Abstract
Model computations were performed for the study of numerical errors which are interjected into local geoid computations byFFT. The gravity field model was generated through the attractions of granitic prisms derived from actual geology. Changes in sampling interval introduced only0.3 cm variation in geoid heights. Although zero padding alone provided an improvement of more than5 cm in theFFT generated geoid, the combination of spectral windowing (tapering) and padding further reduced numerical errors. For theGPS survey of Franklin County, Ohio, the parameters selected as a result of model computations, allow large reduction in local data requirements while still retaining the centimeter accuracy when tapering and padding is applied.
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References
R.N. BRACEWELL, 1978:The Fourier Tranform and its applications. McGraw-Hill Book Company.
J.W. COOLEY and J.W. TUKEY, 1965:An Algorithm for the Machine Calculation of Complex Fourier Series. Mathematics of Computations,19, No. 90, pp. 297–301.
H. DENKER, 1988:Regional Quasigeoid Determination in Northern Germany and Comparison with GPS. Chapman Conference on Progress in the Determination of the Earth’s Gravity Field, Fort Lauderdale, Florida, September.
T. ENGELIS, R.H. RAPP and C.C. T SCHERNING, 1984:The Precise Computation of Geoid Undulation Differences with Comparison to Results Obtained from Global Positioning System. Geophysical Research Letters, Vol. 1, No. 9, September.
R. FORSBERG and D. SOLHEIM, 1988:Performance of FFT Methods in Local Gravity Field Modeling. Chapman Conference on Progress in the Determination of the Earth’s Gravity Field, Fort Lauderdale, Florida, September.
R.J. FURY, 1985:Report on Data Analysis of GPS Survey Project, Franklin County GPS Survey. NGS Report, May.
GEO-HYDRO, 1983:Project Report. Geodetic Survey, Franklin County, Ohio.
R.A. GIBB and J. van BOECKEL, 1970:Three-dimensional gravity interpretation of the Round Lake batholith, northeastern Ontario. Can. J. Earth Sci. 7.
E. GROTEN, 1981:Precise determination of the disturbing potential using alternative boundary values. NOAA Technical Report, NOS 90 NGS 20, Rockville, MD.
A.H.W. KEARSLEY, 1985:Towards the Optimum Evaluation of the Inner Zone Contribution to the Geoid Heights. Australian Journal of Geodesy, Photog. and Surv., No. 42, June.
W.D. McMILAN, 1958:The Theory of the Potential. Dower Publications, Inc., New York.
D. NAGY, 1966:The gravitational attraction of a right rectangular prism. Geophysics,XXXI, No. 2, April, pp. 362–371.
D. NAGY, 1980:Gravity anomalies, deflection of the vertical and geoidal heights for a three-dimensional model. Acta Geodaet. Geophys. et Mont. Acad. Sci. Hung. Tomus15 (1), pp. 17–26.
D. NAGY, 1988:Fast Fourier Transform and Modeling in Geoid Computation. Bolletino di Geodesia e Scienze Affini No. 1, 1988, pp. 33–43.
R.H. RAPP, 1977:The Relationship between Mean Anomaly Block Size and Spherical Harmonic Representation. Journal of Geophysical Research, Vol. 82, pp. 5360–5364.
B.W. REMONDI, 1984:Using the Global Positioning System (GPS) Phase Observable for Relative Geodesy: Modeling, Processing and Results. Ph.D. Dissertation, The University of Texas at Austin.
K.P. SCHWARZ, M.G. SIDERIS, R. FORSBERG, 1990:The Use of FFT Techniques in Physical Geodesy. Geophysical Journal International,100, pp. 485–514.
M.G. SIDERIS and K.P. SCHWARZ, 1986:Improvement of Medium and Short Wavelength Features of Geopotential Solutions by Local Data. Proc. of the Int. Symposium on the Definition of the Geoid, Florence, Italy.
C.C. TSCHERNING, 1989:Achievable Accuracy for Geoid Height Differences Across the Strait of Gibraltar. First Int. Workshop on Geodesy for the Europe-Africa Fixed Link Feasibility Studies in the Strait of Gibraltar, Madrid, March.
C. TSUBOI and T. FUCHIDA, 1937:Relation between gravity values and the corresponding subteranean mass distribution. Earthquake Res. Inst. Bull. Tokyo,15 pp. 636–649.
S. ZHAO, 1989:The Computation of Detailed Geoids Using the Fast Fourier Transform Method. Report No. 400. Dept. of Geodetic Science and Surveying, The Ohio State Univ., August.
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Nagy, D., Fury, R.J. Local geoid computation from gravity using the fast fourier transform technique. Bull. Geodesique 64, 283–294 (1990). https://doi.org/10.1007/BF02519181
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DOI: https://doi.org/10.1007/BF02519181