Boundary-Value Problems for Gravimetric Determination of a Precise Geoid [Paperback]

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.Theoretical approach as basis for measurements and modeling
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