Abstract
The great Russian geodesist Leonard Pavlovich Pellinen (1922–1992) has exerted considerable influence on the development of physical geodesy in both East and West. He has extended the geodetic boundary-value problem according to M.S. Molodensky, seeking relations and cross-connections to other possible solutions, such as the inclusion of gravity reduction and the equivalence of Molodensky’s series to another series solution based on analytical continuation.
L.P. Pellinen worked and thought along very similar lines as the author. Both influenced each other, and at several occasions both found similar results independently and almost simultaneously. As regards the above-mentioned equivalence, it was shown by the author up to degree 2 and by his colleague E. Ecker to degree 3; further progress seemed impossible. By a stroke of genius, Pellinen succeeded in proving the equivalence for arbitrary degrees n. The paper examines this and other examples of direct and indirect mutual influence.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Arnold, K. (1959a). Zur Bestimmung der Geoidundulationen aus Freiluftanomalien, Veröff. No. 12, Geodätisches Institut Potsdam.
Arnold, K. (1959b). Strenge Theorie der absoluten Lotabweichungen als Funktionen der Freiluftanomalien der Schwere, Veröff. No. 13, Geod. Inst. Potsdam.
Arnold, K. (1962). The deflections of the vertical expressed in free—air anomalies and their relationship to the gravimetric—isostatic deflections, Bull. Géod., 65, 259–264.
Ecker, E. (1971). Über die Äquivalenz von Lösungen des geodätischen Randwert-problems, Österr. Z. Vermessungswesen, 59, 97–105.
Heiskanen, W.A., and Moritz, H. (1967). Physical Geodesy, W.H. Freeman, San Francisco.
Hotine, M. (1969). Mathematical Geodesy, ESSA Monograph 2, Washington, D.C.
Krarup, T. (1969). A contribution to the mathematical foundation of physical geodesy, Publ. 44, Danish Geodet. Inst., Copenhagen.
Lelgemann, D. (1970). Untersuchungen zu einer genaueren Lösung des Problems von Stokes, Veröff. Dt. Geod. Komm., C, 155, München.
Marych, M.I. (1969). On the second approximation of M.S. Molodensky for the disturbing potential (in Russian), Geodeziya, Kartografiya i Aerofotosyemka, 10, 17–27, Lvov.
Molodenski, M.S. (1958). Grundbegriffe der geodätischen Gravimetrie, VEB Verlag Technik, Berlin.
Molodenskii, M.S., Eremeev, V.F., and Yurkina, M.I. (1962). Methods for Study of the External Gravitational Field and Figure of the Earth, Transl. from Russian ( 1960 ), Israel Program for Scientific Translations, Jerusalem.
Moritz, H. (1964). The boundary—value problem of physical geodesy, Rept. 46, Inst. Geod. Phot. Cart., Ohio State Univ.
Moritz, H. (1968a). Linear solutions of the geodetic boundary—value problem. Veröff. Dt. Geod. Komm., A, 58, München.
Moritz, H. (1968b). On the use of terrain correction in solving Molodensky’s problem, Rept. 108, Dept. Geodet. Sci., Ohio State Univ.
Moritz, H. (1971). Series solutions of Molodensky’s problem, Veró f. Dt. Geod. Komm., A, 70, München.
Moritz, H. (1980). Advanced Physical Geodesy, Wichmann, Karlsruhe
Moritz, H. (1990). The Figure of the Earth, Wichmann, Karlsruhe.
Pellinen, L.P. (1962). Accounting for topography in the calculation of quasigeoidal heights and plumb—line deflections from gravity anomalies, Bull. Géod., 63, 57–65.
Pellinen, L.P. (1964). Expedient formulae for computation of earth’s gravitational field characteristics from gravity anomalies, Bull. Géod., 74, 327–333.
Pellinen, L.P. (1968). Comparison of different methods for computing the plumbline deflections in the mountainous areas, Bull. Géod., 89, 345–354.
Pellinen, L.P. (1972). On the identity of various solutions of the Molodensky’s problem with help of a small parameter, Int. Symp. on Earth Gravity Models and Related Problems, Saint Louis, Missouri, August 1972 (also in Russian, Geod. Aerofotosyemka, 65–71, 1974 ).
Pellinen, L.P. (1981). Effects of the earth ellipticity on solving geodetic boundary value problem, VIII Int. Hotine Symp. on Math. Geodesy, Como, Italy, September 1981.
Pellinen, L.P. (1982). Theoretische Geodäsie, VEB Verlag Bauwesen, Berlin (transi. from Russian (1978) by F. Deumlich).
Sagrebin, D.W. (1956). Die Theorie des regularisierten Geoids, Veröff. No. 9, Geod. Inst. Potsdam.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1993 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Moritz, H. (1993). L.P. Pellinen — Scientific Memories. In: Montag, H., Reigber, C. (eds) Geodesy and Physics of the Earth. International Association of Geodesy Symposia, vol 112. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-78149-0_3
Download citation
DOI: https://doi.org/10.1007/978-3-642-78149-0_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-56572-7
Online ISBN: 978-3-642-78149-0
eBook Packages: Springer Book Archive