Journal of Geodesy最新文献

Inverting fault geometry and slip distribution simultaneously with geodetic observations based on Bayesian theory is becoming increasingly prevalent. A widely used approach, proposed by (Fukuda and Johnson, Geophys J Int 181:1441–1458, 2010) (F-J method), employs the least-squares method to solve the linear parameters of slip distribution after sampling the nonlinear parameters, including fault geometry, data weights and smoothing factor. Here, we present a modified version of the F-J method (MF-J method), which treats data weights and the smoothing factor as hyperparameters not directly linked to surface deformation. Additionally, we introduce the variance component estimation (VCE) method to resolve these hyperparameters. To validate the effectiveness of the MF-J method, we conducted inversion tests using both synthetic data and a real earthquake case. In our comparison of the MF-J and F-J methods using synthetic experiments, we found that the F-J method's inversion results for fault geometry were highly sensitive to the initial values and step sizes of hyperparameters, whereas the MF-J method exhibited greater robustness and stability. The MF-J method also exhibited a higher and more stable acceptance rate, enabling convergence to simulated values and ensuring greater accuracy of the parameter estimation. Furthermore, treating the fault length and width as unknown parameters and solving them simultaneously with other fault geometry parameters and hyperparameters using the MF-J method successfully resolved the issue of non-uniqueness in fault location solutions caused by the excessively large no-slip areas. In the 2017 Mw 7.3 Sarpol-e Zahab earthquake case study, the MF-J method produced a fault slip distribution with low uncertainty that accurately fit surface observation data, aligning with results from other research institutions. This validated the method's applicability and robustness in real-world scenarios. Additionally, we inferred that the second slip asperity was caused by early afterslip.

The spherical radial basis function (SRBF) approach, widely used in gravity modeling, is theoretically surveyed from a viewpoint of random field theory. Let the gravity potential be a random field which is represented as an integral functional of another random field, namely an isotropic Gaussian random field (IGRF) on a sphere inside the Bjerhammar sphere with the SRBF as the integral kernel. When the integration is approximated by a discrete sum within a local region, one gets the widely applicable SRBF model. With this theoretical study, the following two findings are made. First, the IGRF implies a Gaussian prior on the spherical harmonic coefficients (SHCs) of the gravity potential; for this prior the SHCs are independent with each other and their variances are degree-only dependent. This should be reminiscent of two well-known priors, namely the power-law Kaula’s rule and the asymptotic power-law Tscherning-Rapp model. Second, the IGRF-SRBF representation is non-unique. Benefiting from this redundant representation, one can employ a simple IGRF, e.g., the simplest white field, and then design the SRBF accordingly to represent a potential with desired prior statistical properties. This can simplify the corresponding SRBF modeling significantly; to be more specific, the regularization matrix in parameter estimation of the SRBF modeling can be chosen to be a diagonal matrix, or even the naïve identity matrix.

The 3D ionosphere structure is of interest in many fields such as radio frequency communication and global navigation satellite system (GNSS) applications. However, the limited temporal and spatial coverage of measurements poses a challenge for 3D electron density modeling. To overcome this challenge, we explore the use of kriging interpolation technique. The kriging interpolation is performed to obtain 3D representation of the ionosphere over electron density measurements retrieved by GNSS radio-occultation (RO) data. RO measurements are first reduced to “shape function,” the ratio of electron density to vertical total electron content (VTEC), aiming to create a background model. Then, the empirical residual semivariogram is analyzed for variation characteristics of the shape functions under different solar geomagnetic conditions. Finally, 3D kriging is adopted for shape function interpolation. Compared to the modeling results without kriging, the maximum root mean square error (RMSE) reduction reaches (3.4times {10}^{-4}~text {km}^{-1}), which amounts to (3.4times {10}^{11}~text {el/m}^{3}) of electron density when VTEC is assumed as 100 TECU. This improvement accounts for 17.8% of root mean square (RMS) of shape function.

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.