National Report for the IAG of the IUGG 2019-2022

Abstract: Major results of researches conducted by Russian geodesists in 2019-2022 on the topics of the International Association of Geodesy (IAG) of the International Union of Geodesy and Geophysics (IUGG) are presented in this issue. This report is prepared by the Section of Geodesy of the National Geophysical Committee of Russia. In the report prepared for the XXVII General Assembly of IUGG (Germany, Berlin, 11-20 July 2023), the results of principal researches in geodesy, geodynamics, gravimetry, in the studies of geodetic reference frame creation and development, Earth's shape and gravity field, Earth's rotation, geodetic theory, its application and some other directions are briefly described. For some objective reasons not all results obtained by Russian scientists on the field of geodesy are included in the report.

• The paper presents a comprehensive synthesis of Russian advances in geodetic reference frames, gravity modeling, and geodynamic monitoring.
• It details rigorous network adjustments and innovative methods in satellite, GNSS, and SAR interferometry to enhance measurement precision.
• Practical insights include improved hazard and seismic monitoring, real-time positioning support, and enhanced integration of multi-sensor data.

National Report for the IAG of the IUGG 2019-2022: Synthesis and Technical Analysis

Overview and Scope

The report "National Report for the IAG of the IUGG 2019-2022" (2307.11117) presents a comprehensive synthesis of Russian research advances in geodesy, gravimetry, geodynamics, geodetic reference frames, and related domains over the 2019–2022 period. With contributions from leading Russian academic and applied geodesy institutions, the compendium systematically covers fundamental progress on geodetic reference frame realization, novelty in gravity field modeling, evolution in Earth's rotation parameter estimation, physical and analytical geodesy, integration of geodesy with seismology, and satellite-based applications.

Geodetic Reference Frames and National Geodetic Infrastructure

An emphasis is placed on the development and rigorous adjustment of national coordinate, height, and gravimetric frames, notably in the Russian context. The Fundamental Astronomical-Geodetic Network (FAGN) underwent comprehensive adjustment in the ITRF2014 realization for the period 2014–2022. The derivation of inter-annual and intra-annual variations in station coordinates achieved homogeneous geodetic reference across Russia with a reported normal height measurement accuracy of ~2 mm/km for class II leveling and acceleration of gravity monitored using top-tier gravimeters.

The operational structure is captured in a three-tier reference system: FAGN, the High-Precision Geodetic Reference Network (PGN), and the first-class Satellite Geodetic Network (SGN-1) with respective mean site separation of 150–650 km, 150–300 km, and 25–35 km. These networks are continually densified and up-to-date coordinates and velocities are computed, delivering real-time geodetic support for applied and scientific purposes.

The deployment and continuous expansion of the Federal Network of Differential Geodetic Stations (FNGS; >2000 stations as of 2023) is highlighted, facilitating real-time, high-precision positioning, with joint adjustment to the State FAGN network as the metrological backbone.

Advances in Reference Frame Theory and Methods

At the international level, Russian scientists contributed to the IAG Sub-commission 1.4, focusing on minimizing inconsistencies between terrestrial (e.g., ITRF) and celestial (e.g., ICRF) frames. Significant methodical advances include:

• A spherical equal-area isolatitudinal grid for data uniformization in reference frame analysis, advantageous for both celestial and terrestrial applications (SREAG grid).
• Robust orientation parameter estimation between frames, utilizing binning and median filtering on SREAG-distributed cells with subsequent VSH decomposition, which enhances outlier insensitivity in frame comparison.
• Practical recommendations for galactic aberration modeling in ICRF implementations at the few μas/yr level.
• Ongoing scrutiny of modeling deficiencies and processing strategies across SLR, VLBI, and GNSS datasets.

Gravity Field, Geoid Modeling, and Physical Geodesy

Substantial progress is documented in both global and regional gravity field investigations:

• Satellite altimetry is leveraged for cost-effective geoid and gravity anomaly determination in marine domains. In specific regional experiments (e.g., Black Sea section), the method yielded residuals within 6 mGal relative to EGM2008, validating satellite altimetry as an essential tool for gravity field recovery in difficult environments.
• Airborne gravimetry, augmented by SRBF-based downward continuation techniques, demonstrated RMS errors of 1.18 mGal in the Vietnam region—superior to earlier efforts.
• Theoretical developments led to advances in the Hotine-Koch integral kernel, incorporating frequency response operators and SRBF approximations for regional transformation. Correction of classical errors in the Molodensky mixed anomaly formulation ensures improved high-order accuracy.

Notably, strong claims are made regarding the superiority of normal heights (per the Molodensky approach) versus orthometric heights in large states, based on the criterion of constancy along level surfaces and independence from unknown internal mass distributions.

Geodynamics: GNSS, Seismicity, and Integrated Observation

Long-term GNSS observation networks provided a foundation for advanced geodynamic analyses:

• The introduction of "geosynoptics"—kinematic mapping of temporal deformation fields, linked to seismicity—enabled empirical extraction of precursory deformation patterns prior to major seismic events (e.g., detected displacement deficits in areas later affected by the 2023 Karamanmarash earthquakes).
• Migration of total shear deformation (TSD) waves, with velocities up to 20 km/year, was identified as a possible earthquake trigger. Evidence indicates anomalous TSD development 1–7 years before high-magnitude earthquakes (Ridgecrest 2019, Napa 2014).
• Retrospective analysis demonstrates that regions of internal displacement deficit, inferred from GNSS kinematics, are predictive of subsequent strong earthquake loci.
• The use of integrated GNSS networks at the Russian-Chinese border and Kuril-Kamchatka is shown to increase efficiency and reliability of seismic- and tsunami-early warning.
• Joint inversion techniques assimilating GRACE, SAR, GNSS, and bottom pressure observations achieved refined rupture surface models for recent mega-thrust earthquakes, and demonstrated that postseismic displacements often require a dominant role for aseismic slip rather than solely viscoelastic relaxation, especially above rupture zones.

SAR Interferometry and Remote Sensing Applications

The report details extensive SAR interferometry-based studies covering:

• Monitoring and modeling of post-eruption lava subsidence (e.g., Tolbachik, Shiveluch volcanoes), using thermomechanical models to connect remote deformation data with internal magma dynamics.
• Detection and mapping of vertical crustal movements due to both natural (e.g., active volcanism, landsliding in Sochi) and anthropogenic causes (e.g., mine-induced subsidence in Berezniki).
• Validation of SAR-derived displacement magnitudes against in-situ geodetic measurements, substantiating remote techniques as reliable surveillance for disaster risk management.

Earth's Rotation, EOP Combination, and Interconnections

The Russian Main Metrological Center maintains state-level time, frequency, and EOP services. The report describes:

• The routine combination of VLBI, GNSS, and SLR for EOP, with statistically significant gains in UT1 accuracy, particularly with the addition of IAA RAS VGOS antenna data.
• Novel pilot methods for satellite clock calibration and laser time transmission.
• Identification and analysis of non-linear periodicities in Earth's rotation (Chandler wobble, LOD variations), supported by Kalman and Panteleev filtering, and updated models for phase relationships (e.g., between Chandler pole and lunar perigee).
• Cross-domain effects: strong earthquakes have shown detectable signatures in optical latitude and timing records, suggesting potential for earthquake prediction.

Importantly, no strong trend improvement in celestial pole prediction accuracy was seen over the last decade, although Russian institutes achieve approximately double the predictive accuracy (for both short and long-term) compared to other major centers.

A novel result is the wavelet-based identification of coherence between free core nutation and geomagnetic secular variation, strengthening the argument for their geophysical coupling.

Positioning, Atmospheric Sensing, and Applications

Advances in satellite geodesy underpin a range of application areas:

• Development of robust outlier rejection and pre-processing algorithms for GNSS and SLR, minimizing data loss without sacrificing end accuracy.
• Creation and public release of a homogenously processed East European GNSS station velocity database for regional geodynamics.
• Demonstrated calibration and performance of Galileo and GPS space-borne oscillators, identifying stability and noise characteristics fundamental to timekeeping and geodesy.
• Operational GNSS-based troposphere water vapor monitoring; high-correlation (r > 0.9, at analysis epoch) with GFS forecast model data except at longer lead times and in cold seasons, establishing GNSS meteorology as an accurate tool for operational hydrometeorology.

Theoretical and Technical Contributions

The report includes:

• Mathematical corrections to the Molodensky theory for geopotential anomalies.
• Rigorous developments in network adjustment using least squares and correlated equalization, applied to the adjustment of the national geodetic infrastructure.
• In-depth analysis of the relativity-based Sagnac effect for frequency standard synchronization, critical for high-precision timing applications.

Implications and Future Prospects

Practically, these research outputs allow:

• Enhanced hazard monitoring (seismic, volcanic, landslide) and rapid warning systems using multi-sensor fusion.
• Sub-centimeter level maintenance and expansion of national and regional geodetic networks, essential for navigation, engineering, and surveying.
• Improved metrological support and integration with international reference frame maintenance.
• Next-generation geodetic theory development, focused on robustness in network adjustment, optimal reference surface realization, and orientation parameter estimation.

Theoretically, results from the geodynamics, Earth's rotation, and gravimetric work challenge and refine standard assumptions about postseismic processes and geodynamic precursors, and open further inquiry into physical interrelation in Earth's deep interior and geomagnetic field dynamics.

Future research directions can be anticipated in quantum geodetic standards, satellite-satellite tracking for gravity recovery, dense GNSS and SAR fusion for urban and natural hazards, and further international harmonization of geodetic reference frames.

Conclusion

The 2019–2022 Russian National Report for the IAG of IUGG (2307.11117) provides a robust and detailed snapshot of achievements in reference frame realization, gravity field modeling, geodynamic monitoring, and advanced applications in positioning and atmospheric sensing. It documents both extensive empirical results and targeted methodological innovations with direct impact for national infrastructural needs and international geoscientific standards. The continued integration of multi-sensor measurements, enhancement of physical and mathematical modeling, and strengthening of the international geodetic framework are expected to remain pivotal agendas in the coming research cycles.