# Combining InSAR and GNSS to Track Magma Transport at Bastic Volcano
## 7 Conclusions  
InSAR and GNSS data provide complementary information on the spatial distribution of displacements and their temporal evolution, respectively. Combining these data, we successfully inverted the source of observed displacements in order to track magma transport in the volcanic edifice of Piton de la Fournaise. We showed that four different LOS are sufficient to invert the static geometry of the emplaced magma intrusion. The addition of campaign and permanent GNSS displacement covering the same period does not remove the ambiguity pertaining to the non-uniqueness of inversions. Inversion of InSAR data covering a time period shorter to the other InSAR data indicates a pre-eruptive phase of deformation which is not detectible in the longer time period. Systematic discrepancies in data fitting between ascending and descending LOS are indicative of seaward flank displacement accompanying the magma intrusion. We also show that, in order to track magma propagation from GNSS time series, the intrusion geometry derived from InSAR measurements should be used as an a priori. A new graph-based method (the Subgraph method) is proposed to invert the pressurized part of the final geometry from GNSS time series. It provides a better fit for intermediate InSAR data than the two other methods: the Ellipse method which has no a priori and the Projected Disk method which uses the same final geometry as for the Subgraph method. It also leads to a more physically viable model where magma starts beneath the summit crater and propagates towards the surface, opening up eruptive fissures. When static inversions of InSAR data lead to equally well fitting models due to the inherent non-uniqueness of inversions, the GNSS temporal inversion may favor one family of models over the other. Systematic studies of new cases of propagating intrusions imaged by InSAR and GNSS times series would help increase our understanding of magma propagation. The shorter return time (of 6 days) for Sentinel-1 should make this possible in the coming years. Another possible approach for future studies would be to integrate the physics of magma propagation into a model before jointly inverting InSAR data and GNSS time series. Conceptualization, D.S., V.C. and V.P. ; methodology, D.S. ; software, V.C., D.S. and Q.D. ; validation, V.C., V.P. ; formal analysis, D.S. ; investigation, D.S. ; resources, V.P., V.C. ; data curation, A.P., J.-L.F.; writing--original draft preparation, D.S., V.C. and V.P. ; writing--review and editing, V.C., V.P. and A.P. ; visualization, D.S. ; supervision, V.C., V.P. ; project administration, V.P., V.C. ; funding acquisition, V.C., V.P., A.P. and J.-L.F. The PhD Fellowship of D.S is funded by the French Ministry for Higher Education and Research. This research was partly supported by the INSU-CNRS ALEAS program, by the ANR through the SLIDEVOLC project (contract ANR-16-CE94-004-01) as well as the MagmaPropagator project (contract ANR-18-CE92-0037-01), by the French Government Laboratory of Excellence initiative ANR-10-LABX-00006, the CNES through the CNES project AssimSAR, the Region Auvergne and the European Regional Development Fund. We thank the team which manage the OVPF, installs, maintains and monitors stations; [PERSON] for proofreading the english of the paper. This paper has also benefited from discussionwith [PERSON] about the graph theory and [PERSON] about GNSS data processing. Raw GNSS data are available on VOLOBSIS website ([[http://volobsis.ipsp.fr](http://volobsis.ipsp.fr)]([http://volobsis.ipsp.fr](http://volobsis.ipsp.fr))). Processed data are available by contacting the OVPF. We thank the European Space Agency for providing the Sentinel-1 data and the Italian Space Agency for providing the Cosmo SkyMed data. All interferograms used in this study were computed with Diapason ((c) TRE ALTAMIRA) by the Indian Ocean InSAR Observatory Service OI2, part of the National Service for Volcanological Observations (SNOV) of the French National Research Council Institute for Earth Sciences and Astronomy (CNRS/INSU).