Coeruptive crustal deformation associated with the 2018 Kusatsu-Shirane phreatic eruption based on PALSAR-2 time-series analysis


 Coeruptive deformation helps to interpret physical processes associated with volcanic eruptions. Because phreatic eruptions cause small, localized coeruptive deformation, we sometimes fail to identify plausible deformation signals. Satellite synthetic aperture radar (SAR) data allow us to identify extensive deformation fields with high spatial resolutions. Herein, we report coeruptive crustal deformation associated with the 2018 Kusatsu-Shirane phreatic eruption detected by time series analyses of L-band satellite SAR (ALOS-2/PALSAR-2) data. Coeruptive deformation maps derived from SAR time series analyses show that subsidence and eastward displacement dominate the southwestern side of an eruptive crater with a spatial extent of approximately 2 km in diameter. Although we were unable to identify any significant deformation signals before the 2018 eruption, posteruptive deformation on the southwestern side of the crater has been ongoing until the end of 2019. This prolonged deformation implies the progression of posteruptive physical processes within a confined hydrothermal system, such as volcanic fluid discharge, similar to the processes observed during the 2014 Ontake eruption. Although accumulated snow and dense vegetation hinder the detection of deformation signals on Kusatsu-Shirane volcano using conventional InSAR data, L-band SAR with various temporal baselines allowed us to successfully extract both coeruptive and posteruptive deformation signals. The extracted coeruptive deformation events are well explained by normal faulting with a left-lateral slip component along a southwest-dipping fault plane rather than by a point source deflation. The inferred fault plane can be considered as a degassing pathway from the shallow hydrothermal system to the surface. We reconfirmed that SAR data is a robust tool for detecting coeruptive and posteruptive deformations, which are helpful for understanding shallow physical processes associated with phreatic eruptions at active volcanoes.


Introduction
A phreatic eruption is a hazardous volcanic activity event that includes sporadic ejections of volcanic ash, steam and volcanic gases induced by transient pressure changes in the hydrothermal systems of active volcanoes. The episodic pressure changes are generally induced by injections of volcanic gases into a con ned shallow hydrothermal system or by the abrupt boiling of con ned overheated geothermal water due to sudden depressurization. In general, phreatic eruptions cause less damage than magmatic eruptions, but can sometimes produce destructive hazards such as lahars that wash out infrastructure (e.g., Naranjo et al. 1986).
Ground deformation of active volcanoes is usually helpful for interpreting the physical processes of volcanic activity; however, most of ground deformation associated with phreatic eruptions is characterized as small and localized ones with a sudden onset. These characteristics hinder the detection of plausible deformation signals related to phreatic eruptions due to sparse observation networks or limited measurement accuracy. Recently, satellite synthetic aperture radar (SAR) data have allowed us to identify displacement elds with high spatial resolution without ground-based instruments. Several studies have successfully detected coeruptive deformation associated with phreatic eruptions using satellite SAR data (e.g., Hamling 2017; Doke et al. 2018;Narita and Murakami 2018). If precursors of phreatic eruptions, such as overpressure in shallow hydrothermal systems, persist for a long time, satellite SAR data can identify precursory deformation signals of the phreatic eruption (Kobayashi et al. 2018).
Kusatsu-Shirane volcano is an active volcanic complex located in central Japan (Fig. 1). It comprises Yugama crater lake, Ainomine volcano, and Moto-Shirane volcano, which are aligned in the north-south direction (Fig. 1 Some research institutes have reported conventional interferometric SAR (InSAR) data for the coeruptive ground deformation associated with the 2018 phreatic eruption (PPCVE report 2018b, 2018c). However, some InSAR data were contaminated by decorrelation noises due to variations in the back-scatter characteristics on the ground, such as snow and volcanic tephra coverage. Here, we investigate both the coeruptive and posteruptive deformation signals associated with the 2018 Kusatsu-Shirane phreatic eruption by applying SAR time series analyses to L-band SAR data. We also propose a schematic model that explains the extracted coeruptive deformation.

Sar Data Processing
In this study, we employed L-band SAR data acquired from the Phased Array type L-band SAR 2 (PALSAR-2) sensor onboard the Advanced Land Observation Satellite 2 (ALOS-2) to detect crustal deformation signals on Kusatsu-Shirane volcano. The L-band microwaves (wavelength: 23.6 cm) that PALSAR-2 uses are suitable for monitoring deformation signals on volcanoes covered by dense vegetation, such as those in Japan. In general, decorrelation problems can be caused by variations in scattering characteristics on the ground such as snow coverage or dense vegetation. Shorter-wavelength microwaves, such as C-band (wavelength: 5.6 cm) and X-band (wavelength: 3.1 cm) microwaves, scatter on shallower parts of the snow/ice layer and on leaves or branches, Thus, we expect shorter-wavelength microwaves to suffer from decorrelation problems in this case. In contrast, longer-wavelength microwaves, such as L-band microwave, can penetrate to deeper parts of a snow/ice layer and through dense vegetation. The region around Kusatsu-Shirane volcano is covered by dense vegetation in the summer and by snow in the winter (Additional le 1; Figure S1). Thus, we expect that the PALSAR-2 data are suitable for extracting deformation signals around Kusatsu-Shirane volcano through the year.
All InSAR data were generated using the GAMMA software (Wegmüller and Werner 1997). We corrected the topography-dependent fringes using a 10 m mesh digital elevation model released by the Geospatial Information Authority of Japan (GSI). Tropospheric artifacts were corrected using zenith tropospheric delays provided by Generic Atmospheric Correction Online Service for InSAR (GACOS; Yu et al. 2017;Yu et al. 2018). Long-wavelength signals across the InSAR data were corrected by tting 2D polynomial functions. We discarded some PALSAR-2 data that were contaminated by strong ionospheric artifacts.
We employed a multi-temporal InSAR (MTI) analysis, one of the SAR time-series analyses, to infer spatiotemporal variations in the crustal deformation at Kusatsu-Shirane volcano (e.g., Schmidt and Bürgmann 2003). The MTI analysis infers mean displacement rates during each image acquisition interval by using the InSAR data with various temporal baselines, assuming constant displacement rates during each image acquisition interval. Figure S2 in Additional le 1 shows a plot of perpendicular baselines and SAR data combinations for the MTI analysis is shown. We did not set the criteria for spatial and temporal baselines in estimating the displacement time-series, unlike the small baseline subset approach (Berardino et al. 2002). One reason for this is that L-band SAR data tend to avoid decorrelation problems even when a pair of SAR images with a temporal baseline of more than a year are used. Another reason is that the ALOS-2 satellite has been operating within 500 m of the perpendicular baseline since the satellite was launched. The Laplacian operators for the smoothing temporal variations in line-of-sight (LOS) changes were optimized by using the L-curve criterion (e.g., Hansen 1992; Additional le 1; Figure S3). We did not infer any temporal variations in the LOS changes for discarded pixels where the coherence of any individual InSAR data point was below 0.1. After we estimated the time-series of LOS changes using the MTI analysis, we extracted the cumulative coeruptive deformation associated with the 2018 phreatic eruption until the end of 2019. Using pairs of cumulative coeruptive LOS changes in paths 19/125 and 19/126, we decomposed them into quasi-east-west (QEW) and quasi-up-down (QUD) components to better understand the spatial characteristics of the coeruptive LOS changes (Fujiwara et al. 2000).

Results
Coeruptive deformation associated with the 2018 phreatic eruption Figure 2 shows the cumulative LOS changes in paths 19, 125, and 126 until the end of 2019. In the path 19 MTI results, a positive LOS change was dominant on the southwestern side of the 2018 crater. The maximum amplitude of the positive LOS change was ~ 6 cm near the 2018 crater. The standard deviation of the inferred displacement velocity in the undeformed region in path 19 was ~ 1 cm (Additional le 1; Figure S4a). In the path 19 averaged InSAR data, we identi ed a displacement discontinuity with a WNW-ESE strike at the 2018 crater where the path 19 MTI data show missing data (Additional le 1; Figure S5). The four averaged individual interferograms in path 19 showed the same location of the displacement discontinuity (red arrows in Figure S5a in Additional le1); thus, this displacement discontinuity is likely a plausible characteristic of the coeruptive deformation (Additional le 1; Table S2). The location of the displacement discontinuity is identical to that of the 2018 crater. Unlike the MTI data, and 4). We expect that the spatial characteristics of the coeruptive deformation can be explained by a dislocation along a plane, rather than by volume changes of a point source, because of the observed asymmetry of the coeruptive displacement eld. We used the analytical solutions of surface deformation caused by either planar dislocation (Model A) or volume changes of a point source (Model B) to t the observed data (Mogi 1958;Okada 1985). We adopted a grid search algorithm to infer the following parameters: width, length, dip angle, rake angle, and the amount of slip for the planar dislocation and location, depth, and volume change for the point source. Table S3 in Additional le 1 lists the ranges and intervals of the grid search parameters used. We set the top location of the dislocation plane to that of the 2018 eruptive crater, xed the strike angle at 105 degrees, and set the shallowest depth at 50 m. We regarded the best-t solution as a combination of parameters that minimized the total root-mean-square (RMS) of the residuals between the observed and the computed deformations. We assigned a rigidity of 0.1 GPa with a Poisson's ratio of 0.4, assuming a uid-saturated clay as the medium (Sas et al. 2013; Kobayashi et al. 2018). We resampled the LOS change maps in each path using concentric grids (e.g., Fukushima et al. 2005). The 95% con dence intervals of the best-t parameters were estimated by bootstrap with 300 iterative nonparametric re-samplings (Efron 1979).
We rst tried to retrieve the coeruptive LOS changes using the analytical solutions of surface deformation due to a plane dislocation (Model A; Additional le 1; Figure S10). Figure S11a in Additional le 1 shows a map of the total RMS residuals. The best-t parameters were a dip angle of 49 degrees, a rake angle of -67 degrees, and a slip of 0.21 m, which represents normal faulting with a left-lateral slip component on a southwest-dipping plane (Table 1) Table 1). The best-t parameters suggest 2.0 × 10 13 Nm of a geodetic moment release, which corresponds to the moment magnitude of 2.8 (Kanamori 1977). Standard errors are shown in parentheses.
We also t the observed data using an analytical solution of surface displacement due to an isotropic de ation of a point source (Model B; Additional le 1; Figure S12). A de ation volume of 70000 m 3 and a source depth of 360 m minimized the total RMS residuals (Table 1; Additional le 1; Figure S11b). The best-t parameters of Model B resulted in positive LOS changes on not only the southwestern side, but also the northeastern side of the 2018 crater; however, it did not show negative LOS changes on the northeastern side of the 2018 crater in the path 19. The RMS of all paths in Model B were larger than those in Model A (Table 1). We also con rmed smaller values of Akaike's Information Criterion of Model A than that of Model B (Akaike 1974) ( Table 1; Additional le 1; Table S5). Therefore, we propose that normal faulting with left-lateral slip along a southwest-dipping plane (Model A), rather than point source de ation (Model B), is a favorable solution that can explain the extracted coeruptive deformation patterns.

Data and model interpretations
The most plausible interpretation of our best-t model is that the dislocation was induced by a path formation of a sudden steam plume and/or a volcanic gas ejection from the shallow hydrothermal system to the surface. The geometry of the best-t plane dislocation can be considered as a degassing pathway (Additional le 1; Figure S13). The best-t width of the plane is 1600 m, which means that the bottom of the plane reaches approximately 1100 m depth. A previous magnetotelluric survey proposed a low-resistivity subsurface structure from Moto-Shirane volcano to Yugama crater lake at 1500-3000 m below the surface and alternating thin laminae of low-and high-resistivity layers between the surface and the large conductor (Nurhasan et al. 2006;Matsunaga et al. 2020). The large conductor implies the emplacement of volcanic uids that originated from the deep magma source and are con ned in a thick impermeable layer. The assemblage of materials ejected from the 2018 eruption likely originated from the basement rock of Moto-Shirane volcano, with an upper location of a few hundred meters below the surface (Yaguchi et al. 2019). While the best-t dislocation plane in Model A is inferred to reach a depth of 1100 m, Model B (point source de ation) suggests that the deformation source depth was 360 m. Therefore, we speculate that the extracted deformation was mainly caused by near-surface physical processes but also at greater depths because we can identify the signi cant difference in the depth of the dislocation plane and the point source de ation.
The increased posteruptive subsidence on the southwestern side of the 2018 crater can be interpreted by a depressurization of hydrothermal system, mass discharge and thermoelastic compaction (e.g., phreatic eruption, the coeruptive craters formed at the northern rim of the Kagamiike-kita pyroclastic cone. Our modeling suggests that the southwest-dipping dislocation plane from the eruptive crater is a favorable solution to explain the coeruptive deformation. Considering that the observed asymmetric subsidence can be interpreted as trapdoor faulting, we can presume abrupt pressure changes within the aquifer of the peripheral hydrothermal system before and after the phreatic eruption. Several historical WNW-ESE aligned craters detected by the GSI LIDAR mapping are distributed perpendicular to the distribution axis of the pyroclastic cones on Kusatsu-Shirane volcano (CCPVE report 2018c). A geological survey suggested that the sequence of pyroclastic cones formed due to magmatic eruptions ~ 3000 years ago, although phreatic eruptions are the dominant eruption type recently (Hayakawa and Yui 1989). The orthogonal distribution of small craters and pyroclastic cones may suggest a rotation of the stress regime from a depth at which a magma body is emplaced, to a shallower depth where the hydrothermal system is developed. Additionally, the distributions of small craters imply that the physical processes of historical phreatic eruptions were similar to those of the 2018 eruption. The left-lateral component of our best-t solution can be considered as a stress accommodation in the shallow brittle part stimulated by breaking seals or weaknesses from normal stress due to episodic degassing. Considering that paths of ejected volcanic uid usually form along pre-existing fractures or low-energy pathways, the distribution axis of the aligned WNW-ESE craters implies a peripheral stress regime in the shallow part of the crust above the magma source.

Conclusions
We successfully extracted coeruptive and posteruptive deformation signals associated with the 2018 Kusatsu-Shirane phreatic eruption based on ALOS-2/PALSAR-2 MTI data. The PALSAR-2 MTI data show that the coeruptive deformation elds are dominantly characterized by ~ 10 cm of subsidence and eastward movement on the southwestern side of the 2018 crater, which formed on the northern side of Kagamiike-kita pyroclastic cone. We identi ed approximately 2-3 cm of posteruptive deformation that lasted for approximately two years following the 2018 eruption, while few plausible deformations were observed before the 2018 eruption. Normal faulting with a left-lateral slip component on a southwestdipping plane is favorable solution that ts the spatial characteristics of the extracted coeruptive deformation. The inferred best-t parameters of the dislocation plane can be interpreted as a pathway for volcanic uid transport from the deformation source to the surface. To our knowledge, this is the rst report regarding crustal deformation associated with the 2018 Kusatsu-Shirane eruption using SAR data.
We recon rmed that satellite SAR data allow us to detect high-spatial-resolution crustal deformation on active volcanoes even if the eruption occurs at an unexpected site or in a region with a sparse groundbased network. Although the coeruptive deformation due to the 2018 Kusatsu-Shirane phreatic eruption was small in magnitude (~ 10 cm) and in spatial extent (~ 2 km in diameter), similar to deformation caused by other previous phreatic eruptions, the observation data contribute to an understanding of the shallow physical processes related to the 2018 phreatic eruption. Although we only present SAR image processing associated with the 2018 Kusatsu-Shirane eruption in this study, these data will be helpful for supporting other observational dataset.

Funding
This study is funded by "Integrated program for next generation volcano research and human resource development" led by the Ministry of Education, Culture, Sport, Science and Technology, Japan (MEXT).
Authors' contributions YH performed SAR image processing and constructed the model. All authors managed this study, discussed the results, and approved the nal manuscript.