Smooth approximation of potential fields from noisy scattered data
Michael Rauth and Thomas StrohmerDepartment of Geophysics, University of Vienna
Nordbergstr.17, A-1090 Wien, Austria
e-mail: Mitch Rauth
Dept.of Mathematics, University of Vienna
Strudlhofgasse 4, A-1090 Vienna, Austria
Keywords: algorithms, irregular sampling, potential
fields, scattered data approximation
Geophysical potential-field data are in general observed at scattered sampling points and are contaminated by measurement- and preprocessing errors. Analysis and further treatment require a representation of the underlying potential fields on a regular grid.
In the presence of noise an approximation of the data is more appropriate than an exact interpolation. Analysis of the smoothness of potential fields indicates an approximation by band-limited functions.
We show that the resulting least squares problem can be formulated as a linear system of equations, where the system matrix is of block-Toeplitz type. This special structure allows a computational attractive and robust solution via the Fast Fourier transform and the conjugate gradient algorithm. We show how additional knowledge about the physical properties of potential fields and the statistics of the data are easily incorporated in our algorithm.
Experimental results for synthetic and real world gravity data demonstrate good performance for highly irregularly spaced noisy data.