Molodensky's series and analytical continuation
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Date
1970-09
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Ohio State University. Division of Geodetic Science
Abstract
It is shown that the Molodensky series solution and the solution of OSU Report 126, based on analytical continuation, are asymptotic series satisfying the basic equations in terms of which the problems are formulated. For the investigation of the second solution, analytical continuation to a level surface completely outside the topographic masses is used. The result provides a logical completion of the proof of equivalence of these two series solutions. It is also shown that the results of the method of Report 126 are the same regardless of the level surface to which analytical continuation is made. This completes the justification of the formal use of analytical continuation into the interior of the topographic masses.
Description
Prepared for Air Force Cambridge Research Laboratories, Air Force Systems Command, United States Air Force, Bedford, Massachusetts: Contract No. F19628-69-C-0127, Project No. 7600, Task No. 760002, 04