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The geoid errors for the Canadian Gravimetric Geoid 2005 (CGG05) model are estimated from the error information of the satellite
and terrestrial gravity data. Calibration is conducted through the application of variance component estimation (VCE) with
GPS-leveling data and their associated covariance matrices. Preliminary results suggest that the e...
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Context 1
... total geoid error is finally computed from the scaled CV matrices (after variance component estimation) of the three estimated components corresponding to SG, TG and CG. Assuming that the variance factors in Table 1 are applicable for non-GPS/leveling points (albeit a bold assumption), the total calibrated geoid error for CGG05 is illustrated in Figure 6 on a 2' × 2' grid. This assumption will be further tested using additional data that was not implemented in this study. ...
Context 2
... progress made in this study represents a significant step forward to achieving realistic error estimates for the Canadian gravimetric geoid model. However, it should be stated that the total geoid errors shown in Figure 6 are preliminary and refinements are ongoing. In particular, major improvements are expected on three fronts, namely (i) the inclusion of additional GPS-leveling data for a regional calibration based on the geographical heterogeneity of the data, (ii) the incorporation of the correlation between the terrestrial gravity data and (iii) the verification of the reliability of the estimated variance components, through an external validation process. ...
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Citations
... Aiming at a geoid model estimated with a sub-centimetre internal error implies that the mean value of the estimated STD of the geoid height σ N needs to be smaller than 1 cm. The range of the internal error estimate may be larger, especially in the high mountains (Huang et al., 2007;Huang and Véronneau, 2013;Ågren and Sjöberg, 2014;Farahani et al., 2017;Featherstone et al., 2018;Foroughi et al., 2019). Looking at Fig. 8, the errors of the EGM-generated values (reference gravity disturbances and reference geoid heights) are negligibly small compared to the other two terms and since they cannot be controlled by gravimetric surveys, we do not discuss them any further. ...
... A GGM supports the conversion of ellipsoidal heights to orthometric heights with accuracies varying between few centimetres to even a metre (Denker et al. 2009;Pavlis et al. 2012;Alcaras et al. 2022). There are also local geoid models that present higher level of accuracy: they are generally developed using local (surface or aerial) gravity data compared with the GNSS/levelling measurements (Sideris and She 1995;Huang et al. 2007). In fact, to determine an accurate local geoid, it is necessary to take full advantage of all types of data/information in an integrated solution (Chen and Luo 2004). ...
Local geoid models presenting higher resolution than global ones are generally derived by a combination of different datasets, integrating individual pure astrogeodetic, gravimetric and GNSS/levelling solutions. To define local geoid, different interpolators may be applied starting from dataset of geoid height values. It is well known that the accuracy of the resulting models depends not only by interpolation method, but also by points numerosity and distribution. This article aims to analyse the performance of Kriging approaches in dependence of the density of the dataset. The experiments are carried out on geoid heights extracted in random way from an already existing local geoid model: different subsets are organized containing an increasing number of points in the same area and each of them is submitted to Kriging interpolations (Universal Kriging and Ordinary Kriging). The resulting models are compared with the original one and residuals are calculated to evaluate the accuracy in dependence of point density. The results demonstrate the efficiency of the Kriging methods, highlighting the possibility to achieve higher accuracy (a few centimetres) using a point density of 1 point/100 sqkm, in absence of gravity anomalies. Ordinary Kriging provides better results than Universal Kriging but the undulations between the resulting models are minimal (a few millimetres) when a high number of points is involved. Furthermore, the results highlight the limit of the leave one out Cross validation since it supplies higher residuals than direct comparison for both Universal Kriging and Ordinary Kriging, when few points are used.
... His results were based on Molodensky's approach applied for estimation of the geoid-to-quasigeoid separation. Huang et al. (2007) estimated errors in the geoidal heights over Canada by propagating of the noise in satellite and ground gravity data through the Stokes integral. According to their results, the average error in the geoidal heights over Canada was in the range of 1.57.5 cm. ...
The uncertainties of the geoidal heights estimated from ground gravity data caused by their spatial distribution and noise are investigated in this study. To test these effects, the geoidal heights are estimated from synthetic ground gravity data using the Stokes- Helmert approach. Five different magnitudes of the random noise in ground gravity data and three types of their spatial distribution are considered in the study, namely grid, semigrid and random. The noise propagation is estimated for the two major computational steps of the Stokes-Helmert approach, i.e., the downward continuation of ground gravity and Stokes’s integration. Numerical results show that in order to achieve the 1-cm geoid, the ground gravity data should be distributed on the grid or semi-grid with the average angular distance less than 2′. If they are randomly distributed (scattered gravity points), the 1-cm geoid cannot be estimated if the average angular distance between scattered gravity points is larger than 1′. Besides, the noise of the gravity data for the tree types of their spatial distribution should be below 1 mGal to estimate the 1-cm geoid. The advantage of interpolating scattered gravity points onto the regular grid, rather than using them directly, is also investigated in this study. Numerical test shows that it is always worth interpolating the scattered points to the regular grid except if the scattered gravity points are sparser than 5′.
... 1). Notwithstanding least squares collocation (LSC), few previous studies have propagated uncertainties through Stokes's integral (e.g., Sideris and She 1995;Pavlis and Saleh 2005;Huang et al. 2007). LSC was not used for the Australian gravimetric quasigeoid computations simply because of the sheer size and extent of the Australian datasets (Sect. ...
... Sideris and She (1995) provide error propagation formulas for the 1D-FFT (Haagmans et al. 1993) when using the RCR technique over a region. Huang et al. (2007) provide a spectral form when using the RCR technique and a modified integration kernel over a spherical integration cap. Common to both these approaches is the need to use a satellite-only EGM so that errors in the terrestrial gravity data are independent and thus combined without the need to consider correlations. ...
... Instead, the error degree variances (diagonal of the VCV matrix) are often used to approximate σ 2 (ζ EGM ). In our error propagation, however, we use the error grids of σ 2 (ζ EGM ) and σ 2 ( g EGM ) that accompany EGM2008, and not the error degree variances of a satellite-only EGM (as used by, e.g., Sideris and She 1995;Huang et al. 2007;Huang and Véronneau 2013) and assume independence between error values at grid nodes. For a global integration with an unmodified Stokes kernel, Eq. (20) degenerates to Eq. (15) because the first, third, fourth, fifth and sixth terms on the right-hand side cancel, and the error propagation is solely from the terrestrial gravity data variances σ 2 ( g) (cf. ...
We describe the computation of the first Australian quasigeoid model to include error estimates as a function of location that have been propagated from uncertainties in the EGM2008 global model, land and altimeter-derived gravity anomalies and terrain corrections. The model has been extended to include Australia’s offshore territories and maritime boundaries using newer datasets comprising an additional \({\sim }\)280,000 land gravity observations, a newer altimeter-derived marine gravity anomaly grid, and terrain corrections at \(1^{\prime \prime }\times 1^{\prime \prime }\) resolution. The error propagation uses a remove–restore approach, where the EGM2008 quasigeoid and gravity anomaly error grids are augmented by errors propagated through a modified Stokes integral from the errors in the altimeter gravity anomalies, land gravity observations and terrain corrections. The gravimetric quasigeoid errors (one sigma) are 50–60 mm across most of the Australian landmass, increasing to \({\sim }100\) mm in regions of steep horizontal gravity gradients or the mountains, and are commensurate with external estimates.
... A major challenge is the development of a geoid model with an accuracy of 1-3 cm homogenously across Canada. The latest official geoid model CGG05 is estimated at an accuracy of better than 6 cm nationally and generally about 4 cm regionally (Huang et al. 2007). A new geoid model CGG10 is under development by taking advantage of the early release of GOCE models and new gravity and DEM data. ...
... In combination with the accuracy of the satellite gravity models, the formal error of the geoid can be estimated (see e.g. Huang et al. 2007). NGS is working on such a first test line in the Texas area ). ...
The United States adopted the North American Vertical Datum of 1988 (NAVD 88) for its official vertical datum in the 1990s. Canada has been using the Canadian Geodetic Vertical Datum (CGVD28) for its height applications since the 1930s. The use of the different datums causes inconsistent heights across the border between the two countries, and the topographic height data from the two countries are not compatible. Both datums rely on passive control and significant pre-modern survey data, yielding not only misalignment of the datums to the best known global geoid at approximately 1–2 m, but also local uplift and subsidence issues which may significantly exceed 1–2 m in extreme cases.
Today, the GNSS provides the geometric (ellipsoidal) height to an accuracy of 1–2 cm globally. The use of current inaccurate vertical datums no longer serves the purpose it once did. Because of this, users have begun to demand a physical height system that is closely related to the Earth’s gravity field to a comparable accuracy. To address this need, government agencies of both countries are preparing the next generation of vertical datums. Even if the new datums are based on the same concepts and parameters, it is possible to have inconsistent heights along the borders due to the differences in the realization of the datums. To avoid inconsistency, it is in the interest of both countries to have a united, seamless, highly accurate vertical datum. The proposed replacements for CGVD28 and NAVD88 shall be based on GNSS positioning and a high accuracy gravimetric geoid that covers the territories of the United States, Canada, Mexico and the surrounding waters (to include all of Alaska, Hawaii, the Caribbean and Central America). To account for the effect of the sea level change, postglacial rebound, earthquakes and subsidence, this datum will also provide information on these changes. Detailed description of the definition, realization and maintenance of the datum is proposed. The challenges in realization and maintaining the datum are also discussed.
... The errors originating from the terrestrial gravity anomalies are due to the errors in the gravity measurements, topographic reduction applied, gridding and interpolation of gravity values, DEM and the actual topographical density distribution ( Huang et al., 2007). The error coming from the terrestrial data can be expressed by: ...
The aim of this study is to investigate the current vertical datums in North America and to assess the possible improvements to them coming from the recently obtained satellite gravity models. The study is conducted in two steps. First, the geoid models computed from the first and the second generation GOCE-only and GRACE-GOCE combined satellite-only models and truncated for different spherical harmonic degrees are compared to the GPS/leveling geoid heights which are reduced to the same spectral band of the gravity field. The GPS/leveling-derived geoid heights are used as independent controls in the assessment of the geoid models. The comparison results indicate that the GOCE models show a full power of gravity signal in terms of geoid undulation up to about spherical harmonic degree 150. Second, one of the first generation GOCE satellite-only models developed by the time-wise approach, TW01, is complemented with local terrestrial data and tested against the GPS/leveling-derived geoid undulations in full spectrum of the gravity field and compared with the official global and regional geoid models. Based on these results there is not enough evidence indicating significant improvement (cm level) from the first generation GOCE models to the geoid modeling in Canada and the two sub-regions, the Great Lakes area and Rocky Mountains investigated, compared to EGM2008 and the existing regional geoid models. One important contribution is the evaluation of the GOCE-only and complementary terrestrial data combined geoid model in Canada without any effect of the other satellite and geodetic techniques. The preliminary investigations on the second generation GOCE models show that the future GOCE-only and combined GRACE-GOCE models can provide more accurate and consistent geoid solutions for Canada. iii ACKNOWLEDGEMENTS
... EGM08 [Pavlis et al., 2008] is truncated to spherical harmonic degree and order 360 and combined with the PCG08I gravity grid to realize the 2 min by 2 min resolution geoid model. The computational process makes use of the remove-restore approach with a degree 90 modified degree-banded Stokes kernel [Huang et al., 2007]. The low-degree part of EGM08 (degree 2 to degree 90) is dominated by the GRACE data. ...
... The total geoid error is mostly between 1 and 5 cm for the study area. The approach for estimating geoid error is described by Huang et al. [2007]. ...
A new mean sea surface topography (MSST) is used to estimate the surface
circulation of the subpolar gyre of the northwest Atlantic. The MSST is
produced using a new geoid model derived from a blend of gravity data
from the Gravity Recovery and Climate Experiment (GRACE) satellite
mission, satellite altimeters, and terrestrial measurements. The MSST is
compared with a topography produced by an ocean model which is
spectrally nudged to a new Argo period temperature and salinity
climatology. The mean surface circulation associated with the geodetic
MSST is compared with estimates of the circulation from surface
drifters, moorings, and other in situ measurements. The geodetic MSST
and circulation estimate are found to be in good agreement with the
other estimates, both qualitatively and quantitatively. The topography
is found to be an improvement over an earlier geodetic estimate with
better resolution of the coastal currents. Deficiencies are identified
in the ocean model's estimate of flow over shelf regions.
... One must further consider long wavelength uncertainties in the geoid model used to convert from ellipsoidal heights measured by GPS to the orthometric heights derived from traditional optical levelling used in older surveys when comparing the new Bouguer anomaly values to old data in the area. Huang et al. (2006), presenting a GSD-led study of regional geoid errors across Canada, has estimated this uncertainty at less than 3-4 cm in the region of our survey. This is encouraging as it would translate to a regional bias of less than 0.01 mGal in the combined Free Air and Bouguer slab corrections that would be calculated based on GPSderived elevations versus the elevations derived from optical levelling. ...
... When comparing the new Bouguer anomaly values with the old data from the report area, it is important to consider long-wavelength uncertainties in the geoid model used to convert ellipsoidal heights obtained from present-day GPS measurements to the elevations derived from traditional optical levelling methods of earlier surveys. A GSD-led study of regional geoid errors across Canada (Huang et al. 2006) estimated this uncertainty to be <3 cm to 4 cm in the survey area. This is encouraging, as it translates to a regional bias of <0.01 mGal in the Bouguer anomaly that would be calculated on the basis of GPS-derived elevations versus those derived from optical levelling. ...
A regional, land-based gravity survey was undertaken in the fall of 2009 in a roughly
triangular area of eastern New Brunswick delineated by the communities of Richibucto,
Shediac, and Stilesville. The ~1000 km2 survey area, situated within the late Paleozoic
Maritimes Basin, extends approximately 54 km along the Northumberland Strait coast
and, from there, reaches between 11 km and 23 km inland. The survey encompassed,
and extended north of, the northeastern part of the Late Devonian to Early
Carboniferous Cocagne Subbasin, a graben-like structure that appears as a welldefined
gravity low (herein, the ‘Cocagne gravity low’) within the survey area. The
survey objectives were 1) to better define multiple northeast-trending gravity anomalies
that intersect the Northumberland Strait subperpendicular to the coast, and 2) to gain a
better understanding of the sedimentary cover thickness and underlying basement
structure in a region that is prospective for hydrocarbon and evaporite deposits.
A total of 708 gravity stations were acquired using a Scintrex CG-5 gravimeter and two
high-precision, dual-frequency GPS receivers. The targeted station spacing was
approximately 1 km, but coverage was coarser in areas with restricted road access and
denser along profiles of particular interest. Repeated gravity and GPS observations
attest to a high degree of precision (± 0.01 mGal standard deviation) in the reduced
Bouguer anomaly values.
Bouguer anomaly and vertical gravity gradient maps were produced by merging the new
and old data. These maps confirm the presence of significant anomalies evident in the
old data but offer improved precision and spatial resolution that allow for more confident
interpretations. The Cocagne gravity low is bounded to the south by a relatively broad
gravity high associated with uplifted Early Carboniferous sedimentary rocks and
crystalline basement of the Indian Mountain Deformed Zone. In contrast, the Cocagne
anomaly’s northern boundary is defined by abrupt changes in both gravity and vertical
gravity gradient, indicating that the subbasin is asymmetrical in cross-section. It is
proposed that this linear northeast-trending boundary represents the Belleisle Fault,
defining the northern limit of the Cocagne Subbasin beneath Late Carboniferous cover.
The trajectory of the Belleisle Fault was previously extrapolated through this area along
a pronounced magnetic anomaly that is now recognized to bisect the better resolved
Cocagne gravity low. The new gravity data support the presence of a significant fault
near this trajectory, herein renamed the Cormierville Fault so as to allow the Belleisle Fault
to retain its originally defined significance as the southern margin of the New
Brunswick Platform. Simple 2D forward modelling of two gravity profiles suggests that
the Cocagne Subbasin in the survey area is 3 km to 4 km deep north of the Cormierville
Fault and 2 km to 3 km deep south of it. Earlier gravity data from regions adjacent to the
survey area indicate that the Cocagne Subbasin deepens toward the southwest.
... When comparing the new Bouguer anomaly values with the old data from the report area, it is important to consider long-wavelength uncertainties in the geoid model used to convert ellipsoidal heights obtained from present-day GPS measurements to the elevations derived from traditional optical levelling methods of earlier surveys. A GSD-led study of regional geoid errors across Canada (Huang et al. 2006) estimated this uncertainty to be <3 cm to 4 cm in the survey area. This is encouraging, as it translates to a regional bias of <0.01 mGal in the Bouguer anomaly that would be calculated on the basis of GPS-derived elevations versus those derived from optical levelling. ...
A regional, land-based gravity survey was undertaken in the fall of 2009 in a roughly triangular area of eastern New Brunswick delineated by the communities of Richibucto, Shediac, and Stilesville. The ~1000 km 2 survey area, situated within the late Paleozoic Maritimes Basin, extends approximately 54 km along the Northumberland Strait coast and, from there, reaches between 11 km and 23 km inland. The survey encompassed, and extended north of, the northeastern part of the Late Devonian to Early Carboniferous Cocagne Subbasin, a graben-like structure that appears as a well-defined gravity low (herein, the 'Cocagne gravity low') within the survey area. The survey objectives were 1) to better define multiple northeast-trending gravity anomalies that intersect the Northumberland Strait subperpendicular to the coast, and 2) to gain a better understanding of the sedimentary cover thickness and underlying basement structure in a region that is prospective for hydrocarbon and evaporite deposits. A total of 708 gravity stations were acquired using a Scintrex CG-5 gravimeter and two high-precision, dual-frequency GPS receivers. The targeted station spacing was approximately 1 km, but coverage was coarser in areas with restricted road access and denser along profiles of particular interest. Repeated gravity and GPS observations attest to a high degree of precision (± 0.01 mGal standard deviation) in the reduced Bouguer anomaly values. Bouguer anomaly and vertical gravity gradient maps were produced by merging the new and old data. These maps confirm the presence of significant anomalies evident in the old data but offer improved precision and spatial resolution that allow for more confident interpretations. The Cocagne gravity low is bounded to the south by a relatively broad gravity high associated with uplifted Early Carboniferous sedimentary rocks and crystalline basement of the Indian Mountain Deformed Zone. In contrast, the Cocagne anomaly's northern boundary is defined by abrupt changes in both gravity and vertical gravity gradient, indicating that the subbasin is asymmetrical in cross-section. It is proposed that this linear northeast-trending boundary represents the Belleisle Fault, defining the northern limit of the Cocagne Subbasin beneath Late Carboniferous cover. The trajectory of the Belleisle Fault was previously extrapolated through this area along a pronounced magnetic anomaly that is now recognized to bisect the better resolved Cocagne gravity low. The new gravity data support the presence of a significant fault near this trajectory, herein renamed the Cormierville Fault so as to allow the Belleisle 99 Fault to retain its originally defined significance as the southern margin of the New Brunswick Platform. Simple 2D forward modelling of two gravity profiles suggests that the Cocagne Subbasin in the survey area is 3 km to 4 km deep north of the Cormierville Fault and 2 km to 3 km deep south of it. Earlier gravity data from regions adjacent to the survey area indicate that the Cocagne Subbasin deepens toward the southwest. ___________________________________ Un levé gravimétrique régional terrestre a été réalisé à l'automne 2009 dans une zone plus ou moins triangulaire dans le centre-est du Nouveau-Brunswick, comprise entre les localités de Richibucto, Shediac et Stilesville. Cette zone de plus ou moins 1 000 km 2 se trouve dans le bassin des Maritimes, de la fin du Paléozoïque, et s'étend sur une bande d'environ 54 km qui longe la côte du détroit de Northumberland, et s'enfonce à l'intérieur des terres sur une distance comprise entre 11 et 23 km. Le secteur examiné par le levé a porté, vers le nord et dans la partie nord-est sur le sous-bassin de Cocagne, qui date de la fin du Dévonien au début du Carbonifère, une structure qui s'apparente au graben et qui apparaît comme un creux gravimétrique bien défini (d'où la désignation de « creux gravimétrique » de Cocagne). Les objectifs du levé étaient les suivants : 1) mieux définir plusieurs anomalies gravimétriques orientées au nord-est qui entrecoupent de manière sous-perpendiculaire le détroit de Northumberland par rapport à la côte; et 2) mieux comprendre l'épaisseur des roches sédimentaires de recouvrement et la structure du socle sous-jacent dans une région prospective pour des gisements d'hydrocarbures et d'évaporites. En tout, 708 points de relevé gravimétrique ont été établis à l'aide d'un gravimètre Scintrex CG-5 et de deux récepteurs GPS de grande précision à double fréquence. L'espacement de points de relevé recherché était d'environ un kilomètre, mais l'intervalle de quadrillage a été plus grand dans des secteurs où les chemins d'accès faisaient défaut et plus resserré dans les secteurs comportant des points d'intérêt particuliers. Les mesures de répétitions gravimétriques et par GPS ont donné lieu à un grand degré de précision (écart type de ± 0,01 mGal) dans les valeurs de l'anomalie de Bouguer. Des cartes de l'anomalie de Bouguer et de gradients gravimétriques verticaux ont été établies par le recoupement des données anciennes et nouvelles. Ces cartes confirment la présence d'anomalies importantes et manifestes dans les anciennes données. Par ailleurs, leur plus grande précision et la limite de résolution spatiale améliorée permettent une interprétation plus sûre. Le creux gravimétrique de Cocagne est bordé au sud par une crête gravimétrique relativement large, associée aux roches sédimentaires du début du Carbonifère ayant subi un soulèvement et au socle cristallin de la zone de déformation d'Indian Mountain. En revanche, la limite nord de l'anomalie de Cocagne se caractérise par des changements abrupts sur le plan gravimétrique et du gradient gravimétrique vertical, ce qui indiquerait que le sous-bassin a un contexte géologique asymétrique sur le plan transversal. On suppose que cette démarcation linéaire orientée vers le nord-est correspond à la faille de Belleisle et forme la limite nord du sous-bassin de Cocagne, sous la structure de recouvrement de la fin du Carbonifère. Le tracé de la faille de Belleisle a déjà fait l'objet d'une extrapolation dans cette zone. Elle longerait une forte anomalie magnétique dont on sait maintenant qu'elle coupe le creux gravimétrique de Cocagne, mieux défini. Les nouvelles données gravimétriques attesteraient la présence d'une importante faille près de ce tracé, qui est renommée 100 dans cet exposé la faille de Cormierville. Ce faisant, il est possible de préserver l'importance d'origine de la faille de Belleisle, en tant que limite sud de la plate-forme du Nouveau-Brunswick. La modélisation simple bidimensionnelle de deux profils gravimétriques porte à croire que le sous-bassin de Cocagne dans le secteur à l'étude se trouve dans une zone comprise entre 3 à 4 km au nord de la faille de Cormierville et 2 à 3 km au sud. Les données gravimétriques antérieures des régions adjacentes indiquent que le sous-bassin de Cocagne gagne en profondeur vers le sud-ouest.
