Analytical Method for Designing and Analyzing 1D Search Programs

Investigation programs are intended to reduce uncertainty in site conditions that impact design performance. However, existing theoretical tools for assessing uncertainty reduction, such as Bayes' theorem, have seen limited practical use because cumbersome numerical solutions are usually required. A first-order, second-moment Bayesian method (FSBM) that overcomes this limitation is described in this paper. FSBM is a practical, analytical approximation to Bayes' theorem that helps estimate the reduction in uncertainty achieved for a particular investigation outcome (inverse analysis) and the reduction expected to result for proposed programs (design or forward analysis). In this initial application, FSBM is formulated and applied to updating uncertainty in the geometry of a single subsurface feature for 1D search programs. Uncertainty in the existence of the feature is also addressed. FSBM provides solutions for example cases that are generally within 10% of solutions obtained by Monte Carlo simulation. The method is intended and shows promise for more general applications such as the design of 3D investigation programs or building probabilistic models of 3D subsurface features.