Stable Computation of Potential Field Vertical Derivative - A Modification of Conventional FFT Algorithm

A variant of the frequently used FFT algorithm is described, to calculate the vertical derivative of potential field data. This modification of FFT algorithm is very stable and has a reduced sensitivity to noise. By this method, we take into account the spectral properties of the signal and introduce a regularization parameter estimated by computing the standard deviation of the modules of the second-order field horizontal gradient. The algorithm can be implemented to compute the field vertical derivatives of high order, avoiding the amplification of high frequency noise. Application of the modified FFT algorithm to the synthetic data set confirms its stability and efficiency upon the conventional FFT algorithm and also to the ISVD technique.