Gravity and magnetic exploration areas are usually irregular,and there is some data deficiency.Missing data must be interpolated before the vertical derivative conversion in the wavenumber domain.Meanwhile,for improved processing precision,the data need to be edge-padded to the length required by the fast Fourier transform algorithm.For conventional vertical derivative conversion of potential field data(PFD),only vertical derivative conversion is considered,or interpolation,border padding,and vertical derivative conversion are executed independently.In this paper,these three steps are considered uniformly,and a vertical derivative conversion method for irregular-range PFD based on an improved projection onto convex sets method is proposed.The cutoff wavenumber of the filter used in the proposed method is determined by fractal model fitting of the radial average power spectrum(RAPS)of the potential field.Theoretical gravity models and real aeromagnetic data show the following:(1)The fitting of the RAPS with a fractal model can separate useful signals and noise reasonably.(2)The proposed iterative method has a clear physical sense,and its interpolation,border padding error,and running time are much smaller than those of the conventional kriging and minimum curvature methods.