# Journal of Geodesy

The latest content available from Springer
Updated: 2 days 19 hours ago

### Error propagation for the Molodensky G 1 term

Sat, 06/01/2019 - 00:00
Abstract

Molodensky G terms are used in the computation of the quasigeoid. We derive error propagation formulas that take into account uncertainties in both the free air gravity anomaly and a digital elevation model. These are applied to generate G1 terms and their errors on a 1″ × 1″ grid over Australia. We use these to produce Molodensky gravity anomaly and accompanying uncertainty grids. These uncertainties have average value of 2 mGal with maximum of 54 mGal. We further calculate a gravimetric quasigeoid model by the remove–compute–restore technique. These Molodensky gravity anomaly uncertainties lead to quasigeoid uncertainties with a mean of 4 mm and maximum of 80 mm when propagated through a deterministically modified Stokes’s integral over an integration cap radius of 0.5°.

### Empirically derived model of solar radiation pressure for BeiDou GEO satellites

Sat, 06/01/2019 - 00:00
Abstract

A key limitation in the precise orbit determination (POD) of BeiDou geostationary Earth orbit (GEO) satellites is the relatively static observation geometry, which results in strong correlations between orbital elements, solar radiation pressure (SRP) parameters, and ambiguities. Satellite laser ranging (SLR) residuals of BeiDou G01 satellite orbits display a clear dependence on the Sun elongation angle ε, as well as a bias of approximately − 40 cm. These indicate the low performance of BeiDou GEO orbits. In this study, we confirmed that the perturbation caused by the communication antenna generates the ε-angle-dependent variation and the bias of approximately − 14.9 cm in BeiDou G01 SLR residuals. Besides, the orbit-normal (ON) attitude mode used by BeiDou GEO satellites as well as an orbital inclination of nearly 0° results in strong linear correlations between the POD estimated parameters, i.e., satellite’s initial position on the Z-axis and the constant Y-bias along the cross-track direction. Hence, the solar pressure models, such as Extended CODE Orbit Model (ECOM) in ON mode, with the Y-axis along the cross-track direction are deficient for SRP estimation of BeiDou GEO satellites. In this study, an empirical a priori SRP model was established for BeiDou GEO satellites to enhance the ECOM using an empirical fitting approach. This proposed model is expressed in DYB frame using eight parameters. With this model, precise BeiDou GEO orbits in 2016 were determined. SLR validation indicated that the systematic ε-angle-dependent error was reduced and the large negative bias almost vanished. In general, better than 10-cm root-mean-square of SLR validation was achieved, and also an improvement of 4–5 times over the five-parameter ECOM model was obtained.

### The cause of the 2011 Hawthorne (Nevada) earthquake swarm constrained by seismic and InSAR methods

Sat, 06/01/2019 - 00:00
Abstract

We used both seismic and InSAR data to investigate the mechanism behind the 2011 Hawthorne (Nevada) earthquake swarm that occurred between March 15 and August 17, 2011. Regional seismic data were used to estimate the centroid depth and focal mechanism for nine earthquakes that occurred in this swarm, with magnitudes between $$M_w$$ 3.9 and $$M_w$$ 4.8. The inferred focal mechanisms indicate that the source of these earthquakes is normal faulting with a small left-lateral strike-slip component along the southwest direction. Three InSAR displacement maps covering the epicentral zone of the 2011 Hawthorne earthquakes were inverted to get a slip model. The slip distribution shows that the deformation source is characterized by normal faulting, consistent with our inferred focal mechanisms. Our results suggest that the seismogenic zone was in the tensile stress environment. The temporal and spatial evolutions of seismicity suggest that the 2011 Hawthorne swarm might be caused by aseismic slip. Therefore, the 2011 Hawthorne earthquake swarm may have been the result of aseismic slip under the regional tectonic stress, and had nothing to do with volcanic activity. However, the quantitative evidence for aseismic slip is limited to the indication that the geodetic moment is 15% greater than the seismic moment, which is near the level of uncertainty.

### Sub-centimetre geoid

Sat, 06/01/2019 - 00:00
Abstract

This paper represents a milestone in the UNB effort to formulate an accurate and self-consistent theory for regional geoid determination. To get the geoid to a sub-centimetre accuracy, we had to formulate the theory in a spherical rather than linear approximation, advance the modelling of the effect of topographic mass density, formulate the solid spherical Bouguer anomaly, develop the probabilistic downward continuation approach, incorporate improved satellite determined global gravitational models and introduce a whole host of smaller improvements. Having adopted Auvergne, an area in France as our testing ground, where the mean standard deviation of observed gravity values is 0.5 mGal, according to the Institute Geographique Nationale (Duquenne in Proceedings of the 1st international symposium of the international gravity field service “gravity field of the earth”, International gravity field service meeting, Istanbul, Turkey, 2006), we obtained the standard deviation of the gravity anomalies continued downward to the geoid, as estimated by minimizing the L2 norm of their residuals, to be in average 3 times larger than those on the surface with large spikes underneath the highest topographic points. The standard deviations of resulting geoidal heights range from a few millimetres to just over 6 cm for the highest topographic points in the Alpine region (just short of 2000 m). The mean standard deviations of the geoidal heights for the whole region are only 0.6 cm, which should be considered quite reasonable even if one acknowledges that the area of Auvergne is mostly flat. As one should expect, the main contributing factors to these uncertainties are the Poisson probabilistic downward continuation process, with the maximum standard deviation just short of 6 cm (the average value of 2.5 mm) and the topographic density uncertainties, with the maximum value of 5.6 cm (the average value of 3.0 mm). The comparison of our geoidal heights with the testing geoidal heights, obtained for a set of 75 control points (regularly spaced throughout the region), shows the mean shift of 13 cm which is believed to reflect the displacement of the French vertical datum from the geoid due to sea surface topography. The mean root square error of the misfit is 3.3 cm. This misfit, when we consider the estimated accuracy of our geoid, indicates that the mean standard deviation of the “test geoid” is about 3 cm, which makes it about 5 times less accurate than the Stokes–Helmert computed geoid.

### M-estimation using unbiased median variance estimate

Sat, 06/01/2019 - 00:00
Abstract

This paper first proves that the traditional median variance estimate is biased when the sample number is small and then proposes an unbiased median variance estimate to calibrate for the bias of the variance estimate. The scaled median variance estimate is firstly derived, and the unbiased median variance estimate is formed with independent residuals in an adjustment model no matter whether the measurements are contaminated by outliers or not. Using the unbiased median variance estimate, the M-estimate is constructed to mitigate for the biases caused by the variance estimate. The IGGIII reduction factor is used to verify the proposed algorithms by a levelling network example. Numerical analysis confirms that the proposed median variance estimate can achieve better unbiasedness for contaminated measurement set, but the dispersion of our estimate is unfortunately larger than that for the least-squares estimate.

### High-resolution models of tropospheric delays and refractivity based on GNSS and numerical weather prediction data for alpine regions in Switzerland

Sat, 06/01/2019 - 00:00
Abstract

The tropospheric delay of a microwave signal affects all space geodetic techniques. One possibility of modeling the delay is by introducing tropospheric models from external data sources. In this study, we present high-resolution models of tropospheric total refractivity and zenith total delay (ZTD) for the alpine area in Switzerland. The troposphere models are based on different combinations of data sources, including numerical weather prediction (NWP) model COSMO-1 with high spatial resolution of $$1.1~\hbox {km}~\times ~1.1~\hbox {km}$$ , GNSS data from permanent geodetic stations and GPS L1-only data from low-cost permanent stations. The tropospheric parameters are interpolated to the arbitrary locations by the least-squares collocation method using the in-house developed software package COMEDIE (Collocation of Meteorological Data for Interpretation and Estimation of Tropospheric Pathdelays). The first goal of this study is to validate the obtained models with the reference radiosonde and GNSS data to show the improvement w.r.t. the previous studies that used lower resolution input data. In case of total refractivity, the profiles reconstructed from COSMO-1 model show the best agreement with the reference radiosonde measurements, with an average bias of 1.1 ppm (0.6% of the total refractivity value along a vertical profile) and standard deviation of 2.6 ppm (1.6%) averaged from the whole profile. The radiosondes are assimilated into COSMO-1 model; thus, a high correlation is expected, and this comparison is not independent. In case of ZTD, the GNSS-based model shows the highest agreement with the reference GNSS data, with an average bias of 0.2 mm (0.01%) and standard deviation of 4.3 mm (0.2%). For COSMO-based model, the agreement is also very high, especially compared to our previous studies with lower resolution NWPs. The average bias is equal to − 2.5 mm (0.1%) with standard deviation of 9.2 mm (0.5%). The second goal of this study is to test the feasibility of calculating high-resolution troposphere models over a limited area from coarser data sets. We calculate the ZTD models with spatial resolution of 20 m for a test area in Matter Valley. We include the information from the low-cost GPS stations (X-Sense), to also assess the performance and future usability of such stations. We validate the models based on three data sources w.r.t. the reference GNSS data. For the station located inside the area of the study, the models have an agreement of few mm with the reference data. For stations located further away from the study area, the agreement for X-Sense is smaller, but the standard deviations of residuals are still below 15 mm. We consider also another factor of evaluating the high-resolution models, i.e., spatial variability of the data. For designing a GNSS network, also for the tropospheric estimates, the height variability of the network may be as important as the horizontal distribution. The GNSS-based models are built from the coarsest network; thus, their variability is the lowest. The variability of X-Sense-based stations is the highest; thus, such data may be suitable for building troposphere models for very high-resolution applications.

### Helmert-VCE-aided fast-WTLS approach for global ionospheric VTEC modelling using data from GNSS, satellite altimetry and radio occultation

Sat, 06/01/2019 - 00:00
Abstract

Vertical total electron content (VTEC) global ionospheric maps (GIM) are commonly used to correct the ionospheric delay of global navigation satellite system (GNSS) signals for single-frequency positioning and other ionospheric studies. The measurements observed by inhomogeneously distributed ground reference stations are the only data used to generate the GIMs. Thus the accuracy of the GIMs over ocean and polar regions is relatively poor due to the lack of measurements over these regions. In this study, space-borne VTECs obtained from ocean-altimetry and GNSS radio occultation measurements are incorporated into the modelling process. Since the three types of VTEC data have different qualities, the weight for each type of data is determined using the Helmert-variance component estimation (Helmert-VCE) method. In addition, unlike the traditional weighted least squares (WLS) estimation method in which the design matrix of observation equations is fixed, in this study, the design matrix, especially those elements in design matrix that are derived from the coordinates of either tangent point or ionospheric pierce point, are considered to be inaccurate. Thus they are adjusted together with the unknown coefficient parameters of the fitting model using the fast-weighted total least squares (fast-WTLS) technique. The proposed approach, named Helmert-WTLS, was tested using the data in the period of day of year (DOY) 217–224, 2016 and validated using GIMs produced by the research team for ionosphere and precise positioning based on BDS/GNSS (GIPP) at the Academy of Opto-Electronics, Chinese Academy of Sciences (CAS). Comparison results showed that the GIMs (with a 2 h temporal resolution) generated using the new approach can improve the determination of ionospheric TEC by 0.28 TEC units (TECU) over those from the Helmert-VCE-aided WLS approach (w.r.t CAS references, respectively) and by 1.61 TECU better than those from WLS, in terms of the mean of all root-mean-squares errors of all 2 h time slots in the 8-day testing period. In addition, in comparison with out-of-sample Jason-3 observations, results from the proposed method also outperformed Helmert-VCE-aided WLS, CAS and CODE models by 1.5, 2.4 and 2.4 TECU, respectively.

### Modeling and performance analysis of precise time transfer based on BDS triple-frequency un-combined observations

Sat, 06/01/2019 - 00:00
Abstract

In this study, a model of precise time transfer is developed based on the triple-frequency un-combined observations of the BeiDou navigation satellite system, known as UC-PPP. In this model, except for the traditional position, troposphere delay and receiver clock parameters, ionosphere delays are estimated as unknown parameters by adding the prior, spatial and temporal constraints. In addition, receiver differential code biases (DCB) are also estimated as unknown parameters. The standard triple-frequency ionosphere-free model is also introduced, named as IF-PPP. To assess the performance of the model, datasets with short baseline and common external time frequency are used. The results show that the triple-frequency UC-PPP model can be used for precise time transfer, with accuracy and stability identical to those of the IF-PPP model. The model can also provide the receiver DCB and ionosphere total electron content products.

### Precise point positioning with mixed use of time-differenced and undifferenced carrier phase from multiple GNSS

Sat, 06/01/2019 - 00:00
Abstract

A multi-GNSS kinematic precise point positioning (PPP) approach that is based on the mixed use of time-differenced and undifferenced carrier phase observations is presented. The approach reduces the number of constant parameters, such as ambiguities and hardware biases, and mitigates quasi-constant systematic errors including residual atmospheric refractions and multipath effects. The effectiveness and efficiency of the proposed approach are validated in some PPP tests of running and vehicle driving. The proposed method requires an accurate initial position. When that is available, up to 71% improvement in positioning accuracy can be achieved compared with traditional PPP. The proposed approach is also computationally efficient, especially for high-rate positioning applications.

### The Smithsonian Astrophysical Observatory (SAO) and the Centre National d’Études Spatiales (CNES): contributions to the international laser ranging network

Sat, 06/01/2019 - 00:00
Abstract

The Smithsonian Astrophysical Observatory (SAO) and the Centre National d’Études Spatiales (CNES) worked closely together in the early years of the space program to deploy satellite laser ranging (SLR) systems at overseas sites to enhance global coverage to support specific missions. The data were routinely made available for use by the science community for programs in geodesy, gravity field, atmospheric physics, and ultimately for oceanography and geodynamics. SAO and CNES organized campaigns for international participation and loaned each other equipment to enhance the network. SAO and CNES provided technical expertise and advice to a number of other groups as they planned and deployed SLR systems. In this paper, we will discuss the history and the role of the two institutions in the building of the international SLR network.

Sat, 06/01/2019 - 00:00

### Determination of GNSS pseudo-absolute code biases and their long-term combination

Fri, 05/10/2019 - 00:00
Abstract

With the modernization of GPS and the establishment of additional global navigation satellite system (GNSS) constellations, such as Galileo, Beidou, and QZSS, more and more GNSS satellites are available transmitting on various frequencies with multiple signal modulations. In order to cope with the increasing number of observation types, the commonly used differential approach becomes more and more difficult regarding book-keeping. The actually processed original observation types have to be known in advance to define a linearly independent set of differential signal biases (DSB) while processing GNSS data. An alternative treatment of code biases is the usage of observable-specific signal biases (OSB) where the setup and correction of biases become trivial. Potential dependencies of the bias parameters can be considered after the setup of normal equations (NEQs), e.g., immediately before it is inverted. The code bias results are retrieved on a daily basis and their NEQs stored. This allows to combine bias results from various sources (or analysis lines) and different time periods. By combining all daily bias NEQs, we have generated a coherent multi-year bias solution from 2000 to 2017 with one common datum. If absolute receiver calibrations are available, the multi-year solution could be aligned to those receivers and thus could lead to an absolute estimation of the code biases. Finally, the estimated satellite OSBs are used for the receiver compatibility grouping testing which receivers are compatible with which bias sets. This may be achieved by solving for so-called OSB multipliers.

### Fourier-domain modeling of gravity effects caused by polyhedral bodies

Wed, 05/01/2019 - 00:00
Abstract

We present 2D and 3D Fourier-domain modeling of gravity effects, including the gravity potential and its first- and second- order derivatives, generated by an arbitrary polyhedron with constant and exponential density distributions. Fourier-domain expressions are obtained using Gauss’s divergence theorem repeatedly to transform the volume integral first into surface integrals and then to line integrals in the wave number domain. Both the derivation and the final expressions are simpler and more compact than space-domain ones. The highly accurate and efficient Gauss-FFT algorithm is then applied to transform the Fourier-domain expressions back to space-domain gravity fields. Synthetic and real model tests show that the Fourier-domain algorithm presented can provide forward results almost identical to space-domain analytical or numerical solutions at places where the exact solution changes smoothly. However, high-frequency truncation errors do become noticeable in the near vicinity of the source body, where the exact solution changes abruptly, or even discontinuously. The Fourier-domain algorithm captures almost all frequency components of the exact solution that are lower than the Nyquist frequency, which is determined by the chosen grid intervals. The algorithm offers a more efficient solution for 2D and 3D modeling of gravity fields on large and densely sampled regular grids than classical space-domain solutions, at the cost of a small loss of accuracy.

### Multi-GNSS triple-frequency differential code bias (DCB) determination with precise point positioning (PPP)

Wed, 05/01/2019 - 00:00
Abstract

Differential code biases (DCBs) account for the most significant systematical biases when sensing the earth’s ionosphere with GNSS observations and are also important correction parameters in GNSS applications of positioning, navigation and timing. With the continuous modernization of the American GPS and Russian GLONASS systems, and also the rapid developments of the European Galileo and Chinese BeiDou systems, there is a strong demand of precise satellite DCB products for multiple constellations and frequencies. This study proposes a new method for the precise determination of multi-GNSS triple-frequency DCBs, which can be divided into three steps. The first step is to precisely retrieve slant ionospheric delays and “additional code biases” based on a newly established full-rank triple-frequency precise point positioning (PPP) model with raw observations. Both the slant ionospheric delays and “additional code biases” containing the DCBs need to be estimated. Then, an enhanced IGGDCB (IGG stands for Institute of Geodesy and Geophysics) method is used to estimate the DCBs between the first and second frequency bands with the PPP-derived slant ionospheric delays. At last, the previously estimated DCBs between the first and second frequency bands are substituted into the “additional code biases” and DCBs between the first and third frequency bands are estimated. Multi-GNSS slant ionospheric delays from the triple-frequency PPP method are compared with those from the traditional dual-frequency carrier-to-code level (CCL) method, in terms of formal precision and zero-baseline experiment. Quad-system average formal precisions are 0.08 and 0.41 TECU, for PPP and CCL methods, respectively, indicating the obvious improvements of PPP over CCL. One month of data from 60 globally distributed multi-GNSS experiment stations are selected, and totally eight types of DCBs are estimated for GPS, GLONASS, Galileo and BeiDou. Multi-GNSS satellite DCBs generated with the proposed method are compared with the products from different agencies, including Center for Orbit Determination in Europe (CODE), Deutsches zentrum für Luft-und Raumfahrt (DLR) and Chinese Academy of Sciences (CAS). For GPS C1WC2 W DCBs, RMS values with respect to CODE products are 0.24, 0.07 and 0.09 ns for DLR, CAS and IGG (this study), respectively. RMS values are 0.31/0.25 and 0.19/0.15 ns, for GPS C1WC5X and C1WC5Q DCBs and with respect to DLR/CAS, respectively. For GLONASS C1PC2P DCBs, RMS values with respect to CODE are 0.68, 0.49 and 0.33 ns for DLR, CAS and IGG, respectively. For Galileo, RMS values are 0.16/0.20 and 0.13/0.14 ns, for C1XC5X and C1XC7X DCBs and with respect to DLR/CAS, respectively. For BeiDou, RMS values are 0.32/0.25 and 0.34/0.41, for C2IC7I and C2IC6I DCBs and with respect to DLR/CAS. These results show that the proposed method can provide multi-GNSS and multi-frequency satellite DCB estimation with high precision, processing efficiency and flexibility.

### An assessment of smartphone and low-cost multi-GNSS single-frequency RTK positioning for low, medium and high ionospheric disturbance periods

Wed, 05/01/2019 - 00:00
Abstract

The emerging GNSSs make single-frequency (SF) RTK positioning possible. In this contribution two different types of low-cost (few hundred USDs) RTK receivers are analyzed, which can track L1 GPS, B1 BDS, E1 Galileo and L1 QZSS, or any combinations thereof, for a location in Dunedin, New Zealand. These SF RTK receivers can potentially give competitive ambiguity resolution and positioning performance to that of more expensive (thousands USDs) dual-frequency (DF) GPS receivers. A smartphone implementation of one of these SF receiver types is also evaluated. The least-squares variance component estimation (LS-VCE) procedure is first used to formulate a realistic stochastic model, which assures that our receivers at hand can achieve the best possible ambiguity resolution and RTK positioning performance. The best performing low-cost SF RTK receiver types are then assessed against DF GPS receivers and survey-grade antennas. Real data with ionospheric disturbances at low, medium and high levels are analyzed, while making use of the ionosphere-weighted model. It will be demonstrated that when the presence of the residual ionospheric delays increases, instantaneous RTK positioning is not possible for any of the receivers, and a multi-epoch model is necessary to use. It is finally shown that the low-cost SF RTK performance can remain competitive to that of more expensive DF GPS receivers even when the ionospheric disturbance level reaches a Kp-index of 7−, i.e. for a strong geomagnetic storm, for the baseline at hand.

### A gravitational telescope deformation model for geodetic VLBI

Wed, 05/01/2019 - 00:00
Abstract

We have measured the geometric deformations of the Onsala 20 m VLBI telescope utilizing a combination of laser scanner, laser tracker, and electronic distance meters. The data put geometric constraints on the electromagnetic raypath variations inside the telescope. The results show that the propagated distance of the electromagnetic signal inside the telescope differs from the telescope’s focal length variation, and that the deformations alias as a vertical or tropospheric component. We find that for geodetic purposes, structural deformations of the telescope are more important than optic properties, and that for geodetic modelling the variations in raypath centroid rather than focal length should be used. All variations that have been identified as significant in previous studies can be quantified. We derived coefficients to model the gravitational deformation effect on the path length and provide uncertainty intervals for this model. The path length variation due to gravitational deformation of the Onsala 20 m telescope is in the range of 7–11 mm, comparing elevation 0 $$^{\circ }$$ and 90 $$^{\circ }$$ , and can be modelled with an uncertainty of 0.3 mm.

### LEO constellation-augmented multi-GNSS for rapid PPP convergence

Wed, 05/01/2019 - 00:00
Abstract

The fast motion of low earth orbit (LEO) satellite contributes to the geometric diversity, allowing for rapid convergence of precise point positioning (PPP). In this contribution, we investigate the PPP performance of the LEO constellation-augmented full operational capability (FOC) multi-GNSS. We design six LEO constellations with different satellite numbers, orbit altitudes and orbit types, together with the FOC multi-GNSS constellations, and then simulate both the onboard LEO and ground-based observations. The multi-GNSS POD result shows much better orbit accuracy of 3.3, 2.7 and 2.6 cm in radial, along-track and cross-track components, respectively, compared with that of 10.3, 9.2 and 8.9 cm for GPS-only POD. Furthermore, the performance of LEO-augmented multi-GNSS PPP is evaluated. With the augmentation of 60-, 96-, 192- and 288-satellite LEO constellation, the multi-GNSS PPP convergence time can be shortened from 9.6 to 7.0, 3.2, 2.1 and 1.3 min, respectively, in midlatitude region. For LEO-augmented GPS- and BDS-only PPP, the improvement is more significant with the convergence time dramatically shortened by 90% from about 25 to within 3 min with 192- or 288-satellite constellation. The augmentation capability is also found to be associated with station latitude, and the higher latitude, the better performance. To enable about more than 70% significant reduction on convergence time, as well as considering the cost, the 192-satellite LEO constellation scheme is suggested. In terms of orbit altitude, the scheme of 1000 km presents better performance than that of 600 km. As for orbit type, the performances are comparable for polar and sun-synchronous orbits. Additionally, LEO-only PPP can be achieved with the convergence time of about 6.5 min.

### Bayesian approach for network adjustment for gravity survey campaign: methodology and model test

Wed, 05/01/2019 - 00:00
Abstract

The drift rate of relative gravimeters differs from time to time and from meter to meter. Furthermore, it is inefficient to estimate the drift rate by returning them frequently to the base station or stations with known gravity values during gravity survey campaigns for a large region. Unlike the conventional gravity adjustment procedure, which employs a linear drift model, we assumed that the variation of drift rate is a smooth function of lapsed time. Using this assumption, we proposed a new gravity data adjustment method by means of objective Bayesian statistical inference. Some hyper-parameters were used as trade-offs to balance the fitted residuals of gravity differences between station pairs and the smoothness of the temporal variation of the drift rate. We employed Akaike’s Bayesian information criterion (ABIC) to estimate these hyper-parameters. A comparison between results from applying the classical and the Bayesian adjustment methods to some simulated datasets showed that the new method is more robust and adaptive for solving problems caused by irregular nonlinear meter drift. The new adjustment method is capable of determining the time-varying drift rate function of any specific gravimeter and optimizing the weight constraints for every gravimeter used in a gravity survey. We also carried out an error analysis for the inverted gravity value at each station based on the marginal distribution. Finally, we used this approach to process actual gravity survey campaign data from an observation network in North China.

### The IERS EOP 14C04 solution for Earth orientation parameters consistent with ITRF 2014

Wed, 05/01/2019 - 00:00
Abstract

The Earth Orientation Center of the International Earth Rotation and Reference Systems Service (IERS) has the task to provide the scientific community with the international reference time series of Earth orientation parameters (EOP), referred to as IERS EOP C04 or C04. These series result from a combination of operational EOP series derived from VLBI, GNSS, SLR, and DORIS. The C04 series were updated to provide EOP series consistent with the set of station coordinates of the ITRF 2014. The new C04, referred to as IERS EOP 14C04, is aligned onto the most recent versions of the conventional reference frames (ITRF 2014 and ICRF2). Additionally, the combination algorithm was revised to include an improved weighting of the intra-technique solutions. Over the period 2010–2015, differences to the IVS combination exhibit standard deviations of 40  $$\upmu$$ as for nutation and 10  $$\upmu$$ s for UT1. Differences to the IGS combination reveal a standard deviation of 30  $$\upmu$$ as for polar motion. The IERS EOP 14C04 was adopted by the IERS directing board as the IERS reference series by February 1, 2017.

### On the computation of gravitational effects for tesseroids with constant and linearly varying density

Wed, 05/01/2019 - 00:00
Abstract

The accurate computation of gravitational effects from topographic and atmospheric masses is one of the core issues in gravity field modeling. Using gravity forward modeling based on Newton’s integral, mass distributions are generally decomposed into regular mass bodies, which can be represented by rectangular prisms or polyhedral bodies in a rectangular coordinate system, or tesseroids in a spherical coordinate system. In this study, we prefer the latter representation because it can directly take the Earth’s curvature into account, which is particularly beneficial for regional and global applications. Since the volume integral cannot be solved analytically in the case of tesseroids, approximation solutions are applied. However, one well-recognized issue of these solutions is that the accuracy decreases as the computation point approaches the tesseroid. To overcome this problem, we develop a method that can precisely compute the gravitational potential $$\left( V\right)$$ and vector $$\left( V_x, V_y, V_z\right)$$ on the tesseroid surface. In addition to considering a constant density for the tesseroid, we further derive formulas for a linearly varying density. In the near zone (up to a spherical distance of 15 times the horizontal tesseroid dimension from the computation point), the gravitational effects of the tesseroids are computed by Gauss–Legendre quadrature using a two-dimensional adaptive subdivision technique to ensure high accuracy. The tesseroids outside this region are evaluated by means of expanding the integral kernel in a Taylor series up to the second order. The method is validated by synthetic tests of spherical shells with constant and linearly varying density, and the resulting approximation error is less than $$10^{-4}\,\hbox {m}^2\,\hbox {s}^{-2}$$ for V, $$10^{-5}\,\hbox {mGal}$$ for $$V_x$$ , $$10^{-7}\,\hbox {mGal}$$ for $$V_y$$ , and $$10^{-4}\,\hbox {mGal}$$ for $$V_z$$ . Its practical applicability is then demonstrated through the computation of topographic reductions in the White Sands test area and of global atmospheric effects on the Earth’s surface using the US Standard Atmosphere 1976.

Theme by Danetsoft and Danang Probo Sayekti inspired by Maksimer