Dr Helmut Moritz has been at OSU regularly as a visiting researcher. He worked there hosted by Urho Votila and other geodesist. In 1977 Moritz wrote a report entitled “Recent developments in the GBVP”.
The report reviews progress in the mathematical formulation and treatment of the goedetic boundary-value problem, in particular, the existence and uniqueness theorems of L. Hormander and the gravity space approach due to Sanso. The method of Hormander uses a very advanced inverse function theorem of nonlinear functional analysis. Sanso has transformed Molodensky’s free boundary-value problem into a fixed boundary-value problem in “gravity space”, thereby essentially reducing the mathematical complexity. As a linear approximation, the gravity space approach gives identical superior for treating questions of existence and uniqueness of the solution, although it is restricted to the pure gravitational case without centrifugal force.
In the introduction Moritz wrote;
The last five ears have brought considerable advances in the theory of the boundary-value problem of physical geodesy in the formulation of Molodensky, which is the determination of the physical earth ’ s surface from gravity. These advances have been accomplished mainly through the work of Krarup, Hörmander and Sanso. The present report is devoted to a review of this work.
Hormander (1975) The boundary-value problem of physical geodesy. Technical Report 9 Mittag-Leffler Institute, of Lund, Sweden.
Moritz’s Report – OSU (Dec 1977)
No comments:
Post a Comment