Geodetic Boundary Value Problem: the Equivalence between Molodensky’s and Helmert’s Solutions

  • Fernando Sansò
  • Michael G.  Sideris

Part of the SpringerBriefs in Earth Sciences book series (BRIEFSEARTH)

Table of contents

  1. Front Matter
    Pages i-v
  2. Fernando Sansò, Michael G. Sideris
    Pages 1-5
  3. Fernando Sansò, Michael G. Sideris
    Pages 7-15
  4. Fernando Sansò, Michael G. Sideris
    Pages 17-25
  5. Fernando Sansò, Michael G. Sideris
    Pages 47-54
  6. Fernando Sansò, Michael G. Sideris
    Pages 55-60
  7. Fernando Sansò, Michael G. Sideris
    Pages 61-66
  8. Back Matter
    Pages 67-81

About this book


This book offers a new approach to interpreting the geodetic boundary value problem, successfully obtaining the solutions of the Molodensky and Stokes boundary value problems (BVPs) with the help of downward continuation (DC) based methods. Although DC is known to be an improperly posed operation, classical methods seem to provide numerically sensible results, and therefore it can be concluded that such classical methods must in fact be manifestations of different, mathematically sound approaches.

Here, the authors first prove the equivalence of Molodensky’s and Stoke's approaches with Helmert’s reduction in terms of both BVP formulation and BVP solutions by means of the DC method. They then go on to show that this is not merely a downward continuation operation, and provide more rigorous interpretations of the DC approach as a change of boundary approach and as a pseudo BVP solution approach.


Molodensky's Problem Stokes's Problem Helmert Reduction Geoid/quasi-Geoid Determination Analytical/Downward Continuation Change of Boundary Approach

Authors and affiliations

  • Fernando Sansò
    • 1
  • Michael G.  Sideris
    • 2
  1. 1.Politecnico di Milano - Polo Territoriale di ComoComoItaly
  2. 2.Department of Geomatics EngineeringSchulich School of EngineeringCalgaryCanada

Bibliographic information

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