Combining the geodetic models of vertical crustal deformation

Different kinds of analytical models of vertical curstal deformation have both advantages and disadvantages, and are appropriate to different deformation patterns. It is difficult to identify which deformation model is most suitable for a particular deformation area. In order to obtain a more precise and reliable analytical result, the combined model based on forecast theory has been approached. As a result, the fitting ability of single models is significantly improved. The combined model still possesses the same important features as the single models, which enable transferal of the derived crustal deformation information, within or even outside the time span of the data coverage, from geodetic sites to any user-specified locations where geodetic data may not exist. Examples are presented of both numerical simulation and a real-life situation, and the results are analysed in detail to demonstrate the efficiency of the proposed methodology. Received: 26 January 1998 / Accepted 14 August 1998     

Devising stable geometrical reference frames for use in geodetic studies of vertical crustal motion

We present a method for constructing and assessing the stability of a geometrical reference frame for use in vertical crustal motion studies. Our approach exploits the fact that when we transform GPS velocity solutions from one reference frame (RF) to another one using a Helmert transformation, only the frame translation rate parameters produce significant changes in the vertical station velocities expressed in the final RF. Loosely speaking, one can select and impose a ‘vertical RF’ from an ensemble of candidate frames, without any reference to the ‘horizontal RF’ (which can be selected and imposed afterwards), by seeing how the frame translation rates vary as one moves across the ensemble of frames. We order this ensemble according to the number of stations, N, incorporated into the set VREF whose RMS vertical motion is minimized in order to realize each frame. The value of N controls the level of scatter in, and hence the degree of similarity between the vertical velocities of the stations composing VREF. We characterize a specific vertical RF as stable if all of the frames located in a large neighborhood of the ensemble which includes the specific frame are characterized by very small relative frame translation rates. In this case, the expression of vertical GPS station velocities in any of these frames would lead to very similar results. We present a case study using a very large global time series in which we find a large RF neighborhood in which vertical station velocities are globally stable at the $\sim $ 0.2 mm/year level, and a slightly smaller neighborhood in which vertical stability improves to $\sim $ 0.1 mm/year level in polar regions.     

The role of frame definitions in the geodetic determination of crustal deformation parameters

A study of the role of coordinate frame definitions in the determination of crustal deformation parameters is first carried out for the theoretical case where displacement information between two discrete time epochs is continuously available for all area points. The obtained results are next applied to the realistic case where the required continuous information is derived by means of an interpolation of the known coordinate variations at the points of a horizontal geodetic network. The problem is different from the usual one of frame-invariant interpolation, since not only the domain of definition, but also the interpolated quantities, depend on independent choices of coordinate frames. Specific necessary and sufficient conditions for the invariance of derived crustal deformation parameters are given for linear type of interpolations of either the coordinates at the second epoch or of the displacements. With the help of the above conditions the invariance characteristics of two commonly used types of linear interpolations are finally derived, in order to illustrate the practical significance of the results.     

Propagation of error in precise levelling and its bearing on the assessment of recent crustal movements

Inference from repeated levellings regarding recent crustal movements is discussed in connection with the assessment of indications of local vertical movements and regional tilts. The recommended procedure of evaluating the propagation of error in large levelling networks is given together with the system of statistical tests leading to the determination of the level of significance of apparent changes in height. A practical example is analysed to show that when the changes are too small to be individually significant the probabilities of uplift and subsidence can be combined to indicate the most probable trend. Another example illustrates the testing of the possible influence of outlying differences on conclusions drawn from the comparison of repeated levellings in search of indications of gradual tilting.     

Long-arc analyses of SLR observations of the Etalon geodetic satellites

In this paper we describe the results of an analysis of a 2.5-year set of satellite laser range observations of the two Etalon geodetic satellites. We fit continuous orbits to the range observations, and map the range residuals into series of equivalent orbital element residuals, considering in detail the orbital longitude, eccentricity and nodal residuals. We use the longitude residuals to study thermal effects acting on the satellites and compare the results with those published for the Lageos satellites. We discuss the differences between the two series of eccentricity residuals, and again compare the results with those from Lageos. Finally we use the nodal residuals to investigate the potential for determination of UT1 of the reference frame defined by the orbits of the Etalon satellites. Received: 30 January 1997 / Accepted: 11 December 1997     

Contemporary crustal velocity field in Alpine Mediterranean area of Italy from new geodetic data

A new crustal velocity field for the Alpine Mediterranean area was determined by using a time series spanning 6.5 years of 113 global navigation satellite system (GNSS) permanent stations. This area is characterized by a complex tectonic setting driven by the interaction of Eurasian and African plates. The processing was performed by using a state-of-the-art absolute antenna phase center correction model and by using recomputed precise International GNSS Service orbits, available since April 2014. Thus, a new and more accurate tropospheric mapping function for geodetic applications was adopted. Results provide a new detailed map of the kinematics throughout the entire study area. In some area of the Italian peninsula, such as in the central Apennines, the velocity vector orientation appears rotated with respect to previous results. These discrepancies suggest that the geodynamic setting of this sector of Mediterranean area should be revised in accordance with these new results.     

Analysis of geodetic satellite (Geos I) observations in North America

Geos I observations made at thirty optical and four Secor stations were analyzed in the geometric and short-arc modes for the purpose of detecting systematic distortions in the North American Datum. The results indicate that the Nad at its origin (Meades Ranch, Kansas) requires an easterly rotation in azimuth and a westerly rotation in the prime vertical plane, both in the magnitude of one second of arc to fit the satellite data. There is also evidence of the need for a reduction in scale of about 1:200.000.     

利用天测与测地VLBI观测建立天球与地球参考架

本文讨论了利用天测与测地 VLBI观测建立天球与地球参考架过程中所面临的问题及解决的技术途径 ,涉及天球参考架与地球参考架原点与定向的确定、地球参考架时间演变的确定等。并通过实测数据分析与结果比对证明解决途径的有效性。     

Simulations of VLBI observations of a geodetic satellite providing co-location in space

We performed Monte Carlo simulations of very-long-baseline interferometry (VLBI) observations of Earth-orbiting satellites incorporating co-located space-geodetic instruments in order to study how well the VLBI frame and the spacecraft frame can be tied using such measurements. We simulated observations of spacecraft by VLBI observations, time-of-flight (TOF) measurements using a time-encoded signal in the spacecraft transmission, similar in concept to precise point positioning, and differential VLBI (D-VLBI) observations using angularly nearby quasar calibrators to compare their relative performance. We used the proposed European Geodetic Reference Antenna in Space (E-GRASP) mission as an initial test case for our software. We found that the standard VLBI technique is limited, in part, by the present lack of knowledge of the absolute offset of VLBI time to Coordinated Universal Time at the level of microseconds. TOF measurements are better able to overcome this problem and provide frame ties with uncertainties in translation and scale nearly a factor of three smaller than those yielded from VLBI measurements. If the absolute time offset issue can be resolved by external means, the VLBI results can be significantly improved and can come close to providing 1 mm accuracy in the frame tie parameters. D-VLBI observations with optimum performance assumptions provide roughly a factor of two higher uncertainties for the E-GRASP orbit. We additionally simulated how station and spacecraft position offsets affect the frame tie performance.     

Space orientation and geodetic azimuths of long lines from observations of the ANNA Satellite

The space orientation and geodetic azimuths of lines ranging from 300 km to 1400 km have been determined from simultaneous optical observations of the ANNA Flashing Satellite. The results of this test prove that the azimuth and the space direction between two stations can be achieved to an accuracy of 0.5″ and 0.8″ second respectively with only a limited amount of data. The reason for the high accuracy is attributed to two factors: [1] the metric quality of the PC-1000's stellar cameras, and [2] the “perfect” simultaneity in the observations provided by the ANNA flashing light. Much of this work was accomplished by the writer while employed by the Geodesy and Gravity Branch of Cambridge Research Laboratories.     

Effect of the selection of reference radio sources on geodetic estimates from VLBI observations

This paper evaluates the effect of the accuracy of reference radio sources on the daily estimates of station positions, nutation angle offsets, and the estimated site coordinates determined by very long baseline interferometry (VLBI), which are used for the realization of the international terrestrial reference frame (ITRF). Five global VLBI solutions, based on VLBI data collected between 1979 and 2006, are compared. The reference solution comprises all observed radio sources, which are treated as global parameters. Four other solutions, comprising different sub-sets of radio sources, were computed. The daily station positions for all VLBI sites and the corrections to the nutation offset angles were estimated for these five solutions. The solution statistics are mainly affected by the positional instabilities of reference radio sources, whereas the instabilities of geodetic and astrometric time-series are caused by an insufficient number of observed reference radio sources. A mean offset of the three positional components (Up, North, East) between any two solutions was calculated for each VLBI site. From a comparison of the geodetic results, no significant discrepancies between the respective geodetic solutions for all VLBI sites in the Northern Hemisphere were found. In contrast, the Southern Hemisphere sites were more sensitive to the selected set of reference radio sources. The largest estimated mean offset of the vertical component between two solutions for the Australian VLBI site at Hobart was 4 mm. In the worst case (if a weak VLBI network observed a limited number of reference radio sources) the daily offsets of the estimated height component at Hobart exceeded 100 mm. The exclusion of the extended radio sources from the list of reference sources improved the solution statistics and made the geodetic and astrometric time-series more consistent. The problem with the large Hobart height component offset is magnified by a comparatively small number of observations due to the low slewing rate of the VLBI dish (1°/ s). Unless a minimum of 200 scans are performed per 24-h VLBI experiment, the daily vertical positions at Hobart do not achieve 10 mm accuracy. Improving the slew rate at Hobart and/or having an increased number of new sites in the Southern Hemisphere is essential for further improvement of geodetic VLBI results for Southern Hemisphere sites.     

数值流形方法及在川滇地区地壳运动研究中的应用

The numerical manifold method （NMM） can calculate the movements and deformations of structures or materials. Both the finite element method （FEM） for continua and the discontinuous deformation analysis （DDA） for block systems are special cases of NMM. NMM has separate mathematical covers and physical meshes： the mathematical covers define only fine or rough approximations; as the real material boundary, the physical mesh defines the integration fields. The mathematical covers are triangle units; the physical mesh includes the fault boundaries, joints, blocks and interfaces of different crust zones on the basis of a geological tectonic background. Aiming at the complex problem of continuous and discontinuous deformation across the Chinese continent, the numerical manifold method （NMM） is brought in to study crustal movement of the Stchuan-Yunnan area. Based on the GPS velocity field in the Sichuan-Yunnan area, a crustal strain and stress field is simulated and analyzed. Moreover, results show that the NMM is a more suitable method than DDA in simulating the movement of the Sichuan-Yunnan area. Finally, a kind of mechanism of crustal motion in the Sichuan-Yunnan area is discussed in the paper.     

The deflection of the vertical of major geodetic datums and the semimajor axis of the Earth's ellipsoid as obtained from satellite observations

The geocentric (terrestrial) coordinates of the 12 Baker-Nunn stations are derived from an analysis of 46,535 observations of 13 different satellites, and the absolute deflection of the vertical for 7 datums is determined. Based on those deflections of the vertical and through geoidal fit, the value of a=6.378169 Mm for the semimajor axis of the earth's ellipsoid is derived. Smithsonian Institution Astrophysical Observatory