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1.
Following our earlier definition of the rigorous orthometric height [J Geod 79(1-3):82–92 (2005)] we present the derivation and calculation of the differences between this and the Helmert orthometric height, which is embedded in the vertical datums used in numerous countries. By way of comparison, we also consider Mader and Niethammer’s refinements to the Helmert orthometric height. For a profile across the Canadian Rocky Mountains (maximum height of ~2,800 m), the rigorous correction to Helmert’s height reaches ~13 cm, whereas the Mader and Niethammer corrections only reach ~3 cm. The discrepancy is due mostly to the rigorous correction’s consideration of the geoid-generated gravity disturbance. We also point out that several of the terms derived here are the same as those used in regional gravimetric geoid models, thus simplifying their implementation. This will enable those who currently use Helmert orthometric heights to upgrade them to a more rigorous height system based on the Earth’s gravity field and one that is more compatible with a regional geoid model.  相似文献   
2.
In regional gravimetric geoid determination, it is customary to use the modified Stokes formula that combines local terrestrial data with a global geopotential model. This study compares two deterministic and three stochastic modification methods for computing a regional geoid over the Baltic countries. The final selection of the best modification method is made by means of two accuracy estimates: the expected global mean square error of the geoid estimator, and the statistics of the post-fit residuals between the computed geoid models and precise GPS-levelling data. Numerical results show that the modification methods tested do not provide substantially different results, although the stochastic approaches appear formally better in the selected study area. The 2.8–5.3 cm (RMS) post-fit residuals to the GPS-levelling points indicate the suitability of the new geoid model for many practical applications. Moreover, the numerical comparisons reveal a one-dimensional offset between the regional vertical datum and the geoid models based upon the new GRACE-only geopotential model GGM01s. This gives an impression of a greater reliability of the new model compared to the earlier, EGM96-based and somewhat tilted regional geoid models for the same study area.  相似文献   
3.
Ship-board global navigation satellite system (GNSS) measurements are widely used to determine sea surface heights, marine geoid validation, and/or satellite altimetry calibration. However, the use of a vessel could be complicated near coastal areas due to shallow water. Therefore, in the area of sea ice formation, GNSS measurements on the ice surface could be a viable alternative to vessel-borne surveys. Importantly, the ice-covered water is not affected by short-term winds, which otherwise could have systematic influence on the instantaneous sea surface topography. This study tackles methodology and validation of marine geoid models by profile-wise GNSS measurements on ice in an archipelago of the Baltic Sea. The GNSS measurements were carried out on the three ice roads with total length 48 kilometers. The along-route standard deviation between the gravimetric geoid model and profile-wise GNSS heights remained within ±2.1 centimeters.  相似文献   
4.
This paper revisits several aspects of defining and computing the anomalous gravity data for purposes of gravimetric inversion/interpretation. Attention is paid to evaluation of a refined global topographic correction to the gravity disturbance based on the reference ellipsoid (RE) and constant reference density for solid topography onshore and sea water density for liquid topography offshore. The global bathymetric correction is discussed. Two issues associated with compilation and inversion of bathymetrically and topographically corrected gravity disturbances in regions of negative ellipsoidal (geodetic) heights are pointed out: the evaluation of normal gravity and the harmonic continuation of the gravity data. Stripping, the removal of an effect of a known density contrast, is considered also for additional geological elements such as lakes, glaciers, sedimentary basins, isostatic mountain roots, etc. The stripping corrections are discussed in the context of the gravimetric inverse problem.  相似文献   
5.
We report on testing the UNB (University of New Brunswick) software suite for accurate regional geoid model determination by use of Stokes-Helmert’s method against an Australian Synthetic Field (ASF) as “ground truth”. This testing has taken several years and has led to discoveries of several significant errors (larger than 5mm in the resulting geoid models) both in the UNB software as well as the ASF. It was our hope that, after correcting the errors in UNB software, we would be able to come up with some definite numbers as far as the achievable accuracy for a geoid model computed by the UNB software. Unfortunately, it turned out that the ASF contained errors, some of as yet unknown origin, that will have to be removed before that ultimate goal can be reached. Regardless, the testing has taught us some valuable lessons, which we describe in this paper. As matters stand now, it seems that given errorless gravity data on 1′ by 1′ grid, a digital elevation model of a reasonable accuracy and no topographical density variations, the Stokes-Helmert approach as realised in the UNB software suite is capable of delivering an accuracy of the geoid model of no constant bias, standard deviation of about 25 mm and a maximum range of about 200 mm. We note that the UNB software suite does not use any corrective measures, such as biases and tilts or surface fitting, so the resulting errors reflect only the errors in modelling the geoid.  相似文献   
6.
The deduction of a regularly spaced gravity anomaly grid from scattered survey data is studied, addressing mainly two aspects: reduction of gravity to anomalies and subsequent interpolation by various methods. The problem is illustrated in a heterogeneous study area and contrasting test areas including mountains, low terrains, and a marine area. Provided with realistic error estimates, Least Squares Collocation interpolation of Residual Terrain Model anomalies yields the highest quality gravity grid. In most cases, the Bouguer reduction and other interpolation methods tested are equally viable. However, spline-based interpolation should be avoided in marine areas with trackwise survey data.  相似文献   
7.
Geoid and quasigeoid modelling from gravity anomalies by the method of least squares modification of Stokes’s formula with additive corrections is adapted for the usage with gravity disturbances and Hotine’s formula. The biased, unbiased and optimum versions of least squares modification are considered. Equations are presented for the four additive corrections that account for the combined (direct plus indirect) effect of downward continuation (DWC), topographic, atmospheric and ellipsoidal corrections in geoid or quasigeoid modelling. The geoid or quasigeoid modelling scheme by the least squares modified Hotine formula is numerically verified, analysed and compared to the Stokes counterpart in a heterogeneous study area. The resulting geoid models and the additive corrections computed both for use with Stokes’s or Hotine’s formula differ most in high topography areas. Over the study area (reaching almost 2 km in altitude), the approximate geoid models (before the additive corrections) differ by 7 mm on average with a 3 mm standard deviation (SD) and a maximum of 1.3 cm. The additive corrections, out of which only the DWC correction has a numerically significant difference, improve the agreement between respective geoid or quasigeoid models to an average difference of 5 mm with a 1 mm SD and a maximum of 8 mm.  相似文献   
8.
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9.
In mountainous regions with scarce gravity data, gravimetric geoid determination is a difficult task that needs special attention to obtain reliable results satisfying the demands, e.g., of engineering applications. The present study investigates a procedure for combining a suitable global geopotential model and available terrestrial data in order to obtain a precise regional geoid model for Konya Closed Basin (KCB). The KCB is located in the central part of Turkey, where a very limited amount of terrestrial gravity data is available. Various data sources, such as the Turkish digital elevation model with 3 ?? × 3?? resolution, a recently published satellite-only global geopotential model from the Gravity Recovery and Climate Experiment satellite (GRACE) and the ground gravity observations, are combined in the least-squares sense by the modified Stokes?? formula. The new gravimetric geoid model is compared with Global Positioning System (GPS)/levelling at the control points, resulting in the Root Mean Square Error (RMS) differences of ±6.4 cm and 1.7 ppm in the absolute and relative senses, respectively. This regional geoid model appears to be more accurate than the Earth Gravitational Model 2008, which is the best global model over the target area, with the RMS differences of ±8.6 cm and 1.8 ppm in the absolute and relative senses, respectively. These results show that the accuracy of a regional gravimetric model can be augmented by the combination of a global geopotential model and local terrestrial data in mountainous areas even though the quality and resolution of the primary terrestrial data are not satisfactory to the geoid modelling procedure.  相似文献   
10.
To reduce the numerical complexity of inverse solutions to large systems of discretised integral equations in gravimetric geoid/quasigeoid modelling, the surface domain of Green’s integrals is subdivided into the near-zone and far-zone integration sub-domains. The inversion is performed for the near zone using regional detailed gravity data. The farzone contributions to the gravity field quantities are estimated from an available global geopotential model using techniques for a spherical harmonic analysis of the gravity field. For computing the far-zone contributions by means of Green’s integrals, truncation coefficients are applied. Different forms of truncation coefficients have been derived depending on a type of integrals in solving various geodetic boundary-value problems. In this study, we utilise Molodensky’s truncation coefficients to Green’s integrals for computing the far-zone contributions to the disturbing potential, the gravity disturbance, and the gravity anomaly. We also demonstrate that Molodensky’s truncation coefficients can be uniformly applied to all types of Green’s integrals used in solving the boundaryvalue problems. The numerical example of the far-zone contributions to the gravity field quantities is given over the area of study which comprises the Canadian Rocky Mountains. The coefficients of a global geopotential model and a detailed digital terrain model are used as input data.  相似文献   
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