Abstract: The vertical derivatives of the total field magnetic anomaly (TMA) plays an important role in the interpretation process of magnetic objects. Owing to the filter characteristic of vertical derivative operator, the conversion of vertical derivative is inherently unstable and any high-frequency noise present in the surveying data gets strongly magnified in the transformed map in such a way to mask any useful signal. Based on the harmonic properties of the vertical integral and derivatives of TMA which are confirmed theoretically in this paper, an algorithm is presented to perform calculation of vertical derivatives using both frequency and space domain transformations. The algorithm involves following steps: vertically integrating the field by using a frequency domain operator; and then, according to the Laplace equation, computing its second vertical derivative by means of the sum of its second horizontal derivatives which is approximated with three-point finite-differences or bicubic splines method; finally, all the other vertical derivatives are again computed by the Laplace equation starting from the TMA (even derivatives) and its first vertical derivative (odd derivatives). The effectiveness of the suggested techniques had been illustrated by synthetic sphere magnetic model whose total field magnetic anomaly’s first and second vertical derivative expressions are deduced for the first time when the geomagnetic direction is different from magnetization direction. The conclusion indicates that the presented vertical derivatives calculation method provides better results and allows a lower degrading of the signal-to-noise ratio than the standard Fourier method, especially when the order of computed derivatives increases, as the vertical integration filter is a smoothing filter.