Boundary-Value Problems for Gravimetric Determination of a Precise Geoid

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.

The stokes two-boundary-value problem for geoid determination.- The zeroth- and first-degree spherical harmonics in the Helmert 2nd condensation technique.- Topographical effects.- Planar approximation.- Taylor series expansion Newton kernel of the.- The effect of anomalous of topographical masses density.- Formulation of the Stokes two-boundary-value problem with a higher-degree reference field.- A discrete downward continuation problem determination for geoid.- The Stokes boundary-value problem on an ellipsoid of revolution.- The external Dirichlet boundary-value problem for the Laplace equation on an ellipsoid of revolution.- The Stokes boundary-value problem with ellipsoidal corrections in boundary condition.- The least-squares solution to the discrete altimetry-gravimetry boundary-value problem for determination of the global gravity model.