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First Brazilian Real Time Network DGPS through the Internet: Development, Application and Availability Analyses The Global Positioning System (GPS) is widely used by the civil community. Differential GPS (DGPS) was developed to provide better accuracy than autonomous GPS. The DGPS concept is based on the high correlation of errors due to atmospheric effects, satellite clocks and orbits. However, as the baseline grows, its efficiency decreases because the error correlation is reduced. This limitation can be handled by using a reference station network and applying the network DGPS concept (called NDGPS). In this paper, the goal is to present aspects related to the development and application of NDGPS in real time at the São Paulo state network in Brazil. The NDGPS corrections were computed from data received via the Internet using NTRIP (Networked Transport of RTCM via Internet Protocol). Our implementation was based on BNC (BKG Ntrip Client ) software. NDGPS provided RMS improvements of up to 59% in horizontal components and 31% in vertical components when compared to DGPS. The availability of the system, the first of this nature in Brazil, was also analyzed within the context of the SP State GNSS Network, located in the southeastern region of Brazil. The results also serve as an indication of the quality of local internet infrastructure for using in geodetic positioning.

Application of the BEM approach for a determination of the regional marine geoid model and the mean dynamic topography in the Southwest Pacific Ocean and Tasman Sea We apply a novel approach for the gravimetric marine geoid modelling which utilise the boundary element method (BEM). The direct BEM formulation for the Laplace equation is applied to obtain a numerical solution to the linearised fixed gravimetric boundary-value problem in points at the Earth's surface. The numerical scheme uses the collocation method with linear basis functions. It involves a discretisation of the Earth's surface which is considered as a fixed boundary. The surface gravity disturbances represent the oblique derivative boundary condition. The BEM approach is applied to determine the marine geoid model over the study area of the Southwest Pacific Ocean and Tasman Sea using DNSC08 marine gravity data. The comparison of the BEM-derived and EGM2008 geoid models reveals that the geoid height differences vary within -25 and 18 cm with the standard deviation of 6 cm. The DNSC08 sea surface topography data and the new marine geoid are then used for modelling of the mean dynamic topography (MDT) over the study area. The local vertical datum (LVD) offsets estimated at 15 tide-gauge stations in New Zealand are finally used for testing the coastal MDT. The average value of differences between the MDT and LVD offsets is 1 cm.

Performance of High-Rate Kinematic GPS During Strong Shaking: Observations from Shake Table Tests and the 2010 Chile Earthquake Over the last decade, the 1-sample-per-second kinematic Global Positioning System (GPS) has been used as a displacement sensor in earthquake observations and for structural health monitoring. Many researchers in both seismology and engineering have expressed the desire for higher-sample-rate (10-sample-per-second or higher) GPS data to acquire high-frequency displacement information. We performed several shake table tests of GPS observation on 29 April, 2009 for the purpose of evaluating the performance of high-rate kinematic GPS. We found that the accuracy of high-rate kinematic GPS depended on antenna movement, but was independent of receiver sampling rate. The errors in kinematic GPS measurements during the periods of strong shaking were systematically larger than those during the static periods. Furthermore, we found that these large errors were coincident with large accelerations and jerks in the motions experienced by the GPS receivers and antennas. Observations from the 2010 earthquake in Maule, Chile (M 8.8) indicated that strong ground motions can degrade the accuracy of high-rate kinematic GPS measurements. Significant jerks and/or accelerations can cause GPS units to temporarily lose tracking on satellite signals and lead to gaps in GPS-recorded seismograms.

Solutions to Linear Inverse Problems on the Sphere by Tikhonov Regularization, Wiener filtering and Spectral Smoothing and Combination — A Comparison Solutions to linear inverse problems on the sphere, common in geodesy and geophysics, are compared for Tikhonov's method of regularization, Wiener filtering and spectral smoothing and combination as well as harmonic analysis. It is concluded that Wiener and spectral smoothing, although based on different assumptions and target functions, yield the same estimator. Also, provided that the extra information on the signal and error degree variances is available, the standard Tikhonov method is inferior to the other methods, which, in contrast to Tikhonov's approach, match the spectral errors and signals in an optimum way. We show that the corresponding Tikhonov matrix for optimum regularization can only be determined approximately. Moreover, as Tikhonov's method solves an integral equation, it is less computationally efficient than the other methods, which use forward integration. Also harmonic analysis uses direct integration and is not hampered, as previous methods, with spectral leakage. Spectral combination, in addition to filtering, has the advantage of combining different data sets by least squares spectral weighting.

Comments to X. Li and Y. M. Wang (2011) Comparisons of geoid models over Alaska computed with different Stokes' kernel modifications, JGS 1(2): 136-142 Li and Wang recently compared geoid determination by various gravimetric methods for modifying Stokes' formula vs. using GPS/levelling geoid heights as a reference model. Possible large systematic errors in the differences of gravimetric and GPS/levelling geoid models deteriorate the results and conclusions. Moreover, spectral combination, the only stochastic method in the study, was applied in an unrealistic way.

Reply to Comments to X. Li and Y. M. Wang (2011) Comparisons of geoid models over Alaska computed with different Stokes' kernel modifications, JGS 1(2): 136-142 by L. E. Sjöberg The authors thank professor Sjöberg for having interest in our paper. The main goal of the paper is to test kernel modification methods used in geoid computations. Our tests found that Vanicek/Kleusberg's and Featherstone's methods fit the GPS/leveling data the best in the relative sense at various cap sizes. At the same time, we also pointed out that their methods are unstable and the mean values change from dm to meters by just changing the cap size. By contrast, the modification of the Wong and Gore type (including the spectral combination, method of Heck and Grüninger) is stable and insensitive to the truncation degree and cap size. This feature is especially useful when we know the accuracy of the gravity field at different frequency bands. For instance, it is advisable to truncate Stokes' kernel at a degree to which the satellite model is believed to be more accurate than surface data. The method of the Wong and Goretype does this job quite well. In contrast, the low degrees of Stokes' kernel are modified by Molodensky's coefficients t n in Vanicek/Kleusberg's and Featherstone's methods (cf. Eq. (6) in Li and Wang (2011)). It implies that the low degree gravity field of the reference model will be altered by less accurate surface data in the final geoid. This is also the cause of the larger variation in mean values of the geoid.

Interdecadal oscillations in Atmospheric Angular Momentum variations Global Atmospheric Angular Momentum (AAM) is an intrinsic index for describing processes that affect the atmospheric circulation on time scales ranging from intraseasonal to secular. It is associated with length-of-day (LOD) variability through conservation of global angular momentum in planet Earth and thus is of considerable importance for quantifying how the Earth acts as a system. The availability of lengthy AAM time series computed from the recent 20 th Century atmospheric reanalyses (1870-2008), complemented by the NCAR-NCEP reanalysis in the overlapping period of 1948-2008 allows the investigation of the role of decadal and interdecadal cycles as well as the recent overall trend in AAM. Thus, we extend to the entire 20 th century (and prior, back to 1870) results concerning decadal time scales and a secular positive trend detected over recent decades by different authors. In addition, we also note that AAM has features of interdecadal time scales that modulate the lower frequency variability. These interdecadal time signals oscillate with periods of about 30-50 years, and we found an indication of an 80-90 year period. Short term signals interact with the long-term (secular) trend. Particularly over the years 1950-1985 the global positive trend in AAM appears to result from a conjunction of constructive positive slopes from all lower frequency signals (interdecadal short-term trends and the long-term positive secular trend). Since the mid 1980s, however, the interdecadal oscillation short-term trend contribution decreases, as does the total signal in global AAM. These oscillations appear as two interdecadal modes originating within the Pacific (associated principally with the Pacific Decadal Oscillation and also ENSO) from which they propagate poleward, with differing characteristics in each hemisphere.

Comparison of remove-compute-restore and least squares modification of Stokes' formula techniques to quasi-geoid determination over the Auvergne test area The remove-compute-restore (RCR) technique for regional geoid determination implies that both topography and low-degree global geopotential model signals are removed before computation and restored after Stokes' integration or Least Squares Collocation (LSC) solution. The Least Squares Modification of Stokes' Formula (LSMS) technique not requiring gravity reductions is implemented here with a Residual Terrain Modelling based interpolation of gravity data. The 2-D Spherical Fast Fourier Transform (FFT) and the LSC methods applying the RCR technique and the LSMS method are tested over the Auvergne test area. All methods showed a reasonable agreement with GPS-levelling data, in the order of a 3-3.5 cm in the central region having relatively smooth topography, which is consistent with the accuracies of GPS and levelling. When a 1-parameter fit is used, the FFT method using kernel modification performs best with 3.0 cm r.m.s difference with GPS-levelling while the LSMS method gives the best agreement with GPS-levelling with 2.4 cm r.m.s after a 4-parameter fit is used. However, the quasi-geoid models derived using two techniques differed from each other up to 33 cm in the high mountains near the Alps. Comparison of quasi-geoid models with EGM2008 showed that the LSMS method agreed best in term of r.m.s.

A numerical method for solving the horizontal resection problem in Surveying The three-point resection problem, i.e., the problem of obtaining the position of an unknown point from relative angular measurements to three known stations is a basic operation in surveying engineering. In the last centuries, a number of approaches to solve this problem have been developed. In this note, a new numerical approach to solve this problem is presented. The method uses only basic formulae from coordinate geometry. We present also numerical simulations that show the good performance and accuracy of this approach.

Extraction of the deterministic ingredient of a dynamic geodetic control network A minimum constraints solution, which resolves the datum defect of a control network, is an arbitrary solution that may result in a systematic error in the estimation of the deformation parameters. This error is not derived from measurements and is usually inconsistent with the geophysical reality. A free network is affected only by errors of measurement and, therefore, a free network is an accepted way of coping with this problem. Study of deformations, which is based on the use of geodetic measurements, is usually performed today by defining a kinematic model. Such a model, when used to describe a complex geophysical environment, can lead to the partial estimation of the deterministic dynamics, which characterize the entire network. These dynamics are themselves expressed in measurements, as the adjustment systems' residuals. The current paper presents an extension of the definition of the parameters that are revalued. This extension enables the cleaning of measurements by means of the extraction of datum elements that have been defined by geodetic measurement. This cleaning minimizes the effects of these elements on the revaluated deformation. The proposed algorithm may be applied to achieve the simultaneous estimation of the physical parameters that define the geophysical activity in the network.