# Combining InSAR and GNSS to Track Magma Transport at Bastic Volcano
## 5 Results
### Temporal Inversion
#### 5.2.1 A Need for Geometrical a Priori to Invert for the GNSS Time Series

Table 4: Comparison of the inverted source characteristics for different methods for tracking magma propagation and different data: continuous GNSS data from the permanent network and an intermediate Sentinel-1 interferogram S1 D1 covering the first part of the eruption (before 01:45). % explained data (%_Ed_, see Equation (9)) computed with data used in the inversions are in bold, while those computed a posteriori using data omitted in the inversion are in small italics. 5.2.2 Inversion of GNSS Time Series to Improve Discrimination between Families of Intrusion Geometry  
Two best-fit model families (F1 and F2) were determined with the static inversion: F1 characterized by curved sources dipping eastward and F2 characterized by a sill-to-dike geometry. We conducted the inversion of the GNSS time series with the Projected Disk method on geometries characteristic of F1  
Figure 10: Comparison of inversion results for validation test using interferogram S1 D1. Wrapped interferogram S1 D1 (**first column**) and modeled interferograms computed with the best models determined with the Ellipse method (**2 nd column**), Projected Disk method (**3 rd column**) and Subgraph method (**4 th column**). Inversion is done with continuous GNSS data alone (**top**) or with SAR S1 D1 data alone (**bottom**). Black segment markss the location of the eruptive fissure. Diamonds represent the location of permanent GNSS stations. Figure 9: Comparison between the intrusion determined from InSAR data covering the whole eruption (grey) and the best model intrusion geometry (blue) resulting from the temporal inversion of GNSS data at 01:45. Results for the three different methods for inverting the pressure source are shown. (**Top**) Ellipse; (**Middle**) Projected Disk and (**bottom**) Subgraph methods. (inversion 04a) and F2 (inversion 02a). Inversions from F2 give a better fit than those of F1 (Figure 11) for all time steps with a larger difference at the beginning of the time series at 21:00 the misfits for F1 and F2 are \(\chi^{2}\sim\)30 and \(\chi^{2}\sim\)20, respectively and at 4:00 the misfits for F1 and F2 are \(\chi^{2}\sim\)30 and \(\chi^{2}\sim\)25, respectively. Pressures and openings determined for F1 are overestimated, reaching 10 MPa, while areas are underestimated, as indicated by the comparison with the result determined from the inversion of the intermediate interferogram (compare the blue curves with the open symbols at 1:45 in Figure 11). On the contrary, inversions of GNSS times series from F2 (Projected circle or Subgraph) show consistent results. Time series inversions also confirm that the Ellipse method leads to unreliable results in terms of pressure, area and average openings. For both families, evolution of the source location with time (Figure 12) shows an increase in the source area and a migration from centrally beneath the Dolomieu crater to the southeast region of this crater. However, only the magma path determined from inversions with model F2 is consistent with a feeding system beneath the Dolomieu crater, followed by a lateral transport to the vent. With F1, magma travels back down, accumulates in the curved part of the source and never reaches the surface. The Subgraph method used with F2 has the greatest potential to give rise to an opening of the dike part of the eruptive fissure. The analysis of time series contributes critical information that helps resolve the non-uniqueness of deformation modeling. The F2 geometry is therefore considered to be the most realistic. Figure 11: Results of inversions of the GNSS time series for 29 time steps between 20:40 and 4:00 a.m. Green line is the Ellipse method. Blue and red dashed lines are the Projected Disk method on a priori meshes for families F1 and F2, respectively. Solid black circles are the Subgraph method for family F2. Open symbols are for inversions from the intermediate Sentinel-1 interferogram S1 D1, green star corresponds to the Ellipse method, red square to the Projected Disk on family F2 and black circle to the Subgraph method on family F2.