This study investigates the post-seismic deformation following the October 30, 2020 MW7.0 Samos earthquake using Copernicus Sentinel-1 Interferometric Synthetic Aperture Radar (InSAR) time series and continuous Global Navigation Satellite System (GNSS) observations spanning more than four years after the main shock. Prior to the post-seismic analysis, a reference co-seismic slip model was derived from co-seismic GNSS offsets within a seismologically constrained finite-fault geometry. Post-seismic deformation is largely confined to Samos Island, with no resolvable signal detected on adjacent islands or along the Turkish coast, indicating a near-field-dominated response. The post-seismic deformation within Samos Island is spatially asymmetric, characterized by sharp displacement gradients in the western and central parts of the island and smoother deformation towards the east. The joint inversion of GNSS and InSAR data indicates that post-seismic deformation is dominated by shallow afterslip concentrated primarily up-dip and laterally adjacent to the co-seismic rupture. Peak cumulative afterslip reaches ∼0.6 m, releasing a post-seismic moment equivalent to approximately 20% of the co-seismic one. The spatial relationship between the co-seismic slip, afterslip, and aftershocks suggests efficient stress release during the main rupture, followed by aseismic afterslip on shallow parts of the fault plane. Localized deviations from the afterslip model, particularly in coastal areas, imply that poroelastic rebound may have contributed secondarily to the post-seismic deformation.
Landslides are destructive geological disasters that can cause heavy casualties and huge economic losses. Global navigation satellite system (GNSS) can provide real-time, continuous, and high-precision three-dimensional deformation information all weather and all time, and thus has been widely used in landslide deformation monitoring. However, the strong multipath effect that exists under the practical observational environment will seriously affect the accuracy and reliability of GNSS real-time landslide monitoring. In this contribution, we aim to evaluate the performance of the multipath hemispherical map (MHM) model for multipath correction in landslide monitoring with GNSS real-time kinematic (RTK) positioning. Both the performance of the single-differenced MHM (SD-MHM) and double-differenced MHM (DD-MHM) models are preliminarily evaluated and compared with two GNSS datasets collected in practical landslide monitoring scenarios. The experimental results verify the spatial repeatability of the multipath error with the DD-MHM and SD-MHM models. It is also demonstrated that both the SD-MHM and DD-MHM models can effectively reduce the impact of low-frequency multipath error and improve RTK positioning accuracy. Moreover, the SD-MHM model outperforms the DD-MHM model. Compared with RTK positioning with no multipath correction (NON-MHM), the root-mean-square (RMS) errors of the phase and code residuals for the SD-MHM model are reduced by approximately 49.4% and 24.4%, respectively, and are reduced by approximately 39.8% and 18.6% for the DD-MHM model, respectively. Moreover, compared with the NON-MHM model, the positioning accuracy of the DD-MHM model is improved by approximately 25.9% and 46.5% in the horizontal and vertical components, respectively, and is further improved by approximately 37.0% and 54.2% with the SD-MHM model, respectively. The results verify the effectiveness of the MHM model in improving the RTK performance in practical GNSS landslide monitoring applications.
Extracting seasonal signals accurately from Global Navigation Satellite System (GNSS) coordinate time series is essential for investigating geophysical processes such as crustal deformation and plate motion. The coexistence of time-varying periodic signals and colored noise with fluctuating amplitudes significantly complicates this task, rendering flexible and robust methods imperative. Leveraging the low-rank property of the Hankel matrix constructed from noise-free signals, this paper proposes a Truncated Reweighted Nuclear Norm Minimization (TRNM) method for reconstructing GNSS coordinate time series. TRNM integrates truncation and reweighting strategies to better approximate the rank of the original matrix, and employs a modified Accelerated Proximal Gradient (APG) technique incorporating an adaptive momentum updating criterion and Reweighting Singular Value Thresholding (RSVT) to reduce computational cost induced by full SVD. Simulation experiments and real data analysis are conducted by comparing TRNM with five State Of The Art (SOTA) methods. It is observed that TRNM performs as well as the SOTA methods for low noise level condition while outperforms the compared methods for high noise level condition with respect to residual spectral index, residual amplitude, Trend Uncertainty (TU), and misfit. Moreover, TRNM demonstrates the minimal deviation of TU from theoretical values across all evaluation metrics for missing rates ranging from 0.1 to 0.5 or data length increasing from 1000 to 6000 days, while keeping nearly the smallest misfit value, without requiring data interpolation. Finally, real GNSS time series experiments show that the residual analysis results are consistent with those obtained by simulation experiments, and TRNM exhibits robustness against noise with varying levels. Therefore, this paper proposes a competitive and robust method for reconstructing GNSS coordinate time series.
We use the hydrological model WaterGAP v2.2e in the range of 1901–2019, incorporating climate forcings and direct human impacts to calculate the hydrologically-induced perturbations in the Earth’s axial moment of inertia and rotation rate of the mantle, thereby deriving deviations in Length of Day (ΔLOD) from the nominal value of 86,400 s. This study presents 10 individual components of this Terrestrial Water Storage (TWS), namely, water storage in canopies, snow, soil, groundwater, local lakes, global lakes, local wetlands, global wetlands, reservoirs, and rivers. The changes in snowfall patterns and melting of glaciers under climate change, groundwater usage due to direct human influence, as well as impoundment of reservoirs, are the three most important long-term contributors, exhibiting trends as large as 0.19 ms per century. However, the results show that this trend differs from that derived from satellite gravity measurements, revealing a missing contribution from the polar ice sheets. We demonstrate that the estimates are consistent with an independent data series generated by the German Research Center for Geosciences during 1976–2019. In addition, by comparing the results with the observed ΔLOD from space geodesy, we explain a considerable portion of this observed signal on seasonal to interannual timescales, although the agreement is incomplete (about 37%). The results provide daily hydrological excitations of ΔLOD, extending the temporal range of the currently available excitation series to the early 20th century and including individual contributors to TWS under climate change and direct human influence. This proves useful in better constraining other important contributors to ΔLOD, particularly the core dynamics.
Achieving centimeter-level or higher-precision vertical datum unification is pivotal for addressing both scientific and societal needs. This study presents a preliminary vertical datums unification in Chinese mainland, Hong Kong, and Taiwan of China. Leveraging the classical theory of physical geodesy, the geopotential values and vertical datum offsets are derived. Gravity field models and the residual terrain model (RTM) are integrated to generate refined Global Geopotential Models (GGMs), which capture high-precision medium-to-long wavelength signals and preserve short-wavelength signals from topography. Numerical comparison results demonstrate that the refined EIGEN-6C4_RTM model shows superior consistency with GNSS/leveling verification data, exhibiting excellent (quasi-)geoid accuracy with standard deviations (STDs) of 7.4 cm in Shandong, 5.7 cm in Taiwan region, and 3.0 cm in Hong Kong. The zero-height geopotential values of Chinese mainland, Taiwan region, Hong Kong were obtained by combining GNSS/levelling data and the EIGEN-6C4_RTM model. The estimated values are 62636853.05 m2s-2 for the National Vertical Datum 1985 (NVD1985), 62636850.43 m2s-2 for the Taiwan Vertical Datum 2001 (TWVD2001), and 62653860.22 m2s-2 for the Hong Kong Principal Datum (HKPD). The resulting vertical datum offsets indicate that NVD1985 is approximately 26.7 ± 9.3 cm lower than TWVD2001, approximately 73.3 ± 8.0 cm higher than HKPD, and TWVD2001 is approximately 100.0 ± 6.4 cm higher than HKPD. These results suggest that the refined GGMs enable the unification of vertical datums with few-centimeter-level precision, underscoring their significant potential for contributing to the implementation of the International Height Reference System (IHRS).
The Kongur Extensional System (KES) plays a crucial role in accommodating regional crustal deformation of the northeastern Pamir, where sparse geodetic observations limit detailed kinematic characterization. Herein, we constructed a high-resolution 3D velocity field by integrating Sentinel-1 Interferometric Synthetic Aperture Radar (InSAR) and Global Navigation Satellite System (GNSS) data. Using a Bayesian inversion approach on ten profiles across the KES, we derived the segmented geometric and kinematic characteristics along the main fault. Our results reveal the ongoing uplift and inhomogeneous deformation on the northeastern Pamir. The E-W-trending Muji Fault (MF) exhibits a dextral strike-slip rate of about 7.6–10.8 mm/yr with a shallow locking depth (about 5 km), consistent with the unruptured zone of the 2016 Aketao earthquake. The present-day crustal deformations on the other segments of the KES are dominated by normal faulting, with relatively high extension rates (about 5.3–7.6 mm/yr) on the northern part of the fault and comparatively low (about 3 mm/yr) on the southern segments, exhibiting a progressive southward decay. Furthermore, the South Kungai Shan Fault represents a potential seismic gap, with an accumulated seismic moment equivalent to an earthquake of about MW7.0, highlighting the regional seismic hazard. Our findings provide new geodetic evidence for the limited effect of gravitational collapse on the northeastern Pamir. Rather, the formation and evolution of the KES are more likely driven by large-scale asymmetric radial thrusting beneath the Pamir Plateau in the context of the long-lasting India-Eurasia collision.
Landslide hazards occur frequently in the Three Gorges Reservoir Region. Therefore, landslide susceptibility assessment is of great importance for hazard identification and risk control. Traditional assessment methods that rely only on static environmental factors cannot fully reflect recent slope activity. This study focused on the Zigui to Yiling section of the Three Gorges Reservoir area. It used the SBAS-InSAR technique to obtain surface deformation information from 2021 to 2024. PCC, VIF, TOL, and IGR were then used to select nine conditioning factors. Based on these factors, CNN, SVM, and RF models were constructed for landslide susceptibility assessment. On this basis, InSAR deformation information was further incorporated into the assessment. The results showed that most deformation rates in the study area fell within the range of -10 to 10 mm/a, while strong deformation was mainly distributed along the riverbanks in Zigui County and in its mountainous areas. Analysis of typical reservoir bank areas showed that slope deformation became significantly stronger during periods of rapid reservoir water level fluctuation. When the monthly rise rate of the reservoir water level reached its maximum, the deformation rates at the three representative points all reached their peak values. Among the three models, the CNN model performed best, with an AUC of 87.1%, which was higher than those of SVM (86.0%) and RF (86.7%). The very high susceptibility zones were mainly distributed along the riverbanks in Zigui County, in the mountainous area of southwestern Zigui County, and in central Yiling District. After InSAR deformation information was incorporated, the very high susceptibility zones became more concentrated in slopes with stronger deformation, while some relatively stable areas were adjusted to lower susceptibility levels. These results provide support for landslide monitoring, risk identification, and field investigation in the reservoir area.
In recent years, precise point positioning (PPP) technology has undergone rapid development. In particular, since the International GNSS Service (IGS) began providing multi-system real-time products, real-time PPP has been widely applied in areas such as displacement monitoring, atmospheric sounding, and geodetic surveying. Although real-time products generally demonstrate stable performance and meet application requirements under most conditions, anomalies in the real-time product are inevitable. These anomalies include low product availability, degraded accuracy, and even abnormal results. Currently, several IGS analysis centers provide real-time products; however, none of them include corresponding integrity information. In this study, we first developed a real-time PPP augmentation service, which utilizes globally distributed tracking stations to determine satellite orbits, clocks, and uncalibrated phase delays (UPDs). Furthermore, this study provides a detailed analysis of integrity information, such as quality indicators (QI) for each system based on characterization of phase residuals. Finally, validation of the real-time PPP augmentation system using 24 globally distributed stations demonstrates average positioning accuracies of 0.012 m, 0.014 m, and 0.031 m in the North, East, and Height components, respectively, with an average convergence time of 129 s and a wrong-fix rate of 2.225%. The results indicate that under nominal service conditions, integrity information has minimal impact on positioning accuracy, though it slightly reduces the probability of wrong-fix rate and the time-to-first-fix (TTFF). However, during satellite orbital maneuvers or periods of degraded accuracy and anomalies, QI significantly enhances both positioning precision and solution reliability.
Following the Wenchuan MS8.0 earthquake, numerous studies have sought to determine the sliding friction coefficient of the Longmenshan fault (LMSF) zone. However, results have varied widely (0.02–0.61), deviating significantly from traditional understandings (0.6–0.85). As a critical parameter governing fault strength, the sliding friction coefficient influences coseismic stress drop and the recurrence interval of large earthquakes. To better constrain this coefficient, we constructed a two-dimensional finite-element contact model extending 300 km in length and 104 km in depth that includes the LMSF. Constrained by GPS observations, we controlled fault activity using static and dynamic friction constitutive relations, and conducted multiple numerical simulations by assigning different sliding friction coefficients to the fault to simulate regional deformation and the recurrence of strong earthquakes. Comparison between the simulation results and observational data, along with lateral comparisons across different simulation results, allowed us to constrain the sliding friction coefficient of the LMSF. The main conclusions are as follows: the LMSF exhibits a relatively low sliding friction coefficient around 0.08. The recurrence interval for magnitude 8.0 earthquakes on the LMSF is approximately 5,460 ± 130 years. Coseismic shear stress drop is a key factor in controlling the spatial distribution of mainshocks and aftershocks. Additionally, the rapid uplift along the eastern Qinghai-Xizang Plateau is likely driven by upper mantle creep beneath the Songpan–Garzê block.
Benefiting from significant advances in modern geodetic technologies, Global Navigation Satellite System (GNSS) measurements provide a new means to quantify terrestrial water storage (TWS) and to reveal hydrological-climate interaction mechanisms. This study integrates observational data from GNSS and Interferometric Synthetic Aperture Radar (InSAR), two advanced geodetic techniques, to jointly invert TWS variations in coastal Texas. The results reveal the spatiotemporal fluctuations of TWS and their linkage with large-scale drought and climate processes. Comparisons with GLDAS hydrological model outputs, GRACE-derived gravity solutions, and precipitation observations demonstrate strong consistency, while highlighting the higher spatial resolution and improved sensitivity of the joint inversion approach to local hydrological changes. The correlation coefficient between the TWS derived from the joint inversion of GNSS and InSAR and GRACE-EWH is 0.857, which is slightly higher than the value of 0.825 obtained with GLDAS-EWH. Our findings indicate pronounced seasonal variations in TWS across the study area and highlight the significant impact of drought events on regional hydrological conditions. By incorporating multi-source drought severity index (DSI) data, we further quantify wet and dry conditions, which align well with precipitation anomalies. These results provide a reliable observation and analysis framework for refined monitoring of coastal water cycle dynamics and for advancing the understanding of hydrological-climate interactions.
Waveform clipping, sensor tilting, and saturation in traditional seismic data often lead to systematic underestimation in rapid magnitude estimation for strong earthquakes. High-rate Global Navigation Satellite Systems (GNSS) offer an effective alternative by capturing coseismic displacements without being affected by these issues. However, in tectonically complex regions such as the Qinghai-Xizang Plateau, the scarcity of observational data limits the application of data-driven methods. In this study, we constructed 4200 rupture scenarios ranging from MW5.37 to MW8.06 and generated 617,400 three-component waveforms with realistic noise to simulate magnitude variations in northeastern Xizang. Based on this dataset, we developed a deep learning network framework combining dense layers and Long Short-Term Memory (LSTM) for time-evolving magnitude estimation. Validation on the synthetic test set showed that the percentages of predictions within the ±0.3 magnitude tolerance reached 95.7%, 96.6%, and 97.4% at 32 s, 64 s, and 128 s, respectively, with a mean absolute error of 0.103 at 128 s. Sensitivity tests based on station distribution further indicate that the model can reliably estimate magnitudes even with only four stations or uneven station distributions. Ablation experiments confirmed that the LSTM captures temporal dependencies, whereas the dropout layer enhances model stability. Compared with empirical PGD scaling laws and the CNN-based model, the proposed framework provides faster convergence, improved temporal stability, and reduced early-stage underestimation. Retrospective tests using the strike-slip (2022 MW6.6 Menyuan and 2021 MW7.4 Maduo) and thrust (2013 MW6.6 Lushan) earthquakes further confirm the robustness and generalization capability of the proposed framework under different tectonic environments and faulting styles. These results demonstrate that the proposed framework provides a practical and robust approach for high-rate GNSS-based earthquake early warning in tectonically complex active continental regions.
We study the western North Patagonian region of Argentina using gravity and geological methods. The first derivative of the Bouguer anomaly shows a gravity high west of the Limay River and Arroyo Comallo, forming a semicircular pattern, all linked to the Devonian Colohuincul Complex and older rocks. In contrast, the gravity lows are due to Permian granites, Jurassic volcanic rocks, and Jurassic and Cretaceous sedimentary rocks of the Neuquén Basin, with the latter reaching a thickness of 2 km but restricted to the northern part of the area. We identified five groups of geological and Euler lineaments, some possibly formed in the Devonian, with episodic movements during the Permian and Jurassic, and connected to the Limay Fault Zone. Between 257 and 250 Ma, a second group linked to strike-slip regional faults helped form the volcanically derived Los Menucos and Laguna Blanca complexes. From 191 to 187 Ma, the third system of lineaments, marked by rift structures and volcanic calderas and associated with the second rifting episode in the Neuquén basin, was active in the region. The development of pull-apart basins associated with strike-slip faults occurred between 192 and 185 Ma, representing the fourth group. The last group comprises several fault- and curved-acidic-dike swarms, dated at 188 Ma and 187 Ma, and extensional fractures related to dextral movement of the Limay Fault Zone. The Río Limay and Arroyo Comallo between the Piedra del Águila and Comallo localities form the dextral strike-slip Limay fault zone, potentially marking the boundary between the North Patagonian region and the Neuquén Basin.
The deflection of the vertical (DOV) reflects the discrepancy between the Earth's actual gravity field and reference models (e.g., WGS84, GRS80). The Chinese mainland exhibits highly complex topography and geomorphology, active crustal deformation, and pronounced spatial heterogeneity in the gravity field, creating an urgent need for large-scale, high-precision analyses of DOV to deepen understanding of regional gravity-field characteristics. We utilize long-term GRACE satellite data, together with the XGM_2019e static gravity model and GRACE RL06 time-varying data, to compute the meridional and prime-vertical components of the DOV (including the contribution of water mass variations) for the period 2002 to 2016 at 3328 grid points across the Chinese mainland. The results show larger DOV variations in western China (±10″) and smaller variations in the eastern region (0–5″), with opposite trends in the meridional and prime vertical components in the east. Three regions with anomalous DOV variations were identified: the Ordos-Taihang Mountains, the Sichuan-Yunnan region, and the Yadong-Gulu fault zone. By constructing an absolute DOV model and comparing it with the GPS velocity field in the corresponding region, the relationships among DOV, geoid morphology, and regional tectonic motions are revealed.
The 2025 Balıkesir earthquake sequence in western Turkey, consisting of an MW6.1 event on 10 August and an MW6.0 event on 27 October, occurred within an extensional transition zone between the southern Marmara region and western Anatolia. To investigate the rupture characteristics, seismogenic structure, and earthquake interaction of this sequence, we integrate Sentinel-1 InSAR coseismic deformation, geodetic fault-slip inversion, aftershock relocation, shallow slip-deficit (SSD) analysis, Coulomb stress modeling, and regional strain-rate constraints. The August earthquake was characterized by a compact rupture patch with a peak slip of ∼1.5 m, concentrated mainly at 8–10 km depth, whereas the October event showed a broader, more distributed rupture pattern with a peak slip of ∼1.4 m and principal slip concentrated at 10–12 km depth. Inversions based on the preferred fault planes also fit the observed deformation better than alternative nodal-plane solutions. Relocated aftershocks and slip models together indicate that both coseismic rupture and subsequent seismicity were mainly confined to a vertically limited seismogenic layer in the middle upper crust. SSD estimates show strongly reduced shallow slip for both events, reaching 93% and 87% within the upper 3 km, implying inefficient upward rupture propagation and possible rheological weakening in the shallow crust. Coulomb stress modeling further suggests that stress interaction within the sequence was depth-dependent, and that static stress loading likely contributed to failure in the shallow-to-intermediate seismogenic layer. Regional strain-rate results indicate that the source area is situated in an actively deforming extensional to transtensional setting. Overall, the Balıkesir sequence highlights the importance of depth-dependent rupture behavior, shallow rheological effects, and nonuniform stress interaction in controlling moderate earthquake sequences in continental extensional transition zones, with implications for seismic hazard assessment in western Anatolia.
Terrestrial Water Storage (TWS) represents all sources of water on land, including polar ice sheets (Greenland and Antarctica), mountain glaciers, and hydrological components. Understanding the spatio-temporal evolution of TWS and the sea-level change remains a challenge in climate science, but is important in a variety of domains, including water resource management and sea-level rise in coastal areas. Machine learning has recently emerged as a viable technique for analyzing and predicting TWS. However, these models often lack interpretability, ignore uncertainty quantification, and are useful mainly for short-term prediction horizons of up to 1 year. Our study sets itself apart from previous attempts by presenting a novel probabilistic Physics-Informed Neural Networks (PINNs) methodology to (i) incorporate the physics of continental-ocean mass redistribution, (ii) quantify prediction uncertainty, and (iii) extend the prediction horizon of TWS to decadal (10-year) timescales. We present numerical experiments in the range 1900–2024 to show that our predictions are consistent with satellite gravimetry observations and improve on the projections of climate models by up to 42%, particularly for mountain glaciers. Furthermore, the predicted sea-level change agrees with the independent observations by satellite altimetry during 2003–2024, both in terms of fluctuations and the long-term trend within 0.1 mm/yr. These findings can advance our understanding of the spatio-temporal evolution of TWS and the corresponding sea-level change, both of which are of significant societal relevance.
Nonlinear and non-stationary noise is a major cause of instability in GNSS coordinate time series velocity estimation. Effectively reducing noise in the time series is crucial to improving the accuracy of velocity estimation accuracy. To effectively remove noise from time series, this paper proposes a combined denoising model, ICEEMDAN-TCN, which integrates improved complete ensemble empirical mode decomposition with adaptive noise (ICEEMDAN), multiscale permutation entropy (MPE), and temporal convolutional network (TCN). The study selects vertical coordinate time series from 394 stations across Chinese mainland for experimental verification and compares the results with ICEEMDAN, wavelet domain denoising (WD) and ICEEMDAN-WD methods. The results show that, whether using the unified optimal noise model or the evaluated optimal noise model for velocity estimation before and after denoising, ICEEMDAN-TCN outperforms ICEEMDAN, WD, and ICEEMDAN-WD in noise suppression, with an average suppression rate exceeding 90%. When the optimal noise model is used, both WD and ICEEMDAN-WD suppress noise but also increase velocity uncertainty, indicating over-denoising. In contrast, the proposed ICEEMDAN-TCN does not exhibit such issues.
Historically affected by land subsidence resulting from excessive groundwater withdrawal, the Dezhou region is currently experiencing a significant hydrological transition following the implementation of the South-to-North Water Diversion Project. This study retrieves Groundwater Storage (GWS) variations from April 2002 to June 2025 using data from the Gravity Recovery and Climate Experiment (GRACE)/GRACE-FO missions and the Global Land Data Assimilation System (GLDAS), and validates them against in-situ well observations. Concurrently, vertical surface deformation from 2020 to 2025 is monitored using Small Baseline Subset Interferometric Synthetic Aperture Radar (SBAS-InSAR). Time-Varying Set Pair Potential (SPP) theory is integrated with the Load-Unload Response Ratio (LURR) to assess the stability and integrity of the soil structure. Furthermore, cross-correlation techniques are employed to quantify the hysteresis effect between groundwater changes and surface deformation. Results show that GWS exhibited three distinct phases: “fluctuating rise, continuous deficit, and rapid recovery.” Following a peak deficit in May 2021, GWS recovered at a rate of 4.46 mm/month. Surface deformation exhibits significant spatial heterogeneity: Qihe and Wucheng remain the primary subsidence bowls (with a maximum cumulative subsidence of approximately 150 mm), whereas Pingyuan and Xiajin exhibit uplift (with a maximum uplift of approximately 53 mm). Mechanistically, LURR anomalies observed between 2021 and 2022 indicated plastic deformation; however, post-2024 data suggest a gradual recovery of elastic energy, despite persistent risks in deep geothermal extraction zones. Hysteresis analysis reveals distinct variability: shallow sandy soils respond rapidly (lag <30 days), while deep clay layers exhibit lag times concentrated between 150 and 250 days. These findings quantify surface response mechanisms under groundwater recharge conditions, providing a theoretical basis for subsidence prediction.
The determination of the short-wavelength components of the Earth’s gravity field is crucial for regional quasigeoid modeling within the remove-compute-restore (RCR) framework. Residual terrain modeling (RTM) estimates these high-frequency signals by calculating the gravitational effects of masses between the topography/bathymetry and a smoother reference, referred to as the RTM surface. This study evaluates two RTM approaches for quasigeoid modeling in five regions surrounding the Argentinean stations of the International Height Reference Frame (IHRF). The first approach, named classical (CL), is based on numerical integration with an RTM surface derived from a moving-average operator applied to the SRTM v4.1 and SRTM15+ v2.5.5 models. The second approach, denoted spectral (SP), employs a spherical harmonic representation of the topographic gravity field based on dV_ELL_Earth 2014 and numerically-integrated RTM effects from ERTM2160. Both approaches are used along with the XGM2019e global geopotential model (GGM) at four truncation degrees. Height anomalies are computed from residual gravity anomalies by employing the Molodensky integral with a Wong–Gore kernel modification. The results show that the SP approach yields residual gravity anomalies up to 75% smoother than the CL approach and reduces the GGM truncation ringing effects. The models' agreement with GNSS/leveling data shows an improvement of up to 0.04 m between the lowest and highest truncation degrees. The highest estimated precisions range from 0.165 m in regions with more complex topography down to 0.052 m in flat areas. Overall, the SP approach has a comparable or slightly higher performance than the CL approach.
Sumatra Island is an active subduction margin controlled by the subduction of the Indo-Australian Plate beneath Sundaland, oblique deformation, and the activity of the Great Sumatran Fault; thus, it is an important region for examining regional crustal structure. This study aims to determine the three-dimensional Moho topography beneath Sumatra using the cross-gravity gradient components from the GOCE satellite, namely Γxy, Γxz, and Γyz. The approach used was the Vening Meinesz–Moritz isostatic inversion with Tikhonov regularization, while the regularization parameter was selected using the L-curve method. Each component was inverted separately to produce the Mxy, Mxz, and Myz models, then combined into a multi-component model Mxyz. The results showed that all cross-gradient components displayed a regional northwest–southeast pattern aligned with the physiographic orientation and tectonic framework of Sumatra. The Moho models from the inversion showed similar regional geometry, but the combined Mxyz model provided the most stable solution with a depth range of 27.1–46.9 km. Spatially, the Moho was relatively shallower in the oceanic forearc domain to the southwest and became deeper beneath the main landmass of Sumatra, especially in North Sumatra, West Sumatra, South Sumatra, Bengkulu, and Lampung. Compared with the reference model, all GOCE-based models tended to produce a deeper Moho, but Mxyz showed the smallest residual distribution with a standard deviation of 7.05 km and an RMS of 11.85 km. Spectral analysis also showed that Mxyz best preserved the regional signal while suppressing extreme local fluctuations. These results confirm that GOCE cross-gravity gradients are effective for reconstructing the regional Moho topography and revealing crustal segmentation beneath Sumatra.
Gravity gradients are important for underwater navigation, seafloor topography inversion, and submarine geological investigation. In this study, a global marine full-tensor gravity gradient model, named GMGGD1, is derived using a differential method based on deflection of the vertical and gravity anomaly products incorporating Surface Water and Ocean Topography (SWOT) satellite altimetry observations. The reliability and consistency of GMGGD1, and the contribution of SWOT data are evaluated through comparisons with existing gravity-gradient products and ultra-high-degree gravity field models. The mean and standard deviation (STD) of the differences between the vertical gravity gradient component of GMGGD1 and SIO curv_SWOT_03 are approximately 0.05 E and 1.47 E, respectively. Comparisons with SGG-UGM-2 show that the absolute mean differences of all components are smaller than 0.01 E, with STDs below 8.0 E, and larger differences occur mainly in regions with sharp seafloor topographic variations, such as trenches and seamount chains. Further comparisons with CUGB2023GRAD, GMGG1, and GMGGD-V32 indicate that GMGGD1 shows good overall consistency while exhibiting stronger short-wavelength signals. In particular, compared to GMGGD-V32, which was derived without using SWOT observations, GMGGD1 displays significantly stronger signals at wavelength shorter than 20 km, highlighting the contribution of SWOT observations.
