Plate kinematics of Nubia–Somalia using a combined DORIS and GPS solution

We have used up to 12 years of data to assess DORIS performance for geodynamics applications. We first examine the noise characteristics of the DORIS time-series of weekly station coordinates to derive realistic estimates of velocity uncertainties. We find that a combination of white and flicker noise best explains the DORIS time-series noise characteristics. Second, weekly solutions produced by the Institut Géographique National/Jet Propulsion Laboratory (IGN/JPL) DORIS Analysis Centre are combined to derive a global velocity field. This solution is combined with two independent GPS solutions, including 11 sites on Nubia and 5 on the Somalia plate. The combination indicates that DORIS horizontal velocities have an average accuracy of 3 mm/year, with best-determined sites having velocity accuracy better than 1 mm/year (one-sigma levels). Using our combined velocity field, we derive an updated plate kinematics model with a focus on the Nubia–Somalia area. Including DORIS data improves the precision of the angular velocity vector for Nubia by 15%. Our proposed model provides robust bounds on the maximum opening rates along the East African Rift (4.7–6.7 mm/year). It indicates opening rates 15 and 7% slower than values predicted by NUVEL-1A for the southern Atlantic Ocean and Indian Ocean, respectively. These differences are likely to arise from the fact that NUVEL-1A considered Africa as a single non-deforming plate, while here we use a more refined approach.     

Estimating the noise in space-geodetic positioning: the case of DORIS

The noise spectrum in DORIS ground- station motion is investigated by means of the Allan variance method applied to the decomposition of the 3D signal into its principal components in the time domain. Sets of weekly position time-series from 1994 to 2005 derived by three IDS Analysis Centres (IGN-JPL, INASAN, and LEGOS-CLS) for 119 stations at 69 sites are considered. The observing satellites are SPOT-2, SPOT-3, SPOT-4, and SPOT-5, TOPEX/Poseidon, and ENVISAT. Annual and semi-annual perturbations, as well as the 117.3-day term associated with the TOPEX/Poseidon orbit, are found at most stations. Their amplitudes reach up to 19.3, 23.7, and 13.3 mm, respectively, for the three analysis centres (ACs). When corrected for these components and a linear drift, the time-series dominantly show white noise (WN) at the 10–45mm level the noise level is the highest in the East direction, probably in connection with the high orbit inclinations. The noise level is minimum for the high latitude stations, mostly and intensively observed by the SPOT satellites, and the determination of the noise type is unclear; longer observation spans would be needed to decide between interannual variations and flicker noise. The improvement in positioning due to the DORIS constellation extension from three to five satellites in 2002, and the network rejuvenation program initiated in 2000, results in a decrease of the noise level by a factor of 1.7 in a WN context, both before and after the changes. One example of the benefit of studying the signal in the time eigenspace domain is the detection of anomalously large WN in the East direction for station HBKB (Hartebeesthoek, Africa) that masks the above-mentioned improvement. Studying the projection on the local frame of the second and third time-eigenspace components, a noise excess is detected in the North direction for some of the ACs. Station stability derived from our time-series analysis confirms, in general, the expected performance based on the careful technical review of the station components (antenna, pillar, etc.). The respective merits of our noise qualification method, based on direct time-series analysis in the time-eigenspace domain without any a priori statistical model, in comparison with other methods, such as the selection of a mixed-noise model by maximum likelihood estimation, are discussed.     

DORIS Contribution to ITRF2005

We examine the contribution of the Doppler Orbit determination and Radiopositioning Integrated by Satellite (DORIS) technique to the International Terrestrial Reference Frame (ITRF2005) by evaluating the quality of the submitted solutions as well as that of the frame parameters, especially the origin and the scale. Unlike the previous versions of the ITRF, ITRF2005 is constructed with input data in the form of time-series of station positions (weekly for satellite techniques and daily for VLBI) and daily Earth orientation parameters (EOPs), including full variance–covariance information. Analysis of the DORIS station positions’ time-series indicates an internal precision reaching 15 mm or better, at a weekly sampling. A cumulative solution using 12 years of weekly time-series was obtained and compared to a similar International GNSS Service (IGS) GPS solution (at 37 co-located sites) yielding a weighted root mean scatter (WRMS) of the order of 8 mm in position (at the epoch of minimum variance) and about 2.5 mm/year in velocity. The quality of this cumulative solution resulting from the combination of two individual DORIS solutions is better than any individual solution. A quality assessment of polar motion embedded in the contributed DORIS solutions is performed by comparison with the results of other space-geodetic techniques and in particular GPS. The inferred WRMS of polar motion varies significantly from one DORIS solution to another and is between 0.5 and 2 mas, depending on the strategy used and in particular estimating or not polar motion rate by the analysis centers. This particular aspect certainly needs more investigation by the DORIS Analysis Centers.     

Systematic errors in the Z-geocenter derived using satellite tracking data: a case study from SPOT-4 DORIS data in 1998

Within the scope of the Global Geodetic Observing System, Doppler Orbit Determination and Radiopositioning Integrated by Satellite – as a geodetic technique – can provide precise and continuous monitoring of the geocenter motion related to mass redistribution in the Earth, ocean and atmosphere system. We have reanalyzed 1998 DORIS/SPOT-4 (Satellite pour l’ Observation de la Terre) data that were previously generating inconsistent geocenter positions (?65 cm offset). We show here that this error is due to an incorrect phase center correction provided with the DORIS preprocessed data resulting from a +12 cm offset in the cross-track direction that has been confirmed since. We also conclude that a 1 mm error in the cross-track offset of non-yawing sun-synchronous SPOT satellites will generate a ?6.5 mm error in the derived Z-geocenter. Other non-yawing satellites would also be affected by a similar effect whose amplitude could be easily estimated from the orbit inclination     

Tectonic plate motion and co-seismic steps surveyed by DORIS field beacons: the New Hebrides experiment

 The New Hebrides experiment consisted of setting up a pair of DORIS beacons in remote tropical islands in the southwestern Pacific, between 1993 and 1997. Because of orbitography requirements on TOPEX/Poséidon, the beacons were only transmitting to SPOT satellites. Root-mean-square (RMS) scatters at the centimeter level on the latitude and vertical components were achieved, but 2-cm RMS scatters affected the longitude component. Nevertheless, results of relative velocity (123 mm/year N250°) are very consistent with those obtained using the global positioning system (GPS) (126 mm/yr N246°). The co-seismic step (12 mm N60°) related to the Walpole event (M _W = 7.7) is consistent with that derived from GPS (10 mm N30°) or from the centroid moment tensor (CMT) of the quake (12 mm N000°). Received: 19 November 1999 / Accepted: 17 May 2000     

地表质量负载对格陵兰岛区域GPS站点坐标时序特征的影响

选取ITRF2008框架下格陵兰岛区域12个GPS站2013年1月-2016年12月期间的日解坐标时间序列作为研究对象,并利用极大似然估计分析地表质量负载改正前后各站点的噪声特性、速度场及周期项振幅。结果表明：站点最优噪声模型主要为白噪声+幂律噪声与白噪声+闪烁噪声,地表质量负载形变修正GPS坐标时序后,明显增加U方向闪烁噪声的成分,平均降低其速度约0.36 mm/a,对水平方向影响较小;同时分别降低高程方向44.1%、14.2%的1 a项、0.5 a项振幅,相反,却增加了水平方向的周期项振幅。     

顾及共模误差的大区域GPS网坐标时间序列噪声分析

噪声分析对GPS时间序列分析有着重要影响,然而针对时间跨度较长的大尺度GPS网的共模误差相关研究较少。本文选取了平均基线长度大于2000 km的欧洲地区9个GPS台站2006-2014年的数据,使用主成分分析法剔除坐标时间序列的共模误差,同时利用极大似然估计的方法对滤波前后的时间序列进行了噪声分析。结果表明,欧洲地区广域GPS网的噪声模型存在多样性,各个分量具有不同的噪声特性,主要表现为白噪声+闪烁噪声、白噪声+幂率噪声,少部分台站N、E两个方向含有随机漫步噪声。经过空间滤波后,部分台站最优噪声模型发生改变,但仍以白噪声+闪烁噪声、白噪声+幂率噪声为主。滤波对N、E方向速度场影响为0.2 mm/a,U方向速度场影响为0.5 mm/a。     

An investigation of GNSS atomic clock behavior at short time intervals

A technique for obtaining clock measurements from individual GNSS satellites at short time intervals is presented. The methodology developed in this study allows for accurate satellite clock stability analysis without an ultra-stable clock at the ground receiver. Variations in the carrier phase caused by the satellite clock are isolated using a combination of common GNSS carrier-phase processing techniques. Furthermore, the white phase variations caused by the thermal noise of the collection and processing equipment are statistically modeled and removed, allowing for analysis of clock performance at subsecond intervals. Allan deviation analyses of signals collected from GPS and GLONASS satellites reveal distinct intervals of clock noise for timescales less than 100 s. The clock data collected from GPS Block IIA, IIR, IIR-M, and GLONASS satellites reveal similar stability performance at time periods greater than 20 s. The GLONASS clock stability in the 0.6–10 s range, however, is significantly worse than GPS. Applications that rely on ultra-stable clock behavior from the GLONASS satellites at these timescales may therefore require high-rate corrections to estimate and remove oscillator-based errors in the carrier phase.     

Multi-technique comparison of tropospheric zenith delays derived during the CONT02 campaign

In October 2002, 15 continuous days of Very Long Baseline Interferometry (VLBI) data were observed in the Continuous VLBI 2002 (CONT02) campaign. All eight radio telescopes involved in CONT02 were co-located with at least one other space-geodetic technique, and three of them also with a Water Vapor Radiometer (WVR). The goal of this paper is to compare the tropospheric zenith delays observed during CONT02 by VLBI, Global Positioning System (GPS), Doppler Orbitography Radiopositioning Integrated by Satellite (DORIS) and WVR and to compare them also with operational pressure level data from the European Centre for Medium-Range Weather Forecasts (ECMWF). We show that the tropospheric zenith delays from VLBI and GPS are in good agreement at the 3–7 mm level. However, while only small biases can be found for most of the stations, at Kokee Park (Hawaii, USA) and Westford (Massachusetts, USA) the zenith delays derived by GPS are larger by more than 5 mm than those from VLBI. At three of the four DORIS stations, there is also a fairly good agreement with GPS and VLBI (about 10 mm), but at Kokee Park the agreement is only at about 30 mm standard deviation, probably due to the much older installation and type of DORIS equipment. This comparison also allows testing of different DORIS analysis strategies with respect to their real impact on the precision of the derived tropospheric parameters. Ground truth information about the zenith delays can also be obtained from the ECMWF numerical weather model and at three sites using WVR measurements, allowing for comparisons with results from the space-geodetic techniques. While there is a good agreement (with some problems mentioned above about DORIS) among the space-geodetic techniques, the comparison with WVR and ECMWF is at a lower accuracy level. The complete CONT02 data set is sufficient to derive a good estimate of the actual precision and accuracy of each geodetic technique for applications in meteorology.     

Total Electron Content Variations Observed by a DORIS Station During the 2004 Sumatra–Andaman Earthquake

For about 40 years, ionospheric variations [including total electron content (TEC)] have been observed from time to time during large earthquakes. The TEC is the integrated electron density between a ground beacon and a satellite. It is a by-product of the International DORIS Service (IDS), which is also used for precise orbit determination of altimetric satellites. This paper reports the study of TEC variations observed by the DORIS station Cibinong, Indonesia (CICB, latitude: 6.48°S; longitude: 106.85°E) at the time of the Sumatra–Andaman earthquake (magnitude 9.2), which occurred on December 26, 2004. Numerous and intense aftershocks followed for several months after the main shock. An analysis was done to compare the variation of the TEC intensity observed by several satellites with the occurrence of these earthquakes. For comparison, the same study was also performed for another earthquake occurred very close to CICB but at a very different time. The main result is that the DORIS data show a TEC perturbation during night time close to the epicenter prior to the main Sumatra–Andaman earthquake event.     

Estimating rate uncertainty with maximum likelihood: differences between power-law and flicker–random-walk models

Recent studies have documented that global positioning system (GPS) time series of position estimates have temporal correlations which have been modeled as a combination of power-law and white noise processes. When estimating quantities such as a constant rate from GPS time series data, the estimated uncertainties on these quantities are more realistic when using a noise model that includes temporal correlations than simply assuming temporally uncorrelated noise. However, the choice of the specific representation of correlated noise can affect the estimate of uncertainty. For many GPS time series, the background noise can be represented by either: (1) a sum of flicker and random-walk noise or, (2) as a power-law noise model that represents an average of the flicker and random-walk noise. For instance, if the underlying noise model is a combination of flicker and random-walk noise, then incorrectly choosing the power-law model could underestimate the rate uncertainty by a factor of two. Distinguishing between the two alternate noise models is difficult since the flicker component can dominate the assessment of the noise properties because it is spread over a significant portion of the measurable frequency band. But, although not necessarily detectable, the random-walk component can be a major constituent of the estimated rate uncertainty. None the less, it is possible to determine the upper bound on the random-walk noise.     

Plate Motion of India and Interseismic Strain in the Nepal Himalaya from GPS and DORIS Measurements

We analyse geodetically estimated deformation across the Nepal Himalaya in order to determine the geodetic rate of shortening between Southern Tibet and India, previously proposed to range from 12 to 21 mm yr^?1. The dataset includes spirit-levelling data along a road going from the Indian to the Tibetan border across Central Nepal, data from the DORIS station on Everest, which has been analysed since 1993, GPS campaign measurements from surveys carried on between 1995 and 2001, as well as data from continuous GPS stations along a transect at the logitude of Kathmandu operated continuously since 1997. The GPS data were processed in International Terrestrial Reference Frame 2000 (ITRF2000), together with the data from 20 International GNSS Service (IGS) stations and then combined using quasi- observation combination analysis (QOCA). Finally, spatially complementary velocities at stations in Southern Tibet, initially determined in ITRF97, were expressed in ITRF2000. After analysing previous studies by different authors, we determined the pole of rotation of the Indian tectonic plate to be located in ITRF2000 at 51.409±1.560° N and ?10.915±5.556°E, with an angular velocity of 0.483±0.015°. Myr^?1. Internal deformation of India is found to be small, corresponding to less than about 2 mm yr^?1 of baseline change between Southern India and the Himalayan piedmont. Based on an elastic dislocation model of interseismic strain and taking into account the uncertainty on India plate motion, the mean convergence rate across Central and Eastern Nepal is estimated to 19±2.5 mm yr^?1, (at the 67% confidence level). The main himalayan thrust (MHT) fault was found to be locked from the surface to a depth of about 20 km over a width of about 115 km. In these regions, the model parameters are well constrained, thanks to the long and continuous time-series from the permanent GPS as well as DORIS data. Further west, a convergence rate of 13.4±5 mm yr^?1, as well as a fault zone, locked over 150 km, are proposed. The slight discrepancy between the geologically estimated deformation rate of 21±1.5 mm yr^?1 and the 19±2.5 mm yr^?1 geodetic rate in Central and Eastern Nepal, as well as the lower geodetic rate in Western Nepal compared to Eastern Nepal, places bounds on possible temporal variations of the pattern and rate of strain in the period between large earthquakes in this region.     

The effect of seasonal and long-period geopotential variations on the GPS orbits

We examine the impact of using seasonal and long-period time-variable gravity field (TVG) models on GPS orbit determination, through simulations from 1994 to 2012. The models of time-variable gravity that we test include the GRGS release RL02 GRACE-derived 10-day gravity field models up to degree and order 20 (grgs20x20), a 4 × 4 series of weekly coefficients using GGM03S as a base derived from SLR and DORIS tracking to 11 satellites (tvg4x4), and a harmonic fit to the above 4 × 4 SLR–DORIS time series (goco2s_fit2). These detailed models are compared to GPS orbit simulations using a reference model (stdtvg) based on the International Earth Rotation Service (IERS) and International GNSS Service (IGS) repro1 standards. We find that the new TVG modeling produces significant along, cross-track orbit differences as well as annual, semi-annual, draconitic and long-period effects in the Helmert translation parameters (Tx, Ty, Tz) of the GPS orbits with magnitudes of several mm. We show that the simplistic TVG modeling approach used by all of the IGS Analysis Centers, which is based on the models provided by the IERS standards, becomes progressively less adequate following 2006 when compared to the seasonal and long-period TVG models.     

First results of DORIS data analysis at Geodetic Observatory Pecný

In a cooperation between the Astronomical Institute, University of Bern (AIUB), the Geodetic Observatory Pecný (GOPE), and the Institut Géographique National (IGN), DORIS data analysis capabilities were implemented into a development version of the Bernese GPS software. The DORIS Doppler observables are reformulated such that they are similar to global navigation satellite system (GNSS) carrier-phase observations, allowing the use of the same observation models and algorithms as for GNSS carrier-phase data analysis with only minor software modifications. As such, the same algorithms may be used to process DORIS carrier-phase observations. First results from the analysis of 3 weeks of DORIS data (September 2004, five DORIS-equipped satellites) at GOPE are promising and are presented here. They include the comparison of station coordinates with coordinate estimates derived by the Laboratoire d’Etudes en Géophysique et Océanographie Spatiale/Collecte Localisation Satellites analysis centre (LCA) and the Institut Géographique National/Jet Propulsion Laboratory (IGN/JPL), and the comparison of Earth orientation parameters (EOPs) with the International Earth Rotation and Reference Frames Service (IERS) C04 model. The modified Bernese results are of a slightly lower, but comparable, quality than corresponding solutions routinely computed within the IDS (International DORIS Service). The weekly coordinate repeatability RMS is of the order of 2–3 cm for each 3D station coordinate. Comparison with corresponding estimates of station coordinates from current IDS analysis centers demonstrates similar precision. Daily pole component estimates show a mean difference from IERS-C04 of 0.6  mas in X _p and  ? 0.5  mas in Y _p and a RMS of 0.8  mas in X _p and 0.9  mas in Y _p (mean removed). An automatic analysis procedure is under development at GOPE, and routine DORIS data processing will be implemented in the near future.     

有色噪声对东南极区域GPS测站三维速度估计的影响

近年来,有研究发现在GPS测站坐标时间序列中既存在白噪声,也存在有色噪声。为了研究有色噪声对东南极区域GPS测站三维速度估计的影响,本文使用GAMIT/GLOBK10.5软件对东南极区域6个连续GPS测站2005—2014年的实测数据进行解算和平差,并利用最大似然法（MLE）分别估计了在两种假设噪声模型条件下的测站三维运动速度及其不确定性。结果表明：在进行参数估计时,考虑两种有色噪声（闪烁噪声和随机游走噪声）对东南极区域GPS测站三维速度估计的量级影响不大,水平方向最大影响量级为0.3 mm/a,垂直方向最大影响量级为0.8 mm/a;但如果不考虑有色噪声,会严重低估参数估计的真实不确定性。     

Characterization of periodic variations in the GPS satellite clocks

The clock products of the International Global Navigation Satellite Systems (GNSS) Service (IGS) are used to characterize the timing performance of the GPS satellites. Using 5-min and 30-s observational samples and focusing only on the sub-daily regime, approximate power-law stochastic processes are found. The Block IIA Rb and Cs clocks obey predominantly random walk phase (or white frequency) noise processes. The Rb clocks are up to nearly an order of magnitude more stable and show a flicker phase noise component over intervals shorter than about 100 s. Due to the onboard Time Keeping System in the newer Block IIR and IIR-M satellites, their Rb clocks behave in a more complex way: as an apparent random walk phase process up to about 100 s and then changing to flicker phase up to a few thousand seconds. Superposed on this random background, periodic signals have been detected in all clock types at four harmonic frequencies, n × (2.0029 ± 0.0005) cycles per day (24 h coordinated universal time or UTC), for n = 1, 2, 3, and 4. The equivalent fundamental period is 11.9826 ± 0.0030 h, which surprisingly differs from the reported mean GPS orbital period of 11.9659 ± 0.0007 h by 60 ± 11 s. We cannot account for this apparent discrepancy but note that a clear relationship between the periodic signals and the orbital dynamics is evidenced for some satellites by modulations of the spectral amplitudes with eclipse season. All four harmonics are much smaller for the IIR and IIR-M satellites than for the older blocks. Awareness of the periodic variations can be used to improve the clock modeling, including for interpolation of tabulated IGS products for higher-rate GPS positioning and for predictions in real-time applications. This is especially true for high-accuracy uses, but could also benefit the standard GPS operational products. The observed stochastic properties of each satellite clock type are used to estimate the growth of interpolation and prediction errors with time interval.     

基于滑动L2优化准则的GPS坐标时间序列重构

GPS坐标时间序列中不仅包含白噪声,还包含闪烁噪声、随机漫步噪声等有色噪声,这些噪声将影响GPS应用的可靠性,甚至可能对一些地球物理现象做出错误的解释,因此降低GPS坐标时间序列中有色噪声的影响、提高GPS精度是一个重要和基本的问题。提出了一种滑动L₂优化估计方法(ML₂),通过选取合适的窗口建立L₂优化模型,再利用交替迭代乘子法求解每段时间序列的优化问题,并逐年滑动得到整段GPS坐标时间序列的估计。实验结果表明,ML₂方法与奇异谱分析、小波分解、滑动普通最小二乘法相比具有更好的重构效果。     

A model of present-day tectonic plate motions from 12 years of DORIS measurements

In the frame of the International DORIS Service (IDS), the Laboratoire d’Etudes en Géophysique et Océanographie Spatiales (LEGOS)/Collecte Localisation Satellites (CLS) Analysis Center (LCA) processes DORIS measurements from the SPOT, TOPEX/Poseidon and Envisat satellites and provides weekly station coordinates of the whole network to the IDS. Based on DORIS measurements, the horizontal and vertical velocities of 57 DORIS sites are computed. The 3D positions and velocities of the stations with linear motion are estimated simultaneously from the 12-year (1993–2004) combined normal equation matrix. We include 35 DORIS sites assumed to be located in the stable zones of 9 tectonic plates. For the motion of these plates, we propose a model (LCAVEL-1) of angular velocities in the ITRF2000 reference frame. Based on external comparison with the most recent global plate models (PB2002, REVEL, GSRM-1 and APKIM2000) and on internal analysis, we estimate an average velocity error of the DORIS solution of less than 3 mm/year. The LCAVEL-1 model presents new insights of the Somalia/Nubia pair of plates, as the DORIS technique has the advantage of having a few stations located on those two plates. We also computed (and provide in this article) the horizontal motion of the sites located close to plate boundaries or in the deformation zones defined in contemporary models. These computations could be used in further analysis for these particular regions of the Earth not moving as rigid plates.     

GPS position time-series analysis based on asymptotic normality of M-estimation

The efficacy of robust M-estimators is a well-known issue when dealing with observational blunders. When the number of observations is considerably large—long time series for instance—one can take advantage of the asymptotic normality of the M-estimation and compute reasonable estimates for the unknown parameters of interest. A few leading M-estimators have been employed to identify the most likely functional model for GPS coordinate time series. This includes the simultaneous detection of periodic patterns and offsets in the GPS time series. Estimates of white noise, flicker noise, and random walk noise components are also achieved using the robust M-estimators of (co)variance components, developed in the framework of the least-squares variance component estimation (LS-VCE) theory. The method allows one to compute confidence interval for the (co)variance components in asymptotic sense. Simulated time series using white noise plus flicker noise show that the estimates of random walk noise fluctuate more than those of flicker noise for different M-estimators. This is because random walk noise is not an appropriate noise structure for the series. The same phenomenon is observed using the results of real GPS time series, which implies that the combination of white plus flicker noise is well described for GPS time series. Some of the estimated noise components of LS-VCE differ significantly from those of other M- estimators. This reveals that there are a large number of outliers in the series. This conclusion is also affirmed by performing the statistical tests, which detect (large) parts of the outliers but can also leave parts to be undetected.