A KERNEL ESTIMATOR FOR STOCHASTIC SUBSURFACE CHARACTERIZATION

A nonparametric statistical methodology based on kernel function estim ation is developed for assessing the probability that a particular loc ation in the aquifer has high or low conductivity using borehole infor mation. The approach presented is an alternative to indicator Kriging, Soils are classified through a binary indicator function defined as 0 for low and as 1 for a high conductivity soil. Estimates of the proba bility of occurrence of a high or low conductivity soil are made on a three-dimensional grid. Each such estimate is formed as a local weight ed average of the indicator function values that lie within an averagi ng interval or bandwidth of the point of estimate. A different vertica l bandwidth is chosen at each borehole log. Horizontal bandwidths are selected independently at each horizontal level. These bandwidths are chosen by cross validation. Observations closer to the point of estima te are weighted higher using a kernel or weight function. Unlike Krigi ng, the underlying stochastic process is not assumed to be stationary. An application using data from Lake Bonneville deposits in Davis Coun ty, Utah is presented.