## 1 Introduction  
Lava flows emitted during volcanic events can continue to deform for years after their emplacements, generating measureable ground displacement on and adjacent to lava flow fields [1; 2; 3; 4]. This displacement is mainly driven by processes such as [3;4]: (1) thermal contraction associated with cooling and consolidation; (2) compaction of vesicles and void space within the lava body; and (3) depression of flow substrate in response to surface load. The characterization and interpretation of displacement in lava fields is one of the key factors for the assessment of volcanic hazards. Piton de la Fournaise is a hotspot shield volcano located in the south-eastern part of La Reunion Island, Indian Ocean (Figure 1 inset). It presently hosts the Enclos Fouque caldera (\(\sim\)13 \(\times\) 9 km in size), where an active volcanic cone founded by two pit-craters (Bory crater to the west and Dolomieu crater to the east) is located inside (Figure 1). The Eastern Flank of Piton de la Fournaise, which is open to the sea, involves the Grandes Pentes and the Grand Brule areas (Figure 1). Being one of the most active basaltic volcanoes in the world, Piton de la Fournaise erupts frequently and produces significant lava flows. It erupted 25 times and emitted nearly 450 Mm\({}^{3}\) of magma to the surface between March 1998 and April 2007, preceded by a six-years of quiescence [5; 6; 7]. The lava fields emplaced between March 1998 and April 2007 are illustrated in Figure 1. They have mainly covered the north-eastern, eastern, and south-eastern flanks of the volcano. Characteristics of these lava flows, including the geometric parameter (surface, volume, and flux), location and elevation, have been investigated and presented by [PERSON] et al. [5]. Continuous ground displacements recorded at the GNSS stations located in these lava fields (Figure 1) have also been reported by [PERSON] et al. [7] and Staudacher & Peltier [8]. However, few analyses focusing on the long-term post-emplacement displacement in lava fields at a large spatial extent have yet been performed. Figure 1: Location of lava flow fields emplaced between 1998 and 2007 at Piton de la Fournaise, superimposed on a shaded relief map with the main areas mentioned in the paper, modified from Servadio [9]: the Enclos Fouque caldera, the Dolomieu and Bory caters, the Plaine des Osmondes, the Grandes Pentes, and the Grand Brule areas. Location of flank GNSS stations, GPNG, GPSG, HDLG, and GBNG, installed on these lava fields is indicated by black triangles. The inset shows the location of La Reunion Island in the Indian Ocean and that of the Piton des Neiges and Piton de la Fournaise volcanoes in La Reunion Island, with the location of the REUN IGS station used in this study for subtraction of the plate motion from GNSS data. Coordinates in Geographic Lat/Lon WGS84. Interferometric Synthetic Aperture Radar (InSAR), a rapidly developed technique, has been widely and successfully applied to monitor the surface displacements at volcanoes worldwide, such as the Etna, Kilaea, and Piton de la Fournaise (e.g., [10; 11; 12; 13; 14; 15]). However, the number of InSAR studies focusing on the displacement due to the post- lava emplacement processes is very limited with respect to those focusing on the displacement associated with magmatic processes [16]. Among those few InSAR studies detecting lava displacement after emplacement (e.g., [16; 17; 18; 19; 20; 21; 22; 23; 24; 25; 26; 27; 28; 29; 30; 31; 32; 33; 34; 35; 36; 37; 38; 39; 40; 41; 42;  
where \(\phi_{sb}\) are the interferometric phases from SB subset, \(\phi_{ts}\) the time series to be inverted and G the design matrix with zeros, plus and minus ones [28]. The time series were temporally referenced to the first acquisition date and spatially referenced to non-displacement areas about 10 km away from volcanic craters.