Syllabus
* Boundary-value problem for geoid determination
Gravity and gravitational potentials, the geoid, formulation of the problem for geoid determination, Bruns' formula, its accuracy, linearizations in gravity and geometry spaces, spherical and ellipsoidal approximations, ellipsoidal corrections, free-air gravity anomaly, reference satellite gravity model.
* Helmert's condensation and isostatic reductions
Airy-Heiskanen and Pratt-Hayford compensation models, Helmert's condensation, direct and indirect topographical effects, co-geoid.
* Stokes's problem
Its formulation, existence and uniqueness of a solution, Stokes's integral, Stokes-function - spectral and spatial forms, removing of weak singularity of Stokes's function, truncated Stokes's integration, near- and far-zone contributions, role of the reference gravity field, spheroidal Stokes's function, Molodenskij's truncation coefficients, Paul's coefficients.
* Poisson's integral and continuation of a harmonic function
External and internal Dirichlet's BVP for the Laplace equation on a sphere, Poisson's kernel - spectral and spatial forms, expansion of the delta-function in spherical harmonics, truncation of Poisson integral, near- and far-zone contributions, downward continuation of gravity, instability of a continuous problem, regularization by discretization, Tikhonov regularization.
* Stokes and Dirichlet problem on an ellipsoid of revolution
Formulation of boundary-value problems, the uniqueness of a solution, ellipsoidal harmonics, their computation, generalized addition theorems, ellipsoidal Stokes and Poisson kernels, their spatial representations, behavior at the point psi=0.
* Literature:
- W. A. Heiskanen, H. Moritz: Physical Geodesy, Freeman, San Francisco 1967.
- H. Moritz: Advanced Physical Geodesy, Wichmann, Karlsruhe 1980.
Annotation
Stokes problem for the Laplace equation, geoid, orthometric heights. Molodensky problem, quasigeoid, normal heights.
Dirichlet problem, harmonic downward continuation, stabilization. Ellipsoidal approximation, ellipsoidal corrections.
Gradiometric problem.