A two- or three-dimensional treatment of magnetic anomaly data generally requires that the data be interpolated onto a regular grid, especially when the analysis involves transforming the data into the Fourier domain. We present an algorithm for interpolation and downward continuation of magnetic anomaly data that works within a statistical framework. We assume that the magnetic anomaly is a realization of a random stationary field whose power spectral density (PSD) we can estimate; by using the PSD the algorithm produces an array incorporating as much of the information contained in the data as possible while avoiding the introduction of unnecessary complexity. The algorithm has the added advantage of estimating the uncertainty of every interpolated value. Downward continuation is a natural extension of the statistical algorithm. We apply our method to the interpolation of magnetic anomalies from the region around the 95.5 ¿W Galapagos propagating rift onto a regular grid and also to the downward continuation of these data to a depth of 2200 m. We also note that the observed PSD of the Galapagos magnetic anomalies has a minimum at low wave numbers and discuss how this implies that intermediate wavelength (65 km<λ<1500 km) magnetic anomalies are weaker than suggested by one dimensional spectral analysis of single profiles. ¿ American Geophysical Union 1989