Subsurface characterization using a D-optimality based pilot point method

Abstract

Detailed hydraulic conductivity estimation is a difficult problem as the number of direct measurements available at a typical field site is relatively few and sparse. A common approach to estimate hydraulic conductivity is to combine direct hydraulic conductivity measurements with secondary measurements such as hydraulic head and tracer concentrations in an inverse modeling approach. Even with secondary measurements this may constitute an underdetermined (or over-parameterized) inverse problem giving rise to ‘non-unique’ and incorrect estimates. One approach to reduce over-parameterization is to estimate hydraulic conductivity at a few carefully chosen points called ‘pilot points’ (i.e. reduction in parameter space). This paper develops a D-optimality based criterion method (DBM) for pilot point selection and tests its effectiveness for estimating hydraulic conductivity fields using several synthetic cases. Results show that the selected pilot points using this approach lead to a more accurate hydraulic conductivity characterization than either random or sequential pilot point location selection methods.