The Importance of Using Deviations of the Vertical for the Reduction of Survey Data to a Geocentric Datum

Featherstone, Will; Rüeger, J. M.

doi:10.1080/00050354.2000.10558815

Cited by 28 publications

(34 citation statements)

References 12 publications

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“…Models like EurAlpGM2011 are suitable for planning of gravity field surveys, or detection of gross-errors in gravity data bases, and the construction principles are useful for simulated gravity field modelling. It can also be a convenient source of (i) quasigeoid height differences for GNSS (global navigation satellite system)-based height transfer (e.g., Hirt et al 2010b), (ii) vertical deflections for reduction of survey data (e.g., Featherstone and Rüeger 2000) and (iii) medium-accuracy gravity values for the re-construction of gravity values at surveying benchmarks (Filmer 2011) and the computation of levelling reductions (Meyer et al 2006), without the need to perform observations. Importantly, the gradient approach investigated in this paper is a key to constructing similar models over other parts of Earth which may be beneficial for a range of potential applications.…”

Section: Application Of Euralpgm2011mentioning

confidence: 99%

Efficient and accurate high-degree spherical harmonic synthesis of gravity field functionals at the Earth’s surface using the gradient approach

Hirt

2012

J Geod

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Spherical harmonic synthesis (SHS) of gravity field functionals at the Earth's surface requires the use of heights. The present study investigates the gradient approach as an efficient yet accurate strategy to incorporate height information in SHS at densely-spaced multiple points. Taylor series expansions of commonly used functionals quasigeoid heights, gravity disturbances and vertical deflections are formulated, and expressions of their radial derivatives are presented to arbitrary order. Numerical tests show that first-order gradients, as introduced by Rapp (J Geod 71(5): 282-289, 1997) for degree-360 models, produce cm-to dm-level RMS approximation errors over rugged terrain when applied with EGM2008 to degree 2190. Instead, higher-order Taylor expansions are recommended that are capable of reducing approximation errors to insignificance for practical applications. Because the height information is separated from the actual synthesis, the gradient approach can be applied along with existing highly-efficient SHS routines to compute surface functionals at arbitrarily dense grid points. This confers considerable computational savings (above or well above one order of magnitude) over conventional point-by-point SHS. As an application example, an ultrahigh resolution model of surface gravity functionals (EurAlpGM2011) is constructed over the entire European Alps that incorporates height information in the SHS at 12,000,000 surface points. Based on EGM2008 and residual topography data, quasigeoid heights, gravity disturbances and vertical deflections are estimated at ~200 m resolution. As a conclusion, the gradient approach is efficient and accurate for high-degree SHS at multiple points at the Earth's surface.

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Section: Application Of Euralpgm2011mentioning

confidence: 99%

Efficient and accurate high-degree spherical harmonic synthesis of gravity field functionals at the Earth’s surface using the gradient approach

Hirt

2012

J Geod

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“…AUSGeoid98 ) has served Australia reasonably well for over a decade, principally for the determination of Australian Height Datum (AHD; Roelse et al 1971) heights from GNSS (Global Navigation Satellite Systems) surveys (e.g., Featherstone 2008), but also for the reduction of terrestrial geodetic-surveying data to the Geocentric Datum of Australia 1994 (GDA94) (Featherstone 1997;Featherstone and Rüeger 2000). It has also found applications in geology (Miranda et al 2008), environmental geoscience (McLaren and Wallace 2010) and physical oceanography (Deng et al 2009).…”

Section: Motivationmentioning

confidence: 99%

The AUSGeoid09 model of the Australian Height Datum

Featherstone

Kirby

Hirt

et al. 2010

J Geod

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Abstract. AUSGeoid09 is the new Australia-wide gravimetric quasigeoid model that has been a posteriori fitted to the Australian Height Datum (AHD) so as to provide a product that is practically useful for the more direct determination of AHD heights from Global Navigation Satellite Systems (GNSS). This approach is necessary because the AHD is predominantly a third-order vertical datum that contains a ~1 m north-south tilt and ~0.5 m regional distortions with respect to the quasigeoid, meaning that GNSS-gravimetricquasigeoid and AHD heights are inconsistent. Since the AHD remains the official vertical datum in Australia, it is necessary to provide GNSS users with effective means of recovering AHD heights. The gravimetric component of the quasigeoid model was computed using a hybrid of the remove-compute-restore technique with a degree-40 deterministically modified kernel over a one-degree spherical cap, which is superior to the remove-compute-restore technique alone in Australia (with or without a cap). This is because the modified kernel and cap combine to filter long-wavelength errors from the terrestrial gravity anomalies. The zero-tide EGM2008 global gravitational model to degree and order 2190 was used as the reference field. Other input data are: ~1.4 million land gravity anomalies from Geoscience Australia, 1'x1' DNSC2008GRA altimeter-derived gravity anomalies offshore, the 9"x9" GEODATA-DEM9S Australian digital elevation model, and a readjustment of Australian National Levelling Network (ANLN) constrained to the CARS2006 dynamic ocean topography model. In order to determine the numerical integration parameters for the modified kernel, the gravimetric component of AUSGeoid09 was compared with 911 GNSS-observed ellipsoidal heights at benchmarks. The standard deviation of fit to the GNSS-AHD heights is ±222 mm, which dropped to ±134 mm for the readjusted GNSS-ANLN heights, showing that careful consideration now needs to be given to the quality of the levelling data used to assess gravimetric quasigeoid models. The publicly released version of AUSGeoid09 also includes a geometric component that models the difference between the gravimetric quasigeoid and the zero surface of the AHD at 6,794 benchmarks. This a posteriori fitting used least-squares collocation (LSC) in cross-validation mode to determine a correlation length of 75 km for the analytical covariance function, whereas the noise was taken from the estimated standard deviation of the GNSS ellipsoidal heights. After this LSC surface-fitting, the standard deviation of fit reduced to ±30 mm, one third of which is attributable to the uncertainty in the GNSS ellipsoidal heights.

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“…To pomeni, da moramo klasična terestrična opazovanja reducirati na normalo ter na površino ploskve referenčnega elipsoida, ki jih opravimo z uporabo odklonov navpičnic in geoidnih višin točk. Tako s postopki terestrične geodetske izmere pridobimo koordinate točk, ki so enakovredne koordinatam, določenim na podlagi opazovanj GNSS (Featherstone, Rüger, 2000). Z odklonom navpičnice in geoidno višino je podana lega geoida glede na elipsoid v točki.…”

Section: Uvodunclassified