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Monograph available for loan

Geoid determination : theory and methods (2013)

Sansò, Fernando [Hrsg.] ; Sideris, Michael G. [Hrsg.]

Berlin [u.a.] : Springer

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Call number: 6/M 15.0285

In: Lecture notes in earth system sciences, volume 110

Description / Table of Contents: Based on the material of the lecture notes in several International Schools for the determination and use of the Geoid, organized by the International Geoid Service of the International Association of Geodesy. the book consolidates, unifies, and streamlines this material in a unique way not covered by the few other books that exist on this subject. More specifically, the book presents (for the first time in a single volume) the theory and methodology of the most common technique used for precise determination of the geoid, including the computation of the marine geoid from satellite altimetry data. These are illustrated by specific examples and actual computations of local geoids. In addition, the book provides the fundamentals of estimating orthometric heights without spirit levelling, by properly combining a geoid with heights from GPS. Besides the geodectic and geophysical uses, this last application has made geoid computation methods very popular in recent years because the entire GPS and GIS user communities are interested in estimating geoid undulations in order to convert GPS heights to physically meaningful orthometric heights (elevations above mean sea level). The overall purpose of the book is, therefore, to provide the user community (academics, graduate students, geophysicists, engineers, oceanographers, GIS and GPS users, researchers) with a self-contained textbook, which will supply them with the complete roadmap of estimating geoid undulations, from the theoretical definitions and formulas to the available numerical methods and their implementation and the test in practice.

Type of Medium: Monograph available for loan

Pages: xxi, 734 S. : Ill. graph. Darst.

ISBN: 9783540746997

Series Statement: Lecture notes in earth system sciences 110

Classification:

Geodesy

Location: Upper compact magazine

Branch Library: GFZ Library

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2

Electronic Resource

Fourier geoid determination with irregular data (1995)

Sideris, Michael G.

Springer

Journal of geodesy 70 (1995), S. 2-12

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ISSN: 1432-1394

Source: Springer Online Journal Archives 1860-2000

Topics: Architecture, Civil Engineering, Surveying

Notes: Abstract The fast Fourier transform (FFT) and, recently, the fast Hartley transform (FHT) have been extensively used by geodesists for efficient geoid determination. For this kind of efficiency, data must be given on a regular grid and, consequently, a pre-processing step of interpolation is required when only point measurements are available. This paper presents a way of computing a grid of geoid undulations N without explicitly gridding the data. The method is applicable to all FFT or FHT techniques of geoid or terrain effects determination, and it works with planar as well as spherical formulas. This method can be used not only for, e.g., computing a grid of undulations from irregular gravity anomalies Δg but it also lends itself to other applications, such as the gridding of gravity anomalies and, since the contribution of each data point is computed individually, the update of N- or Δg-grids as soon as new point measurements become available. In the case that there are grid cells which contain no measurements, the results of gravity interpolation or geoid estimation can be drastically improved by incorporating into the procedure a frequency-domain interpolating function. In addition to numerical results obtained using a few simple interpolating functions, the paper presents briefly the mathematical formulas for recovering missing grid values and for transforming values from one grid to another which might be rotated and/or scaled with respect to the first one. The geodetic problems where these techniques may find applications are pointed out throughout the paper.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF00863415

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3

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Evaluation of deflections of the vertical on the sphere and the plane: a comparison of FFT techniques (1997)

Liu, Q. W. ; Li, Y. Cai ; Sideris, Michael G.

Springer

Journal of geodesy 71 (1997), S. 461-468

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ISSN: 1432-1394

Keywords: Key words. Fast Fourier transform ; Vertical deflections ; Terrain corrections

Source: Springer Online Journal Archives 1860-2000

Topics: Architecture, Civil Engineering, Surveying

Notes: Abstract. This paper presents a set of efficient formulas to evaluate the deflections of the vertical on the sphere using gridded data. The Vening-Meinesz formula, the topographic indirect effect on the deflections of the vertical as well as the terrain corrections are expressed as both 2D and 1D convolutions on the sphere, and consequently can be evaluated by the 2D and the 1D fast Fourier transform (FFT). When compared with the results obtained from pointwise integration, the use of the 1D FFT gives identical results, and therefore these results were used as control values in this paper. The use of the spherical 2D FFT improves significantly the computational efficiency with little sacrifice of accuracy (0.6″ rms difference from the 1D FFT results). The planar 2D FFT, which is as efficient as the spherical 2D FFT, gives worse results (1.2″ rms difference from the 1D FFT results) because of the extra approximations.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/s001900050114

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A new, high-resolution geoid for Canada and part of the U.S. by the 1D-FFT method (1995)

Sideris, Michael G. ; She, Bin Bin

Springer

Journal of geodesy 69 (1995), S. 92-108

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ISSN: 1432-1394

Source: Springer Online Journal Archives 1860-2000

Topics: Architecture, Civil Engineering, Surveying

Notes: Abstract A new, high-resolution and high-precision geoid has been computed for the whole of Canada and part of the U.S., ranging from 35°N to about 90°N in latitude and 210°E to 320°E in longitude. The OSU91A geopotential model complete to degree and order 360 was combined with a 5′ × 5′ mean gravity anomaly grid and 1km × 1km topographical information to generate the geoid file. The remove-restore technique was adopted for the computation of terrain effects by Helmert's condensation reduction. The contribution of the local gravity data to the geoid was computed strictly by the 1D-FFT technique, which allows for the evaluation of the discrete spherical Stokes integral without any approximation, parallel by parallel. The indirect effects of up to second order were considered. The internal precision of the geoid, i.e. the contribution of the gravity data and the model coefficients noise, was also evaluated through error propagation by FFT. In a relative sense, these errors seem to agree quite well with the external errors and show clearly the weak areas of the geoid which are mostly due to insufficient gravity data coverage. Comparison of the gravimetric geoid with the GPS/levelling-derived geoidal heights of eight local GPS networks with a total of about 900 stations shows that the absolute agreement with respect to the GPS/levelling datum is generally better than 10 cm RMS and the relative agreement ranges, in most cases, from 4 to 1 ppm over short distances of about 20 to 100km, 1 to 0.5 ppm over distances of about 100 to 200 km, and 0.5 to 0.1 ppm for baselines of 200 to over 1000 km. Other existing geoids, such as UNB90, GEOID90 and GSD91, were also included in the comparison, showing that the new geoid achieves the best agreement with the GPS/levelling data.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF00819555

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A numerical investigation on height anomaly prediction in mountainous areas (1995)

Li, Ye Cai ; Sideris, Michael G. ; Schwarz, Klaus-Peter

Springer

Journal of geodesy 69 (1995), S. 143-156

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ISSN: 1432-1394

Source: Springer Online Journal Archives 1860-2000

Topics: Architecture, Civil Engineering, Surveying

Notes: Abstract This paper provides numerical examples for the prediction of height anomalies by the solution of Molodensky's boundary value problem. Computations are done within two areas in the Canadian Rockies. The data used are on a grid with various grid spacings from 100 m to 5 arc-minutes. Numerical results indicate that the Bouguer or the topographicisostatic gravity anomalies should be used in gravity interpolation. It is feasible to predict height anomalies in mountainous areas with an accuracy of 10 cm (1σ) if sufficiently dense data grids are used. After removing the systematic bias, the differences between the geoid undulations converted from height anomalies and those derived from GPS/levelling on 50 benchmarks is 12 cm (1σ) when the grid spacing is 1km, and 50 cm (1σ) when the grid spacing is 5′. It is not necessary, in most cases, to require a grid spacing finer than 1 km, because the height anomaly changes only by 3 cm (1σ) when the grid spacing is increased from 100 m to 1000 m. Numerical results also indicate that, only the first two terms of the Molodensky series have to be evaluated in all but the extreme cases, since the contributions of the higher order terms are negligible compared to the objective accuracy.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF00815483

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Assessment of the GOCE-Based Global Gravity Models in Canada (2012)

Ince, E. Sinem ; Sideris, Michael G. ; Huang, Jianliang ; [et al.]

Canadian Science Publishing

In: Geomatica. 2012; 66(2): 125-140. Published 2012 Jun 01. doi: 10.5623/cig2012-025.

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Publication Date: 2012-06-01

Description: The aim of this study is to test the first, second and third generation GOCE geoid solutions, obtained from the first 2, 8 and 18-month observations, respectively. These solutions are assessed over Canada and for two sub-regions (the Great Lakes and Rocky Mountains). The Canadian GPS/leveling-derived geoid heights are used as independent control values in the assessment of the GOCE geoid models. The study is conducted in two steps. First, the geoid models are computed from satellite-only models and truncated to different spherical harmonic degrees. These models are compared with the GPS/leveling geoid heights which are reduced to the same spectral band as the satellite models by EGM2008 predicted frequency components higher than the truncation degrees. The results suggest that the GOCE models show a full power of signal up to about spherical harmonic degree 180. Moreover, the second and third generation GOCE models (with the exception of the direct approach models) provide better agreement with the GPS/leveling-derived geoid undulations than the first generation models due to the longer observation period. The second step involves the combination of the two third generation GOCE models with terrestrial data. These models are tested against to the GPS/leveling-derived geoid undulations in full spectrum. EGM2008 global geopotential model and Canadian gravimetric geoid model CGG2005 are also included in the comparisons to measure improvement provided by the GOCE models. The GOCE-combined models yielded GPS/leveling results that are comparable with those obtained from EGM2008 and CGG2005 models. The best comparative results with the combined models give standard deviations of 4.8 cm, 6.0 cm and 12.2 cm for the Great Lakes, Rocky Mountains and Canada, respectively. These results indicate that the third generation GOCE models conform to the Canadian terrestrial gravity data from degrees 90 to 180. The new generation models show evident improvement over the first and second generation models.

Print ISSN: 1195-1036

Electronic ISSN: 1925-4296

Topics: Architecture, Civil Engineering, Surveying