In potential-field inversion problems, it can be dicult to obtain reliable information about the source distribution with respect to depth. Moreover, spatial resolution of the reconstructions decreases with depth, and in fact the more ill-posed the problem - and the more noisy the data - the less reliable the depth information. Based on earlier work using the singular value decomposition, we introduce a tool ApproxDRP which uses approximations of the singular vectors obtained by the iterative Lanczos bidiagonalization algorithm, making it well suited for large-scale problems. This tool allows a computational/visual analysis of how much the depth resolution in a computational potential-field inversion problem can be obtained from the given data. Through synthetic and real data examples we demonstrate that ApproxDRP, when used in combination with a plot of the approximate SVD quantities, may successfully show the limitations of depth resolution resulting from noise in the data. This allows a reliable analysis of the retrievable depth information and effectively guides the user in choosing the optimal number of iterations, for a given problem.