The Rupture Surface Model of the July 29, 2025 Mw 8.8 Kamchatka Earthquake Based on Satellite Geodesy and Interferometry Data

In October 2002, 15 continuous days of Very Long Baseline Interferometry (VLBI) data were observed in the Continuous VLBI 2002 (CONT02) campaign. All eight radio telescopes involved in CONT02 were co-located with at least one other space-geodetic technique, and three of them also with a Water Vapor Radiometer (WVR). The goal of this paper is to compare the tropospheric zenith delays observed during CONT02 by VLBI, Global Positioning System (GPS), Doppler Orbitography Radiopositioning Integrated by Satellite (DORIS) and WVR and to compare them also with operational pressure level data from the European Centre for Medium-Range Weather Forecasts (ECMWF). We show that the tropospheric zenith delays from VLBI and GPS are in good agreement at the 3–7 mm level. However, while only small biases can be found for most of the stations, at Kokee Park (Hawaii, USA) and Westford (Massachusetts, USA) the zenith delays derived by GPS are larger by more than 5 mm than those from VLBI. At three of the four DORIS stations, there is also a fairly good agreement with GPS and VLBI (about 10 mm), but at Kokee Park the agreement is only at about 30 mm standard deviation, probably due to the much older installation and type of DORIS equipment. This comparison also allows testing of different DORIS analysis strategies with respect to their real impact on the precision of the derived tropospheric parameters. Ground truth information about the zenith delays can also be obtained from the ECMWF numerical weather model and at three sites using WVR measurements, allowing for comparisons with results from the space-geodetic techniques. While there is a good agreement (with some problems mentioned above about DORIS) among the space-geodetic techniques, the comparison with WVR and ECMWF is at a lower accuracy level. The complete CONT02 data set is sufficient to derive a good estimate of the actual precision and accuracy of each geodetic technique for applications in meteorology.

The understanding of forced temporal variations in celestial pole motion (CPM) could bring us significantly closer to meeting the accuracy goals pursued by the Global Geodetic Observing System (GGOS) of the International Association of Geodesy (IAG), i.e., 1 mm accuracy and 0.1 mm/year stability on global scales in terms of the Earth orientation parameters. Besides astronomical forcing, CPM excitation depends on the processes in the fluid core and the core–mantle boundary. The same processes are responsible for the variations in the geomagnetic field (GMF). Several investigations were conducted during the last decade to find a possible interconnection of GMF changes with the length of day (LOD) variations. However, less attention was paid to the interdependence of the GMF changes and the CPM variations. This study uses the celestial pole offsets (CPO) time series obtained from very long baseline interferometry (VLBI) observations and data such as spherical harmonic coefficients, geomagnetic jerk, and magnetic field dipole moment from a state-of-the-art geomagnetic field model to explore the correlation between them. In this study, we use wavelet coherence analysis to compute the correspondence between the two non-stationary time series in the time–frequency domain. Our preliminary results reveal interesting common features in the CPM and GMF variations, which show the potential to improve the understanding of the GMF’s contribution to the Earth’s rotation. Special attention is given to the corresponding signal between FCN and GMF and potential time lags between geomagnetic jerks and rotational variations.

To achieve the 1 mm accuracy and 0.1 mm/year stability of Terrestrial Reference Frame (TRF) required by Global Geodetic Observing System (GGOS), various surface displacements have to be precisely modeled. Non-tidal atmosphere, ocean, and hydrology loading displacements are major sources causing stochastic and systematic effects in station coordinates estimated by space geodetic techniques such as Global Navigation Satellite Systems (GNSS). Studies show that the correction of non-tidal loading displacements in GNSS station coordinate time series reduces coordinate repeatability and thereby improves stability. Currently, non-tidal loading displacements are corrected on the observation level in Very Long Baseline Interferometry (VLBI) data analysis for standard IVS (International VLBI Service for Geodesy and Astrometry) products, but not in GNSS data analysis. We applied the ESMGFZ non-tidal atmosphere and ocean loading displacements (NTAOL) on the observation, normal equation, and parameter levels for global GNSS network solutions in 2005-2019. We demonstrate that the station coordinate repeatability can be significantly improved when correcting NTAOL displacements, especially in the up component where a reduction of 20-30% can be observed at middle and high latitudes. Whereas for other geodetic parameters, such as satellite orbits, Earth Rotation Parameters (ERP), and geocenter motion, however, the impact of NTAOL displacements is insignificant. The difference between applying NTAOL displacements on the observation to that on the normal equation level is on sub-daily scales and we show that most of these differences are absorbed by receiver clocks. As for the differences of applying NTAOL on the observation and on the parameter levels, small but systematic effects on the horizontal components of station coordinates appear, which are mainly due to network alignment. We also demonstrate that the a priori tropospheric delay modeling affects the non-tidal atmosphere loading signals in station coordinates, i.e., when applying empirical tropospheric delay models, e.g., GPT3, NTAL correction introduces a significantly smaller improvement of station coordinate repeatabilities (below 5% in up component). Hence, we recommend always using discrete tropospheric delay products from Numerical Weather Model (NWM) as a priori values when NTAL corrections are applied.

A precise geodetic measurement network using three modern space geodetic techniques, i.e. Very Long Baseline Interferometry, Satellite Laser Ranging, and Global Positioning System, is being established around Tokyo, Japan by the Communications Research Laboratory. The Key Stone Project, which is the name of the project, was started to obtain precise relative positions of four stations using these three space geodetic techniques on a daily basis. The system was designed to make frequent observations possible with minimum human operations and to provide analyzed results as fast as possible. This paper describes various aspects of new features and the performance of the automatic geodetic Very Long Baseline Interferometry observation and data analysis system designed for the Key Stone Project. This automated design has allowed daily Very Long Baseline Interferometry experiments to be conducted since January 1995 and the results to be immediately made available for public use after each experiment.

An assessment of the tropospheric parameters independently derived from the analysis of Very Long Baseline Interferometry (VLBI) and Global Navigation Satellite Systems (GNSS) data serves as a cross-validation of the two space geodetic techniques on the parameter level. Time series of the tropospheric parameters are studied for the most frequently observed VLBI stations at 7 co-located sites covering a time span between 2019 and middle of 2023. These sites are equipped in total with 10 small and fast-slewing antennas that have been specifically built to satisfy the concept of the VLBI Global Observing System (VGOS). Next to the VGOS antennas, 5 legacy VLBI antennas are located providing an additional source of the VLBI observations for comparison. VLBI conducts observations on a session-wise basis of 24 hours at least twice a week, whereas GNSS observes continuously. As a consequence, the paired tropospheric parameters are restricted to epochs where VLBI data are available. The closest GNSS receivers are chosen next the VGOS or VLBI antennas to ensure the same path propagation delays. For the sake of a meaningful comparison, the parameterization of the troposphere is homogenized between the two techniques in favor of the VLBI analysis: the VLBI observations are scheduled to provide even sky-coverage within every hour. After omitting modelled offsets between the reference points of the VLBI and GNSS antennas expected due to the height differences, the obtained tropospheric estimates of two independent techniques show a good agreement level, which lays within their scatter. The remaining tropospheric variations are averaged at the level of 4-6 mm in terms of root mean square differences. A larger scatter of these tropospheric variations is obtained for a few stations at the level between 8–10 mm. These extreme cases can be explained by specific issues at each individual station, i.e. the short paired time series.

Since more accurate and precise measurements are available in space geodetic techniques, there is a growing interest for the scientific community in studying the short periodic fluctuation of the Earth’s rotation axis. In particular subtle nearly diurnal variations of the orientation of the rotation axis, as viewed from the Earth, reflect dynamical properties of the deep interior of the Earth. Recently Very Long Baseline Interferometry (VLBI) data analysis sets a stringent upper limit to the nearly diurnal wobble whose amplitude is well below the milliarc second (mas) level [Herring et al., 1991].

<p>Numerous active low Earth orbiters (LEOs) and Global Navigation Satellite System (GNSS) satellites, including the Galileo constellation, are equipped with laser retroreflectors used for Satellite Laser Ranging (SLR). Moreover, most of LEOs are equipped with GNSS receivers for precise orbit determination. SLR measurements to LEOs, GNSS, and geodetic satellites vary in terms of the number of registered normal points (NPs) or registered satellite passes. In 2016-2018, SLR measurements to LEOs constituted 81% of all NPs and 59% of all registered satellite passes, whereas 10% of NPs and 30% of satellite passes, respectively, were assigned to GNSS. The remaining SLR measurements were completed by geodetic satellites, including LAGEOS-1/2, and LARES-1.</p><p>In this study, we show that the SLR observations to Galileo, passive geodetic and active LEO satellites together with precise GNSS-based orbits of LEOs and Galileo, can be used for the determination of global geodetic parameters, such as geocenter coordinates (GCC) and Earth rotation parameters (ERPs), i.e. pole coordinates, and length-of-day parameter.</p><p>GCC are typically determined using SLR observations to passive geodetic satellites, such as LAGEOS-1/2. Also, the SLR observations to LAGEOS-1/2 together with GNSS and Very Long Baseline Interferometry data are used for the determination of ERPs. Here, we use SLR observations to Galileo, LAGEOS-1/2, LARES-1, Sentinel-3A, SWARM-A/B/C, TerraSAR-X, Jason-2, GRACE-A/B satellites to investigate whether they can be applied for the reference frame realization and for deriving high-quality global geodetic parameters.</p><p>We present various types of solutions to investigate the best solution set-up. The studied solutions differ in terms of solution lengths, the combination of different sets of satellites and the relative weights for the variance scaling factors of technique and satellite-specific normal equations. We compare our results with the standard LAGEOS-based solutions, the combined EOP-14-C04 products and show the consistency of the results.</p>

The relationship between seismic deformation and deep-seated gravitational movements during the 1997 Umbria–Marche (Central Italy) earthquakes

This study investigates the kinematic behavior and deformation patterns of the Psathopyrgos normal fault in the Western Gulf of Corinth (GoC) using space geodetic techniques such as InSAR and GNSS time-series analysis. The Psathopyrgos fault is the main onshore tectonic structure of the north-dipping fault system and is located near the western tip of GoC (Tsimi et al. 2007). The crustal extension across the Corinth rift increases from east to west and reaches its maximum value in the western GoC where the Psathopyrgos fault is located.  Our analysis covers the period from 2016 to 2022 and leverages LiCSBAS, an open-source package, for InSAR time series analysis with the N-SBAS method. We combine our InSAR results with GNSS velocities in order to obtain a more accurate estimation of the deformation field. Through the InSAR time-series analysis, the E-W fault trace of the Psathopyrgos fault was mapped in detail as the ground motion pattern is affected by the long-term displacement of the fault. An offset across the fault trace was detected in the LOS position time series. The Up-Down component of InSAR confirms the LOS findings thus indicating a mainly vertical component of motion and shows an average velocity offset of 4.5 mm/yr between the two blocks across the fault, i.e., the footwall and the hanging-wall. This geodetic evidence confirms the creeping behavior of the fault. The E-W cross-sections of the InSAR velocity data also show contrasting patterns of motion. The E-W component of InSAR reveals a right-lateral slip along the western segment of the fault. An additional finding was provided by the examination of the time-series of the pixels that are located on the hanging wall of the Psathopyrgos fault. These pixels include offsets related to possible co-seismic or passive slip of Psathopyrgos fault because of the 17 February 2021 M5.3 offshore earthquake (Zahradnik et al. 2022). The offset in the time-series was about 0.01 m. The geodetic data indicate a possible surface rupture or passive slip along the Psathopyrgos fault plane, together with continuous motion that could relate to migration of fluids and aseismic creep. These new findings suggest a combination of slip history including fault rupture, aseismic creep, and fluid migration, thus, contributing to a better understanding of the interseismic and co-seismic dynamics of the Psathopyrgos active fault. Tsimi, Ch., Ganas, A., Soulakellis, N., Kairis, O., and Valmis, S., 2007. Morphotectonics of the Psathopyrgos active fault, western Corinth rift, central Greece. Bulletin of the Geological Society of Greece, vol. 40, 500-511 http://dx.doi.org/10.12681/bgsg.16657  .Zahradník, J., Aissaoui, E. M., Bernard, P., Briole, P., Bufféral, S., De Barros, L., et al. (2022). An atypical shallow Mw 5.3, 2021 earthquake in the western Corinth rift (Greece). Journal of Geophysical Research: Solid Earth, 127, e2022JB024221. https://doi.org/10.1029/2022JB02422

A critical point in the analysis of ground displacement time series, as those recorded by space geodetic techniques, is the development of data-driven methods that allow the different sources of deformation to be discerned and characterized in the space and time domains. Multivariate statistic includes several approaches that can be considered as a part of data-driven methods. A widely used technique is the principal component analysis (PCA), which allows us to reduce the dimensionality of the data space while maintaining most of the variance of the dataset explained. However, PCA does not perform well in finding the solution to the so-called blind source separation (BSS) problem, i.e., in recovering and separating the original sources that generate the observed data. This is mainly due to the fact that PCA minimizes the misfit calculated using an $$L_{2}$$ norm ( $$\chi ^{2})$$ , looking for a new Euclidean space where the projected data are uncorrelated. The independent component analysis (ICA) is a popular technique adopted to approach the BSS problem. However, the independence condition is not easy to impose, and it is often necessary to introduce some approximations. To work around this problem, we test the use of a modified variational Bayesian ICA (vbICA) method to recover the multiple sources of ground deformation even in the presence of missing data. The vbICA method models the probability density function (pdf) of each source signal using a mix of Gaussian distributions, allowing for more flexibility in the description of the pdf of the sources with respect to standard ICA, and giving a more reliable estimate of them. Here we present its application to synthetic global positioning system (GPS) position time series, generated by simulating deformation near an active fault, including inter-seismic, co-seismic, and post-seismic signals, plus seasonal signals and noise, and an additional time-dependent volcanic source. We evaluate the ability of the PCA and ICA decomposition techniques in explaining the data and in recovering the original (known) sources. Using the same number of components, we find that the vbICA method fits the data almost as well as a PCA method, since the $$\chi ^{2}$$ increase is less than 10 % the value calculated using a PCA decomposition. Unlike PCA, the vbICA algorithm is found to correctly separate the sources if the correlation of the dataset is low ( $$<$$ 0.67) and the geodetic network is sufficiently dense (ten continuous GPS stations within a box of side equal to two times the locking depth of a fault where an earthquake of $$M_\mathrm{{w}} >6$$ occurred). We also provide a cookbook for the use of the vbICA algorithm in analyses of position time series for tectonic and non-tectonic applications.

Geodesy is a branch of applied mathematics and Earth sciences, the scientific discipline and technology dealing with measurement and representation of Earth, including its gravitational field, in three-dimensional, time-varying space. Geodesy can be divided into applied, physical, geometric, and satellite geodesy and is associated with the fields of photogrammetry, remote sensing, and cartography, because one has to start with measuring in order to produce a map. In other words, a map is the final result of surveying and geodesy. Sphere is often taken as a model of the Earth’s surface. Another model frequently taken for the Earth’s surface is rotational ellipsoid. While determination of the Earth’s figure and size is one of the fundamental tasks of geodesy, map projections include the study of spherical or ellipsoidal transformation from the Earth’s or another planet’s surface model to a two dimensional representation. The chapter deals with basic mathematics of an ellipsoid or a sphere required to understand map projections.

The troposphere is one of the most important error sources for space geodetic techniques relying on radio signals. Since it is not possible to model the wet part of the tropospheric delay with sufficient accuracy, it needs to be estimated from the observational data. In the analysis of very long baseline interferometry (VLBI) data, the parameter estimation is routinely performed using a least squares adjustment. In this paper, we investigate the application of a Kalman filter for parameter estimation, specifically focusing on the tropospheric delays. The main advantages of a Kalman filter are its real-time capability and stochastic approach. We focused on the latter and derived stochastic models for VLBI zenith wet delays, taking into account temporal and location-based differences. Compared to a static noise model, the quality of station coordinates, also estimated in the Kalman filter, increased as a result. In terms of baseline length and station coordinate repeatabilities, this improvement amounted to 2.3 %. Additionally, we compared the Kalman filter and least squares results for VLBI with zenith wet delays derived from GPS (Global Positioning System), water vapor radiometers, and ray tracing in numerical weather models. The agreement of the Kalman filter VLBI solution with respect to water vapor radiometer data was larger than that of the least squares solution by 6–15 %. Our investigations are based on selected VLBI data (CONT campaigns) that are closest to how future VLBI infrastructure is designed to operate. With the aim for continuous and near real-time parameter estimation and the promising results which we have achieved in this study, we expect Kalman filtering to grow in importance in VLBI analysis.

Soil creep is characterised by slow displacement, with depths of a few meters and loosely defined limits. Buildings and infrastructure located on slopes affected by such landslides may suffer significant damages if their foundations are poorly dimensioned. The presence of soil creep in urban areas makes it necessary to develop landslide activity maps, derive hazard maps, and implement risk management plans. Even though both geological and geomorphological analyses can provide basic information, it is often necessary to use additional techniques to obtain information about ground displacements. This paper proposes a method to derive a soil creep activity map using a multi-approach analysis based on geological, geomorphological, and persistent scatterer interferometry (PSI) data. PSI is a satellite-based technique to estimate land displacement velocity. The work described in this paper was carried out in the town of El Papiol, in the metropolitan area of Barcelona (Spain). This is an urban area that has been heavily affected by soil creep over the past decades. The results achieved show that PSI data substantially improve the information provided by the geological and geomorphological analyses and make it possible to accurately define the landslide area and estimate its activity.

This study aims to investigate the occurrence of surface displacements in the Canto do Amaro (CAM) onshore oil field, situated in Rio Grande do Norte, Brazil, using Sentinel-1 data. The persistent scatterer interferometry (PSI) technique was used to perform the analysis based on 42 Sentinel-1 images, acquired from 23 July 2020 to 21 December 2021. Moreover, information regarding the structural geology of the study area was collected by referencing existing literature datasets. Additionally, a study of the water, gas, and oil production dynamics in the research site was conducted, employing statistical analysis of publicly available well production data. The PSI points results were geospatially correlated with the closest oil well production data and the structural geology information. The PSI results indicate displacement rates from −20.93 mm/year up to 14.63 mm/year in the CAM region. However, approximately 90% of the deformation remained in the range of −5.50 mm/year to 4.95 mm/year, indicating low levels of ground displacement in the designated research area. No geospatial correlation was found between the oil production data and the zones of maximum deformation. In turn, ground displacement demonstrates geospatial correlation with geological structures such as strike-slip and rift faults, suggesting a tectonic movement processes. The PSI results provided a comprehensive overview of ground displacement in the Canto do Amaro field, with millimeter-level accuracy and highlighting its potential as a complementary tool to field investigations.

We have successfully detected widely distributed ground displacements for the 2015 Gorkha earthquake by applying a ScanSAR-based interferometry analysis of Advanced Land Observing Satellite 2 (ALOS-2) L-band data. A major displacement area extends with a length of about 160 km in the east-west direction, and the most concentrated crustal deformation with ground displacement exceeding 1 m is located 20–30 km east from Kathmandu. A quasi-vertical displacement estimated by combining the ascending and the descending data indicates upheaval of about 1.4 m at maximum. We inverted the synthetic aperture radar interferometry (InSAR) data including both of the main shock (moment magnitude (Mw) 7.8) and the largest aftershock (Mw 7.3) to construct a slip distribution model. Our model shows a nearly pure reverse fault motion with a slip amount of approximately 6 m at maximum, and the spatial extent is zonally distributed within a distance of 50 to 100 km from the surface along downdip direction. The downdip end of the slip is quite consistent with that of the interseismic coupling area geodetically inferred in previous studies. On the other hand, there is no significant slip at shallow depth in spite of the fact that the plate interface is thought to be fully locked there, may be suggesting that there still remains a potential of fault slip. The slip distribution unnaturally bifurcates in the east, and we can identify a clear-cut slip deficit area with a radius of ~10 km just west side of the Mw 7.3 event, where the slip amount reaches only 20 cm at most. This area is presumably subjected to a strong shear stress which should promote a reverse fault slip. There is a possibility to produce a fault slip equivalent to Mw ~7.0 in the future although we do not know if the slip heterogeneity would be smoothed out by a seismic event or an aseismic event.