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Are the National Geodetic Survey’s surface gravity data sufficient for supporting the computation of a 1 cm-accurate geoid? This paper attempts to answer this question by deriving a few measures of accuracy for this data and estimating their effects on the US geoid. We use a data set which comprises million gravity observations collected in 1,489 surveys. Comparisons to GRACE-derived gravity and geoid are made to estimate the long-wavelength errors. Crossover analysis and -nearest neighbor predictions are used for estimating local gravity biases and high-frequency gravity errors, and the corresponding geoid biases and high-frequency geoid errors are evaluated. Results indicate that 244 of all 1,489 surface gravity surveys have significant biases  mGal, with geoid implications that reach 20 cm. Some of the biased surveys are large enough in horizontal extent to be reliably corrected by satellite-derived gravity models, but many others are not. In addition, the results suggest that the data are contaminated by high-frequency errors with an RMS of  mGal. This causes high-frequency geoid errors of a few centimeters in and to the west of the Rocky Mountains and in the Appalachians and a few millimeters or less everywhere else. Finally, long-wavelength ( ) surface gravity errors on the sub-mGal level but with large horizontal extent are found. All of the south and southeast of the USA is biased by +0.3 to +0.8 mGal and the Rocky Mountains by to  mGal. These small but extensive gravity errors lead to long-wavelength geoid errors that reach 60 cm in the interior of the USA.

The “non-harmonicity” problem in residual terrain modelling (RTM) is a challenging issue, causing errors exceeding 200 mGal in the RTM gravity anomaly in rugged areas. Although various methods have been proposed to address this problem, including the condensation method, regularized downward continuation methods with Taylor series expansions (TS) and spherical harmonics (SH), complete harmonic correction (HC) method, closed-form complete HC method, and Kadlec's method, their performances in gravity field determination have not been directly validated. In this study, we reviewed and evaluated these methods, especially for their performance in regional geoid determination. We found that the HC's expression for the closed-form complete method is identical to that under the unlimited Bouguer plate approximation, and Kadlec’s method is equivalent to the condensation method with the same approximation for Bouguer masses. However, the HC associated with the complete HC method shows large differences compared to other methods. This is because the upward and downward continuations in the complete HC method consider an Earth with changing total mass. To address it, we propose a new three-step approach, proved to be equivalent to the HC using the TS method. Then the performance of various HC methods is evaluated in gravity anomaly synthesis and geoid determination over a select region in Colorado, USA. The best result is achieved when using the SH method to compute RTM gravity anomalies, resulting in a geoid accuracy of ~ 1.62 cm. Involving the HC for the height anomaly in the restore procedure slightly improves the accuracy to ~ 1.56 cm.

Numerical methods, like the finite element method (FEM) or finite volume method (FVM), are widely used to provide solutions in many boundary value problems. In previous studies, these numerical methods have also been applied in geodesy but demanded extensive computations because the upper boundary condition was usually set up at the satellite orbit level, hundreds of kilometers above the Earth. The relatively large distances between the lower boundary of the Earth's surface and the upper boundary exacerbate the computation loads because of the required discretization in between. Considering that many areas, such as the US, have uniformly distributed airborne gravity data just a few kilometers above the topography, we adapt the upper boundary from the satellite orbit level to the mean flight level of the airborne gravimetry. The significant decrease in the domain of solution dramatically reduces the large computation demand for FEM or FVM. This paper demonstrates the advantages of using FVM in the decreased domain in simulated and actual field cases in study areas of interest. In the simulated case, the FVM numerical results show that precision improvement of about an order of magnitude can be obtained when moving the upper boundary from 250 to 10 km, the upper altitude of the GRAV-D flights. A 2–3 cm level of accurate quasi-geoid model can be obtained for the actual datasets depending on different schemes used to model the topographic mass. In flat areas, the FVM solution can reach to about 1 cm precision, which is comparable with the counterparts from classical methods. The paper also demonstrates how to find the upper boundary if no airborne data are available. Finally, the numerical method provides a 3D discrete representation of the entire local gravity field instead of a surface solution, a (quasi) geoid model.

In situ airborne gravity data at altitudes of 11, 6.3, and 1.7 km over a smooth area of Alabama are used to assess gravity accuracy and errors in upward and downward continuations. Analysis of the Alabama free-air anomaly gravity data at crossover points at the three altitudes suggests 1 - 2 mgal accuracy for the dataset. Gravity data at each altitude are then expanded into local 3D Fourier series, to prepare for continuation. This Fourier representation results in continuation errors at few-mgal level in Alabama, even in the extreme case of downward continuation from 11 km to sea level. The result in Alabama inspires an airborne gravity survey over the rough, inaccessible terrain of Tibet. Similar investigations as in Alabama are made in Tibet using EGM08-derived airborne gravity data at flight altitudes of 10, 5, and 0 km. Bouguer anomalies at the 10-km altitude preserve the major tectonic features of Tibet. Downward continuation errors increase with terrain roughness, but the survey can enhance local tectonic features. This study highlights the value of a future Tibetan airborne gravity survey and points out the expected gravity accuracy and spatial resolution from this survey.

A terrestrial survey, called the Geoid Slope Validation Survey of 2011 (GSVS11), encompassing leveling, GPS, astrogeodetic deflections of the vertical (DOV) and surface gravity was performed in the United States. The general purpose of that survey was to evaluate the current accuracy of gravimetric geoid models, and also to determine the impact of introducing new airborne gravity data from the ‘Gravity for the Redefinition of the American Vertical Datum’ (GRAV-D) project. More specifically, the GSVS11 survey was performed to determine whether or not the GRAV-D airborne gravimetry, flown at 11 km altitude, can reduce differential geoid error to below 1 cm in a low, flat gravimetrically uncomplicated region. GSVS11 comprises a 325 km traverse from Austin to Rockport in Southern Texas, and includes 218 GPS stations ( σ Δ h = 0.4 cm over any distance from 0.4 to 325 km) co-located with first-order spirit leveled orthometric heights ( σ Δ H = 1.3 cm end-to-end), including new surface gravimetry, and 216 astronomically determined vertical deflections ( σ DOV = 0 . 1 ″ ) . The terrestrial survey data were compared in various ways to specific geoid models, including analysis of RMS residuals between all pairs of points on the line, direct comparison of DOVs to geoid slopes, and a harmonic analysis of the differences between the terrestrial data and various geoid models. These comparisons of the terrestrial survey data with specific geoid models showed conclusively that, in this type of region (low, flat) the geoid models computed using existing terrestrial gravity, combined with digital elevation models (DEMs) and GRACE and GOCE data, differential geoid accuracy of 1 to 3 cm (1 σ ) over distances from 0.4 to 325 km were currently being achieved. However, the addition of a contemporaneous airborne gravity data set, flown at 11 km altitude, brought the estimated differential geoid accuracy down to 1 cm over nearly all distances from 0.4 to 325 km.

The gravity-geologic method (GGM) was implemented for 2′ by 2′ bathymetric determinations in a 1.6° longitude-by-1.0° latitude region centered on the eastern end of the Shackleton Fracture Zone in the Drake Passage, Antarctica. The GGM used the Bouguer slab approximation to process satellite altimetry-derived marine free-air gravity anomalies and 6,548 local shipborne bathymetric sounding measurements from the Korea Ocean Research and Development Institute to update the surrounding off-track bathymetry. The limitations of the Bouguer slab for modeling the gravity effects of variable density, rugged bathymetric relief at distances up to several kilometers, were mitigated by establishing ‘tuning’ densities that stabilized the GGM predictions. Tests using two-thirds of the shipborne bathymetric measurements to estimate the remaining third indicated that the tuning densities minimized root-mean-square deviations to about 29 m. The optimum GGM bathymetry model honoring all the ship observations correlated very well with widely available bathymetry models, despite local differences that ranged up to a few kilometers. The great analytical simplicity of GGM facilitates accurately and efficiently updating bathymetry as new gravity and bathymetric sounding data become available. Furthermore, the availability of marine free-air gravity anomaly data ensures that the GGM is more effective than simply extrapolating or interpolating ship bathymetry coverage into unmapped regions.

Available marine free-air gravity anomalies (FAGA) derived from multiple satellite altimetry missions have had geologically useful, short wavelength features removed during processing. An approach is described for augmenting these FAGA in the high latitude region with coherent higher frequency data. This added-value approach is demonstrated over the Barents Sea in the Arctic using existing FAGA predictions from the Danish National Cadastre (KMS98) as a reference. Short wavelength components between 4 and 111 km were added from reduced and correlation-filtered ERS1 168-day mission altimetry that had been sorted into ascending and descending datasets for separate processing. The processed data were then recombined by spectral quadrant swapping to generate a correlated, high frequency gravity field related to the local geologic sources. This added-value surface adjusted the reference FAGA to better reflect features at wavelengths related to the distances between altimetry tracks.

This is the final paper in a four-part series examining the fundamental question, \"What does the word height really mean?\" The creation of this series was motivated by the National Geodetic Survey's (NGS) embarking on a height modernization program as a result of which NGS will publish measured ellipsoid heights and computed Helmert orthometric heights for vertical bench marks. Practicing surveyors will therefore encounter Helmert orthometric heights computed from Global Positioning System (GPS) ellipsoid heights and geoid heights determined from geoid models as their published vertical control coordinate, rather than adjusted orthometric heights determined by spirit leveling. It is our goal to explain the meanings of these terms in hopes of eliminating confusion and preventing mistakes that may arise over this change. The first paper in the series reviewed reference ellipsoids and mean sea level datums. The second paper reviewed the physics of heights culminating in a simple development of the geoid in order to explain why mean sea level stations are not all at the same orthometric height. The third paper introduced orthometric heights, geopotential numbers, dynamic heights, normal heights, and height systems. This fourth paper is composed of two sections. The first considers the stability of the geoid as a datum. The second is a review of current best practices for heights measured with the Global Positioning System (GPS), essentially taking the form of a commentary on NGS' guidelines for high-accuracy ellipsoid and orthometric height determination using GPS.

To facilitate geological analyses of the Ulleung Basin in the East Sea (Japan Sea) between Korea and Japan, shipborne and satellite altimetry-derived gravity data are combined to derive a regionally coherent anomaly field. The 2-min gridded satellite altimetry-based gravity predicted by Sandwell and Smith [Sandwell DT, Smith WHF (1997) J Geophys Res 102(B5):10,039-10,054] are used for making cross-over adjustments that reduce the errors between track segments and at the cross-over points of shipborne gravity profiles. Relative to the regionally more homogeneous satellite gravity anomalies, the longer wavelength components of the shipborne anomalies are significantly improved with minimal distortion of their shorter wavelength components. The resulting free-air gravity anomaly map yields a more coherent integration of short and long wavelength anomalies compared to that obtained from either the shipborne or satellite data sets separately. The derived free-air anomalies range over about 140 mGals or more in amplitude and regionally correspond with bathymetric undulations in the Ulleung Basin. The gravity lows and highs along the basin's margin indicate the transition from continental to oceanic crust. However, in the northeastern and central Ulleung Basin, the negative regional correlation between the central gravity high and bathymetric low suggests the presence of shallow denser mantle beneath thinned oceanic crust. A series of gravity highs mark seamounts or volcanic terranes from the Korean Plateau to Oki Island. Gravity modeling suggests underplating by mafic igneous rocks of the northwestern margin of the Ulleung Basin and the transition between continental and oceanic crust. The crust of the central Ulleung Basin is about a 14-15 km thick with a 4-5 km thick sediment cover. It may also include a relatively weakly developed buried fossil spreading ridge with approximately 2 km of relief.[PUBLICATION ABSTRACT]