Journal of Geodesy最新文献

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.

When conducting coseismic slip distribution inversion with interferometric synthetic aperture radar (InSAR) data, there is no universal method to objectively determine the appropriate size of InSAR data. Currently, little is also known about the computing efficiency of variance component estimation implemented in the inversion. Therefore, we develop a variance component adaptive estimation algorithm to determine the optimal sampling number of InSAR data for the slip distribution inversion. We derived more concise variation formulae than conventional simplified formulae for the variance component estimation. Based on multiple sampling data sets with different sampling numbers, the proposed algorithm determines the optimal sampling number by the changing behaviors of variance component estimates themselves. In three simulation cases, four evaluation indicators at low levels corresponding to the obtained optimal sampling number validate the feasibility and effectiveness of the proposed algorithm. Compared with the conventional slip distribution inversion strategy with the standard downsampling algorithm, the simulation cases and practical applications of five earthquakes suggest that the developed algorithm is more flexible and robust to yield appropriate size of InSAR data, thus provide a reasonable estimate of slip distribution. Computation time analyses indicate that the computational advantage of variation formulae is dependent of the ratio of the number of data to the number of fault patches and can be effectively suitable for cases with the ratio smaller than five, facilitating the rapid estimation of coseismic slip distribution inversion.

Electronic distance measurements (EDM) represent one of the first methods to detect ground deformation on volcanoes. Used since 1964, they enable acquiring precise distance measurements, whose time repetition may highlight changes related to volcanic activity. This technique was widely used on volcanoes from the 1970s to the early 2000s and has been used many times to model position, geometry, and volumes of magmatic and hydrothermal sources. This paper reports the EDM experiences, results and data acquired on Sicilian volcanoes (Etna, Vulcano, Stromboli and Pantelleria) from the early 1970s, which have played a major role in the birth of the volcano-geodesy for volcanic process knowledge, making the Sicilian volcanoes among those with the longest geodetic record in the world.

Troposphere’s asymmetry can introduce errors ranging from centimeters to decimeters at low elevation angles, which cannot be ignored in high-precision positioning technology and meteorological research. The traditional two-axis gradient model, which strongly relies on an open-sky environment of the receiver, exhibits misfits at low elevation angles due to their simplistic nature. In response, we propose a directional mapping function based on cyclic B-splines named B-spline mapping function (BMF). This model replaces the conventional approach, which is based on estimating Zenith Wet Delay and gradient parameters, by estimating only four parameters which enable a continuous characterization of the troposphere delay across any directions. A simulation test, based on a numerical weather model, was conducted to validate the superiority of cyclic B-spline functions in representing tropospheric asymmetry. Based on an extensive analysis, the performance of BMF was assessed within precise point positioning using data from 45 International GNSS Service stations across Europe and Africa. It is revealed that BMF improves the coordinate repeatability by approximately (10%) horizontally and about (5%) vertically. Such improvements are particularly pronounced under heavy rainfall conditions, where the improvement of 3-dimensional root mean square error reaches up to (13%).

We reconstructed the Chandler Wobble (CW) from 1962 to 2022 by combining the Eigen-oscillator excited by geophysical fluids of atmospheric and oceanic angular momentums (AAM and OAM). The mass and motion terms for the AAM are further divided with respect to the land and ocean domains. Particular attention is placed on the time span from 2012 to 2022 in relation to the observable reduction in the amplitude of the CW. Our research indicates that the main contributor to the CW induced by AAM is the mass term (i.e., the pressure variations over land). Moreover, the phase of the AAM-induced CW remains relatively stable during the interval of 1962–2022. In contrast, the phase of the OAM-induced CW exhibits a periodic variation with a cycle of approximately 20 years. This cyclic variation would modulate the overall amplitude of the CW. The noticeable amplitude deduction over the past ten years can be attributed to the evolution of the CW driven by AAM and OAM, toward a state of cancellation. These findings further reveal that the variation in the phase difference between the CW forced by AAM and OAM, may be indicative of changes in the interaction between the solid Earth, atmosphere, and ocean.

Removing stripe noise from the GRACE (Gravity Recovery and Climate Experiment) monthly gravity field model is crucial for accurately interpreting temporal gravity variations. The conventional parameter filtering (CPF) approach expresses the signal components with a harmonic model while neglecting non-periodic and interannual signals. To address this issue, we improve the CPF approach by incorporating those ignored signals using a first-order Gauss–Markov process. The improved parameter filtering (IPF) approach is used to filter the monthly spherical harmonic coefficients (SHCs) of the Tongji-Grace2018 model from April 2002 to December 2016. Compared to the CPF approach, the IPF approach exhibits stronger signals in low-degree SHCs (i.e., degrees below 20) and lower noise in high-order SHCs (i.e., orders above 40), alongside higher signal-to-noise ratios and better agreement with CSR mascon product and NOAH model in global and basin analysis. Across the 22 largest basins worldwide, the average Nash–Sutcliffe coefficients of latitude-weighted terrestrial water storage anomalies filtered by the IPF approach relative to those derived from CSR mascon product and NOAH model are 0.90 and 0.21, significantly higher than 0.17 and − 0.71, filtered by the CPF approach. Simulation experiments further demonstrate that the IPF approach yields the filtered results closest to the actual signals, reducing root-mean-square errors by 30.1%, 25.9%, 45.3%, 30.9%, 46.6%, 32.7%, 39.6%, and 38.2% over land, and 2.8%, 54.4%, 70.1%, 15.3%, 69.2%, 46.5%, 40.4%, and 23.6% over the ocean, compared to CPF, DDK3, least square, RMS, Gaussian 300, Fan 300, Gaussian 300 with P4M6, and Fan 300 with P4M6 filtering approaches, respectively

The issue of outliers has been a research focus in the field of geodesy. Based on a statistical testing method known as the w-test, data snooping along with its iterative form, iterative data snooping (IDS), is commonly used to diagnose outliers in linear models. However, in the case of multiple outliers, it may suffer from the masking and swamping effects, thereby limiting the detection and identification capabilities. This contribution is to investigate the cause of masking and swamping effects and propose a new method to mitigate these phenomena. First, based on the data division, an extended form of the w-test with its reliability measure is presented, and a theoretical reinterpretation of data snooping and IDS is provided. Then, to alleviate the effects of masking and swamping, a new outlier diagnostic method and its iterative form are proposed, namely data refining and iterative data refining (IDR). In general, if the total observations are initially divided into an inlying set and an outlying set, data snooping can be considered a process of selecting outliers from the inlying set to the outlying set. Conversely, data refining is then a reverse process to transfer inliers from the outlying set to the inlying one. Both theoretical analysis and practical examples show that IDR would keep stronger robustness than IDS due to the alleviation of masking and swamping effect, although it may pose a higher risk of precision loss when dealing with insufficient data.