## 3 Characteristic Deformation and Associated Physical Processes at Piton de la Fournaise volcano
### Short-Term Rapid Variations and Typical Deformation Patterns Associated with Eruptions
#### 3.2.1 Co-Eruptive Displacements  
The first dedicated InSAR study at Piton de la Fournaise was published in 1999 by [PERSON] et al. [23], who detected ground displacements associated with the 9 March 1998-21 September 1998 eruption of Piton de la Fournaise using satellite data collected by the Canadian RADARSAT-1 satellite (RSAT1). The authors could explain the co-eruptive displacements by means of a 1.5 km-long, dipping dislocation with 60 cm of opening in the north that they extended another 1 km towards the south, allowing for only 40 cm of opening there. Edifice inflation prior to this 1998 event was not observed. According to [PERSON] et al. [23], the eruption was accompanied by seawater displacement of the eastern flank. The authors concluded that over time the accumulation of displacements caused by similar eruptions contributed to the destabilization of the volcano's eastern flank. [PERSON] et al. [39] used a combination of a boundary element model (including the topography) and a neighborhood algorithm inversion in order to invert for the source geometry that fed the February 2000 eruption based on RSAT1 InSAR data from two ascending and two descending orbits. The authors explained the deformation associated with this eruption by a seaward dipping (61.0\({}^{\circ}\)-67.3\({}^{\circ}\)) trapezoid, oriented parallel to the rift zone that initiated at 800-1000 m beneath the Dolomieu summit crater. The authors emphasized the importance of taking into account the topography in order to realistically infer for the geometry and overpressure at depth. [PERSON] et al. [41] used ENVISAT ASAR data to describe the deformation field associated with the August 2003 Piton de la Fournaise eruption, and inverted for the associated deformation source. This eruption, too, caused the unsupported eastern flank of the volcano to move seaward (or vice versa). The authors stressed the previous findings of [PERSON] et al. [23], who stated that successive dike intrusions contribute to the destabilization of the volcanic edifice. [PERSON] et al. [40] then analyzed the first five eruptions that occurred since early 1998 using 10 interferograms computed from RSAT1 satellite images. According to these authors, all eruptions apart from the March 1998 event were fed by shallow dikes initiating at depths of less than 1000 m. By taking into account tilt data and seismicity in addition to the InSAR data, [PERSON] et al. [40] concluded that vertical magma propagation preceded lateral material ascent prior to eruptions. [PERSON] [42] studied both co- and post-eruptive displacements associated with the 2007 eruption. [PERSON] et al. [43] used four propagation phase-spanning interferograms in combination with continuous GNSS data to invert for the intrusion geometry (by means of InSAR data) and the magma propagation dynamics (by means of GNSS data) during the eight hours before the 26 May 2016 eruption. According to these authors, the observed deformation was best explained by a 2700-m-long sill that located 800 m above sea level and that connected to the eruptive fissure by a subvertical dike [43]. In contrast to the above-described numerical and geodetic inversion models that explained co-intrusion and/or co-eruption surface deformation at Piton de la Fournaise volcano as elastic-walled, inclined, or (sub-) horizontal dislocations, [PERSON] et al. [44] argued that linear elasticity, which is often assumed in numerical models, might be too general and not representative for the rheology of the highly unconsolidated uppermost part of the volcano's edifice. As mentioned in Section 2, a total of 52 of the 58 eruptions that occurred between 9 March 1998 and 31 December 2019 are covered by interferometric SAR data (Figure 3). Co-eruptive interferograms from both ascending and descending viewing geometries are routinely calculated directly upon data availability for all recent Piton de la Fournaise eruptions, and they are converted into near-3D displacements using the method suggested by [PERSON] et al. [45].