A frequency domain approach to the recovery of geophysical potentials
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
A major difficulty in the recovery of geophysical potentials arises from the fact that the available data are in general noisy and irregularly spaced. Analysis and further processing require a representation of the potential field on a regular grid.
An analysis of the Fourier transform of potential fields suggests an approximation by band-limited functions. We show that the resulting discrete least squares problem can be formulated as a linear system of equations, where the system matrix is of block-Toeplitz type. The properties of potential fields in the frequency domain together with the special structure of the system matrix lead to a robust and computationally attractive solution via the Fast Fourier transform and the conjugate gradient algorithm.
We show how additional knowledge about the statistics of the data can be incorporated in our algorithm. Experimental results for synthetic gravity data demonstrate good performance for irregularly spaced noisy sampling sets.