# Combining InSAR and GNSS to Track Magma Transport at Bastic Volcano
## 1 Introduction
Here, we compare two strategies, one where we invert interferograms that most closely capture an event and one that uses interferograms covering a specific time period. Inverse models are used to analyze displacements, combining forward models and inversions. Inversion of surface displacements is inherently non unique. For instance, [PERSON] and [PERSON] [23] showed that, when sources are axi-symmetrical, the source shape and depth can not be determined using vertical displacements alone but that both the vertical and horizontal displacements are needed to accurately determine these characteristics. Here, the problematic is different because the sources are non axi-symmetrical and 3D displacements can be computed. Since, this study is of a fissure eruption, the source of unrest is a fracture, which is a non axi-symmetrical source. Non uniqueness in the surface response may be caused by material properties [24; 25] but for a given material response, there is a unique surface displacement for each individual fracture. Moreover InSAR provides displacements along several ascending and descending LOS and GNSS gives 3D displacements, thus the combined use of these two types of data can be used to describe 3D displacements [26]. Non unique source determination comes from inverse modeling, which inherently accounts for errorsin data and models. The main sources of error in InSAR and GNSS data derive from atmospheric conditions (water content of the troposphere and ionosphere) and models are simplifications of a complex reality: the number of sources is unknown and their shapes are probably more complex than assumed. A previous study of the 26 May 2016 eruption at Piton de la Fournaise [16] showed that, despite the very dense network of permanent GNSS stations present on this volcano, magma propagation could only be successfully tracked when adding a priori information on the intrusion shape provided by the inversion of co-eruptive interferograms. This conclusion was reached using the intermediate Sentinel-1 acquisition, which allowed different strategies to invert GNSS data to be quantitatively evaluated. Here, we extend our previous study on the combined use of InSAR and GNSS data and we investigate the usefulness of GNSS time series in resolving the non-unique inverse models obtained from InSAR data. Time series of displacements, whether provided by continuous GNSS and tilt measurements [27] or by InSAR [28], are usually analyzed using kinematic inversions, where amplitudes of dislocation sources [29] are determined from minimizing the sum of the L2 norm of the weighted residual on displacements and spatially smoothed dislocation amplitudes. This requires as many parameters as there are dislocations, which leads to statistically less likely solutions [30] and solutions physically less meaningful than pressure sources [31]. In our previous study [16], we addressed these issues by determining the pressurized area corresponding to the active intrusion, where the a priori intrusion was derived from InSAR and a circular pressure source was projected onto the mesh representing this intrusion. This method had two drawbacks: 4 parameters were needed when the number of permanent GNSS measurements is 30 and a projection from a plane on the intrusion geometry was needed, which could exclude part of the intrusion and thus induce errors if the intrusion geometry was curved. In this study, we focus on the methodological aspects of jointly inverting InSAR and GNSS (campaign and time series) data covering the May 2016 Piton de la Fournaise eruption in order to track magma propagation. Because of the non-unique nature of inversions, data covering the whole eruption leads to two families of equally well fitting intrusion models. The influence of the data weightings on the inverted intrusion is also studied. We next use times series of GNSS data to determine the dynamics of the magma propagation for these families of models and to investigate if time series help in the determination of the most likely family of models.