Noise Suppression in Reduction to Pole of Magnetic Data

In geophysical data processing, the noise suppression capability of the applied algorithm is a key characteristic. The often used Discrete Fourier Transformation has the disadvantage, that the noise registered in the time domain is directly transformed into the frequency domain. On the other hand there are robust methods to solve the overdetermined inverse problem with excellent noise rejection capabilities. In this paper, the Fourier transformation is solved as an inverse problem. The continuous frequency spectrum is discretized by series expansion. With the use of Hermit functions as basis function system, the algorithm will be faster. Due to the special feature of the Hermit functions - namely, that they are the eigenfunctions of the FT - the determination of Jacobian matrix does not require the calculation of complex integrals. The applicability of the method was proved on synthetic magnetic data set, where the Fourier transformation is used during the reduction to pole. The application of Iteratively Reweighted Least Squares (IRLS) algorithm using the so-called Cauchy-Steiner weights provides a robust and resistant method.