Investigation of tidal effects in lunar laser ranging

 The analysis of lunar laser ranging (LLR) data enables the determination of many parameters of the Earth–Moon system, such as lunar gravity coefficients, reflector and station coordinates which contribute to the realisation of the International Terrestrial Reference Frame 2000 (ITRF 2000), Earth orientation parameters [EOPs, which contribute to the global EOP solutions at the International Earth Rotation Service (IERS)] or quantities which parameterise relativistic effects in the solar system. The big advantage of LLR is the long time span of lunar observations (1970–2000). The accuracy of the normal points nowadays is about 1 cm.  The capability of LLR to determine tidal parameters is investigated. In principle, it could be assumed that LLR would contribute greatly to the investigation of tidal effects, because the Moon is the most important tide-generating body. In this respect some special topics such as treatment of the permanent tide and the effect of atmospheric loading are addressed and results for the tidal parameters h ₂ and l ₂ as well as values for the eight main tides are given. Received: 14 August 2000 / Accepted: 15 October 2001     

On determination of heights by using terrestrial clocks and GPS signals

 Considering a GPS satellite and two terrestrial stations, two types of equations are derived relating the heights of the two stations to the measured data (frequency ratio or clock rate differences) and the coordinates and velocity components of all three participating objects. The potential possibilities of using such relations for the determination of heights (in terms of geopotential numbers or orthometric heights) are discussed. Received: 6 December 2000 / Accepted: 9 July 2001     

Unification of vertical datums by GPS and gravimetric geoid models with application to Fennoscandia

The second Baltic Sea Level (BSL) GPS campaign was run for one week in June 1993. Data from 35 tide gauge sites and five fiducial stations were analysed, for three fiducial stations (Onsala, Mets?hovi and Wettzell) fixed at the ITRF93 system. On a time-scale of 5 days, precision was several parts in 10⁹ for the horizontal and vertical components. Accuracies were about 1 cm in comparison with the International GPS Geodynamical Service (IGS) coordinates in three directions. To connect the Swedish and the Finnish height systems, our numerical application utilises three approaches: a rigorous approach, a bias fit and a three-parameter fit. The results between the Swedish RH70 and the Finnish N 60 systems are estimated to −19.3 ± 6.5, −17 ± 6 and −15 ± 6 cm, respectively, by the three approaches. The results of the three indirect methods are in an agreement with those of a direct approach from levelling and gravity measurements. Received: 3 April 1996 / Accepted: 4 August 1997     

Linear drift and periodic variations observed in long time series of polar motion

 Two long time series were analysed: the C01 series of the International Earth Rotation Service and the pole series obtained by re-analysis of the classical astronomical observations using the HIPPARCOS reference frame. The linear drift of the pole was determined to be 3.31 ± 0.05 milliarcseconds/year towards 76.1 ± 0.80° west longitude. For the least-squares fit the a priori correlations between simultaneous pole coordinates x _p , y _p were taken into account, and the weighting function was calculated by estimating empirical variance components. The decadal variations of the pole path were investigated by Fourier and wavelet analysis. Using sliding windows, the periods and amplitudes of the Chandler wobble and annual wobble were determined. Typical periods in the variable Chandler wobble and annual wobble parameters were obtained from wavelet analyses. Received: 21 January 2000 / Accepted: 28 August 2000     

Accuracy of GPS-derived relative positions as a function of interstation distance and observing-session duration

 Ten days of GPS data from 1998 were processed to determine how the accuracy of a derived three-dimensional relative position vector between GPS antennas depends on the chord distance (denoted L) between these antennas and on the duration of the GPS observing session (denoted T). It was found that the dependence of accuracy on L is negligibly small when (a) using the `final' GPS satellite orbits disseminated by the International GPS Service, (b) fixing integer ambiguities, (c) estimating appropriate neutral-atmosphere-delay parameters, (d) 26 km ≤ L ≤ 300 km, and (e) 4 h ≤T ≤ 24 h. Under these same conditions, the standard error for the relative position in the north–south dimension (denoted S _n and expressed in mm) is adequately approximated by the equation S _n =k _n /T ^0.5 with k _n =9.5 ± 2.1 mm · h^0.5 and T expressed in hours. Similarly, the standard errors for the relative position in the east–west and in the up-down dimensions are adequately approximated by the equations S _e =k _e /T ^0.5 and S _u =k _u /T ^0.5, respectively, with k _e =9.9 ± 3.1 mm · h^0.5 and k _u =36.5 ± 9.1 mm · h^0.5. Received: 5 February 2001 / Accepted: 14 May 2001     

ITRS, PZ-90 and WGS 84: current realizations and the related transformation parameters

 The first results of the International GLONASS Experiment 1998 (IGEX-98) campaign have provided significant material to illustrate the mutual benefits of the GLONASS system and the realization of the International Terrestrial Reference System (ITRS). A specific aspect, namely the relationship between the World Geodetic System 1984 (WGS 84) and the PZ-90 system using ITRS as a primary standard, is investigated. A review of current works is carried out. A transformation strategy is proposed for the three systems based on recent results from IGEX-98 and an independent set of transformation parameters derived by the Jet Propulsion Laboratory from ITRF97 and PZ-90 coordinates for 16 global stations. Received: 9 June 2000 / Accepted: 12 June 2001     

An estimate of the geodetic accuracy attainable with a transportable lunar laser station

A transportable lunar laser ranging station can be expected to measure the range to the lunar corner retroreflectors from a site on the Earth's surface with an uncertainty of about 3 cms. The accuracy with which that station can infer its geocentric position is influenced by many factors including the uncertainties in the pole position and rotation rate of the Earth and the data loss due to weather. The results of a simplified modelling study intended to include these factors are presented in cartographic form. The modelling indicates that, assuming the successful operation of three or more widely separated fixed laser stations, the transportable station will be able to determine its relative geocentric position in all three coordinates with an accuracy comparable to the original range uncertainty.     

W0: an estimate in the Finnish Height Datum N60, epoch 1993.4, from twenty-five GPS points of the Baltic Sea Level Project

Based upon a data set of 25 points of the Baltic Sea Level Project, second campaign 1993.4, which are close to mareographic stations, described by (1) GPS derived Cartesian coordinates in the World Geodetic Reference System 1984 and (2) orthometric heights in the Finnish Height Datum N60, epoch 1993.4, we have computed the primary geodetic parameter W ₀(1993.4) for the epoch 1993.4 according to the following model. The Cartesian coordinates of the GPS stations have been converted into spheroidal coordinates. The gravity potential as the additive decomposition of the gravitational potential and the centrifugal potential has been computed for any GPS station in spheroidal coordinates, namely for a global spheroidal model of the gravitational potential field. For a global set of spheroidal harmonic coefficients a transformation of spherical harmonic coefficients into spheroidal harmonic coefficients has been implemented and applied to the global spherical model OSU 91A up to degree/order 360/360. The gravity potential with respect to a global spheroidal model of degree/order 360/360 has been finally transformed by means of the orthometric heights of the GPS stations with respect to the Finnish Height Datum N60, epoch 1993.4, in terms of the spheroidal “free-air” potential reduction in order to produce the spheroidal W ₀(1993.4) value. As a mean of those 25 W ₀(1993.4) data as well as a root mean square error estimation we computed W ₀(1993.4)=(6 263 685.58 ± 0.36) kgal × m. Finally a comparison of different W ₀ data with respect to a spherical harmonic global model and spheroidal harmonic global model of Somigliana-Pizetti type (level ellipsoid as a reference, degree/order 2/0) according to The Geodesist's Handbook 1992 has been made. Received: 7 November 1996 / Accepted: 27 March 1997     

A model for adjustment of differential gravity measurements with simultaneous gravimeter calibration

 A mathematical model is proposed for adjustment of differential or relative gravity measurements, involving simultaneously instrumental readings, coefficients of the calibration function, and gravity values of selected base stations. Tests were performed with LaCoste and Romberg model G gravimeter measurements for a set of base stations located along a north–south line with 1750 mGal gravity range. This line was linked to nine control stations, where absolute gravity values had been determined by the free-fall method, with an accuracy better than 10 μGal. The model shows good consistence and stability. Results show the possibility of improving the calibration functions of gravimeters, as well as a better estimation of the gravity values, due to the flexibility admitted to the values of the calibration coefficients. Received: 15 November 1999 / Accepted: 31 October 2000     

Prediction of surface horizontal displacements, and gravity and tilt changes caused by filling the Three Gorges Reservoir

 Horizontal displacements, and gravity and tilt changes induced by filling the Three Gorges Reservoir are modeled using elastic loading Green functions. When the water surface reaches its highest level, the effects become maximum on the reservoir banks. The longitudinal and latitudinal components of the horizontal displacements reach −8.2 and 7.7 mm respectively, gravity is increased by up to 3.4 mGal, and the prime vertical and meridian components of the tilt changes are −7.8 and −17.5 arcseconds respectively. Accordingly, the filling of the reservoir will influence values observed from global positioning system (GPS), gravimetry and tilt measurements in the area. The results given can be used to provide important corrections for extracting earthquake-related signals from observed data. Received: 19 January 2001 / Accepted: 3 September 2001     

Iterative vector methods for computing geodetic latitude and height from rectangular coordinates

 Two iterative vector methods for computing geodetic coordinates (φ, h) from rectangular coordinates (x, y, z) are presented. The methods are conceptually simple, work without modification at any latitude and are easy to program. Geodetic latitude and height can be calculated to acceptable precision in one iteration over the height range from −10⁶ to +10⁹ m. Received: 13 December 2000 / Accepted: 13 July 2001     

Apropos laser tracking to GPS satellites

. Laser tracking to GPS satellites (PRN5 and 6) provides an opportunity to compare GPS and laser systems directly and to combine data of both in a single solution. A few examples of this are given in this study. The most important results of the analysis are that (1) daily SLR station coordinate solutions could be generated with a few cm accuracy; (2) coordinates of nine stations were determined in a 2.3-year-long arc solution; (3) the contribution of laser data on the `SLR-GPS' combined orbit, resulting from the simultaneous processing of SLR and GPS data, is significant and (4) laser-only orbits have an accuracy of 10–20 cm, 1-day predictions of SLR orbits differ from IGS orbits by about 20–40 cm, 2-day predictions by 50–60 cm. Received: 1 October 1996 / Accepted: 14 February 1997     

A simulation study of multi-beam altimetry for lunar reconnaissance orbiter and other planetary missions

The combined use of altimetry, Earth-based Doppler and Earth-based range measurements in the lunar reconnaissance orbiter (LRO) mission (Chin et al. in Space Sci Rev 129:391–419, 2007) has been examined in a simulation study. It is found that in the initial phases of the mission orbit and altimeter geolocation accuracies should be better than 10 m in the radial component and 60 m overall. It is demonstrated that LRO’s precise 1-way laser range measurement from Earth-based stations (Smith et al. in Proceedings of the 15th International Laser Ranging Workshop, Canberra, Australia, October 15–20, 2006) will be useful for gravity recovery. The advantages of multiple laser beams are demonstrated for altimeter calibration, orbit determination and gravity recovery in general planetary settings as well as for LRO.     

Geoid undulation modelling and interpretation at Ladak, NW Himalaya using GPS and levelling data

Fast and accurate relative positioning for baselines less than 20 km in length is possible using dual-frequency Global Positioning System (GPS) receivers. By measuring orthometric heights of a few GPS stations by differential levelling techniques, the geoid undulation can be modelled, which enables GPS to be used for orthometric height determination in a much faster and more economical way than terrestrial methods. The geoid undulation anomaly can be very useful for studying tectonic structure. GPS, levelling and gravity measurements were carried out along a 200-km-long highly undulating profile, at an average elevation of 4000 m, in the Ladak region of NW Himalaya, India. The geoid undulation and gravity anomaly were measured at 28 common GPS-levelling and 67 GPS-gravity stations. A regional geoid low of nearly −4 m coincident with a steep negative gravity gradient is compatible with very recent findings from other geophysical studies of a low-velocity layer 20–30 km thick to the north of the India–Tibet plate boundary, within the Tibetan plate. Topographic, gravity and geoid data possibly indicate that the actual plate boundary is situated further north of what is geologically known as the Indus Tsangpo Suture Zone, the traditionally supposed location of the plate boundary. Comparison of the measured geoid with that computed from OSU91 and EGM96 gravity models indicates that GPS alone can be used for orthometric height determination over the Higher Himalaya with 1–2 m accuracy. Received: 10 April 1997 / Accepted: 9 October 1998     

Laser station coordinates and baselines from long-ARC and short-ARC analyses of starlette

Laser ranging to Starlette from April 1983 to April 1984 has been used to determine a coordinate set, UASC.ST1, of laser reference points for 18 tracking stations. The coordinates were derived by application of the least-squares data reduction procedure in a simultaneous solution along with geodynamic parameters for 49 near consecutive 5–6 day arcs. Comparisons with the University of Texas station coordinates,LSC 8112 andLSC 8402, and theRGO, Herstmonceux, coordinates,RGOSC.LG2, reveal consistency to near 30 cm in each coordinate. Furthermore, the translation vectors of the comparisons are not significantly different from zero indicating consistency in the implied origins of the systems. The period of analysis included seven occasions in which STARLETTE was tracked near simultaneously by three or four laser stations in North America. Using the short arcs as reference frameworks, station coordinates were determined by application of two contrasting methods, namely, a multi-arc simultaneous analysis and a weighted mean of the individual pass solutions. The former compared more favourably with baselines from the long-arc solution with anRMS error of near 16 cm. Comparison against theLSC 8402 coordinates confirmed that baselines accurate to within 15 cm can be achieved by satellite laser ranging to Starlette.     

VLBI技术测月的数学模型探讨

近年各国已纷纷制定测月计划,采用何种技术对月球进行定位,变得尤为重要。本文通过对VLBI技术特点进行分析,VLBI是目前大地测量中精度最高的技术手段,但只适用于深空探测,因为深空射电信号到达地面时,可看作平行信号。本文针对VLBI技术特点及数学模型,对存在不可忽略视差的VLBI测月模型,通过级数展开,解决月面射电信号到达地球时的视差问题,并顾及地球自转得出最终数学模型,通过站间一次差分消除钟差等影响,得出VLBI对近轨天体(月球)表面射电源定位的数学模型。     

Accurate absolute GPS positioning through satellite clock error estimation

 An algorithm for very accurate absolute positioning through Global Positioning System (GPS) satellite clock estimation has been developed. Using International GPS Service (IGS) precise orbits and measurements, GPS clock errors were estimated at 30-s intervals. Compared to values determined by the Jet Propulsion Laboratory, the agreement was at the level of about 0.1 ns (3 cm). The clock error estimates were then applied to an absolute positioning algorithm in both static and kinematic modes. For the static case, an IGS station was selected and the coordinates were estimated every 30 s. The estimated absolute position coordinates and the known values had a mean difference of up to 18 cm with standard deviation less than 2 cm. For the kinematic case, data obtained every second from a GPS buoy were tested and the result from the absolute positioning was compared to a differential GPS (DGPS) solution. The mean differences between the coordinates estimated by the two methods are less than 40 cm and the standard deviations are less than 25 cm. It was verified that this poorer standard deviation on 1-s position results is due to the clock error interpolation from 30-s estimates with Selective Availability (SA). After SA was turned off, higher-rate clock error estimates (such as 1 s) could be obtained by a simple interpolation with negligible corruption. Therefore, the proposed absolute positioning technique can be used to within a few centimeters' precision at any rate by estimating 30-s satellite clock errors and interpolating them. Received: 16 May 2000 / Accepted: 23 October 2000     

A new combined European permanent network station coordinates solution

The EUREF [International Association of Geodesy (IAG) Reference Frame Sub-Commission for Europe] network of continuously operating GPS stations (EPN) was primarily established for reference frame maintenance, and also plays an important role for geodynamical research in Europe. The main objective of this paper is to obtain an independent homogeneous time series of the EPN station coordinates, which is also available in SINEX format. A new combined solution of the EPN station coordinates was computed. The combination was performed independently for every week, in three steps: (1) the stated constraints on the coordinates were removed from the individual solutions of the Analysis Centers; (2) the de-constrained solutions were aligned to ITRF2000; (3) the resulting solutions were combined using the Helmert blocking technique. All the data from GPS weeks 900 to 1302 (April 1997–December 2004) were used. We investigated in detail the behavior of the transformation parameters aligning the new combined solution to ITRF2000. In general, the time series of the transformation parameters show a good stability in time although small systematic effects can be seen, most likely caused by station instabilities. A comparison of the new combined solution to the official EUREF weekly combined solution is also presented.     

A new ΔLOD series in monthly intervals (1892.0–1997.0) and its comparison with other geophysical results

Using the ΔT (integrated variation of the Earth's rotation measured in terestrial time) series (1891.5–1955.5) derived from lunar occultation observations and the UT1–UTC (universal time–coordinated universal time) series (1955.5–1997.5) of the Bureau International de L'Heure/International Earth Rotation Service, a new ΔLOD (variation of the length of day) series in monthly intervals from 1892.0 to 1997.0 is calculated. Using digital filtering, the interannual and decadal components of the ΔLOD series are separated and then compared with those inferred from other geophysical quantities. It is shown that, on the interannual time scale, atmospheric processes can play an important role in exciting astronomical ΔLOD. However, the main oscillation with a mean period of about 5.8 years and peak-to-peak amplitude of about 0.3 ms in the residuals of ΔLOD(Astr) −ΔLOD(Wind) for 1968.0–1997.0 suggests that about half of the amplitude in astronomical ΔLOD must be excited by other geophysical processes, while on the decadal time scale the atmospheric excitation is too small. Geomagnetic core–mantle coupling may be a plausible source of the excitation of ΔLOD on the decadal time scale, but the geomagnetic data are still insufficient and an improved model of core–mantle coupling is required. Received: 3 April 1998 / Accepted: 31 May 1999     

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