Another old paper is added to the collection of reproducible documents: Multiple realizations using standard inversion techniques

When solving a missing data problem, geophysicists and geostatisticians have very similar strategies. Each use the known data to characterize the model’s covariance. At SEP we often characterize the covariance through Prediction Error Filters (PEFs) (Claerbout, 1998). Geostatisticians build variograms from the known data to represent the model’s covariance (Issaks and Srivastava, 1989). Once each has some measure of the model covariance they attempt to fill in the missing data. Here their goals slightly diverge. The geophysicist solves a global estimation problem and attempts to create a model whose covariance is equivalent to the covariance of the known data. The geostatistician performs kriging, solving a series of local estimation problem. Each model estimate is the linear combination of nearby data points that best fits their predetermined covariance estimate. Both of these approaches are in some ways exactly what we want: given a problem give me `the answer’…