Journal of Geodesy最新文献

Accurate orientation of geodetic instruments is fundamental for understanding deformation processes within the Earth's interior. Misalignment can lead to significant errors in data interpretation, affecting various geophysical applications. However, accurate alignment of standalone instruments like seismometers, strainmeters and tiltmeters remains a challenge in field geodesy. While numerous seismic-wave-based orientation methods have been successfully applied to seismometers, they are often inapplicable to tiltmeters due to their high-frequency filtering behavior and the requirement for a neighboring, pre-oriented instrument. In response to these challenges, we propose a novel orientation calibration method for borehole tiltmeters based on maximizing the correlation between recorded tilt data and theoretical tides by adjusting azimuthal angles. Our study encompasses two kinds of borehole tiltmeters and four datasets from three different field sites. Using solid and ocean tides modeling together with local topography and cavity disturbances, we obtain coefficient correlations ranging between 0.831 and 0.963, and 95% confidence intervals of azimuthal angles below 3.3°. The correlation-based method demonstrates robustness across various tidal-signal extraction techniques, including different averaging window sizes and band-pass filters. Moreover, it yields azimuthal results in agreement with direct compass measurements for known orientations, while exhibiting a moderate sensitivity to factors such as ocean tides and site-specific topography for the studied cases. This method appears to be advantageous when direct measurements are either unavailable or challenging, and emerges as an accurate tool for determining borehole tiltmeter orientation. Its potential applicability may extend beyond tiltmeters to other instruments that can also record tidal phenomena, such as strainmeters and broadband seismometers. Additionally, its utility could be extended to environments like the seafloor, in order to refine the precision of azimuthal angle estimation and simplify methods for azimuthal angle determination.

The combination of satellite laser ranging (SLR) observations to various low earth orbit (LEO) satellites can enhance the accuracy and robustness of SLR-derived geodetic parameters, benefiting the realization of the International terrestrial reference frames. Observation stochastic models play a critical role in the integrated processing of SLR observations to multiple LEO satellites. The consideration of precision in heterogeneous SLR observations from various satellites is essential. In this study, we aim to improve the combination of multi-LEO SLR observations for geodetic parameters determination by optimizing the stochastic model using variance component estimation (VCE). We perform weekly estimates of the geodetic parameters, including station coordinates, Earth rotation parameters, and geocenter coordinates (GCC), using three years of SLR observations to seven LEO satellites at different orbits. The satellite-dependent, station-dependent, and satellite–station-dependent variance components are separately estimated through VCE processing to refine the stochastic models. Given the fact that the precision of SLR observations significantly differs in satellites and stations, the multiple LEO combination can be significantly improved with the implementation of VCE. Satellite–station-pair-dependent variance components are more suitable to the SLR VCE and the accuracy of station coordinates, pole coordinates, and length of day can be averagely improved by 8.4, 22.6, and 21.9%, respectively, compared to the equal-weight solution. Our result also indicates that the observation insufficiency for some stations may result in an unreliable VCE estimation, and eventually leads to an accuracy degradation for station coordinates. To overcome this deficiency, we adopt the variance components derived from the monthly solutions to build the stochastic model in the weekly solutions. The application of monthly weights can effectively mitigate the accuracy deterioration of station coordinates, improving the repeatability of the station coordinates by 15.9, 14.6, and 9.2% with respect to the equal-weight solution in E, N, and U components. The global geodetic parameters also benefit from this processing. The import of monthly weight decreases the outliers in the GCC series, especially in the X and Y components.

In the geocenter motion determination using the Global Navigation Satellite Systems (GNSS), satellite clock offsets are usually estimated as white noise process. The correlation between geocenter coordinates (GCC) and the epoch-wise satellite clocks brings inferior GCC estimates, especially for the Z component. In this contribution, satellite clock offsets are described by the polynomial model, and the deviation of the model from the truth is estimated as a random parameter whose process noise is described by the variogram. Based on 3.7 years of BDS, Galileo and GPS observations from 98 global stations, we investigate the impact of the atomic clock model on GCC estimates. After employing the proposed model, the formal errors of GCC-Z component are reduced by 23–46%, 15–31% and 3–9% for BDS, Galileo and GPS, respectively. When the 7-parameter extended empirical CODE orbit model with the a priori box-wing model (BE7) is used, the atomic clock model reduces the correlation of the B_1C parameter and GCC-Z component by 0.28, 0.23 and 0.07 for BDS, Galileo and GPS, respectively. Besides, a mitigation of about 60% is obtained at the 3rd and 5th BDS draconitic harmonics and a mitigation of 55% at the 3rd Galileo draconitic harmonic for the GCC-Z component. The proposed model also contributes to reduce the annual amplitudes of single BDS, Galileo and GPS solutions, improving the agreement with the Satellite Laser Ranging solutions. As an additional verification, the resulting satellite orbits are also improved by satellite clock modeling. When the BE7 model is applied, the day boundary discontinuities of daily orbits are reduced by 3.4–3.6%, and the RMS of orbit differences relative to the ESA precise orbits is reduced by 8.2–8.5% for BDS and Galileo.

We perform a statistical sensitivity analysis on a parametric fit to vertical daily displacement time series of 244 European Permanent GNSS stations, with a focus on linear vertical land motion (VLM), i.e., station velocity. We compare two independent corrections to the raw (uncorrected) observed displacements. The first correction is physical and accounts for non-tidal atmospheric, non-tidal oceanic and hydrological loading displacements, while the second approach is an empirical correction for the common-mode errors. For the uncorrected case, we show that combining power-law and white noise stochastic models with autoregressive models yields adequate noise approximations. With this as a realistic baseline, we report improvement rates of about 14% to 24% in station velocity sensitivity, after corrections are applied. We analyze the choice of the stochastic models in detail and outline potential discrepancies between the GNSS-observed displacements and those predicted by the loading models. Furthermore, we apply restricted maximum likelihood estimation (RMLE), to remove low-frequency noise biases, which yields more reliable velocity uncertainty estimates. RMLE reveals that for a number of stations noise is best modeled by a combination of random walk, flicker noise, and white noise. The sensitivity analysis yields minimum detectable VLM parameters (linear velocities, seasonal periodic motions, and offsets), which are of interest for geophysical applications of GNSS, such as tectonic or hydrological studies.

In this paper, we propose a solution of designing a topside broadcast ionospheric model to enable the future low earth orbit (LEO) navigation augmentation (LEO-NA) services. Considering the lack of global station observations to develop the LEO-NA ionosphere model, we utilize abundant global navigation satellite system (GNSS) data from LEO satellites to determine the topside global broadcast ionospheric delay. This delay can be combined with existing GNSS broadcast ionospheric delay correction models to determine LEO-NA ionospheric delay. First, the performance of the different-order spherical harmonic (SH) model is evaluated in generating a global topside ionospheric map. The results indicate that by increasing the order from 1 to 2, the internal and external accuracy of the model improves significantly. However, increasing the order from 2 to 8 leads to a decrease in accuracy of 0.10 and 0.11 TECU (total electron content unit) for the internal and external root mean square error. Taking into account compatibility with the Beidou global ionospheric delay correction model, limited data capacity in the navigation message, ionospheric model accuracy, and computational efficiency, we select the second-order SH model as the topside ionosphere broadcast model and outline the strategy for calculating broadcast coefficients. Finally, the accuracy of the topside global broadcast ionospheric delay correction model is evaluated during periods of high and low solar activity. The mean values of root mean square in 2009 and 2014 are 1.49 and 1.88 TECU, respectively. The model in 2009 and 2014 can correct for 67.30% and 72.49% of the ionospheric delay, respectively.

Abstract

The strong noise of satellite-based Time-Variable Gravity (TVG) field is often suppressed by applying the averaging filters. However, how to appropriately compromise the data blurring and de-noising remains as a challenge. In our hypothesis, the optimum spatial averaging filter expects to contain averaging kernels that capture the same amount of orbital samples everywhere, to avoid introducing excessive data blurring. To achieve the goal, we take advantages of the spherical convolution and introduce extra spatial constraints into a Gaussian kernel: (1) its half-width radius adapts to the global inhomogeneity of satellite orbit, and (2) the kernel is reshaped as an ellipsoid to adapt to the regional anisotropy. In this way, we designed optimal filters that contain a spatially-Varying non-isotropic Gaussian-based Convolution (VGC) kernel. The VGC-based filter is compared against three most popular filters through real TVG fields and another closed-loop simulation. In both scenarios, VGC-based filters retain more realistic secular trend and seasonal characteristics, in particular at high latitudes. The spatial correlation between the VGC estimates and the simulated ground truth is found to be 0.95 and 0.86 over Greenland and Antarctica, which is found to be 10% better than other tested filters. Temporal correlations with the ground truth are also found to be considerably better than the other filters over 90% of the globally distributed river basin. Besides, the VGC-based filters provide tolerable efficiency (3.5 s per month) and sufficient accuracy (integral error less than 3%). The method can be extended to the next generation gravity mission as well.

Plain Language Summary

Time-Variable Gravity (TVG) fields of the Gravity Recovery and Climate Experiment (GRACE) and its Follow-On mission (GRACE-FO) need proper filtering to suppress the noise before being applied for intended geophysical studies. Existing filters are generally designed in the spectral domain. Though they are numerically efficient, they can hardly treat the noise in fairness, globally. As a result, the TVG fields may get over-smoothed after applying those filters, particularly in regions with high-latitudes. However, it would be mathematically simple to design a filter by applying a spherical convolution, whose kernels can be easily constrained and tuned in the spatial domain. This study introduces filters with spatially-Varying non-isotropic Gaussian-based Convolution kernel (VGC) that is enforced to comply with the spatial distribution of the TVG noise. The proposed filter is found to preserve a finer spatial resolution of TVG fields, and at the same time, to be able to de-noise them at a comparable level as the existing techniques. Geophysical applications that use GRACE-like TVG fields might have benefits from this practical filtering technique.

For decades, the residual terrain model (RTM) concept (Forsberg and Tscherning in J Geophys Res Solid Earth 86(B9):7843–7854, https://doi.org/10.1029/JB086iB09p07843, 1981) has been widely used in regional quasigeoid modeling. In the commonly used remove-compute-restore (RCR) framework, RTM provides a topographic reduction commensurate with the spectral resolution of global geopotential models. This is usually achieved by utilizing a long-wavelength (smooth) topography model known as reference topography. For computation points in valleys this neccessitates a harmonic correction (HC) which has been treated in several publications, but mainly with focus on gravity. The HC for the height anomaly only recently attracted more attention, and so far its relevance has yet to be shown also empirically in a regional case study. In this paper, the residual spherical-harmonic topographic potential (RSHTP) approach is introduced as a new technique and compared with the classic RTM. Both techniques are applied to a test region in the central European Alps including validation of the quasigeoid solutions against ground-truthing data. Hence, the practical feasibility and benefits for quasigeoid computations with the RCR technique are demonstrated. Most notably, the RSHTP avoids explicit HC in the first place, and spectral consistency of the residual topographic potential with global geopotential models is inherently achieved. Although one could conclude that thereby the problem of the HC is finally solved, there remain practical reasons for the classic RTM reduction with HC. In this regard, both intra-method comparison and ground-truthing with GNSS/leveling data confirms that the classic RTM (Forsberg and Tscherning 1981; Forsberg in A study of terrain reductions, density anomalies and geophysical inversion methods in gravity field modeling. Report 355, Department of Geodetic Sciences and Surveying, Ohio State University, Columbus, Ohio, USA, https://earthsciences.osu.edu/sites/earthsciences.osu.edu/files/report-355.pdf, 1984) provides reasonable results also for a high-resolution (degree 2160) RTM, yet neglecting the HC for the height anomaly leads to a systematic bias in deep valleys of up to 10–20 cm.

Classically, vertical reference frames were realized as national or continent-wide networks of geopotential differences derived from geodetic leveling, i.e., from the combination of spirit leveling and gravimetry. Those networks are affected by systematic errors in leveling, leading to tilts in the order of decimeter to meter in larger networks. Today, there opens the possibility to establish a worldwide unified vertical reference frame based on a conventional (quasi)geoid model. Such a frame would be accessible through GNSS measurements, i.e., physical heights would be derived by the method of GNSS-leveling. The question arises, whether existing geodetic leveling data are abolished completely for the realization of vertical reference frames, are used for validation purposes only, or whether existing or future geodetic leveling data can still be of use for the realization of vertical reference frames. The question is mainly driven by the high quality of leveled potential differences over short distances. In the following we investigate two approaches for the combination of geopotential numbers from GNSS-leveling and potential differences from geodetic leveling. In the first approach, both data sets are combined in a common network adjustment leading to potential values at the benchmarks of the leveling network. In the second approach, potential differences from geodetic leveling are used as observable for regional gravity field modeling. This leads to a grid of geoid heights based on classical observables like gravity anomalies and now also on leveled potential differences. Based on synthetic data and a realistic stochastic model, we show that incorporating leveled potential differences improves the quality of a continent-wide network of GNSS-heights (approach 1) by about 40% and that formal and empirical errors of a regional geoid model (approach 2) are reduced by about 20% at leveling benchmarks. While these numbers strongly depend on the chosen stochastic model, the results show the benefit of using leveled potential differences for the realization of a modern geoid-based reference frame. Independent of the specific numbers of the improvement, an additional benefit is the consistency (within the error bounds of each observation type) of leveling data with vertical coordinates from GNSS and a conventional geoid model. Even though we focus on geodetic leveling, the methods proposed are independent of the specific technique used to observe potential (or equivalently height) differences and can thus be applied also to other techniques like chronometric or hydrodynamic leveling.

In this contribution we introduce the dual mixed-integer least-squares problem and study it in relation to its primal counterpart. The dual differs from the primal formulation in the order in which the integer ambiguity vector (a in {mathbb {Z}}^{n}) and baseline vector (b in {mathbb {R}}^{p}) are estimated. As not the ambiguities, but rather the entries of b are usually the parameters of interest, the attractiveness of the dual formulation stems from its direct computation of b. It is shown that this potential advantage relies on the ease with which an implicit integer least-squares problem of the dual can be solved. For the convoluted cases, we introduce two methods of simplifying approximations. To be able to describe their quality, we provide a complete distributional analysis of their estimators, thus allowing users to judge whether or not the approximations are acceptable for their application. It is shown that this approach implicitly introduces a new class of admissible integer estimators of which we also determine the pull-in regions. As the dual function is shown to lack convexity, special care is required to be able to compute its global minimizer ({check{b}}). Our proposed method, which has finite termination with a guaranteed (epsilon )-tolerance, is constructed from combining the branch-and-bound principle, with a special convex-relaxation of the dual, to which the projected-gradient-descent method is applied to obtain the required bounds. Each of the method’s three constituents are described, whereby special emphasis is given to the construction of the required continuously differentiable, convex lower bounding function of the dual.