Gridding of geophysical potential fields from noisy scattered data
Michael RauthDepartment of Geophysics, University of Vienna
Nordbergstr.17, A-1090 Wien, Austria
e-mail: Mitch Rauth
Keywords: scattered data approximation, gridding,
irregular sampling, potential fields, gravity, magnetics
Geophysical potential-field data are in general observed at scattered sampling points and are contaminated by measuring and preprocessing errors. Analysis and further treatment require a representation of the underlying potential fields on a regular grid.
In the presence of noise, a smooth 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. 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 computationally attractive and robust solution via the fast Fourier transform and the conjugate gradient algorithm. Based on the work of T.Strohmer, I present a new gridding method that incorporates additional knowledge about the physical properties of potential fields and the statistics of the data.
The new method is compared to five standard algorithms. Synthetic data sets are used to study the influence of the sampling geometry and the sampling error, respectively. Experimental results for real world gravity and magnetic data demonstrate the good performance of the new method for highly irregularly spaced noisy data.
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