Pub Date : 2026-01-17DOI: 10.1007/s00190-025-02017-6
Tao Jiang, Zejie Tu, Jiancheng Li
The accurate modeling of the Earth gravity field and geoid is critical for geodesy, yet traditional methods face limitations in handling the growing complexity and heterogeneity of modern geodetic data. To address these challenges, this study proposes a physics-informed neural network (PINN) framework for high-precision geoid modeling. The PINN employs convolutional neural networks (CNNs) to extract multi-scale features from terrestrial and airborne gravity data, which are then processed by a multilayer perceptron (MLP) to establish an accurate mapping between these features and the disturbing potential. Physical constraints, including Laplace’s equation and differential equations governing gravity anomaly and gravity disturbance, are embedded into the loss function to enhance both accuracy and interpretability. The proposed method is applied to the Colorado 1 cm geoid experiment. Compared to GNSS/leveling data of the Geoid Slope Validation Survey 2017 (GSVS17), the PINN-derived geoid model achieves a standard deviation (STD) of 2.1 cm. This represents a 12.5%–27.6% improvement over traditional methods and purely data-driven networks (DDNs). The PINN exhibits strong generalization under sparse data conditions, achieving 28.5% higher accuracy than the DDN with only 500 samples. Furthermore, analysis of geoid slopes and physical constraint contributions demonstrates that PINN’s dual physical constraints effectively balance global characteristics and localized fidelity of the geoid. This study establishes the PINN as a robust, physically interpretable machine learning approach for geoid modeling, outperforming classical methods and offering a promising pathway for gravity field estimation in regions with sparse or heterogeneous data. By bridging purely data-driven machine learning with fundamental geodetic principles, this work paves the way for future advancements in physics-informed machine learning-based geodetic modeling.
{"title":"Physics-informed neural networks for geoid modeling","authors":"Tao Jiang, Zejie Tu, Jiancheng Li","doi":"10.1007/s00190-025-02017-6","DOIUrl":"https://doi.org/10.1007/s00190-025-02017-6","url":null,"abstract":"The accurate modeling of the Earth gravity field and geoid is critical for geodesy, yet traditional methods face limitations in handling the growing complexity and heterogeneity of modern geodetic data. To address these challenges, this study proposes a physics-informed neural network (PINN) framework for high-precision geoid modeling. The PINN employs convolutional neural networks (CNNs) to extract multi-scale features from terrestrial and airborne gravity data, which are then processed by a multilayer perceptron (MLP) to establish an accurate mapping between these features and the disturbing potential. Physical constraints, including Laplace’s equation and differential equations governing gravity anomaly and gravity disturbance, are embedded into the loss function to enhance both accuracy and interpretability. The proposed method is applied to the Colorado 1 cm geoid experiment. Compared to GNSS/leveling data of the Geoid Slope Validation Survey 2017 (GSVS17), the PINN-derived geoid model achieves a standard deviation (STD) of 2.1 cm. This represents a 12.5%–27.6% improvement over traditional methods and purely data-driven networks (DDNs). The PINN exhibits strong generalization under sparse data conditions, achieving 28.5% higher accuracy than the DDN with only 500 samples. Furthermore, analysis of geoid slopes and physical constraint contributions demonstrates that PINN’s dual physical constraints effectively balance global characteristics and localized fidelity of the geoid. This study establishes the PINN as a robust, physically interpretable machine learning approach for geoid modeling, outperforming classical methods and offering a promising pathway for gravity field estimation in regions with sparse or heterogeneous data. By bridging purely data-driven machine learning with fundamental geodetic principles, this work paves the way for future advancements in physics-informed machine learning-based geodetic modeling.","PeriodicalId":54822,"journal":{"name":"Journal of Geodesy","volume":"45 1","pages":""},"PeriodicalIF":4.4,"publicationDate":"2026-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146005878","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-17DOI: 10.1007/s00190-025-02029-2
Huacan Hu, Haiqiang Fu, JianJun Zhu, Yanzhou Xie, Qijin Han, Aichun Wang, Mingxia Zhang, Jun Hu
LuTan-1 (LT-1) provides unprecedented L-band bistatic interferometric synthetic aperture radar (InSAR) data for terrain mapping. In forested areas, although the L-band exhibits strong penetration capability, the phase center is still located above the bare ground due to forest volume scattering. Furthermore, the bistatic acquisition provides only single-baseline, single-polarization data, leading to an underdetermined issue for existing scattering models in sub-canopy topography inversion. To address these issues, this study proposes a sub-canopy topography estimation framework based on sub-aperture decomposition and the least-squares collocation (LSC) method. The contributions of this study are: 1) assessing the feasibility of sub-aperture decomposition under LT-1’s small azimuth observation angles; 2) using sub-aperture coherence to provide additional observations and address the underdetermination issue of InSAR inversion; and 3) developing an LSC-based method to separate and calibrate LT-1 orbital and scattering model errors, with the latter arising from complex terrain, forest property variations, and model solution. The proposed framework was tested and validated using LT-1 InSAR data acquired over coniferous, evergreen broadleaf, and tropical forests. The estimated sub-canopy topography achieved a root mean square error (RMSE) between 1.22 and 3.85 m, representing an average improvement of over 60% compared to the InSAR DEM and an improvement of over 30% compared to the initial terrain that did not account for scattering model errors. Moreover, the results indicate that the proposed method also exhibits superior performance under varying terrain and forest conditions, further demonstrating its effectiveness and robustness.
{"title":"Sub-canopy topography estimation based on sub-aperture decomposition and least-squares collocation from LuTan-1 InSAR data","authors":"Huacan Hu, Haiqiang Fu, JianJun Zhu, Yanzhou Xie, Qijin Han, Aichun Wang, Mingxia Zhang, Jun Hu","doi":"10.1007/s00190-025-02029-2","DOIUrl":"https://doi.org/10.1007/s00190-025-02029-2","url":null,"abstract":"LuTan-1 (LT-1) provides unprecedented L-band bistatic interferometric synthetic aperture radar (InSAR) data for terrain mapping. In forested areas, although the L-band exhibits strong penetration capability, the phase center is still located above the bare ground due to forest volume scattering. Furthermore, the bistatic acquisition provides only single-baseline, single-polarization data, leading to an underdetermined issue for existing scattering models in sub-canopy topography inversion. To address these issues, this study proposes a sub-canopy topography estimation framework based on sub-aperture decomposition and the least-squares collocation (LSC) method. The contributions of this study are: 1) assessing the feasibility of sub-aperture decomposition under LT-1’s small azimuth observation angles; 2) using sub-aperture coherence to provide additional observations and address the underdetermination issue of InSAR inversion; and 3) developing an LSC-based method to separate and calibrate LT-1 orbital and scattering model errors, with the latter arising from complex terrain, forest property variations, and model solution. The proposed framework was tested and validated using LT-1 InSAR data acquired over coniferous, evergreen broadleaf, and tropical forests. The estimated sub-canopy topography achieved a root mean square error (RMSE) between 1.22 and 3.85 m, representing an average improvement of over 60% compared to the InSAR DEM and an improvement of over 30% compared to the initial terrain that did not account for scattering model errors. Moreover, the results indicate that the proposed method also exhibits superior performance under varying terrain and forest conditions, further demonstrating its effectiveness and robustness.","PeriodicalId":54822,"journal":{"name":"Journal of Geodesy","volume":"63 1","pages":""},"PeriodicalIF":4.4,"publicationDate":"2026-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146005877","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-16DOI: 10.1007/s00190-025-02024-7
Thunendran Periyandy, Michael Bevis
{"title":"The gravitational potential inside, on, and outside of a homogeneous tetrahedron","authors":"Thunendran Periyandy, Michael Bevis","doi":"10.1007/s00190-025-02024-7","DOIUrl":"https://doi.org/10.1007/s00190-025-02024-7","url":null,"abstract":"","PeriodicalId":54822,"journal":{"name":"Journal of Geodesy","volume":"11 1","pages":""},"PeriodicalIF":4.4,"publicationDate":"2025-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145770606","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-11-28DOI: 10.1007/s00190-025-02021-w
Qiqi Shi, Yonghong Zhou, Jianli Chen, Xueqing Xu
Geophysical sources and processes that excite the Earth’s Chandler wobble (CW) have long been debated. Significant discrepancies remain at times between geophysical fluid models, especially regarding inaccurate hydrological and cryospheric estimates, and observed CW series. Recently, the CW experienced anomalous behavior after 2015, with a disappearance and a re-excitation. Understanding hydrological and cryospheric effects on the CW and their contributions to this anomaly requires urgent investigation. Utilizing the Gravity Recovery and Climate Experiment (GRACE) and GRACE Follow-On (GFO) measurements, we reconstruct the CW series contributed from the hydrology and cryosphere for the GRACE period (April 2002 to December 2015) and GFO period (June 2018 to December 2024), respectively. We find that GRACE/GFO measurements can capture more accurate hydrological and cryospheric forcing CW signals than models. For the first time, our reconstructed results successfully account for the recent observed disappearing and re-excited CW phenomenon. Considering global mass conservation associated with barystatic sea-level changes, the GRACE/GFO-derived hydrological and cryospheric effects agree well with geodetic CW observations. The absence of hydrological and cryospheric contributions on the reconstructed CW would lead to the unmanifested CW re-excitation phenomenon. Additionally, the relative contributions of the hydrology and cryosphere to CW amplitudes exhibit temporal variability, with ratios of approximately 3 to 1 and 2 to 1 during the GRACE and GFO periods, respectively. These findings improve our understanding of the Earth’s rotational dynamics under climate change in relation to the effects of hydrological and cryospheric processes.
{"title":"Recent disappearing and re-excited Earth’s Chandler wobble: contributions from GRACE/GFO hydrological and cryospheric mass changes","authors":"Qiqi Shi, Yonghong Zhou, Jianli Chen, Xueqing Xu","doi":"10.1007/s00190-025-02021-w","DOIUrl":"https://doi.org/10.1007/s00190-025-02021-w","url":null,"abstract":"Geophysical sources and processes that excite the Earth’s Chandler wobble (CW) have long been debated. Significant discrepancies remain at times between geophysical fluid models, especially regarding inaccurate hydrological and cryospheric estimates, and observed CW series. Recently, the CW experienced anomalous behavior after 2015, with a disappearance and a re-excitation. Understanding hydrological and cryospheric effects on the CW and their contributions to this anomaly requires urgent investigation. Utilizing the Gravity Recovery and Climate Experiment (GRACE) and GRACE Follow-On (GFO) measurements, we reconstruct the CW series contributed from the hydrology and cryosphere for the GRACE period (April 2002 to December 2015) and GFO period (June 2018 to December 2024), respectively. We find that GRACE/GFO measurements can capture more accurate hydrological and cryospheric forcing CW signals than models. For the first time, our reconstructed results successfully account for the recent observed disappearing and re-excited CW phenomenon. Considering global mass conservation associated with barystatic sea-level changes, the GRACE/GFO-derived hydrological and cryospheric effects agree well with geodetic CW observations. The absence of hydrological and cryospheric contributions on the reconstructed CW would lead to the unmanifested CW re-excitation phenomenon. Additionally, the relative contributions of the hydrology and cryosphere to CW amplitudes exhibit temporal variability, with ratios of approximately 3 to 1 and 2 to 1 during the GRACE and GFO periods, respectively. These findings improve our understanding of the Earth’s rotational dynamics under climate change in relation to the effects of hydrological and cryospheric processes.","PeriodicalId":54822,"journal":{"name":"Journal of Geodesy","volume":"14 1","pages":""},"PeriodicalIF":4.4,"publicationDate":"2025-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145611054","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-11-28DOI: 10.1007/s00190-025-02020-x
Hans Daniel Platz
Traditionally, global navigation satellite system (GNSS) observations in precise point positioning were processed using geometric ionosphere-free (GIF) code and phase linear combinations (LC). With multi-frequency observations of modernized GNSS, the processing of undifferenced and uncombined (UDUC) observations has gained popularity, often attributed to its increased flexibility and generality. Building on the theoretical foundation of UDUC processing, this work derives an equivalent LC-based network processing approach that maintains the full generality of the UDUC approach while offering some practical advantages. The approach makes use of the following types of LCs: (1) geometry-free and ionosphere free (GFIF), (2) geometric ionosphere-free (GIF), and (3) ionospheric geometry-free (IGF). When processing the GFIF LCs, biases and ambiguities can be estimated. The GFIF model enables compact modeling by reducing continuous observation arcs to a single observation and supports (extra-) wide-lane ambiguity resolution. To obtain the ionosphere-free model, i.e., an equivalent reformulation of the UDUC approach where epoch-wise and line of sight specific ionospheric delays are assumed, exactly one GIF LC per line-of-sight and epoch is added to the GFIF LCs. To obtain the geometry-free model, commonly used for ionospheric modeling, exactly one IGF LC is added to the GFIF LCs per line-of-sight and epoch. Adding both the GIF and IGF LCs to the GFIF LCs yields an exact reformulation of the UDUC with no implicit assumptions regarding ionospheric or geometric parameters. Finally, a brief runtime analysis of LC-based models shows case-dependent efficiency gains over UDUC implementations.
{"title":"Generalizing linear combination-based GNSS PPP-RTK network processing: geometry-free, ionosphere-free, and geometry- and ionosphere-free","authors":"Hans Daniel Platz","doi":"10.1007/s00190-025-02020-x","DOIUrl":"https://doi.org/10.1007/s00190-025-02020-x","url":null,"abstract":"Traditionally, global navigation satellite system (GNSS) observations in precise point positioning were processed using geometric ionosphere-free (GIF) code and phase linear combinations (LC). With multi-frequency observations of modernized GNSS, the processing of undifferenced and uncombined (UDUC) observations has gained popularity, often attributed to its increased flexibility and generality. Building on the theoretical foundation of UDUC processing, this work derives an equivalent LC-based network processing approach that maintains the full generality of the UDUC approach while offering some practical advantages. The approach makes use of the following types of LCs: (1) geometry-free and ionosphere free (GFIF), (2) geometric ionosphere-free (GIF), and (3) ionospheric geometry-free (IGF). When processing the GFIF LCs, biases and ambiguities can be estimated. The GFIF model enables compact modeling by reducing continuous observation arcs to a single observation and supports (extra-) wide-lane ambiguity resolution. To obtain the ionosphere-free model, i.e., an equivalent reformulation of the UDUC approach where epoch-wise and line of sight specific ionospheric delays are assumed, exactly one GIF LC per line-of-sight and epoch is added to the GFIF LCs. To obtain the geometry-free model, commonly used for ionospheric modeling, exactly one IGF LC is added to the GFIF LCs per line-of-sight and epoch. Adding both the GIF and IGF LCs to the GFIF LCs yields an exact reformulation of the UDUC with no implicit assumptions regarding ionospheric or geometric parameters. Finally, a brief runtime analysis of LC-based models shows case-dependent efficiency gains over UDUC implementations.","PeriodicalId":54822,"journal":{"name":"Journal of Geodesy","volume":"29 1","pages":""},"PeriodicalIF":4.4,"publicationDate":"2025-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145611055","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-11-25DOI: 10.1007/s00190-025-02018-5
Agustín R. Gómez, Claudia N. Tocho, Ezequiel D. Antokoletz, Sergio R. Cimbaro
{"title":"Local quasigeoid modeling at Argentinean stations of the International Height Reference Frame (IHRF)","authors":"Agustín R. Gómez, Claudia N. Tocho, Ezequiel D. Antokoletz, Sergio R. Cimbaro","doi":"10.1007/s00190-025-02018-5","DOIUrl":"https://doi.org/10.1007/s00190-025-02018-5","url":null,"abstract":"","PeriodicalId":54822,"journal":{"name":"Journal of Geodesy","volume":"107 1","pages":""},"PeriodicalIF":4.4,"publicationDate":"2025-11-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145593536","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-11-11DOI: 10.1007/s00190-025-02009-6
Janusz Bogusz, Paul Rebischung, Anna Klos
A comparison of the three-dimensional annual motions of the global Navigation satellite system (GNSS) stations in two different solutions – the latest reprocessing campaign of the International GNSS Service (IGS), and the station position time series provided by the Nevada Geodetic Laboratory (NGL) – reveals large-scale differences with amplitudes of about 1 mm in horizontal and 3 mm in vertical. We show that these differences are largely explained, in the vertical component, by differences between the alignment strategies of both solutions to the terrestrial reference frame. Further comparisons with the annual displacements predicted by a global loading deformation model suggest that true annual station motions are less subject to aliasing, hence better preserved with the IGS alignment strategy. Considering these results, we urge providers of GNSS station position time series to take measures to minimize the aliasing of geophysical station motions that occur when aligning their daily station position estimates to the reference frame and propose different such measures.
{"title":"Impact of alignment strategy to the reference frame on the 3D annual station motions from different GNSS solutions","authors":"Janusz Bogusz, Paul Rebischung, Anna Klos","doi":"10.1007/s00190-025-02009-6","DOIUrl":"https://doi.org/10.1007/s00190-025-02009-6","url":null,"abstract":"A comparison of the three-dimensional annual motions of the global Navigation satellite system (GNSS) stations in two different solutions – the latest reprocessing campaign of the International GNSS Service (IGS), and the station position time series provided by the Nevada Geodetic Laboratory (NGL) – reveals large-scale differences with amplitudes of about 1 mm in horizontal and 3 mm in vertical. We show that these differences are largely explained, in the vertical component, by differences between the alignment strategies of both solutions to the terrestrial reference frame. Further comparisons with the annual displacements predicted by a global loading deformation model suggest that true annual station motions are less subject to aliasing, hence better preserved with the IGS alignment strategy. Considering these results, we urge providers of GNSS station position time series to take measures to minimize the aliasing of geophysical station motions that occur when aligning their daily station position estimates to the reference frame and propose different such measures.","PeriodicalId":54822,"journal":{"name":"Journal of Geodesy","volume":"164 1","pages":""},"PeriodicalIF":4.4,"publicationDate":"2025-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145485567","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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