We propose a method for inverting the power spectrum of gravity and magnetic data. The method is demonstrated on aeromagnetic and borewell data from the German Continental Deep Drilling Project (KTB). Density and susceptibility distributions in the Earth's crust exhibit scaling behavior with power spectra proportional to f-β, where f is the wavenumber and β is the scaling exponent of the source distribution. We model the sources of the potential field by a random function with scaling properties, defined on a half-space with its top at a specified depth beneath the observation plane. Comparing the theoretical power spectrum for this model with the power spectrum of the measured data, we obtain the best values for the depth to source and the scaling exponent as a global minimum of the misfit function. Despite the simplicity of the model, it offers a new understanding of the factors influencing the shape of the potential field power spectrum. In particular, the low wavenumber part of the power spectrum can be dominated by the scaling properties of the source distribution and not by the depth to some kind of basement. The scaling exponent of the field varies with the type of surface geology. The question of whether the scaling exponent can actually be used to identify different types of geology gives an interesting new aspect to power spectrum inversion. ¿ American Geophysical Union 1995