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Additional file 4: Figure S1. (a) Schematic diagrams of the process of dividing the chirp band. B is the bandwidth of the original synthetic aperture radar image, f0 is its center frequency, N is the number of divisions, fi is the center frequency of each sub-band, and f1 and fN correspond to fhigh and flow in Eqs. (3 and 4), respectively. (b) Schematic diagram for 1-D phase unwrapping along the frequency. Figure S2. Stage of atmospheric delay reduction for Paths 28 and 126. Left column figures are interferograms before atmospheric delay reduction, mid-column figures are the estimated atmospheric delay, and right-column figures are interferograms after the atmospheric delay reduction. Figure S3. Process of ionospheric delay estimation. InSAR, Interferometric Synthetic Aperture Radar; Orb., orbital; Topo., topographic. Figure S4. Process of difference of split-band interferograms (DSI) analysis. InSAR, Interferometric Synthetic Aperture Radar; Orb. Orbital; Atm., atmospheric; Ion., ionospheric. Figure S5. (a), (c) Slant-range change maps from the conventional Interferometric Synthetic Aperture Radar (InSAR) analysis for Paths 28 and 126, respectively. (b), (d) Differences between slant-range change maps from the difference of split-band interferograms (DSI) and conventional InSAR analyses.

Additional file 2: Text S1. Discussion of the discrepancy between the volume change of the point source and the mass discharge.

Additional file 1. Figure S1.Optical true images of Sentinel-2 data in autumn and winter over Kusatsu-Shirane volcano. Figure S2. Plot of PALSAR-2 perpendicular baselines and combinations of SAR data for the multi-temporal InSAR analyses. Figure S3. L-curve plot for determination of optimal temporal smoothness in the multi-temporal InSAR analysis. Figure S4. Standard deviation of the inferred displacement velocity from 2014–2019. Figure S5. Co-eruptive deformations using the averaging InSAR data spanning the 2018 phreatic eruption. Figure S6. Time series of line-of-sight (LOS) change on Yugama crater lake based on the multi-temporal InSAR analyses. Figure S7. Time-series of PALSAR-2 LOS changes in path 19. Figure S8. Time-series of PALSAR-2 LOS changes in path 125. Figure S9. Time-series of PALSAR-2 LOS change in path 126. Figure S10. Data fitting using analytical solutions of the surface deformation caused by both a plane dislocation and an isotropic deflation (Model C). Figure S11. Root-mean-square error (RMSE) distributions for a plane dislocation and an isotropic deflation in Model C. Figure S12. Data fitting using analytical solutions of the surface deformation caused by a planer dislocation (Model A). Figure S13. Data fitting using analytical solutions of the surface deformation caused by an isotropic deflation (Model B). Table S1. Parameters of PALSAR-2 image acquisition and information for the multi-temporal InSAR analysis in this study. Table S2. Pairs of SAR image acquisition date for the averaged InSAR data in Figure S4. Table S3. Range and interval for the searching best-fit parameters. Table S4. Best-fit RMS residuals of Model A (Planar dislocation) and Model B (Point source deflation) in each path.