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Long-term deformation of Kusatsu-Shirane and Asama volcanoes in central Japan were investigated using Global Navigation Satellite System (GNSS) measurements. Large postseismic deformation caused by the 2011 Tohoku earthquake—which obscures the long-term volcanic deformation—was effectively removed by approximating the postseismic and other recent tectonic deformation in terms of quadrature of the geographical eastings/northings. Subsequently, deformation source parameters were estimated by the Markov Chain Monte Carlo (MCMC) method and linear inversion, employing an analytical model that calculates the deformation from an arbitrary oriented prolate/oblate spheroid. The deformation source of Kusatsu-Shirane volcano was found to be a sill-like oblate spheroid located a few kilometers northwest of the Yugama crater at a depth of approximately 4 $$\text {km}$$ km , while that of Asama was also estimated to be a sill-like oblate spheroid beneath the western flank of the edifice at a depth of approximately 12 $$\text {km}$$ km , along with the previously reported shallow east–west striking dike at a depth of approximately 1 $$\text {km}$$ km . It was revealed that (1) volume changes of the Kusatsu-Shirane deformation source and the shallow deformation source of Asama were correlated with the volcanic activities of the corresponding volcanoes, and (2) the Asama deep source has been steadily losing volume, which may indicate that the volcano will experience fewer eruptions in the near future.

Real-time geopotential measurements with two synchronously linked optical lattice clocks are demonstrated. A height difference between the two clocks separated by 15 km is determined, with an uncertainty of 5 cm, by means of a gravitational redshift. According to Einstein's theory of relativity, the passage of time changes in a gravitational field1,2. On Earth, raising a clock by 1 cm increases its apparent tick rate by 1.1 parts in 1018, allowing chronometric levelling3 through comparison of optical clocks1,4,5. Here, we demonstrate such geopotential measurements by determining the height difference of master and slave clocks separated by 15 km with an uncertainty of 5 cm. A subharmonic of the master clock laser is delivered through a telecom fibre6 to synchronously operate7 the distant clocks. Clocks operated under such phase coherence reject clock laser noise and facilitate proposals for linking clocks8,9 and interferometers10. Taken over half a year, 11 measurements determine the fractional frequency difference between the two clocks to be 1,652.9(5.9) × 10−18, consistent with an independent measurement by levelling and gravimetry11. Our system demonstrates a building block for an internet of clocks, which may constitute ‘quantum benchmarks’, serving as height references with dynamic responses.

The sub-daily noise in horizontal global positioning system (GPS) kinematic time series arising from monument tilts is quantitatively evaluated using tiltmeter data at GPS stations from the Japanese nationwide global navigation satellite system network. The estimated tilt-induced monument displacements show characteristics that are typical of those caused by thermal tilts of the monuments. The root mean square of the displacements is typically a few millimetres, with notable inter-seasonal variations. The stacked amplitude spectra of the monument displacements have peaks at the tidal bands S1 and S2, and their higher tones. The peaks at the S1 and S2 bands in the amplitude spectra are reduced by 41 and 43 % for the north–south component and 36 and 53 % for the east–west component, respectively, after correcting for the monument displacements. The monument displacements due to the thermal tilts of the monuments may also be a favourable candidate for sub-daily noise at the S1 and S2 bands found in other GPS networks.

A new continuous GPS station, 06S061, was installed in Tsukuba, Japan, which is directly anchored to the soil at a depth of 190 m, so that it is less affected by seasonal poroelastic deformations of aquifers induced by groundwater extraction for irrigation. A comparison of GPS-derived vertical movements of surrounding GPS stations relative to 06S061 with the independent observations revealed that 06S061 has an observation quality comparable to a standard GPS station in terms of coordinate repeatability. The poroelastic deformations of aquifers below 190 m recorded at 06S061 were estimated to have peak-to-peak values of about 1 cm, which is half of the total poroelastic deformations of aquifers observed at surrounding GPS stations.

Troposphere-induced errors in GPS-derived geodetic time series, namely, height and zenith total delays (ZTDs), over Japan are quantitatively evaluated through the analyses of simulated GPS data using realistic cumulative tropospheric delays and observed GPS data. The numerical simulations show that the use of a priori zenith hydrostatic delays (ZHDs) derived from the European Centre for Medium-Range Weather Forecasts (ECMWF) numerical weather model data and gridded Vienna mapping function 1 (gridded VMF1) results in smaller spurious annual height errors and height repeatabilities (0.45 and 2.55 mm on average, respectively) as compared to those derived from the global pressure and temperature (GPT) model and global mapping function (GMF) (1.08 and 3.22 mm on average, respectively). On the other hand, the use of a priori ZHDs derived from the GPT and GMF would be sufficient for applications involving ZTDs, given the current discrepancies between GPS-derived ZTDs and those derived from numerical weather models. The numerical simulations reveal that the use of mapping functions constructed with fine-scale numerical weather models will potentially improve height repeatabilities as compared to the gridded VMF1 (2.09 mm against 2.55 mm on average). However, they do not presently outperform the gridded VMF1 with the observed GPS data (6.52 mm against 6.50 mm on average). Finally, the commonly observed colored components in GPS-derived height time series are not primarily the result of troposphere-induced errors, since they become white in numerical simulations with the proper choice of a priori ZHDs and mapping functions.