Airborne Gravity Across New Zealand - For An Improved Vertical Datum

<p>It is important to be able to accurately determine the height of a point on the Earth in terms of the Earth's gravitational potential field. These heights predict how water will flow and so they are vital for engineering and surveying purposes. They are determined using a vertical datum which consists of a specif ed height system and a defined reference surface. At present, in New Zealand, the o fficial vertical datum is NZVD2009 which uses a normal-orthometric height system and gravimetric quasigeoid, NZGeoid2009, as the reference surface. The aim of this thesis is to develop a more accurate gravimetric quasigeoid than NZGeoid2009, by incorporating new gravity data and utilising a re fined data processing strategy, to establish a better vertical datum for New Zealand. A new airborne gravimetry data set has been collected which covers the North, South and Stewart Islands of New Zealand with a flight line spacing of 10km. The data were susceptible to short error prone sections of track due to poor (turbulent) flight conditions and mean off sets which separate the recorded gravity data along flight lines by a constant value from neighbouring lines and existing gravity models. The error prone sections of track have been visually identified by assessing the cross track agreement with other flight lines and with the global gravity model EGM2008, and the mean offsets were estimated by a least squares method which takes into consideration the spatially correlated gravity signal. The repeatability of the data was assessed from data collected from five flights along two separate calibration lines. The mean gravity anomaly pro files calculated along the calibration lines each had a standard deviation of around 2.5 mGal. The internal consistency of the data was assessed by evaluating the diff erence between flight line data at intersection points. This accuracy measure was shown to be influenced by the along track filter, anisotropic topography and the relative flight line elevations. After correcting for all these effects the set of all intersecting differences had a standard deviation of approximately 5.9 mGal. From an existing terrestrial gravity database, around 40000 observations have been reprocessed to reduce them to Bouguer gravity anomalies, this was done to ensure consistency in the formulas that have been used. A new national 8 m digital elevation model (DEM) was used to calculate terrain corrections and these were carefully compared with terrain corrections estimated from field observations of the topography to reduce any discrepancies in calculating near zone terrain e ffects. The largest source of error in the terrestrial gravity anomaly data is due to inaccurate height estimates of the marks. The height discrepancies have been estimated by comparing the recorded heights in the database to those determined from the 8 m DEM and have been translated into mGal by calculating the propagated effect on the free air and Bouguer slab corrections. The airborne and terrestrial gravity data, along with a satellite altimetry marine gravity anomaly and existing shipborne gravity data, were assimilated by least squares collocation with a logarithmic covariance function to appropriately deal with the downward continuation of the airborne data, and gridded at 1 arc-minute resolution in the geographical region 25° (S) to 60 ° (S) and 160° (E) to 190° (E). 1 arc-minute block averaged heights were then used to calculate a reverse Bouguer slab correction, which when applied to the gravity data gave a gridded Faye anomaly. Different noise level variances were assigned to the separate data sets to optimally combine them. Forty six of the most contemporary global gravity models (from 2008 onwards) have each been compared to 1422 leveling and GNSS derived quasigeoid height anomalies. Overall the Eigen-6C4 model fitted the leveling and GNSS derived quasigeoid height anomalies best with a root mean squared error of 5.29cm. The Eigen-6C4 gravity model was subtracted from the gridded Faye anomaly (remove) and Stokes integral was evaluated on the residual gravity anomaly grid. A, theoretically optimum, modified Stokes kernel has been used and the modification degree L and spherical cap for the integration Ψ₀ were varied over the ranges L = 20; 40; 60; ..., 320 and Ψ₀ = 1° ; 1:5° ; 2° ; 2:5° ; 3° . The Eigen-6C4 geoid undulations were then added back to the residual geoid undulation grids and the primary indirect topographic effect was restored to obtain 80 quasigeoids for each L and Ψ₀ parameter variation. The optimal parameter choice was determined to be L = 280 and Ψ₀ = 1:5 which had the best agreement with the leveling and GNSS derived quasigeoid height anomalies with a standard deviation of 3.8cm and root mean squared residual of 4.8cm of the differences. This is a 1.25cm improvement on NZGeoid2009. The quasigeoid was also assessed closely in three main urban areas, Auckland, Wellington and Christchurch, where the majority of large scale engineering projects and surveying takes place in New Zealand. Here there were 123, 169 and 125 data points and the standard deviations of the differences were 3.976, 3.385 and 2.071cm and root mean squared differences of 3.58,4.388 and 4.572 cm respectively. This gives an average accuracy of 3.1 cm standard deviation in urban areas which is 1.5 cm better than the average for NZGeoid2009.</p>

Airborne Gravity Across New Zealand - For An Improved Vertical Datum

<p>It is important to be able to accurately determine the height of a point on the Earth in terms of the Earth's gravitational potential field. These heights predict how water will flow and so they are vital for engineering and surveying purposes. They are determined using a vertical datum which consists of a specif ed height system and a defined reference surface. At present, in New Zealand, the o fficial vertical datum is NZVD2009 which uses a normal-orthometric height system and gravimetric quasigeoid, NZGeoid2009, as the reference surface. The aim of this thesis is to develop a more accurate gravimetric quasigeoid than NZGeoid2009, by incorporating new gravity data and utilising a re fined data processing strategy, to establish a better vertical datum for New Zealand. A new airborne gravimetry data set has been collected which covers the North, South and Stewart Islands of New Zealand with a flight line spacing of 10km. The data were susceptible to short error prone sections of track due to poor (turbulent) flight conditions and mean off sets which separate the recorded gravity data along flight lines by a constant value from neighbouring lines and existing gravity models. The error prone sections of track have been visually identified by assessing the cross track agreement with other flight lines and with the global gravity model EGM2008, and the mean offsets were estimated by a least squares method which takes into consideration the spatially correlated gravity signal. The repeatability of the data was assessed from data collected from five flights along two separate calibration lines. The mean gravity anomaly pro files calculated along the calibration lines each had a standard deviation of around 2.5 mGal. The internal consistency of the data was assessed by evaluating the diff erence between flight line data at intersection points. This accuracy measure was shown to be influenced by the along track filter, anisotropic topography and the relative flight line elevations. After correcting for all these effects the set of all intersecting differences had a standard deviation of approximately 5.9 mGal. From an existing terrestrial gravity database, around 40000 observations have been reprocessed to reduce them to Bouguer gravity anomalies, this was done to ensure consistency in the formulas that have been used. A new national 8 m digital elevation model (DEM) was used to calculate terrain corrections and these were carefully compared with terrain corrections estimated from field observations of the topography to reduce any discrepancies in calculating near zone terrain e ffects. The largest source of error in the terrestrial gravity anomaly data is due to inaccurate height estimates of the marks. The height discrepancies have been estimated by comparing the recorded heights in the database to those determined from the 8 m DEM and have been translated into mGal by calculating the propagated effect on the free air and Bouguer slab corrections. The airborne and terrestrial gravity data, along with a satellite altimetry marine gravity anomaly and existing shipborne gravity data, were assimilated by least squares collocation with a logarithmic covariance function to appropriately deal with the downward continuation of the airborne data, and gridded at 1 arc-minute resolution in the geographical region 25° (S) to 60 ° (S) and 160° (E) to 190° (E). 1 arc-minute block averaged heights were then used to calculate a reverse Bouguer slab correction, which when applied to the gravity data gave a gridded Faye anomaly. Different noise level variances were assigned to the separate data sets to optimally combine them. Forty six of the most contemporary global gravity models (from 2008 onwards) have each been compared to 1422 leveling and GNSS derived quasigeoid height anomalies. Overall the Eigen-6C4 model fitted the leveling and GNSS derived quasigeoid height anomalies best with a root mean squared error of 5.29cm. The Eigen-6C4 gravity model was subtracted from the gridded Faye anomaly (remove) and Stokes integral was evaluated on the residual gravity anomaly grid. A, theoretically optimum, modified Stokes kernel has been used and the modification degree L and spherical cap for the integration Ψ₀ were varied over the ranges L = 20; 40; 60; ..., 320 and Ψ₀ = 1° ; 1:5° ; 2° ; 2:5° ; 3° . The Eigen-6C4 geoid undulations were then added back to the residual geoid undulation grids and the primary indirect topographic effect was restored to obtain 80 quasigeoids for each L and Ψ₀ parameter variation. The optimal parameter choice was determined to be L = 280 and Ψ₀ = 1:5 which had the best agreement with the leveling and GNSS derived quasigeoid height anomalies with a standard deviation of 3.8cm and root mean squared residual of 4.8cm of the differences. This is a 1.25cm improvement on NZGeoid2009. The quasigeoid was also assessed closely in three main urban areas, Auckland, Wellington and Christchurch, where the majority of large scale engineering projects and surveying takes place in New Zealand. Here there were 123, 169 and 125 data points and the standard deviations of the differences were 3.976, 3.385 and 2.071cm and root mean squared differences of 3.58,4.388 and 4.572 cm respectively. This gives an average accuracy of 3.1 cm standard deviation in urban areas which is 1.5 cm better than the average for NZGeoid2009.</p>

Quasi Geoid and Geoid Modeling with the Use of Terrestrial and Airborne Gravity Data by the GGI Method—A Case Study in the Mountainous Area of Colorado

This article concerns the development of gravimetric quasigeoid and geoid models using the geophysical gravity data inversion technique (the GGI method). This research work was carried out on the basis of the data used in the Colorado geoid experiment, and the mean quasigeoid (ζm) and mean geoid (Nm) heights, determined by the approaches used in the Colorado geoid experiment, were used as a reference. Three versions of the quasigeoid GGI models depending on gravity data were analyzed: terrestrial-only, airborne-only, and combined (using airborne and terrestrial datasets). For the combined version, which was the most accurate, a model in the form of a 1′×1′ grid was calculated in the same area as the models determined in the Colorado geoid experiment. For the same grid, the geoid–quasigeoid separation was determined, which was used to build the geoid model. The agreement (in terms of the standard deviation of the differences) of the determined models, with ζm and Nm values for the GSVS17 profile points, was ±0.9 cm for the quasigeoid and ±1.2 cm for the geoid model. The analogous values, determined on the basis of all 1′×1′ grid points, were ±2.3 cm and ±2.6 cm for the quasigeoid and geoid models, respectively.

On the uncertainty of height anomaly differences predicted by least-squares collocation

A network of pointwise available height anomalies, derived from levelling and GPS observations, can be densified by adjusting a gravimetric quasigeoid using least-squares collocation. The resulting type of Corrector Surface Model (CSM) is applied by Norwegian surveyors to convert ellipsoidal heights to normal heights expressed in the official height system NN2000. In this work, the uncertainty related to the use of a CSM to predict differences in height anomaly was sought. As previously, the application of variograms to determine the local statistical properties of the adopted collocation model led to predictions that were consistent with their computed uncertainties. For the purpose of predicting height anomaly differences, the effect of collocation was seen to be moderate in general for the small spatial separations considered (< 10 km). However, the relative impact of collocation could be appreciable, and increasing with distance, near the network. At last, it was argued that conservative uncertainties of height anomaly differences may be obtained by rescaling output of a grid interpolation by \sqrt \Delta, where Δ is the spatial separation of the two locations for which the difference is sought.

A Quasigeoid-Derived Transformation Model Accounting for Land Subsidence in the Mekong Delta towards Height System Unification in Vietnam

A vertical offset model for Vietnam and its surrounding areas was determined based on the differences between height anomalies derived from 779 Global Navigation Satellite System (GNSS)/levelling points and those derived from a dedicated high-resolution gravimetric-only quasigeoid model called GEOID_LSC. First, the deterministic transformation model to effectively fit the differences between the quasigeoid and GNSS/levelling heights was based on a third-order polynomial model. Second, the residual height anomalies have been interpolated to a grid employing Least-Squares Collocation. Finally, the distortions were restored to the residual grid. This model can be used for combination with a gravimetric quasigeoid model in GNSS levelling. The quality of GNSS/levelling data in Vietnam was analyzed and evaluated in this study. The annual subsidence rate from ALOS-1 was also used to analyze the effects of subsidence on the quality of GNSS/levelling data in the Mekong Delta. From this we made corrections to improve the accuracy of GNSS/levelling data in this region. The offset model was evaluated using cross-validation technique by comparing with GNSS/levelling data. Results indicate that the offset model has a standard deviation of 5.9 cm in the absolute sense. Based on this offset model, GNSS levelling can be carried out in most of Vietnam’s territory complying third-order levelling requirements, while the accuracy requirements for fourth-order levelling networks is met for the entire country. This model in combination with the developed gravimetric quasigeoid model should also contribute to the modernization of Vietnam’s height system. We also used high-quality GNSS/levelling data and the determined quasigeoid model to determine the geopotential value W0 for the Vietnam Local Vertical Datum. The gravity potential of the Vietnam Local Vertical Datum is estimated equal to W 0 LVD = 62,636,846.81 ± 0.70 m2s−2 with the global equipotential surface realized by the conventional value W0 = 62,636,853.4 m2s−2.

ASSESSMENT OF MARINE GEOID MODELS BY SHIP-BORNE GNSS PROFILES

Even though the entire Baltic Sea is included in previous geoid modelling projects such as the NKG2015 and EGG07, the accuracy of contemporary geoid models over marine areas remains unknown, presumably being offshore around 15–20 cm. An important part of the international cooperation project FAMOS (Finalising Surveys for the Baltic Motorways of the Sea) efforts is conducting new marine gravity observations for improving gravimetric quasigeoid modelling. New data is essential to the project as the existing gravimetric data over some regions of the Baltic Sea may be inaccurate and insufficiently scarce for the purpose of 5 cm accuracy geoid modelling. Therefore, it is important to evaluate geoid modelling outcome by independent data, for instance by shipborne GNSS measurements. Accordingly, this study presents results of the ship-borne marine gravity and GNSS campaign held on board the Estonian Maritime Administration survey vessel “Jakob Prei” in West-Estonian archipelago in June/July 2016. Emphasis of the study is on principles of using the GNSS profiles for validation of existing geoid models, post-processing of GNSS raw data and low-pass filtering of the GNSS results. Improvements in geoid modelling using new gravimetric data are also discussed. For example, accuracy of geoid models including the new marine gravity data increased 11 mm as assessed from GNSS profiles. It is concluded that the marine GNSS profiles have a potential in providing complementary constraints in problematic geoid modelling areas.