Contemporary deformation in the Kashmir–Himachal,Garhwal and Kumaon Himalaya: significant insights from 1995–2008 GPS time series

We present new insights on the time-averaged surface velocities, convergence and extension rates along arc-normal transects in Kumaon, Garhwal and Kashmir–Himachal regions in the Indian Himalaya from 13 years of high-precision Global Positioning System (GPS) time series (1995–2008) derived from GPS data at 14 GPS permanent and 42 campaign stations between $29.5{-}35^{\circ }\hbox {N}$ and $76{-}81^{\circ }\hbox {E}$ . The GPS surface horizontal velocities vary significantly from the Higher to Lesser Himalaya and are of the order of 30 to 48 mm/year NE in ITRF 2005 reference frame, and 17 to 2 mm/year SW in an India fixed reference frame indicating that this region is accommodating less than 2 cm/year of the India–Eurasia plate motion ( ${\sim }4~\hbox {cm/year}$ ). The total arc-normal shortening varies between ${\sim }10{-}14~\hbox {mm/year}$ along the different transects of the northwest Himalayan wedge, between the Indo-Tsangpo suture to the north and the Indo-Gangetic foreland to the south indicating high strain accumulation in the Himalayan wedge. This convergence is being accommodated differentially along the arc-normal transects; ${\sim } 5{-}10~\hbox {mm/year}$ in Lesser Himalaya and 3–4 mm/year in Higher Himalaya south of South Tibetan Detachment. Most of the convergence in the Lesser Himalaya of Garhwal and Kumaon is being accommodated just south of the Main Central Thrust fault trace, indicating high strain accumulation in this region which is also consistent with the high seismic activity in this region. In addition, for the first time an arc-normal extension of ${\sim }6~\hbox {mm/year}$ has also been observed in the Tethyan Himalaya of Kumaon. Inverse modeling of GPS-derived surface deformation rates in Garhwal and Kumaon Himalaya using a single dislocation indicate that the Main Himalayan Thrust is locked from the surface to a depth of ${\sim }15{-}20~\hbox {km}$ over a width of 110 km with associated slip rate of ${\sim }16{-}18~\hbox {mm/year}$ . These results indicate that the arc-normal rates in the Northwest Himalaya have a complex deformation pattern involving both convergence and extension, and rigorous seismo-tectonic models in the Himalaya are necessary to account for this pattern. In addition, the results also gave an estimate of co-seismic and post-seismic motion associated with the 1999 Chamoli earthquake, which is modeled to derive the slip and geometry of the rupture plane.     

Confirming regional 1 cm differential geoid accuracy from airborne gravimetry: the Geoid Slope Validation Survey of 2011

A terrestrial survey, called the Geoid Slope Validation Survey of 2011 (GSVS11), encompassing leveling, GPS, astrogeodetic deflections of the vertical (DOV) and surface gravity was performed in the United States. The general purpose of that survey was to evaluate the current accuracy of gravimetric geoid models, and also to determine the impact of introducing new airborne gravity data from the ‘Gravity for the Redefinition of the American Vertical Datum’ (GRAV-D) project. More specifically, the GSVS11 survey was performed to determine whether or not the GRAV-D airborne gravimetry, flown at 11 km altitude, can reduce differential geoid error to below 1 cm in a low, flat gravimetrically uncomplicated region. GSVS11 comprises a 325 km traverse from Austin to Rockport in Southern Texas, and includes 218 GPS stations ( $\sigma _{\Delta h }= 0.4$ cm over any distance from 0.4 to 325 km) co-located with first-order spirit leveled orthometric heights ( $\sigma _{\Delta H }= 1.3$ cm end-to-end), including new surface gravimetry, and 216 astronomically determined vertical deflections $(\sigma _{\mathrm{DOV}}= 0.1^{\prime \prime })$ . The terrestrial survey data were compared in various ways to specific geoid models, including analysis of RMS residuals between all pairs of points on the line, direct comparison of DOVs to geoid slopes, and a harmonic analysis of the differences between the terrestrial data and various geoid models. These comparisons of the terrestrial survey data with specific geoid models showed conclusively that, in this type of region (low, flat) the geoid models computed using existing terrestrial gravity, combined with digital elevation models (DEMs) and GRACE and GOCE data, differential geoid accuracy of 1 to 3 cm (1 $\sigma )$ over distances from 0.4 to 325 km were currently being achieved. However, the addition of a contemporaneous airborne gravity data set, flown at 11 km altitude, brought the estimated differential geoid accuracy down to 1 cm over nearly all distances from 0.4 to 325 km.     

A high-precision digital astrogeodetic traverse in an area of steep geoid gradients close to the coast of Perth,Western Australia

We present results from a new vertical deflection (VD) traverse observed in Perth, Western Australia, which is the first of its kind in the Southern Hemisphere. A digital astrogeodetic QDaedalus instrument was deployed to measure VDs with \({\sim }\)0.2\(''\) precision at 39 benchmarks with a \({{\sim }}1~\hbox {km}\) spacing. For the conversion of VDs to quasigeoid height differences, the method of astronomical–topographical levelling was applied, based on topographical information from the Shuttle Radar Topography Mission. The astronomical quasigeoid heights are in 20–30 mm (RMS) agreement with three independent gravimetric quasigeoid models, and the astrogeodetic VDs agree to 0.2–0.3\(''\) (north–south) and 0.6–0.9\(''\) (east–west) RMS. Tilt-like biases of \({\sim }1\,\,\hbox {mm}\) over \({\sim }1\,\,\hbox {km}\) are present for all quasigeoid models within \({\sim }20\,\,\hbox {km}\) of the coastline, suggesting inconsistencies in the coastal zone gravity data. The VD campaign in Perth was designed as a low-cost effort, possibly allowing replication in other Southern Hemisphere countries (e.g., Asia, Africa, South America and Antarctica), where VD data are particularly scarce.     

Deformation analysis of the Lake Urmia causeway (LUC) embankments in northwest Iran: insights from multi-sensor interferometry synthetic aperture radar (InSAR) data and finite element modeling (FEM)

This paper presents deformation analysis of Lake Urmia causeway (LUC) embankments in northwest Iran using observations from interferometry synthetic aperture radar (InSAR) and finite element model (FEM) simulation. 58 SAR images including 10 ALOS, 30 Envisat and 18 TerraSAR-X are used to assess settlement of the embankments during 2003–2013. The interferometric dataset includes 140 differential interferograms which are processed using InSAR time series technique of small baseline subset approach. The results show a clear indication of large deformation on the embankments with peak amplitude of \(>\) 50 mm/year in 2003–2010, increasing to \(>\!\!80\)  mm/year in 2012–2013 in the line of sight (LOS) direction from ground to the satellite. 2D decomposition of InSAR observations from Envisat and ALOS satellites that overlap in the years 2007–2010 shows that the rate of the vertical settlement and horizontal motion is not uniform along the embankments; Both eastern and western embankments show significant vertical motion, while horizontal motion plays a more significant role in eastern embankment than western embankment. The InSAR results are then used to simulate deformation using FEM at two cross-sections at the distance of 4 and 9 km from the most western edge of the LUC for which detailed stratigraphy data are available. Results suggest that consolidation due to dissipation of excess pore pressure in embankments can satisfactory predict settlement of the LUC embankments. Our numerical modeling indicates that nearly half of the consolidation since the construction time of the causeway 30 years ago has been done.     

Global height system unification with GOCE: a simulation study on the indirect bias term in the GBVP approach

One of the main objectives of ESA’s Gravity Field and Steady-State Ocean Circulation mission GOCE (Gravity field and steady-state ocean circulation mission, 1999) is to allow global unification of height systems by directly providing potential differences between benchmarks in different height datum zones. In other words, GOCE provides a globally consistent and unbiased geoid. If this information is combined with ellipsoidal (derived from geodetic space techniques) and physical heights (derived from leveling/gravimetry) at the same benchmarks, datum offsets between the datum zones can be determined and all zones unified. The expected accuracy of GOCE is around 2–3 cm up to spherical harmonic degree n _max ≈ 200. The omission error above this degree amounts to about 30 cm which cannot be neglected. Therefore, terrestrial residual gravity anomalies are necessary to evaluate the medium and short wavelengths of the geoid, i.e. one has to solve the Geodetic Boundary Value Problem (GBVP). The theory of height unification by the GBVP approach is well developed, see e.g. Colombo (A World Vertical Network. Report 296, Department of Geodetic Science and Surveying, 1980) or Rummel and Teunissen (Bull Geod 62:477–498, 1988). Thereby, it must be considered that terrestrial gravity anomalies referring to different datum zones are biased due to the respective datum offsets. Consequently, the height reference surface of a specific datum zone deviates from the unbiased geoid not only due to its own datum offset (direct bias term) but is also indirectly affected by the integration of biased gravity anomalies. The latter effect is called the indirect bias term and it considerably complicates the adjustment model for global height unification. If no satellite based gravity model is employed, this error amounts to about the same size as the datum offsets, i.e. 1–2 m globally. We show that this value decreases if a satellite-only gravity model is used. Specifically for GOCE with n _max ≈ 200, the error can be expected not to exceed the level of 1 cm, allowing the effect to be neglected in practical height unification. The results are supported by recent findings by Gatti et al. (J Geod, 2012).     

Canadian gravimetric geoid model 2010

A new gravimetric geoid model, Canadian Gravimetric Geoid 2010 (CGG2010), has been developed to upgrade the previous geoid model CGG2005. CGG2010 represents the separation between the reference ellipsoid of GRS80 and the Earth’s equipotential surface of $W_0=62{,}636{,}855.69~\mathrm{m}^2\mathrm{s}^{-2}$ W 0 = 62 , 636 , 855.69 m 2 s ? 2 . The Stokes–Helmert method has been re-formulated for the determination of CGG2010 by a new Stokes kernel modification. It reduces the effect of the systematic error in the Canadian terrestrial gravity data on the geoid to the level below 2 cm from about 20 cm using other existing modification techniques, and renders a smooth spectral combination of the satellite and terrestrial gravity data. The long wavelength components of CGG2010 include the GOCE contribution contained in a combined GRACE and GOCE geopotential model: GOCO01S, which ranges from $-20.1$ ? 20.1 to 16.7 cm with an RMS of 2.9 cm. Improvement has been also achieved through the refinement of geoid modelling procedure and the use of new data. (1) The downward continuation effect has been accounted accurately ranging from $-22.1$ ? 22.1 to 16.5 cm with an RMS of 0.9 cm. (2) The geoid residual from the Stokes integral is reduced to 4 cm in RMS by the use of an ultra-high degree spherical harmonic representation of global elevation model for deriving the reference Helmert field in conjunction with a derived global geopotential model. (3) The Canadian gravimetric geoid model is published for the first time with associated error estimates. In addition, CGG2010 includes the new marine gravity data, ArcGP gravity grids, and the new Canadian Digital Elevation Data (CDED) 1:50K. CGG2010 is compared to GPS-levelling data in Canada. The standard deviations are estimated to vary from 2 to 10 cm with the largest error in the mountainous areas of western Canada. We demonstrate its improvement over the previous models CGG2005 and EGM2008.     

Impact of seasonal station motions on VLBI UT1 intensives results

UT1 estimates obtained from the very long baseline interferometry (VLBI) Intensives data depend on the station displacement model used during processing. In particular, because of seasonal variations, the instantaneous station position during the specific intensive session differs from the position predicted by the linear model generally used. This can cause systematic errors in UT1 Intensives results. In this paper, we first investigated the seasonal signal in the station displacements for the 5 VLBI antennas participating in UT1 Intensives observing programs, along with the 8 collocated GPS stations. It was found that a significant annual term is present in the time series for most stations, and its amplitude can reach 8 mm in the height component, and 2 mm in horizontal components. However, the annual signals found in the displacements of the collocated VLBI and GPS stations at some sites differ substantially in amplitude and phase. The semiannual harmonics are relatively small and unstable, and for most stations no prevailing signal was found in the corresponding frequency band. Then two UT1 Intensives series were computed with and without including the seasonal term found in the previous step in the station movement model. Comparison of these series has shown that neglecting the seasonal station position variations can cause a systematic error in UT1 estimates, which can exceed 1  $\upmu $ s, depending on the observing program.     

Reducing the draconitic errors in GNSS geodetic products

Systematic errors at harmonics of the GPS draconitic year have been found in diverse GPS-derived geodetic products like the geocenter $Z$ -component, station coordinates, $Y$ -pole rate and orbits (i.e. orbit overlaps). The GPS draconitic year is the repeat period of the GPS constellation w.r.t. the Sun which is about 351 days. Different error sources have been proposed which could generate these spurious signals at the draconitic harmonics. In this study, we focus on one of these error sources, namely the radiation pressure orbit modeling deficiencies. For this purpose, three GPS+GLONASS solutions of 8 years (2004–2011) were computed which differ only in the solar radiation pressure (SRP) and satellite attitude models. The models employed in the solutions are: (1) the CODE (5-parameter) radiation pressure model widely used within the International GNSS Service community, (2) the adjustable box-wing model for SRP impacting GPS (and GLONASS) satellites, and (3) the adjustable box-wing model upgraded to use non-nominal yaw attitude, specially for satellites in eclipse seasons. When comparing the first solution with the third one we achieved the following in the GNSS geodetic products. Orbits: the draconitic errors in the orbit overlaps are reduced for the GPS satellites in all the harmonics on average 46, 38 and 57 % for the radial, along-track and cross-track components, while for GLONASS satellites they are mainly reduced in the cross-track component by 39 %. Geocenter $Z$ -component: all the odd draconitic harmonics found when the CODE model is used show a very important reduction (almost disappearing with a 92 % average reduction) with the new radiation pressure models. Earth orientation parameters: the draconitic errors are reduced for the $X$ -pole rate and especially for the $Y$ -pole rate by 24 and 50 % respectively. Station coordinates: all the draconitic harmonics (except the 2nd harmonic in the North component) are reduced in the North, East and Height components, with average reductions of 41, 39 and 35 % respectively. This shows, that part of the draconitic errors currently found in GNSS geodetic products are definitely induced by the CODE radiation pressure orbit modeling deficiencies.     

Homogeneous reprocessing of GPS,GLONASS and SLR observations

The International GNSS Service (IGS) provides operational products for the GPS and GLONASS constellation. Homogeneously processed time series of parameters from the IGS are only available for GPS. Reprocessed GLONASS series are provided only by individual Analysis Centers (i. e. CODE and ESA), making it difficult to fully include the GLONASS system into a rigorous GNSS analysis. In view of the increasing number of active GLONASS satellites and a steadily growing number of GPS+GLONASS-tracking stations available over the past few years, Technische Universität Dresden, Technische Universität München, Universität Bern and Eidgenössische Technische Hochschule Zürich performed a combined reprocessing of GPS and GLONASS observations. Also, SLR observations to GPS and GLONASS are included in this reprocessing effort. Here, we show only SLR results from a GNSS orbit validation. In total, 18 years of data (1994–2011) have been processed from altogether 340 GNSS and 70 SLR stations. The use of GLONASS observations in addition to GPS has no impact on the estimated linear terrestrial reference frame parameters. However, daily station positions show an RMS reduction of 0.3 mm on average for the height component when additional GLONASS observations can be used for the time series determination. Analyzing satellite orbit overlaps, the rigorous combination of GPS and GLONASS neither improves nor degrades the GPS orbit precision. For GLONASS, however, the quality of the microwave-derived GLONASS orbits improves due to the combination. These findings are confirmed using independent SLR observations for a GNSS orbit validation. In comparison to previous studies, mean SLR biases for satellites GPS-35 and GPS-36 could be reduced in magnitude from \(-35\) and \(-38\)  mm to \(-12\) and \(-13\)  mm, respectively. Our results show that remaining SLR biases depend on the satellite type and the use of coated or uncoated retro-reflectors. For Earth rotation parameters, the increasing number of GLONASS satellites and tracking stations over the past few years leads to differences between GPS-only and GPS+GLONASS combined solutions which are most pronounced in the pole rate estimates with maximum 0.2 mas/day in magnitude. At the same time, the difference between GLONASS-only and combined solutions decreases. Derived GNSS orbits are used to estimate combined GPS+GLONASS satellite clocks, with first results presented in this paper. Phase observation residuals from a precise point positioning are at the level of 2 mm and particularly reveal poorly modeled yaw maneuver periods.     

Evaluation of the third- and fourth-generation GOCE Earth gravity field models with Australian terrestrial gravity data in spherical harmonics

In March 2013, the fourth generation of European Space Agency’s (ESA) global gravity field models, DIR4 (Bruinsma et al. in Proceedings of the ESA living planet symposium, 28 June–2 July, Bergen, ESA, Publication SP-686, 2010b) and TIM4 (Migliaccio et al. in Proceedings of the ESA living planet symposium, 28 June–2 July, Bergen, ESA, Publication SP-686, 2010), generated from the Gravity field and steady-state Ocean Circulation Explorer (GOCE) gravity observation satellite was released. We evaluate the models using an independent ground truth data set of gravity anomalies over Australia. Combined with Gravity Recovery and Climate Experiment (GRACE) satellite gravity, a new gravity model is obtained that is used to perform comparisons with GOCE models in spherical harmonics. Over Australia, the new gravity model proves to have significantly higher accuracy in the degrees below 120 as compared to EGM2008 and seems to be at least comparable to the accuracy of this model between degree 150 and degree 260. Comparisons in terms of residual quasi-geoid heights, gravity disturbances, and radial gravity gradients evaluated on the ellipsoid and at approximate GOCE mean satellite altitude ( $h=250$  km) show both fourth generation models to improve significantly w.r.t. their predecessors. Relatively, we find a root-mean-square improvement of 39 % for the DIR4 and 23 % for TIM4 over the respective third release models at a spatial scale of 100 km (degree 200). In terms of absolute errors, TIM4 is found to perform slightly better in the bands from degree 120 up to degree 160 and DIR4 is found to perform slightly better than TIM4 from degree 170 up to degree 250. Our analyses cannot confirm the DIR4 formal error of 1 cm geoid height (0.35 mGal in terms of gravity) at degree 200. The formal errors of TIM4, with 3.2 cm geoid height (0.9 mGal in terms of gravity) at degree 200, seem to be realistic. Due to combination with GRACE and SLR data, the DIR models, at satellite altitude, clearly show lower RMS values compared to TIM models in the long wavelength part of the spectrum (below degree and order 120). Our study shows different spectral sensitivity of different functionals at ground level and at GOCE satellite altitude and establishes the link among these findings and the Meissl scheme (Rummel and van Gelderen in Manusrcipta Geodaetica 20:379–385, 1995).     

Effect of the processing methodology on satellite altimetry-based global mean sea level rise over the Jason-1 operating period

Determining how the global mean sea level (GMSL) evolves with time is of primary importance to understand one of the main consequences of global warming and its potential impact on populations living near coasts or in low-lying islands. Five groups are routinely providing satellite altimetry-based estimates of the GMSL over the altimetry era (since late 1992). Because each group developed its own approach to compute the GMSL time series, this leads to some differences in the GMSL interannual variability and linear trend. While over the whole high-precision altimetry time span (1993–2012), good agreement is noticed for the computed GMSL linear trend (of $3.1\pm 0.4$  mm/year), on shorter time spans (e.g., ${<}10~\hbox {years}$ ), trend differences are significantly larger than the 0.4 mm/year uncertainty. Here we investigate the sources of the trend differences, focusing on the averaging methods used to generate the GMSL. For that purpose, we consider outputs from two different groups: the Colorado University (CU) and Archiving, Validation and Interpretation of Satellite Oceanographic Data (AVISO) because associated processing of each group is largely representative of all other groups. For this investigation, we use the high-resolution MERCATOR ocean circulation model with data assimilation (version Glorys2-v1) and compute synthetic sea surface height (SSH) data by interpolating the model grids at the time and location of “true” along-track satellite altimetry measurements, focusing on the Jason-1 operating period (i.e., 2002–2009). These synthetic SSH data are then treated as “real” altimetry measurements, allowing us to test the different averaging methods used by the two processing groups for computing the GMSL: (1) averaging along-track altimetry data (as done by CU) or (2) gridding the along-track data into $2^{\circ }\times 2^{\circ }$ meshes and then geographical averaging of the gridded data (as done by AVISO). We also investigate the effect of considering or not SSH data at shallow depths $({<}120~\hbox {m})$ as well as the editing procedure. We find that the main difference comes from the averaging method with significant differences depending on latitude. In the tropics, the $2^{\circ }\times 2^{\circ }$ gridding method used by AVISO overestimates by 11 % the GMSL trend. At high latitudes (above $60^{\circ }\hbox {N}/\hbox {S}$ ), both methods underestimate the GMSL trend. Our calculation shows that the CU method (along-track averaging) and AVISO gridding process underestimate the trend in high latitudes of the northern hemisphere by 0.9 and 1.2 mm/year, respectively. While we were able to attribute the AVISO trend overestimation in the tropics to grid cells with too few data, the cause of underestimation at high latitudes remains unclear and needs further investigation.     

Continental hydrology loading observed by VLBI measurements

Variations in continental water storage lead to loading deformation of the crust with typical peak-to-peak variations at very long baseline interferometry (VLBI) sites of 3–15 mm in the vertical component and 1–2 mm in the horizontal component. The hydrology signal at VLBI sites has annual and semi-annual components and clear interannual variations. We have calculated the hydrology loading series using mass loading distributions derived from the global land data assimilation system (GLDAS) hydrology model and alternatively from a global grid of equal-area gravity recovery and climate experiment (GRACE) mascons. In the analysis of the two weekly VLBI 24-h R1 and R4 network sessions from 2003 to 2010 the baseline length repeatabilities are reduced in 79 % (80 %) of baselines when GLDAS (GRACE) loading corrections are applied. Site vertical coordinate repeatabilities are reduced in about 80 % of the sites when either GLDAS or GRACE loading is used. In the horizontal components, reduction occurs in 70–80 % of the sites. Estimates of the annual site vertical amplitudes were reduced for 16 out of 18 sites if either loading series was applied. We estimated loading admittance factors for each site and found that the average admittances were 1.01 \(\pm \) 0.05 for GRACE and 1.39 \(\pm \) 0.07 for GLDAS. The standard deviations of the GRACE admittances and GLDAS admittances were 0.31 and 0.68, respectively. For sites that have been observed in a set of sufficiently temporally dense daily sessions, the average correlation between VLBI vertical monthly averaged series and GLDAS or GRACE loading series was 0.47 and 0.43, respectively.     

Using DORIS measurements for modeling the vertical total electron content of the Earth’s ionosphere

The Doppler orbitography and radiopositioning integrated by satellite (DORIS) system was originally developed for precise orbit determination of low Earth orbiting (LEO) satellites. Beyond that, it is highly qualified for modeling the distribution of electrons within the Earth’s ionosphere. It measures with two frequencies in L-band with a relative frequency ratio close to 5. Since the terrestrial ground beacons are distributed quite homogeneously and several LEOs are equipped with modern receivers, a good applicability for global vertical total electron content (VTEC) modeling can be expected. This paper investigates the capability of DORIS dual-frequency phase observations for deriving VTEC and the contribution of these data to global VTEC modeling. The DORIS preprocessing is performed similar to commonly used global navigation satellite systems (GNSS) preprocessing. However, the absolute DORIS VTEC level is taken from global ionospheric maps (GIM) provided by the International GNSS Service (IGS) as the DORIS data contain no absolute information. DORIS-derived VTEC values show good consistency with IGS GIMs with a RMS between 2 and 3 total electron content units (TECU) depending on solar activity which can be reduced to less than 2 TECU when using only observations with elevation angles higher than \(50^\circ \) . The combination of DORIS VTEC with data from other space-geodetic measurement techniques improves the accuracy of global VTEC models significantly. If DORIS VTEC data is used to update IGS GIMs, an improvement of up to 12  % can be achieved. The accuracy directly beneath the DORIS satellites’ ground-tracks ranges between 1.5 and 3.5 TECU assuming a precision of 2.5 TECU for altimeter-derived VTEC values which have been used for validation purposes.     

Non-linear station motions in epoch and multi-year reference frames

In the conventions of the International Earth Rotation and Reference Systems Service (e.g. IERS Conventions 2010), it is recommended that the instantaneous station position, which is fixed to the Earth’s crust, is described by a regularized station position and conventional correction models. Current realizations of the International Terrestrial Reference Frame use a station position at a reference epoch and a constant velocity to describe the motion of the regularized station position in time. An advantage of this parameterization is the possibility to provide station coordinates of high accuracy over a long time span. Various publications have shown that residual non-linear station motions can reach a magnitude of a few centimeters due to not considered loading effects. Consistently estimated parameters like the Earth Orientation Parameters (EOP) may be affected if these non-linear station motions are neglected. In this paper, we investigate a new approach, which is based on a frequent (e.g. weekly) estimation of station positions and EOP from a combination of epoch normal equations of the space geodetic techniques Global Positioning System (GPS), Satellite Laser Ranging (SLR) and Very Long Baseline Interferometry (VLBI). The resulting time series of epoch reference frames are studied in detail and are compared with the conventional secular approach. It is shown that both approaches have specific advantages and disadvantages, which are discussed in the paper. A major advantage of the frequently estimated epoch reference frames is that the non-linear station motions are implicitly taken into account, which is a major limiting factor for the accuracy of the secular frames. Various test computations and comparisons between the epoch and secular approach are performed. The authors found that the consistently estimated EOP are systematically affected by the two different combination approaches. The differences between the epoch and secular frames reach magnitudes of $23.6~\upmu \hbox {as}$ (0.73 mm) and $39.8~\upmu \hbox {as}$ (1.23 mm) for the x-pole and y-pole, respectively, in case of the combined solutions. For the SLR-only solutions, significant differences with amplitudes of $77.3~\upmu \hbox {as}$ (2.39 mm) can be found.     

Voxel-optimized regional water vapor tomography and comparison with radiosonde and numerical weather model

Water vapor tomography has been developed as a powerful tool to model spatial and temporal distribution of atmospheric water vapor. Global navigation satellite systems (GNSS) water vapor tomography refers to the 3D structural construction of tropospheric water vapor using a large number of GNSS signals that penetrate the tomographic modeling area from different positions. The modeling area is usually discretized into a number of voxels. A major issue involved is that some voxels are not crossed by any GNSS signal rays, resulting in an undetermined solution to the tomographic system. To alleviate this problem, the number of voxels crossed by GNSS signal rays should be as large as possible. An important way to achieve this is to optimize the geographic distribution of tomographic voxels. We propose an approach to optimize voxel distribution in both vertical and horizontal domains. In the vertical domain, water vapor profiles derived from radiosonde data are exploited to identify the maximum height of tomography and the optimal vertical resolution. In the horizontal domain, the optimal horizontal distribution of voxels is obtained by searching the maximum number of ray-crossing voxels in both latitude and longitude directions. The water vapor tomography optimization procedures are implemented using GPS water vapor data from the Hong Kong Satellite Positioning Reference Station Network. The tomographic water vapor fields solved from the optimized tomographic voxels are evaluated using radiosonde data and a numerical weather prediction non-hydrostatic model (NHM) obtained for the Hong Kong station. The comparisons of tomographic integrated water vapor (IWV) with the radiosonde and NHM IWV show that RMS errors of their differences are 1.41 and 3.09 mm, respectively. Moreover, the tomographic water vapor density results are compared with those of radiosonde and NHM. The RMS error of the density differences between tomography and radiosonde data is 1.05  \(\mathrm{g/m}^{3}\) . For the comparison between tomography and NHM, an overall RMS error of \(1.43\,\mathrm{g/m^{3}}\) is achieved.     

A complete VLBI delay model for deforming radio telescopes: the Effelsberg case

Deformations of radio telescopes used in geodetic and astrometric very long baseline interferometry (VLBI) observations belong to the class of systematic error sources which require correction in data analysis. In this paper we present a model for all path length variations in the geometrical optics of radio telescopes which are due to gravitational deformation. The Effelsberg 100 m radio telescope of the Max Planck Institute for Radio Astronomy, Bonn, Germany, has been surveyed by various terrestrial methods. Thus, all necessary information that is needed to model the path length variations is available. Additionally, a ray tracing program has been developed which uses as input the parameters of the measured deformations to produce an independent check of the theoretical model. In this program as well as in the theoretical model, the illumination function plays an important role because it serves as the weighting function for the individual path lengths depending on the distance from the optical axis. For the Effelsberg telescope, the biggest contribution to the total path length variations is the bending of the main beam located along the elevation axis which partly carries the weight of the paraboloid at its vertex. The difference in total path length is almost \(-\) 100 mm when comparing observations at 90 \(^\circ \) and at 0 \(^\circ \) elevation angle. The impact of the path length corrections is validated in a global VLBI analysis. The application of the correction model leads to a change in the vertical position of \(+120\)  mm. This is more than the maximum path length, but the effect can be explained by the shape of the correction function.     

A technique for routinely updating the ITU-R database using radio occultation electron density profiles

Well credited and widely used ionospheric models, such as the International Reference Ionosphere or NeQuick, describe the variation of the electron density with height by means of a piecewise profile tied to the F2-peak parameters: the electron density, $N_m \mathrm{F2}$ N m F 2 , and the height, $h_m \mathrm{F2}$ h m F 2 . Accurate values of these parameters are crucial for retrieving reliable electron density estimations from those models. When direct measurements of these parameters are not available, the models compute the parameters using the so-called ITU-R database, which was established in the early 1960s. This paper presents a technique aimed at routinely updating the ITU-R database using radio occultation electron density profiles derived from GPS measurements gathered from low Earth orbit satellites. Before being used, these radio occultation profiles are validated by fitting to them an electron density model. A re-weighted Least Squares algorithm is used for down-weighting unreliable measurements (occasionally, entire profiles) and to retrieve $N_m \mathrm{F2}$ N m F 2 and $h_m \mathrm{F2}$ h m F 2 values—together with their error estimates—from the profiles. These values are used to monthly update the database, which consists of two sets of ITU-R-like coefficients that could easily be implemented in the IRI or NeQuick models. The technique was tested with radio occultation electron density profiles that are delivered to the community by the COSMIC/FORMOSAT-3 mission team. Tests were performed for solstices and equinoxes seasons in high and low-solar activity conditions. The global mean error of the resulting maps—estimated by the Least Squares technique—is between $0.5\times 10^{10}$ 0.5 × 10 10 and $3.6\times 10^{10}$ 3.6 × 10 10 elec/m $^{-3}$ ? 3 for the F2-peak electron density (which is equivalent to 7 % of the value of the estimated parameter) and from 2.0 to 5.6 km for the height ( $\sim $ ～ 2 %).     

Ground movements caused by deep underground mining in Guan-Zhuang iron mine,Luzhong, China

It is difficult to calculate the accurate ground movement due to deep underground mining because of the complexity of the geotechnical environment. Guan-Zhuang iron mine is a pillarless sublevel caving mine operated by Luzhong Metallurgical Mining Company, south-east of Jinan, PR China. It mines the Zhangjiawa Seam at a depth of approximately 520 m. Although the towers are outside the conventional ‘angle of draw’ subsidence influence criteria, and have seen only negligible vertical displacement as a result of deep mining, there has been widespread evidence of regional horizontal displacement of the land surface, large distances away from the mining area. Possible explanations of these displacements include one or a combination of mechanisms such as pre-mining stress relaxation, regional joint patterns, soft rock strata, displacement toward active goaf areas. Luzhong Metallurgical Mining Company have been making precise measurements of distances near the shaft towers in the Guan-Zhuang iron mine since 2003. The results show horizontal displacements of up to 96 mm occur even when underground mining is about 0.8 km from the survey displacements. From an analysis of these and other survey results it is concluded that mining effects extend a long way from deep mining. The results also show that ground horizontal displacements are typically at least as great as the vertical component, that the maximum horizontal displacement occurs soon after undermining.     

The effects of frequency-dependent quasar variability on the celestial reference frame

We examine the relationship between source position stability and astrophysical properties of radio-loud quasars making up the International Celestial Reference Frame (ICRF2). Understanding this relationship is important for improving quasar selection and analysis strategies, and therefore reference frame stability. We construct flux density time series, known as light curves, for 95 of the most frequently observed ICRF2 quasars at both the 2.3 and 8.4 GHz geodetic very long baseline interferometry (VLBI) observing bands. Because the appearance of new quasar components corresponds to an increase in quasar flux density, these light curves alert us about potential changes in source structure before they appear in VLBI images. We test how source position stability depends on three astrophysical parameters: (1) flux density variability at X band; (2) time lag between flares in S and X bands; (3) spectral index root-mean-square (rms), defined as the variability in the ratio between S and X band flux densities. We find that the time lag between S and X band light curves provides a good indicator of position stability: sources with time lags $<$ 0.06 years are significantly more stable ( $>$ 20 % improvement in weighted rms) than sources with larger time lags. A similar improvement is obtained by observing sources with low $(<$ 0.12) spectral index variability. On the other hand, there is no strong dependence of source position stability on flux density variability in a single frequency band. These findings can be understood by interpreting the time lag between S and X band light curves as a measure of the size of the source structure. Monitoring of source flux density at multiple frequencies therefore appears to provide a useful probe of quasar structure on scales important to geodesy. The observed astrometric position of the brightest quasar component (the core) is known to depend on observing frequency. We show how multi-frequency flux density monitoring may allow the dependence on frequency of the relative core positions along the jet to be elucidated. Knowledge of the position–frequency relation has important implications for current and future geodetic VLBI programs, as well as the alignment between the radio and optical celestial reference frames.     

Error analysis of the NGS’ surface gravity database

Are the National Geodetic Survey’s surface gravity data sufficient for supporting the computation of a 1 cm-accurate geoid? This paper attempts to answer this question by deriving a few measures of accuracy for this data and estimating their effects on the US geoid. We use a data set which comprises ${\sim }1.4$ million gravity observations collected in 1,489 surveys. Comparisons to GRACE-derived gravity and geoid are made to estimate the long-wavelength errors. Crossover analysis and $K$ -nearest neighbor predictions are used for estimating local gravity biases and high-frequency gravity errors, and the corresponding geoid biases and high-frequency geoid errors are evaluated. Results indicate that 244 of all 1,489 surface gravity surveys have significant biases ${>}2$  mGal, with geoid implications that reach 20 cm. Some of the biased surveys are large enough in horizontal extent to be reliably corrected by satellite-derived gravity models, but many others are not. In addition, the results suggest that the data are contaminated by high-frequency errors with an RMS of ${\sim }2.2$  mGal. This causes high-frequency geoid errors of a few centimeters in and to the west of the Rocky Mountains and in the Appalachians and a few millimeters or less everywhere else. Finally, long-wavelength ( ${>}3^{\circ }$ ) surface gravity errors on the sub-mGal level but with large horizontal extent are found. All of the south and southeast of the USA is biased by +0.3 to +0.8 mGal and the Rocky Mountains by $-0.1$ to $-0.3$  mGal. These small but extensive gravity errors lead to long-wavelength geoid errors that reach 60 cm in the interior of the USA.