Inverse Problems in Groundwater Modeling

This text discusses basic concepts, theory, solution methods and applications of inverse problems in groundwater modelling. The inverse problem is defined and solved in both deterministic and statistic frameworks. Various direct and indirect methods are discussed and compared. The adjoint state method and its applications are described in detail. For a stochastic field, the maximum likelihood estimation and co-kriging techniques are used to estimate unknown parameters. The ill-posed problem of inverse solution is highlighted and the importance of data collection strategy is emphasized. Besides the classical design criteria, the relationships between decision making, prediction, parameter identification and experimental design are considered from the point of view of extended identifiabilities. The problem of model structure identification is also considered. This book is designed as a textbook for graduate students majoring in hydrogeology or related subjects. It is also a reference book for hydrogeologists, petroleum engineers, environmental engineers, mining engineers and applied mathematicians.

1. Forward Problems in Groundwater Modelling. 2. An Introduction to Inverse Problems. 3. Classical Definition of Inverse Problems. 4. Indirect Methods for the Solution of Inverse Problems. 5. Direct Methods for the Solution of Inverse Problems. 6. The Adjoint State Method. 7. The Stochastic Method for Solving Inverse Problems. 8. Experimental Design, Extended Identifiabilities and Model Structure Identification. Appendices: Mapping, Space and Norm. Probabilities and Random Fields. A Fortran Program.