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Boundary-Value Problems for Gravimetric Determination of a Precise Geoid

  • Book
  • © 1998

Overview

Authors:
  1. ZdenĚk Martinec
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  • Theoretical approach as basis for measurements and modeling
  • Solid foundation for the reconstruction of the geoid

Part of the book series: Lecture Notes in Earth Sciences (LNEARTH, volume 73)

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Table of contents (12 chapters)

  1. Front Matter

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  2. The stokes two-boundary-value problem for geoid determination

    Pages 6-27

  3. The zeroth- and first-degree spherical harmonics in the Helmert 2nd condensation technique

    Pages 28-33

  4. Topographical effects

    Pages 34-49

  5. Planar approximation

    Pages 50-55

  6. Taylor series expansion Newton kernel of the

    Pages 56-71

  7. The effect of anomalous of topographical masses density

    Pages 72-83

  8. Formulation of the Stokes two-boundary-value problem with a higher-degree reference field

    Pages 84-98

  9. A discrete downward continuation problem determination for geoid

    Pages 99-131

  10. The Stokes boundary-value problem on an ellipsoid of revolution

    Pages 132-154

  11. The external Dirichlet boundary-value problem for the Laplace equation on an ellipsoid of revolution

    Pages 155-169

  12. The Stokes boundary-value problem with ellipsoidal corrections in boundary condition

    Pages 170-191

  13. The least-squares solution to the discrete altimetry-gravimetry boundary-value problem for determination of the global gravity model

    Pages 192-209

  14. Back Matter

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Keywords

About this book

This book offers a simultaneous treatment of the theory and numerical application of boundary-value problems related to the determination of a precise geoid from gravimetric data. The following subjects are discussed: topographical effects and their computations in precise gravimetric geoid determination, the downward continuation of a harmonic function, Stokes' problem formulated on an ellipsoid of revolution, spherical Stokes' problem with ellipsoidal corrections involved in boundary conditions for an anomalous potential, and the altimetry-gravimetry boundary-value problem. The answer to a number of scientific problems, raised and discussed in geodetic literature over the past years, can be found here. The book is intended for scientists and advanced graduate students.

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