Conditional Distributions of Poisson Processes Given Realisations of InducedPoint Processes

摘要

The location and geometry of hydrocarbon reservoirs are often modeled byperforming conditional simulations of a marked Poisson point process such that intersections of reservoirs observed on line transects (wells) and planar sections (seismic maps) are shown. Conditional distributions for (marked) Poisson processes, given realizations of point processes induced on one or more (lower-dimensional) subsets of the state space, are derived. These problems are approached by disintegrating an appropriately defined Campbell measure. The theory is illustrated for a Boolean model with elliptical grains, given grain intersections on line transects.