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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Journal of geodesy 71 (1997), S. 571-576 
    ISSN: 1432-1394
    Keywords: Key words. Geoid determination ; Stokes's integral ; Terrain corrections.
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying
    Notes: Abstract. A method is presented with which to verify that the computer software used to compute a gravimetric geoid is capable of producing the correct results, assuming accurate input data. The Stokes, gravimetric terrain correction and indirect effect formulae are integrated analytically after applying a transformation to surface spherical coordinates centred on each computation point. These analytical results can be compared with those from geoid computation software using constant gravity data in order to verify its integrity. Results of tests conducted with geoid computation software are presented which illustrate the need for integration weighting factors, especially for those compartments close to the computation point.
    Type of Medium: Electronic Resource
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  • 2
    ISSN: 1432-1394
    Keywords: Key words. Gravimetric geoid determination ; Modified kernels ; Truncation error reduction
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying
    Notes: Abstract. A deterministic modification of Stokes's integration kernel is presented which reduces the truncation error when regional gravity data are used in conjunction with a global geopotential model to compute a gravimetric geoid. The modification makes use of a combination of two existing modifications from Vaníček and Kleusberg and Meissl. The former modification applies a root mean square minimisation to the upper bound of the truncation error, whilst the latter causes the Fourier series expansion of the truncation error to coverage to zero more rapidly by setting the kernel to zero at the truncation radius. Green's second identity is used to demonstrate that the truncation error converges to zero faster when a Meissl-type modification is made to the Vaníček and Kleusberg kernel. A special case of this modification is proposed by choosing the degree of modification and integration cap-size such that the Vaníček and Kleusberg kernel passes through zero at the truncation radius.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Journal of geodesy 74 (2000), S. 239-248 
    ISSN: 1432-1394
    Keywords: Key words: Geoid determination – Integration kernels – Truncation error
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying
    Notes: Abstract.  When Stokes's integral is used over a spherical cap to compute a gravimetric estimate of the geoid, a truncation error results due to the neglect of gravity data over the remainder of the Earth. Associated with the truncation error is an error kernel defined over these two complementary regions. An important observation is that the rate of decay of the coefficients of the series expansion for the truncation error in terms of Legendre polynomials is determined by the smoothness properties of the error kernel. Previously published deterministic modifications of Stokes's integration kernel involve either a discontinuity in the error kernel or its first derivative at the spherical cap radius. These kernels are generalised and extended by constructing error kernels whose derivatives at the spherical cap radius are continuous up to an arbitrary order. This construction is achieved by smoothly continuing the error kernel function into the spherical cap using a suitable degree polynomial. Accordingly, an improved rate of convergence of the spectral series representation of the truncation error is obtained.
    Type of Medium: Electronic Resource
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  • 4
    ISSN: 1432-1394
    Keywords: Key words. Precise geoid determinations ; Gravity anomaly ; Geodetic boundary value problem ; Downward continuation of gravity
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying
    Notes: Abstract.  The definition of the mean Helmert anomaly is reviewed and the theoretically correct procedure for computing this quantity on the Earth's surface and on the Helmert co-geoid is suggested. This includes a discussion of the role of the direct topographical and atmospherical effects, primary and secondary indirect topographical and atmospherical effects, ellipsoidal corrections to the gravity anomaly, its downward continuation and other effects. For the rigorous derivations it was found necessary to treat the gravity anomaly systematically as a point function, defined by means of the fundamental gravimetric equation. It is this treatment that allows one to formulate the corrections necessary for computing the `one-centimetre geoid'. Compared to the standard treatment, it is shown that a `correction for the quasigeoid-to-geoid separation', amounting to about 3 cm for our area of interest, has to be considered. It is also shown that the `secondary indirect effect' has to be evaluated at the topography rather than at the geoid level. This results in another difference of the order of several centimetres in the area of interest. An approach is then proposed for determining the mean Helmert anomalies from gravity data observed on the Earth's surface. This approach is based on the widely-held belief that complete Bouguer anomalies are generally fairly smooth and thus particularly useful for interpolation, approximation and averaging. Numerical results from the Canadian Rocky Mountains for all the corrections as well as the downward continuation are shown.
    Type of Medium: Electronic Resource
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  • 5
    ISSN: 1432-1394
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying
    Notes: Abstract A method is developed with which to predict time variations of the Earth's gravity field and crustal deformation due to mass loading. Using this method, changes to the original geodetic datums can be estimated. This is applied to the Three Gorges area of China, due to the construction of the Yangtze river dam. Results indicate that the probable maximum crustal deformation and changes in gravity, elevation and deflection of the vertical will be 7.8mm, 4.7mgal, 19.0mm and 0.61 arc seconds, respectively. These changes are of importance for the establishment of monitoring operations both during and upon completion of the dam.
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    Springer
    Journal of geodesy 72 (1998), S. 684-697 
    ISSN: 1432-1394
    Keywords: Key words. Geoid determination ; Modified kernels ; Error propagation ; High-pass filtering
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying
    Notes: Abstract. When regional gravity data are used to compute a gravimetric geoid in conjunction with a geopotential model, it is sometimes implied that the terrestrial gravity data correct any erroneous wavelengths present in the geopotential model. This assertion is investigated. The propagation of errors from the low-frequency terrestrial gravity field into the geoid is derived for the spherical Stokes integral, the spheroidal Stokes integral and the Molodensky-modified spheroidal Stokes integral. It is shown that error-free terrestrial gravity data, if used in a spherical cap of limited extent, cannot completely correct the geopotential model. Using a standard norm, it is shown that the spheroidal and Molodensky-modified integration kernels offer a preferable approach. This is because they can filter out a large amount of the low-frequency errors expected to exist in terrestrial gravity anomalies and thus rely more on the low-frequency geopotential model, which currently offers the best source of this information.
    Type of Medium: Electronic Resource
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  • 7
    Publication Date: 2013-07-05
    Description: The spirit-levelling–based British vertical datum (Ordnance Datum Newlyn) implies a south–north apparent slope in mean sea level of up to 53 mm deg –1 latitude, due to the datum falling on heading northwards. Although this apparent slope has been investigated since the 1960s, explanations of its origin have remained inconclusive. It has also been suggested that, rather than a slope, the British vertical datum includes a step of about 240 mm affecting all sites north of about 53°N. In either case, the British vertical datum may be of limited use for any study requiring accurate heights or changes in heights, such as testing geoid models, groundwater and hydrocarbon extraction, the calibration and validation of satellite-based digital terrain models, and the unification of vertical datums internationally. Within the last decade, however, based on an apparent reduction in the slope to only –12 mm deg –1 latitude with respect to recent geoid models, it has been claimed that the British vertical datum does provide a physically meaningful surface for use in scientific applications. In this paper, we reinvestigate the presence of apparent south–north sea slopes around Britain and reported slopes in the vertical datum, using the EGM2008 global gravitational model, together with mean sea level and GPS data from British tide gauges, GPS ellipsoidal heights of 178 fundamental benchmarks across mainland Britain, and vertical deflection observations at 192 stations. We demonstrate a south–north slope in the British vertical datum of –(20–25) mm deg –1 latitude with respect to both mean sea level (corrected for the ocean's mean dynamic topography and the inverse barometer response to atmospheric pressure loading) and the EGM2008 quasigeoid model, while EGM2008 is shown to exhibit a negligible slope of (2 ± 4) mm deg –1 with respect to mean sea level. It is clear, therefore, that the slope can only arise from systematic errors in the levelling, although we are unable to isolate their exact origin. Using an offset detection method based on a penalized likelihood maximization using the Schwarz Information Criterion, we do not detect a step in the vertical datum affecting all sites north of 53°N, but do identify regional distortions that we attribute to the inhomogeneity in both the levelling data used and the least squares adjustment procedures used to realize the datum. We conclude that the British vertical datum remains unsuitable for scientific purposes.
    Print ISSN: 0956-540X
    Electronic ISSN: 1365-246X
    Topics: Geosciences
    Published by Oxford University Press on behalf of The Deutsche Geophysikalische Gesellschaft (DGG) and the Royal Astronomical Society (RAS).
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  • 8
    Publication Date: 2017-05-31
    Description: We have identified a gap in the literature on error propagation in the gravimetric terrain correction. Therefore, we have derived a mathematical framework to model the propagation of spatially correlated digital elevation model errors into gravimetric terrain corrections. As an example, we have determined how such an error model can be formulated for the planar terrain correction and then be evaluated efficiently using the 2D Fourier transform. We have computed 18.3 billion linear terrain corrections and corresponding error estimates for a 1 arc-second ( ~30 m ) digital elevation model covering the whole of the Australian continent.
    Print ISSN: 0016-8033
    Electronic ISSN: 1942-2156
    Topics: Geosciences , Physics
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  • 9
    Publication Date: 2018-08-22
    Description: Leveling remains the most precise technique for measuring changes in heights. However, for the purposes of determining vertical land motion (VLM), a time series of repeat leveling measurements is susceptible to artifacts and aliasing that may arise due to systematic errors, seasonal surface fluctuations, motions occurring during a survey, and any inconsistencies in the observation conditions among epochs. Using measurements from 10 repeat leveling surveys conducted twice yearly along a profile spanning ~40 km across the Perth Basin, Western Australia, we describe the observation, processing, and analysis methods required to mitigate these potential error sources. We also demonstrate how these issues may lead to misinterpretation of the VLM derived from repeat leveling and may contribute to discrepancies between geologically inferred rates of ground motion or those derived from other geodetic measurement techniques. Finally, we employ historical (~40-year-old) leveling data in order to highlight the errors that can arise when attempting to extrapolate VLM derived from a geodetic time series, particularly in cases where the long-term motion may be nonlinear. ©2018. The Authors.
    Print ISSN: 2169-9313
    Electronic ISSN: 2169-9356
    Topics: Geosciences , Physics
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  • 10
    Publication Date: 2017-05-16
    Print ISSN: 0016-8033
    Electronic ISSN: 1942-2156
    Topics: Geosciences , Physics
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