A New Inversion Based 2D Fourier Transformation Method and Its Use in Pole-reduction of Magnetic Data Set

Considering the Fourier Transform as an inverse problem, a new 2D Fourier transformation procedure is proposed by using the Iteratively Reweighted Least Squares method. We use the special property of the Hermite functions that they are eigen-functions of the Fourier transform. This property avoids the calculation of complex integrals and simplifies the determination of the Jacobian matrice. The new method is tested by using synthetic data set. The noise reduction capability of the new inversion-based Fourier transform method is clearly demonstrated. Its application in the pole-reduction of magnetic data shows sufficient improvement in noise rejection capability compared to the traditional algorithm using Discrete Fourier Transform.