Skip to main content
SpringerLink
Log in

Spherical spectral properties of the earth's gravitational potential and its first and second derivatives

  • Part III: From The GBVP Towards A 1 cm Geoid
  • Chapter
  • First Online:
Geodetic Boundary Value Problems in View of the One Centimeter Geoid

Part of the book series: Lecture Notes in Earth Sciences ((LNEARTH,volume 65))

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Albertella, A., F. Migliaccio, F. Sansò (1994). "Application of the Concept of Biorthogonal Series to a Simulation of a Gradiometric Mission", 3rd Hotine-Marussi Symposium on Mathematical Geodesy, L'Aquila.

    Google Scholar 

  • Albertella, A., F. Migliaccio, F. Sansò (1995). "Global Gravity Field Recovery by Use of STEP Observations" in: "Gravity and Geoid" (eds. H. Sünkel & I. Marson), IAG-Symposia 113, 111–116, Springer, Heidelberg.

    Google Scholar 

  • Baarda, W. (1967). "Statistical Concepts in Geodesy", Netherlands Geodetic Commission, New Series, 2, 4, Delft.

    Google Scholar 

  • Baarda, W. (1979). "A Connection Between Geometric and Gravimetric Geodesy", Net herlands Geodetic Commission, New Series, 6, 4, Delft.

    Google Scholar 

  • Baarda, W. (1995). "Linking up Spatial Models in Geodesy — Extended S-Transformations", Netherlands Geodetic Commission, New Series, 41, Delft.

    Google Scholar 

  • Backus, G.E. (1967). "Converting Vector and Tensor Equations to Scalar Equations in Spherical Coordinates", Geophys. J. R. Astr. Soc., 13, 71–101.

    Google Scholar 

  • Bouman, J. (1993). "The Normal Matrix in Gravity Field Determination with Satellite Methods", Delft University of Technology.

    Google Scholar 

  • Brovelli, M., F. Sansò (1990). "Gradiometry: The Study of the Vyy Component in the BVP Approach", manuscripta geodaetica, 15, 4, 240–248.

    Google Scholar 

  • Bruns, H. (1878). "Die Figur der Erde", Publication des Königl. Preussischen Geodätischen Instituts, Berlin.

    Google Scholar 

  • Colombo, O.L. (1981). "Numerical Methods for Harmonic Analysis on the Sphere", Dept. Geodetic Science and Surveying, 310, The Ohio State University, Columbus.

    Google Scholar 

  • Colombo, O.L. (1984). "Altimetry, Orbits and Tides", Report EG&G Washington Analytical Services Inc., NASA Technical Memorandum 86180.

    Google Scholar 

  • Colombo, O.L. (1989). "Advanced Techniques for High-Resolution Mapping of the Gra vitational Field" in: Theory of Satellite Geodesy and Gravity Field Determination (eds. F. Sansò & R. Rummel) Lecture Notes in Earth Sciences, 25, 335–369, Springer, Heidelberg.

    Google Scholar 

  • Freeden, W., T. Gervens, M. Schreiner (1994). "Tensor Spherical Harmonics and Tensor Spherical Splines", manuscripta geodaetica, 19, 70–100.

    Google Scholar 

  • van Gelderen, M., R. Koop (1996). "An Assessment of the Accuracy of Some Error Prediction Methods for Satellite Gradiometry", journal of geodesy (in print).

    Google Scholar 

  • Gerstl, M., R. Rummel (1981). "Stability Investigations of Various Representations of the Gravity Field", Rev. Geoph. Space Phys., 19, 3, 415–420.

    Google Scholar 

  • Grafarend, E. (1986). "Three-Dimensional Deformation Analysis: Global Vector Spheri cal Harmonic and Local Finite Element Representation", Tectonophysics, 130, 337–359.

    Article  Google Scholar 

  • Groten, E., H. Moritz (1964). "On the Accuracy of Geoid Heights and Deflections of the Vertical", Institute of Geodesy, Photogrammetry and Cartography, 38. The Ohio State University, Columbus.

    Google Scholar 

  • Gurtin, M.E. (1971). "Theory of Elasticity", Handbuch der Physik, Bd. VI, 2nd ed., Springer, Berlin.

    Google Scholar 

  • Heck, B. (1987). "Rechenverfahren und Auswertemodelle der Landesvermessung — Klassische und moderne Methoden", Wichmann, Karlsruhe.

    Google Scholar 

  • Heiskanen, W.A., H. Moritz (1967). "Physical Geodesy", Freeman, San Francisco.

    Google Scholar 

  • Hotine, M. (1967). "Downward Continuation of the Gravitational Potential", in: Hotine, M. (1991). "Differential Geodesy" 143–148, Springer, Berlin.

    Google Scholar 

  • Hotine, M. (1969). "Mathematical Geodesy", U.S. Department of Commerce, Washington D.C..

    Google Scholar 

  • Jackson, J.D. (1925; 1975). "Classical Electrodynamics", John Wiley, New York.

    Google Scholar 

  • Jekeli, Ch. (1978). "An Investigation of Two Models for the Degree Variances of Global Covariance Functions", Dept. Geodetic Science, 275, The Ohio State University, Columbus.

    Google Scholar 

  • Jekeli, Ch., R.H. Rapp (1980). "Accuracy of the Determination of Mean Anomalies and Mean Geoid Undulations from a Satellite Gravity Field Mapping Mission", Dept. Geodetic Science and Surveying, 307, The Ohio State University, Columbus.

    Google Scholar 

  • Jones, M.N. (1985). "Spherical Harmonics and Tensors for Classical Field Theory", Wiley, New York.

    Google Scholar 

  • Kaula, W.M. (1966). "Theory of Satellite Geodesy", Blaisdell Publ., Waltham Ma..

    Google Scholar 

  • Keller, W. (1991). "Behandlung eines überbestimmten Gradiometrie-Randwertproblems mittels Pseudodifferentialoperatoren", ZfV, 116, 66–73.

    Google Scholar 

  • Keller, W., M. Hirsch (1994). "A Boundary Value Approach to Downward Continuation", manuscripta geodaetica, 19, 2, 101–118.

    Google Scholar 

  • Koop, R. (1993). "Global Gravity Field Modelling Using Satellite Gravity Gradiometry", Netherlands Geodetic Commission, New Series, 38, Delft.

    Google Scholar 

  • Krarup, T. (1969). "A Contribution to the Mathematical Foundation of Physical Geodesy", Danish Geodetic Institute, 44, Copenhagen.

    Google Scholar 

  • Krarup, T. (1973). "Letters on Molodensky's Problem", Communication to the members of IAG Special Study Group 4.31.

    Google Scholar 

  • Lanczos, C. (1961). "Linear Differential Operators", Van Nostrand, London.

    Google Scholar 

  • Lerch, F.J. (1989). "Optimum Data Weighting and Error Calibration for Estimation of Gravitational Parameters", NASA Technical Memorandum 100737.

    Google Scholar 

  • Meissl, P. (1971). "A Study of Covariance Functions Related to the Earth's Disturbing Potential", Dept. Geodetic Science, 151, The Ohio State University, Columbus.

    Google Scholar 

  • Mikolaiski, H.-W. (1989). "Synthetische Modelle zur Polbewegung eines deformierbaren Körpers", Deutsche Geodätische Kommission, C-354, München.

    Google Scholar 

  • Mochizuki, E. (1988). "Spherical Harmonic Development of an Elastic Tensor", Geophys. J. Int. 93, 521–526.

    Google Scholar 

  • Molodenskii, M.S., V.F. Eremeev, M.I. Yurkina (1962). "Methods for Study of the Ex ternal Gravitational Field and Figure of the Earth", Israel Program for Scientific Translations, Jerusalem.

    Google Scholar 

  • Moritz, H. (1963). "Interpolation and Prediction of Point Gravity Anomalies", Publ. Isost. Int. Assoc. Geod., 40, Helsinki.

    Google Scholar 

  • Moritz, H. (1976). "Covariance Functions in Least Squares Collocation", Dept. Geodetic Science, 240, The Ohio State University, Columbus.

    Google Scholar 

  • Moritz, H. (1980). "Advanced Physical Geodesy", Wichmann, Karlsruhe.

    Google Scholar 

  • Ohanian, H.C. (1976). "Gravitation and Spacetime", Norton, New York.

    Google Scholar 

  • Papoulis, A. (1965). "Probability, Random Variables and Stochastic Processes", McGraw-Hill, New York.

    Google Scholar 

  • Pelka, E.J., D.B. DeBra (1979). "The Effects of Relative Instrument Orientation upon Gravity Gradiometer System Performance", J. Guidance and Control, 2, 1, 18–24.

    Google Scholar 

  • Phinney, R.A. (1973). "Representation of the Elastic-Gravitational Excitation of a Spherical Earth Model by Generalized Spherical Harmonics", Geophys. J. R. Astr. Soc., 34,451–487.

    Google Scholar 

  • Rapp, R.H., Y.M. Wang, N.K. Pavlis (1991). "The Ohio State 1991 Geopotential and Sea Surface Topography Harmonic Coefficient Models", Dept. Geod. Science & Surveying, 410, The Ohio State University, Columbus.

    Google Scholar 

  • Reed, G.B. (1973). "Application of Kinematical Geodesy for Determining the Short Wave Length Components of the Gravity Field by Satellite Gradiometry", Department of Geodetic Science, 201, The Ohio State University, Columbus.

    Google Scholar 

  • Regge, T., J.A. Wheeler (1957). "Stability of a Schwarzschild Singularity", Phys. Rev., 108, 1063–1069.

    Article  Google Scholar 

  • Rummel, R. (1975). "Downward Continuation of Gravity Information from Satellite Gradiometry in Local Areas", Dept. Geodetic Science, 221, The Ohio State University, Columbus.

    Google Scholar 

  • Rummel, R. (1979). "Determination of the Short-Wavelength Components of the Gravity Field from Satellite-to-Satellite Tracking or Satellite Gradiometry", manuscripta geodaetica, 4, 107–148.

    Google Scholar 

  • Rummel, R. (1984). "From the Observational Model to Gravity Parameter Estimation", in: Proc. Beijing Intern. Summer School on Local Gravity Field Approximation, (ed: K.P. Schwarz), Beijing.

    Google Scholar 

  • Rummel, R. (1986). "Satellite Gradiometry",in: Lecture Notes in Earth Sciences, 7 Ma thematical and Numerical Techniques in Physical Geodesy, (ed. H. Sünkel), 318–163, Springer, Berlin.

    Google Scholar 

  • Rummel, R. (1991). "Fysische Geodesy II (Physical Geodesy 2)", Lecture Notes, Delft University of Technology, Delft.

    Google Scholar 

  • Rummel, R. (1992). "On the Principles and Prospects of Gravity Field Determination by Satellite Methods" in: Geodesy and Physics of the Earth (eds. H. Montag & Ch. Reigber), IAG-Symposia 112, 67–70, Springer, Heidelberg.

    Google Scholar 

  • Rummel, R., M. van Gelderen (1992). "Spectral Analysis of the Full Gravity Tensor", Geophys. J. Int., 111, 1, 159–169.

    Google Scholar 

  • Rummel, R., M. van Gelderen (1995). "Meissl Scheme — Spectral Characteristics of Physical Geodesy", manuscripta geodaetica, 20, 379–385.

    Google Scholar 

  • Rummel, R., F. Sansò, M. van Gelderen, M. Brovelli, R. Koop, F. Migliaccio, E.J.O. Schrama, F. Sacerdote (1993). "Spherical Harmonic Analysis of Satellite Gradiometry", Netherlands Geodetic Commission, New Series, 39, Delft.

    Google Scholar 

  • Sansò, F. (1981). "Recent Advances in the Theory of the Geodetic Boundary Value Problem", Rev. Geoph. Space Physics, 19, 3, 437–449.

    Google Scholar 

  • Sansò, F., R. Rummel (1994). "A Discussion on the Correct Way of Representing White Noise on the Sphere and its Propagation from Estimated Quantities", IAG Section IV Bulletin 1, 3–16.

    Google Scholar 

  • Schrama, E.J.O. (1989). "The Role of Orbit Errors in Processing of Satellite Altimeter Data", Netherlands Geodetic Commission, New Series, 33, Delft.

    Google Scholar 

  • Schreiner, M. (1994). "Tensor Spherical Harmonics and Their Application to Satellite Gradiometry", Doktorarbeit, Fachbereich Mathematik, Universität Kaiserslautern.

    Google Scholar 

  • Schuh, W.-D. (1996). "Tailored Numerical Solution Strategies for the Global Determination of the Earth's Gravity Field", Habilitationsschrift, Technische Universität Graz.

    Google Scholar 

  • Schwarz, K.-P. (1971). "Numerische Untersuchungen zur Schwerefortsetzung", Deutsche Geodätische Kommission, C-171, München.

    Google Scholar 

  • Selényi, P. (editor), (1953). "Roland Eötvös gesammelte Arbeiten", Akademiai Kiado, Budapest.

    Google Scholar 

  • Sneeuw, N. (1994). "Global Spherical Harmonic Analysis by Least-Squares and Numeri cal Quadrature Methods in Historical Perspective", Geophys. J. Int., 118, 707–716.

    Google Scholar 

  • Solid-Earth and Ocean Physics (1969). Report of a study at Williamstown, Mass., NASA.

    Google Scholar 

  • Strang van Hees, G. (1986). "Precision of the Geoid, Computed from Terrestrial Gravity Measurements", manuscripta geodaetica, 11, 1–14.

    Google Scholar 

  • Sünkel, H. (1981). "Feasibility Studies for the Prediction of the Gravity Disturbance Vector in High Altitudes", Dept. Geodetic Science, 311, The Ohio State University, Columbus.

    Google Scholar 

  • Svensson, S.L. (1983). "Pseudodifferential Operators — a New Approach to the Boundary Value Problems of Physical Geodesy", manuscripta geodaetica, 8, 1–40.

    Google Scholar 

  • Thorne, K.S. (1980). "Multipole Expansions of Gravitational Radiation", Rev. Mod. Phys., 52, 2-I, 299–339.

    Article  Google Scholar 

  • Tikhonov, A.N., V.Y. Arsenin (1977). "Solutions of Ill-Posed Problems", John Wiley & Sons, New York.

    Google Scholar 

  • Tscherning, C.C. (1976). "Comparison of the Second-Order Derivatives of the Normal Potential Based on the Representation by a Legendre Series", manuscripta geodaetica, 2, 71–92.

    Google Scholar 

  • Tscherning, C.C., R.H. Rapp (1978). "Closed Covariance Expressions for Gravity Ano malies, Geoid Undulations, and Deflections of the Vertical Implied by Anomaly Degree Variance Models", Dept. Geodetic Science, 208, The Ohio State University, Columbus.

    Google Scholar 

  • Xu, P.L. (1992). "The Value of Minimum Norm Estimation of Geopotential Fields", Geophys. J. Int., 110, 321–332.

    Google Scholar 

  • Xu, P.L., R. Rummel (1994a). "Generalized Ridge Regression with Applications in De termination of Potential Fields", manuscripta geodaetica, 20, 1, 8–20.

    Google Scholar 

  • Xu, P.L., R. Rummel (1994b). "A Simulation Study of Smoothness Methods in Recovery of Regional Gravity Fields", Geophys. J. Int., 117, 472–486.

    Google Scholar 

  • Yaglom, A.M. (1962). "Stationary Random Functions", Dover, New York.

    Google Scholar 

  • Zerilli, F.J. (1970). "Tensor Harmonics in Canonical Form for Gravitational Radiation and other Applications", J. Math. Phys., 11, 7, 2203–2208.

    Article  Google Scholar 

Download references

Authors
  1. R. Rummel
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Fernando Sansó Reiner Rummel

Rights and permissions

Reprints and permissions

Copyright information

© 1997 Springer-Verlag

About this chapter

Cite this chapter

Rummel, R. (1997). Spherical spectral properties of the earth's gravitational potential and its first and second derivatives. In: Sansó, F., Rummel, R. (eds) Geodetic Boundary Value Problems in View of the One Centimeter Geoid. Lecture Notes in Earth Sciences, vol 65. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0011710

Download citation

  • DOI: https://doi.org/10.1007/BFb0011710

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-62636-7

  • Online ISBN: 978-3-540-68353-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation