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.
Michael Rauth and Thomas Strohmer
Proc. Conf. SampTA’97, Aveiro/Portugal, pp.109-114, 1997