A k-Nearest Neighbor Simulator of Pseudo-Bore Hole Logs for Subsurface Characterization

Subsurface characterization is important for investigations of groundwater contamination as well as petroleum extraction potential. Bore holes or drill logs are a common source of localized stratigraphic information. Sampling and interpolation uncertainties complicate the characterization of the subsurface from these data. Geostatistical methods (Kriging based) have been used to map subsurface attributes from such data, and to generate conditional simulations that honor observed strata. These methods often require an a priori discretization of the bore hole data along each vertical section into strata types as well as assumptions as to statistical homogeneity of the underlying random field that generated this discretized data. A method for generating likely realizations of subsurface soils by sampling pseudo-drill logs on to a horizontal grid by bootstrapping (resampling) drill logs is presented here. Entire drill logs are resampled on to the grid locations, thus obviating the need for a prior discretization of the sample space. The bootstrapping algorithm used can be interpreted in terms of a nonhomogeneous Random Field description of the data with the necessary probability distributions estimated implicitly using a nonparametric (k-nearest neighbor) probability density estimate for the sampling distribution of the drill logs (real or pseudo) that lie in a neighborhood of a grid point at which resampling is needed. Example applications to a synthetic and to a real data set are provided. Extensions to incorporate other sources of information, as well as potential applications of the method are discussed.