280460 VO Potential theory (2006S)

ECTS: 5 credit points
Potential theory and its application in geophysics
Characteristics of potential fields (divergence, curl, Gauss und Stokes integral theorem, equipotential surfaces)
Source distribution (Newtonian potential, 1/r-function, convolution theorem, Delta-distribution, special source geometries, arbitrary sources, dipole, dipole distribution, Poisson-theorem, multi-pole distribution, magnetic induction)
Green's theorem
Boundary value problem and field continuation (1st and 2nd BVP on the plane, 1st BVP on the sphere, magnetic induction as BVP)
Solution of Laplace DE in Cartesian and polar coordinate system (Fourier integral, characteristics of the Fourier transform)
Spherical harmonics (Legendre functions, series expansion of the 1/r-function, Legendre DE, orthogonality relations, surface spherical harmonics)
Field transformation in Cartesian and polar coordinate system (filtering, convolution, Fourier transform of the gravity field of simply shaped bodies (point mass, vertical mass line, slab, rectangular prism), discrete Fourier transform, Hilbert-transform)
Characteristics of the gravitational potential (equivalent sources)
Continuity property at discontinuities
2D potential fields (logarithmic potential, analytical signal, generalized AS, 2D modelling (Talwani))
Euler- and Werner deconvolution