Gypsy Field project in reservoir characterization. Quarterly report, July 1--September 30, 1995

The overall objective of this project is to use the extensive Gypsy Field laboratory and data set as a focus for developing and testing reservoir characterization methods that are targeted at improved recovery of conventional oil. The overall project consists of four interdisciplinary sub-projects which are closely interlinked: (1) modeling depositional environments; (2) upscaling; (3) sweep efficiency; (4) tracer testing. During this quarter, the main activities involved the ``Modeling Depositional Environments`` Project, for which progress is reported. The authors seek to quantify the resolution of properties of an estimated parameter. In particular they are interested in whether features can be resolved or at least detected from a set of data with a given estimation procedure for a given model. They restrict their attention to finite dimensional systems arising from finite element approximations of elliptic boundary value problem and to optimal estimators in the interior of the set of admissible parameters. The results they obtain rely on the calculation of rank and the eigenvalues/eigenvectors of certain matrices. From these they construct what they call a sensitivity matrix that allows one to consider the effect perturbations from certain subspaces have on the estimated parameters. The contribution of this work is to analyze within the context of interior optimal estimators the sensitivity of the recovery function to perturbations for finite dimensional estimation problems. If one relates the perturbation of the parameter vector to perturbations of the parameter function in the distributed system, then one is led to an approach for using the mathematical model to analyze the sensitivity of estimators to perturbations of the model coefficients. It is hoped that by conducting such analyses one can design better experiments to evaluate information available and to assess the value of additional information perhaps to reduce the cost of expensive data collection