Abstract The inversion of static potential geophysical data by means of the generalized linear inverse of a matrix is discussed. The method provides the unique distribution of anomalous permeability or density, as the case may be, which gives rise to the observed data and which has a minimum total sum of squares of variation. It is shown that the same results can be achieved by the application of Fourier transform theory which leads to a better understanding of the process and reduces the amount of computation. In the case of magnetic data due to a vertical earth's field, it is shown that the method is the same as upward continuation.