Journal of Geodesy最新文献

In recent years, coseismic velocity from high-rate global navigation satellite systems (GNSS) carrier phase data has been widely utilized to estimate instrumental seismic intensity, thereby guiding earthquake early warning and emergency response. However, using carrier phase data only yields displacement, displacement increment, and average velocity but not instantaneous velocity at the epoch level. In large earthquakes, using average velocity over a brief time span (e.g., 1 s) to quantify instantaneous coseismic velocity is less reliable for recovering accurate deformation dynamics, especially for the near-field region. In this study, we first introduce GNSS raw Doppler-based instantaneous velocity into seismology, expanding carrier phase-based traditional GNSS seismology. We also propose a new integrated GNSS velocity estimation method that employs a Kalman filter to integrate raw Doppler-based instantaneous velocity and carrier phase-based average velocity. The GNSS data from shake table experiments and two real-world earthquake events (i.e., the 2016 Mw 6.6 Norcia earthquake and the 2011 Mw 9.1 Tohoku-oki earthquake) are used to investigate the impact of high-rate GNSS raw Doppler on capturing coseismic velocity waveforms and predicting instrumental seismic intensity. The simulated sine wave experiment results indicate that the accuracy of instantaneous and average velocity for the 1 Hz sampling rate case is 1.20 cm/s and 12.67 cm/s, respectively. A similar case holds for the simulated quake wave experiment. The retrospective analysis of the ultra-high-rate (20 Hz) GNSS data for the Norcia earthquake shows the average velocities exhibit more aliasing and have a smaller peak ground velocity value than instantaneous velocities in all cases (i.e., 1, 2, 4, 5, 10, and 20 Hz). For the 2011 Mw 9.1 Tohoku-oki earthquake, results show that incorporating raw Doppler data enhances the consistency between the GNSS intensity map and the United States Geological Survey intensity map for near-field regions. Therefore, high-rate GNSS RD data as it becomes more widely available should be incorporated into data processing of high-rate GNSS seismology to capture more accurate instantaneous coseismic velocity waveforms and predict more realistic instrumental seismic intensity in future analyses.

The current GNSS meteorology literature focuses on ground-based and space-based GNSS observations separately, without exploring potential synergies. In this study, we propose combining the two data sources using GNSS tomography to overcome current limitations in (1) horizontal resolution of GNSS space-based, (2) low vertical resolution of GNSS ground-based tropospheric retrievals when the number of GNSS ground-based observations is limited and (3) instability of the tomography system due to a lack of observations traversing the atmosphere horizontally. Our study on the combination of GNSS ground-based and space-based presents an innovative way for data integration based on uncertainty estimation. The developed integrated tomography operator, based on 3D ray tracing principles, is tested on 30 days of simulated data with 101 ground stations and over 240 radio occultation events, using three different station layouts. The a priori data introduced into the tomography processing is from a deterministic model, while ray tracing uses the ERA5 reanalysis wet refractivity field to obtain input data for individual test cases. The results are verified by comparing tomography output to ERA5 reanalysis. We observed a decrease in tomography RMSE between 2% and 16% in the case of an integrated solution, depending on GNSS station layout and the number and geometry of radio occultation ray paths. We show that a single RO event during one processing epoch can shift the wet refractivity estimates by 2 to 5 ppm closer to the correct solution compared to ground-based-only GNSS tomography.

Global Navigation Satellite Systems (GNSS) applications require computation of the geometric range between the satellite vehicle at the time-of-signal transmission and the receiver antenna location at the time-of-signal reception. This computation requires attention to the frames of reference due to the rotation of the Earth-Centered Earth-Fixed (ECEF) frame during the time-of-signal propagation. Three range computation approaches are commonplace and will be discussed herein. The first is the Global Positioning System Interface Control Document recommendation to rotate the ECEF frames to a common reference time. The other two are forms of the Sagnac correction. The Sagnac derivations already in the literature are either limited to stationary receivers or lack the connection between the Earth-centered inertial (ECI) and ECEF frames. Neither form of the Sagnac correction exactly reproduces the geometric range. They are approximations. The literature does not currently contain an analysis of the error involved in using either form of the Sagnac correction. This article makes two contributions: (1) it presents derivations for both forms of the Sagnac correction that are valid for moving receivers and that maintain the connection between the ECI and ECEF frames; and (2) it analyzes the error of the Sagnac correction for orbits of different radius. The analysis shows that Sagnac corrections introduce range errors less than (7.57times 10^{-4}) meters for GNSS satellites at medium Earth orbit.

The geoid and quasi-geoid serve as the reference surfaces of the orthometric and normal height systems, respectively. In order to improve the accuracy of the (quasi-) geoid determined by the Stokes integral with use of the Remove-Compute-Restore (RCR) technique, various modification methods for the spherical Stokes’ kernels, including the spheroidal, cosine-, power-, and Molodensky-modified kernels, are studied in this paper. In addition to the traditional Molodensky-modified Stokes’ kernel, a more effective Molodensky-modified Stokes’ kernel is put forward. A general formula for spectral decomposition of the Stokes integral in the RCR mode is derived, followed by the spectral analysis to reveal the transfer principles of gravity data when using different Stokes’ kernels. The spheroidal and modified Stokes integrals can cause spectral leakage phenomenon, and a method to eliminate spectral leakage is presented based on spectral analysis. The research indicates the low truncation degree of the spheroidal Stokes’ kernel and the low modification degrees of the modified Stokes’ kernel affect the accuracy of the (quasi-) geoid significantly. Quantitative methods for estimating the empirical values of the parameters of the low-degree spheroidal and modified Stokes’ kernels are proposed and the effectiveness of the methods is validated through numerical tests.

As an important data source for monitoring the behavior and variations of the ionosphere, the accuracy of current real-time global ionospheric maps (RT-GIMs) in low-latitude regions and oceanic regions is usually poor, and the accuracy during geomagnetic storms is not ideal. Therefore, the ionospheric vertical total electron content (VTEC) short-term forecast results were integrated into the global ionospheric real-time modeling process to improve the accuracy of RT-GIMs. Firstly, the preliminary RT-GIMs were established by constructing a virtual grid and determining the number of ionospheric pierce points in the grid. Then, different strategies were used to determine the virtual VTEC observations and filled the preliminary RT-GIMs. Finally, the filled RT-GIMs were modeled using spherical harmonic expansion and generated the final RT-GIMs, XRTG. On this basis, three ways were selected to evaluate the accuracy of XRTG. The GPS dSTEC (differential slant total electron content) assessment results showed that the performance of XRTG was the closest to that of Centre for Orbit Determination in Europe’s final GIMs (CODG), and it outperformed other RT-GIMs during geomagnetic storm periods and low-latitude regions. Compared with Universitat Politècnica de Catalunya’s RT-GIMs (UADG) with better performance in other RT-GIMs, the maximum decrease in root mean square error (RMSE) of XRTG during the geomagnetic storm period exceeds 25%, and the maximum decrease in the overall average RMSE of the 20 stations in low latitudes exceeds 27%. The Jason-3 VTEC assessment results showed that the accuracy of XRTG was closer to that of UADG and CODG, and the performance of XRTG and UADG in the range of 22° N–22° S was significantly better than that of other RT-GIMs. The consistency between XRTG and Universitat Politècnica de Catalunya’s rapid GIMs, Chinese Academy of Sciences’ final GIMs, and CODG was good, and the VTEC deviations from each post-processing GIMs were mainly concentrated in the range of ± 5 TECU.

The power function of (F-) distribution is the complementary cumulative distribution function of the non-central (F-) distribution. It is used to evaluate the power of the test based on the (F) or ({chi }^{2}-) distributed statistics. This paper revisits its computation and solution for the non-centrality parameter in geodetic studies and shows that the power function related to these studies can be computed efficiently and with minimal effort. To facilitate this, we introduce a novel standalone algorithm that consistently computes the power of the test, even for large non-centrality parameters (e.g., (>{10}^{5})) and for ({chi }^{2})-distribution. The solution of the power function for the non-centrality parameter is typically obtained using standard root finding algorithms, such as the bisection or Newton–Raphson methods. However, they may encounter convergence problems, particularly when the non-centrality parameter increases. We demonstrate that a solution can be readily obtained from a logarithmic form of the power function, ensuring convergence and removing the requirement for a precisely defined initial value. Furthermore, we utilize a few geometric relationships during the iteration to expedite the solution process. As a result, we propose a novel solution algorithm that is highly precise, stable, and at least four times faster than standard algorithms, even for the solution interval of (<{0, 10}^{6}>). This efficient solution is published online as a web-based application for geodetic detectability studies in addition to the given MATLAB and Python codes.

The complete set of five Earth Orientation Parameters (EOP) can only be estimated accurately using geodetic Very Long Baseline Interferometry (VLBI). Their precision and accuracy depends on network geometry and station-dependent properties. Atmospheric turbulence poses one of the largest error sources for geodetic VLBI, impacting the precision of EOP. Thus, it becomes imperative to consider this factor while choosing the optimal locations for geodetic VLBI. The magnitude of tropospheric turbulence is approximated through the refractive index structure constant, (C_textrm{n}^textrm{2}). In this study, we simulate the optimal locations for geodetic VLBI in India, considering individual tropospheric turbulence parameters per telescope location. The study identifies 14 potential VLBI stations, co-located with GPS stations and homogeneously distributed all over India, and computes the (C_textrm{n}) values from zenith wet delay variances over 24 h obtained from GPS data. These locations are simulated in addition to three different reference networks, which show the current and future VLBI Global Observing System (VGOS) networks. Multiple schedules have been generated and simulated for each configuration using VieSched++, and the precision of EOP is compared when constant and station-specific tropospheric turbulence parameters are used. The study shows that, for the investigated networks, southern stations are optimal for polar motion and celestial pole offsets estimation, whereas an eastern station is optimal for UT1−UTC estimation. Furthermore, the study highlights that for reference networks with fewer stations, utilizing station-specific (C_textrm{n}) values significantly influences the determination of optimal locations. It further demonstrates how station-specific (C_textrm{n}) values impact the positioning of VGOS telescopes in each network for each EOP differently. The findings show that higher (C_textrm{n}) values generally lead to a degradation in EOP precision. Geometrically, a station might be at a good location, but if the (C_textrm{n}) value is too high, that location is not favorable.

A bridge may displace due to various loadings (e.g., thermal (Xia et al. in Struct Control Health Monit 28(7):e2738, 2013), winds (Owen et al. in J Wind Eng Ind Aerodyn 206:104389, 2020), and vehicles (Xu et al. in J Struct Eng 133(1):3–11, 2007)) acting upon the bridge. Identifying the contributions of individual loading factors to the measured bridge displacements is important for understanding the structural health conditions of the bridge. There is however no effective method to quantify the contributions when multiple loadings act simultaneously on a bridge. We propose a new data-driven method, termed random forest (RF)-assisted variational mode decomposition (RF-AVMD), for more effective identification of dominant loading factors and for quantifying the contributions of individual loading factors to the measured bridge displacements. The proposed method is applicable to studying the displacements of any bridge structures and allows for the first time to separate the contributions of individual loadings. The effectiveness of the proposed method is validated using data from Tsing Ma Bridge (TMB), a large suspension bridge in Hong Kong recorded during two consecutive strong typhoons. The results reveal that the transverse displacements of TMB mid-span were controlled by the crosswinds, the longitudinal displacements were dominated by the temperature and winds along the bridge centerline, and the vertical displacements were mainly due to the winds along the bridge centerline, temperature, and traffic flows. Displacement time series that responded to each loading factor was derived. The proposed method provides important new insights into the impacts of individual loadings on the displacements of long-span bridges.

Currently, the least-square estimation method is the mainstream method for recovering spherical harmonic coefficients from area mean values over equiangular blocks. Since the least-square estimation method involves matrix inversion, it requires great computation power when the maximum degree to be solved is large. In comparison, numerical quadrature methods are faster. Recent numerical quadrature methods designed for spherical harmonic analysis of area mean values over blocks delineated by equiangular and Gaussian grids are both fast and exact for band-limited data. However, for band-limited area mean values over an equiangular grid that has (N) blocks along the colatitude direction and (2N) blocks along the longitude direction, the maximum degree that can be recovered by using current exact numerical quadrature methods is no larger than (N/2-1). In this study, by using Lagrange’s method for polynomial interpolation, recently proposed numerical quadrature methods that employ the recurrence relations for the integrals of the associated Legendre’s functions are modified into two new methods. By using these methods, the maximum degree of recovered spherical harmonic coefficients is (N-1). The results show that these newly proposed methods are comparable in computation speed with the current numerical quadrature methods and are comparable in accuracy with the least-square estimation method for both band-limited and aliased data. Moreover, solving linear systems is not necessary for these two new methods. The error characteristics of these two new methods are quite different from those of methods that employ least-square methods. The spherical harmonic coefficients recovered using these new methods can effectively supplement those recovered using least-square methods.