Geodetic boundary value problem: the equivalence between Molodensky's and Helmert's solutions (Q2374259)

The book consists of the following eight chapters: 1. Physical Geodesy and its Boundary Value Problems; 2. On the Linearization Band; 3. On the Equivalent Linearized BVP's of Molodensky and Helmert; 4. On the Equivalent BVP's of Stokes and Helmert, and Their Relations to the Molodensky BVP by Analytical Continuation; 5. The Downward Continuation Approach: A Long-Lasting Misunderstanding in Physical Geodesy; 6. The Change of Boundary Approach; 7. The Pseudo-Boundary Value Problem (\(\Psi\) - BVP) Interpretation; 8. One Further Example, Some Remarks and Conclusions. In the first Chapter, the statement of the Scalar Non-Linear Molodensky Problem is given. It also considers its linearized versions. In Chapter 2, the authors review the linearization process of the Scalar Molodensky Problem. Chapter 3 describes the Helmert approach to the Earth topography. It considers the conditions under which Molodensky and Helmert Problems are equivalent. In Chapter 4, the authors closely analyze the two different BVP's most often presented in the literature, namely, the Helmert-Stokes (HS) problem and the Helmert-Molodensky (HM) problem, and examine the equivalence of their solutions. Chapters 3 and 4 prove the equivalence of Molodensky's and Helmert's approaches in terms of BVP formulation and of their classical solutions by what is termed the downward continuation method. Chapter 5 gives a detailed investigation of the downward continuation method. Chapter 6 shows the connection between the downward continuation method and some type of iteration method. Chapter 7 considers the procedure of the stabilization of the downward continuation method. Finally, Chapter 8 considers an example to appreciate the difference/analogy between the Molodensky and the Helmert approaches.