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A kernel estimator for stochastic subsurface characterization

Ali, A.I., Lall, U.
Ground water 1996 v.34 no.4 pp. 647-658
aquifers, saturated hydraulic conductivity, groundwater flow, estimation, stochastic processes, sandy soils, sand, clay soils, clay, alluvium, probability analysis, sediments, Utah
A nonparametric statistical methodology based on kernel function estimation is developed for assessing the probability that a particular location in the aquifer has high or low conductivity using borehole information. 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 probability of occurrence of a high or low conductivity soil are made on a three-dimensional grid. Each such estimate is formed as a local weighted average of the indicator function values that lie within an averaging interval or bandwidth of the point of estimate. A different vertical 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 estimate are weighted higher using a kernel or weight function. Unlike Kriging, the underlying stochastic process is not assumed to be stationary. An application using data from Lake Bonneville deposits in Davis County, Utah is presented.