Journal of Geodesy最新文献

Most present-day bathymetric prediction solely addresses the linear mapping relationship between gravity signals and bathymetric data, disregarding nonlinearity’s effects, despite a probable nonlinear mapping between gravity signals and the seafloor topography. This paper investigates the consequences of excluding nonlinear terms in predicting bathymetry and reaches focused conclusions for different types of seafloor topography. The nonlinear effects were assessed by modelling the gravity signals generated by seafloor topographies with different topographic relief, topographic sizes, and basal depths. The results demonstrate that the nonlinear effect is more pronounced in shallow seas compared to deep seas for the same topographic relief. Furthermore, the consequences of ignoring nonlinear terms become more significant as topographic relief increases and topographic sizes decrease. The experiment on topographic sensitivity demonstrates that nonlinear gravity signals are able to detect small-scale topography more acutely, with higher orders corresponding to smaller sensitive topographic sizes. Using the Emperor seamount chain as an illustrative example, the nonlinear mapping is created by employing the eXtreme Gradient Boosting. The prediction accuracy of bathymetry using gravity anomalies has increased by 13%, whereas the predictive precision through vertical gravity gradient anomalies has risen by 7%. These results confirm the conclusions drawn from the simulation experiment. In addition, the results of the global nonlinear effects indicate that the regions most impacted are situated in the trenches along the plate boundaries, the eastern Pacific, and the Atlantic Ridge. The prediction of bathymetry will benefit from the consideration of nonlinear relationships, particularly for shallow sea and small-scale topography.

Space missions to small bodies like asteroids, comets, and moons rely on physics-based simulations to test guidance and control systems. However, accurately modeling their gravitational fields is challenging due to their highly irregular shapes and limited knowledge of their internal structures, complicating orbit planning and landing maneuvers. This study presents a new approach to model realistic density distributions based on Voxel-shaped mass concentrations. We apply body-specific constraints to three-dimensional Perlin noise, supplemented with normalization and segmentation techniques. Additionally, various structural elements can be incorporated into the density distribution. These include centralized and decentralized shells of different thicknesses and densities, as well as anomalies of varying sizes and shapes. Normalization techniques ensure the body’s total mass conservation. We validate our method by calculating the gravitation of a cube and sphere with constant density and comparing it with its analytical solution. We further compare our method with other mascon approaches and the polyhedral method at different Voxel resolutions and conduct additional performance evaluations of our method using test scenarios with focus on geophysical parameters such as the moments of inertia tensor and the gravity field’s spherical harmonics expansion. Our results demonstrate the method’s ability to account for realistic density distributions and to accurately compute the corresponding gravitational fields and geophysical properties.

Ionospheric sporadic E (Es) layers are thin layers with enhanced ionospheric electron densities (IEDs) which occur frequently in ionospheric E region. Previous detecting method based on ground-based global navigation satellite system (GNSS) observations can only obtain the horizontal maps rather than the vertical distributions and structures of Es layers. This study proposes a computerized ionospheric tomography (CIT) method with constraints from GNSS radio occultation data for the reconstruction of three-dimensional (3-D) structure and evolution of Es layers. The strong Es layers that occurred in Australia on January 11, 2021, and in North America on August 4, 2021, are chosen for reconstruction, and the COSMIC-2 IED profiles in the reconstruction region and its surrounding area are used as constraints in the CIT process. The IED distribution in F region is reconstructed at first by using only slant total electron content (STEC) without significant sudden disturbances, and then the E region contribution to STEC is estimated by subtracting the F region contribution, based on which the 3-D structures of Es layers with high spatial and temporal resolutions are reconstructed consequently. The reconstructed results in F and E regions are assessed separately, which show good consistence with GNSS STEC, global ionospheric maps, or ionosonde observations. The evolution of Es layer structures in the reconstructed region is further analyzed, and the large-scale Es structure spanning over more than 10° in longitude and the movement of Es patches are clearly revealed. Particularly, the reconstruction results successfully trace the vertical variation in the altitudes of Es layers.

GNSS integer ambiguity precision point positioning (IPPP) with satellite integer clock products is currently one of the most precise techniques for time and frequency transfer. However, a challenging issue that hampered the long-term performance of IPPP is the day-boundary discontinuity (DBD) that manifests at UTC (Coordinated Universal Time) midnights during the processing of multi-day GNSS observations. Users’ remedy to eliminate such receiver clock DBDs is to identify the integer offset of ambiguities across days, but residual DBDs could still potentially exceed 100 ps. In this study, we propose an alternative but more efficient approach to eliminate the DBDs of satellite orbit/clock/bias products as an integral, while users would directly achieve receiver clocks without DBDs rather than being troubled to fix them through carrier-phase ambiguity connection. Such a post-processing alignment approach is applicable to IGS satellite integer products processed in daily batches and does not rely on the respective smoothness of orbits or clocks. After application to the rapid multi-GNSS Experiment (MGEX) product at Wuhan University, the residual discontinuities of satellite integer clocks for each GPS/Galileo/BDS-3 satellite typically do not exceed 0.05 cycles of narrow-lane wavelengths. In continuous time and frequency transfer over a 31-day period, DBDs in all nine IPPP time links are smaller than 25 ps with a standard deviation of 10 ps, compared to 60–90 ps for the legacy strategy and unaligned products. This day-boundary alignment approach is suitable for common satellite integer products in the International GNSS Service (IGS) and has been routinely implemented in Wuhan University’s rapid MGEX satellite orbit/clock/bias products since January 1, 2023.

In recent years, the fundamental quantity of the gravitational field has been extended from gravitational potential, gravitational vector, and gravitational gradient tensor to gravitational curvature with its first measurement along the vertical direction in laboratory conditions. Previous studies numerically identified the near-zone and polar-region problems for gravitational curvature of a tesseroid, but these issues remain unresolved. In this contribution, we derive the new third-order central and single-sided difference formulas with one, two, and three arguments using the finite difference method. To solve these near-zone and polar-region problems, we apply a numerical approach combining the conditional split, finite difference, and double exponential rule based on these newly derived third-order difference formulas when the computation point is located below, inside, and outside the tesseroid. Numerical experiments with a spherical shell discretized into tesseroids reveal that the accuracy of gravitational curvature is about 4–8 digits in double precision. Numerical results confirm that when the computation point moves to the surface of the tesseroid, the relative and absolute errors of gravitational curvature do not change much, i.e., the near-zone problem can be adequately solved using the numerical approach in this study. When the latitude of the computation point increases, the relative and absolute errors of gravitational curvature do not increase, which solves the polar-region problem with this stable numerical approach. The provided Fortran codes at https://github.com/xiaoledeng/xtessgc-xqtessgc will help with potential applications for the gravitational field of different celestial bodies in geodesy, geophysics, and planetary sciences.

The paper presents 3D numerical modelling of the altimetry-derived marine gravity data with the high horizontal resolution 1 × 1 arc min. The finite volume method (FVM) as a numerical method is used to solve the altimetry–gravimetry boundary-value problem. Large-scale parallel computations result in the disturbing potential in every finite volume of the discretized 3D computational domain between an ellipsoidal approximation of the Earth’s surface and an upper boundary chosen at altitude of 200 km. Afterwards, the first, second or higher derivatives of the disturbing potential in different directions can be numerically derived using the finite differences. A crucial impact on achieved accuracy has the process of preparing the Dirichlet boundary conditions over oceans/seas. It is based on nonlinear filtering of the geopotential generated on a mean sea surface (MSS) from a GRACE/GOCE-based satellite-only global geopotential model. The paper presents different types of the altimetry-derived marine gravity data obtained on the DTU21_MSS as well as at higher altitudes of the 3D computational domain. The altimetry-derived gravity disturbances on the DTU21_MSS are compared with those from recent datasets like DTU21_GRAV or SS_v31.1. Standard deviations of the residuals are about 2.7 and 2.9 mGal, respectively. The obtained altimetry-derived gravity disturbances at higher altitudes are compared with airborne gravity data from the GRAV-D campaign in US showing accuracy about 3 mGal. In addition, the gravity disturbing gradients as the second derivatives or the third derivatives are provided with the same high resolution on the DTU21_MSS as well as at different altitudes.

In urban canyons or natural valleys, diffraction effect occurs when the signal of Global Navigation Satellite Systems (GNSS) transmits to the edge of obstructions, such as buildings, trees, and slopes, resulting in large diffraction error, which is one of the important error sources in carrier-phase-based precise positioning. However, the theoretical formula derivation and numerical modeling of the diffraction error have been rarely studied. In this study, we derived the theoretical formula of the diffraction error based on the geometrical structure of the signal propagation path in satellite-obstruction-antenna geometry. Then, the diffraction error extraction and modeling method were proposed to study the time-varying characteristics of diffraction error and verify the validity of the theoretical formula of the diffraction error. Based on the GNSS data collected in occlusion environment, a designed experiment was carried out. The results show that the diffraction error generally increases or decreases monotonically, and mostly the amplitude of it could be larger than 50 mm and even reach 200 mm. The time-varying characteristics of diffraction error can be precisely simulated with the vertical and horizontal diffraction formulas developed, and the diffraction error model established could be applied in sidereal filtering method to correct the diffraction error. From the experiment, the fixed rate of ambiguity resolution can be improved from 76.8 to 98.87%, and the positioning reliability is improved from 80 to over 98% with the diffraction correction. The results of this paper provided theoretical basis and experience for the processing of GNSS diffraction error and show the significance in applications of high-precision positioning.

Spectral gravity forward modelling delivers gravitational fields of mass distributions by evaluating Newton’s integral in the spectral domain. We generalize its spherical harmonic variant to 3D variable densities and to any integration radius. The former is achieved by expressing the density function as an infinite-degree polynomial in the radial direction with polynomial coefficients varying laterally as a bounded function. The latter generalization builds on Molodensky’s truncation coefficients and allows to evaluate gravitational contribution of masses found up to and beyond some integration radius. In a numerical study, we forward-model lunar topographic masses by first assuming constant and then 3D variable density. Our validation with respect to GRAIL-based models shows that the 3D density model yields superior gravitational field compared to the constant density model. Thanks to the efficiency of FFT-based spherical harmonic transforms, the new technique can be employed in high-resolution modelling of topographic potentials. A numerical implementation is made available through CHarm, which is a C/Python library for high-degree spherical harmonic transforms accessible at https://github.com/blazej-bucha/charm.

The Surface Water and Ocean Topography (SWOT) altimeter mission provides a significant opportunity to improve the accuracy of geoid gradients (GGs) and marine gravity fields. This paper presents a new method, namely LSA3, to determine the north and east ((xi ) and (eta )) components of GGs from simulated and real SWOT data in the northern South China Sea. To fully use SWOT’s fine-scale sea surface height (SSH) measurements, LSA3 first determines GGs in SWOT along-, cross- and oblique-track directions and constructs a grid for each gradient. Least-squares adjustment (LSA), accounting for correlations of the GGs in three directions, is then employed to point-wisely estimate (xi ) and (eta ) components at grid points. The accuracy of estimated (xi ) and (eta ) components is assessed using those computed by numerical differentiations. For comparison, GG components are also estimated using least-squares collocation (LSC) and weighted LSA (WLSA) methods with empirically determined data window sizes and without accounting for correlations. Simulated results show that LSA3-estimated GG components achieve the root-mean-square deviation (RMSD) values of 0.43 and 0.47 microrad for (xi ) and (eta ), respectively, outperforming LSC (0.82 and 0.86 microrad) and WLSA (0.49 and 0.54 microrad). The results from the real SWOT data indicate that LSA3 is comparable to LSC with a mean RMSD of 1.88 mgal for marine gravity anomalies when compared to shipborne gravity data, but LSA3 is more computationally efficient than LSC. Compared to the Sandwell V32.1 gravity field, SWOT improves gravity accuracy by an average of 12.0%, with a maximum improvement of 44.3% for a single ship trajectory.