National Institute of Polar Research （NIPR） has been conducting absolute gravity measurements not only at Japanese Antarctic research station, Syowa since early 1990s, but also other foreign research stations in Antarctica recently. To validate the absolute gravimeter employed, test measurements were conducted at the gravity point located at the machine shop in NIPR usually before and after the measurements in Antarctica. The observed gravity values at the point, however, often varied exceed the expected instrumental errors. To explain the causes of the large gravity variations, we compared the observed gravity values with the precipitations at three AMeDAS（Automated Meteorological Data Acquisition System）stations, groundwater levels at a Tokyo Metropolitan Government observatory, and the height data at four GEONET （GNSS Earth Observation Network System）stations. The result of the comparisons showed that 1） the seasonal or shorter gravity variations were mainly caused by the precipitations and the resultant soil moisture and/or shallow groundwater changes, and 2） the secular or longer period gravity variations were explained by the uplift after the 2011 Tohoku-oki earthquake and the long-term variations of the groundwater level at deeper depths. After removing these effects, the standard deviation of the gravity residuals was less than 3 µGal （1 µGal＝10⁻⁸ m/s²）.

Dense geodetic observation networks have contributed to observing a wide variety of fault slips with different time scales including coseismic slips, slow slip events, afterslips, and stable slips. These slip behaviors may be a result of heterogeneous physical properties, especially frictional properties, along the plate interface. I have conducted a series of studies for understanding and predicting such various fault slip behavior based on geodetic data analysis, numerical simulation, and data assimilation. This article briefly summarizes my works on data assimilation of estimating frictional properties and predicting fault slip in the case of the 2003 Tokachi-oki afterslip, and geodetic data analysis on slow slip events concerning anticipated earthquakes in southwest Japan.

Tidal Love numbers based on the Wang’s Earth model was obtained by solving simultaneous first-order partial differential equations （PDEs） with Runge-Kutta 4th order method considering the frequency dependency of the tidal force. The PDEs are basically according to Alterman et al. （1959） and partly according to Takeuchi & Saito （1972）, and the boundary conditions are improved in order to be applied for the case of small angular velocities, especially between solids and fluids layers. The initial values at the center of the solid core are obtained by converted from the three independent solutions U, V, P calculated based on the method of Pekeris & Jarosh （1958）. The obtained results are considered to be good even when compared with those by the conventional methods, and there is almost no difference between the effects of frequency difference in the range between 6 and 24 hours, where the dominant tidal constituents exist. The power of the Runge-Kutta 4th order method was clear, and good results were obtained even the number of steps in each layer was reduced to 14 to 30. In addition, the number of processes of the integration from the center to the surface of the earth was one enough. The three independent vectors, （0,1,0,0,0,0）, （0,0,0,1,0,0）, （0,0,0,0,0,1） used as the initial values for the Runge-Kutta method were proved to be good enough since almost the appropriate results were obtained in any cycle. It was confirmed that the determinant is almost zero at the periods 6.656, 17.617, and 19.886 hours, and the sign changed across the periods. These zero crossings seem to correspond some eigen periods of such as the fluid core, but since a stable solution was obtained at a distance from these periods, it was not necessary to divide the integration process to dynamic and static ones. Finally, comparison between the results obtained by our method and those by the method of Pekeris & Jarosh （1958） for a simple uniform earth model was made.

Relative gravity measurements are one of the most useful methods for investigating spatiotemporal mass variations in volcanoes. In order to quantify gravity variations accurately, scale factor （SF） and resultant conversion function should be calibrated for each relative gravimeter in advance. Conventionally, the SF value has been treated as a constant for each relative gravimeter. However, a recent study showed that the SF of Scintrex CG5-300500033 gravimeter indicates a dependence on its reading value. The reading value dependence of SFs has not been fully investigated for other relative gravimeters including LaCoste gravimeters, which have long been used for relative gravity measurements in volcanoes. In this study, we made calibration of the SFs for three LaCoste gravimeters （G534, G605 and G680） and one Scintrex gravimeter （CG5-150241330）, by measuring relative and absolute gravity values at four primary gravity points in Japan with the maximal gravity difference of 660 mGal. We found that the SFs vary with reading values almost linearly, by up to 4×10^－4 for the 500 mGal gravity difference. We also estimated the absolute gravity values at five secondary gravity points located near active volcanoes, by measuring relative gravity differences between the primary and secondary gravity points using the four relative gravimeters described above. The SF-derived systematic error was then corrected by considering the reading value dependence of the SFs. As a result, the absolute gravity values at all of the secondary gravity points were precisely determined with < 20 µGal standard deviation by using the reading-value-dependent SFs; the average of the SF’s error became smaller by 72 and 25% than in the cases where the SFs were assumed to be 1.0 and a constant value for each gravimeter, respectively. By comparing the estimated absolute gravity values with those measured by absolute gravimeters, an absolute gravity change of ＋240 µGal was identified at the AVL gravity point in Aso Volcano from May 2010 to April 2021. We conclude that this large change has been caused mainly by the coseismic ground subsidence due to the 2016 Kumamoto earthquake.