Model increases the complexity of this new method compared to the original SISTEM. Specifically, the SISTEM PLUS method requires the estimation of a greater number of unknown variables, which in turn, necessitates a larger set of available data to achieve robust estimations.

The proposed methodology was tested on both synthetic and experimental data, these last from GNSS and DInSAR measurements carried out on Campi Flegrei area during the 2016-2023 period. In order to appreciate the precision achieved on experimental test results, the estimated standard errors computed by Weight Last Square are provided. These new tests also allowed optimising the choice of specific parameters of the algorithm.

Currently the SISTEM PLUS method allows integration of DInSAR data taken from different geometries and different SAR sensors, (e.g. SENTINEL1, ALOS or CSK) and different kind of in situ data (GNSS, Levelling EDM and Tilt). We emphasize that, as the SISTEM PLUS method performs data integration through the resolution of a system of linear in the parameters strain model based equations, each equation being specific for a particular type of data, it has the built-in capability to integrate additional datasets, such as strain-meter and Distributed Fiber Optics to name a few. This is accomplished defining and adding a suitable set of additional strain model based equations, specifically tailored for the new datasets to be integrated, into the system of equations to be solved.

These potentialities will be fully exploited in future developments of the presented methods.