Abstract
In contrast to continuous global considerations of time dependent boundary value problems an attempt is made to define 4D-linear observation equations in the framework of integrated geodesy for discrete, more or less regional and local applications (deformation analysis) where time variations in position and in the gravity field have to be considered. The derivation is a strict analogue and extension of the 3D integrated approach. In addition the construction of time dependent covariance functions is discussed, which are necessary to solve for unknown displacements and changes in the gravity potential in the generalized least squares collocation model.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
K. ARNOLD: Das Gravitationspotential der rezenten Erdkrustenbewegungen. Vermessungstechnik, 28, pp. 417–418, 1980.
R. BARZAGHI, B. BETTI and F. SANSÒ: Integrated Geodesy: A Purely Local Approach, 1985. Manuscript available from the authors.
P. BIR’O: Zur Anwendung der Stokes’schen Formet fuer zeitliche Schwereaenderungen. Zeitschrift fuer Vermessungswesen, 106, pp. 523–531, 1981.
P. BIR’O, N.C. THONG, and E. WEISZ: Modelling of Secular Variations in Gravity and in Geoidal Undulations. Periodica Polytechnica Civil Engineering 30, pp. 23–36, Budapest, 1986.
P. BIR’O, B. HECK and N.C. THONG: On a New Approach into the Solution of the Three Dimensional Geodetic-Geodynamic Boundary Value Problem. Allgemeine Vermessungsnachrichten, Int. Ed., pp. 9–21, 1986.
J. EEG and T. KRARUP: Integrated Geodesy. The Danish Geodetic Institute, Internal Report No. 7, Kopenhagen, 1973.
E. GRAFAREND: Six Lectures on Geodesy and Global Geodynamics. In: H. Moritz and H. Suenkel (eds.), Geodesy and Global Geodynamics. Mitt. der Geod. Inst. der TU Graz, 41, pp. 531–685, 1982.
E. GRAFAREND: Spacetime Telluroid Versus Spacetime Geoid or the Bruns-Love Dialogue. Rep. No. 19, Dept. of Geodesy, Institute of Geophysics, University of Uppsala, pp. 105–126, 1983.
E. GRAFAREND and F. SANSÒ: The Multibody Space-Time Geodetic Boundary Value Problem and the Honkaselo Term. Geophys. Journal of the Royal Astronomical Society, 78, pp. 255–275, 1984.
B. HECK: Combination of Levelling and Gravity Data for Detecting Real Crustal Movements. Proc. Int. Syrup. on Geodetic Networks and Computations, Munich 1981, Vol. VII. Deutsche Geodaetische Kommission, B. 258/VII, pp. 20–30, 1981.
B. HECK: Zur Bestimmung vertikaler rezenter Erdkrustenbewegungen und zeitlicher Aenderungen des Schwerefeldes aus wiederholten Schweremessungen und Nivellements. Deutsche Geodaetische Kommission C 302, 1984.
B. HECK: Time-Dependent Geodetic Boundary Value Problems. In: Proc. Int. Symposium, Figure and Dynamics of the Earth, Moon and Planets, Prague, Czechoslovakia, Sept. pp. 15–20, 1986.
B. HECK end H. MAELZER: Determination of Vertical Recent Crustal Movements by Levelling and Gravity Data. Tectonophysics 97, pp. 251–264, 1983.
G.W. HEIN: A Contribution to 3D-Operational Geodesy. Part 1: Principle and Observational Equations of Terrestrial Type. In: Proc. of the International Symposium on Geodetic Networks and Computations of the International Association of Geodesy, Munich, Aug. 31 to Sept. 5, 1981, Deutsche Geodaetische Kommission, Reihe B, Nr. 258/VII, pp. 31–64, Muenchen, 1982a.
G.W. HEIN: A Contribution to 3D-Operational Geodesy. Part 2: Concepts of Solution. In: Proc. of the International Symposium on Geodetic Networks and Computations of the International Association of Geodesy Munich, Aug. 31 to Sept. 5, 1981. Deutsche Geodaetische Kommission, Reihe B, Nr. 258/VII, pp. 65–85, Muenchen, 1982b.
G.W. HEIN and H. LANDAU: A Contribution to 3D-Operational Geodesy. Part 3: OPERA — A Multi-Purpose Program for Operational Adjustment of Geodetic Observations of Terrestrial Type. Deutsche Geodaetische Kommission, Reihe B. Nr. 264, Muenchen, 1983.
M. HOTINE: Mathematical Geodesy. ESSA Monograph 2, U.S. Department of Commerce, Washington, 1969.
E. KANNGIESER: Modellierung vertikaler Krustenbewegungen dutch Kollokation. Zeitschrift für Vermessungswesen 108, pp. 373–381, 1983.
A.E.H. LOVE: The Yielding of the Earth to Disturbing Forces. Proc. Royal Astronomical Society, London, 1909.
A.E.H. LOVE: Some Problems on Geodynamics. Dover publication, New York, 1911.
H. MORITZ: The Operational Approach to Physical Geodesy. Department of Geodetic Science, Ohio State University, Report No. 277, 1978a.
H. MORITZ: Least Squares Collocation. Reviews of Geophysics and Space Physics, Vol. 16, No. 3, August 1978, pp. 321–430, 1978b.
W.I. REILLY: Complete Determination of Local Crustal Deformation from Geodetic Observation. In P. Vyskocil, R. Green and H. Maelzer (Eds.), Recent Crustal Movements 1979. Tectonophysics 71, pp. 111–123, 1981.
W.I. REILLY: Differential Geometry of a Time-Varying Gravity Field. Bolletino di Geodesia e Scienze Affini 44, pp. 283–293, 1985.
W.I. REILLY: Heterogeneous Strain in Earth Deformation. Geophysics Division Report, Wellington, 1986 a.
W.I. REILLY: Continuum Models in Earth Deformation Analysis. Paper presented for the Symposium on Height Determination and Recent Vertical Crustal Movements in Western Europe, Hannover, Fed. Rep. of Germany, Sept. 15–19, 1986b.
F. SACERDOTE and F. SANSÒ: The Overdetermined Boundary Value Problems of Physical Geodesy. Universita degli Studi di Pisa, Dipartimento di Mathematica, No. 98, 1984.
F. SANSÒ and A. DERMANIS: A Geodynamic Boundary Value Problem. Boll. di Geodesia e Scienze Affini XLI, pp. 65–87, 1982.
T. SHIDA: Horizontal Pendulum Observations of the Change of Plumbline at Kamigano, Kyoto. Mem. Coll. Sci. Eng. Tokyo, 4, pp. 23–174, 1912.
G.L. STRANG VAN HEES: Zur zeitlichen Aenderung von Schwere und Hoehe. Zeitschrift fuer Vermessungswesen, 102, pp. 444–450, 1977.
M.I. YURKINA: Combined Determination of Changes in the Earth’s Gravitational Field and of Vertical Displacements of the Earth’s Crust. Geodesy, Mapping and Photogrammetry, 19, No. 2, pp. 59–62, 1977.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Collier, P.A., Eissfeller, B., Hein, G.W. et al. On a four-dimensional integrated geodesy. Bull. Geodesique 62, 71–91 (1988). https://doi.org/10.1007/BF02519326
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF02519326