Application of a Doubly Stochastic Poisson Model to the Spatial Prediction of Unexploded Ordnance

The efficient characterization of sites contaminated with unexploded ordnance (UXO) is necessary prior to returning these sites to the public domain. Characterization plans must be based on an accurate prediction of the UXO distribution. A doubly stochastic Poisson process is proposed as the underlying model controlling the spatial distribution of UXO. This model allows the single parameter (intensity) of the Poisson distribution to vary spatially across a site. Historical information regarding site use is incorporated as a prior (soft data) estimate of the spatially variable UXO intensity. Limited sampling (hard data) of the site allows the prior estimate to be updated into a posterior estimate using geostatistical estimation techniques. This initial estimate of the UXO intensity can be compared to an intensity threshold specified by a regulatory body. Uncertainty in the initial estimation of the UXO intensity relative to the specified threshold can be quantified and additional sampling can be targeted in areas of greatest uncertainty. An example of this statistically based predictive approach is applied to an exhaustively known UXO data set. Geophysical surveys were used to locate over 15,000 buried objects with a high probability of discriminating scrap metal from UXO. This anomaly data set is used as a test case. Historical information defining the location of the target is used to develop a prior estimate of object intensity. A subset of the exhaustive data set is sampled along linear transects and used to create a variogram model of the intensity of the objects. The variogram model is used to estimate the spatial distribution of object intensity at the unsampled locations. The doubly stochastic Poisson model is assessed by testing the estimates of the Poisson intensity against the known intensity values at each location. Additionally, the actual count of object data at each location is compared to the corresponding value of the Poisson distribution as defined by the estimated intensity. International Association of Mathematical Geology 2001 Annual Meeting, Cancun, Mexico, September 6-12