Large scale inverse problems

More about the book

This book is the second volume of a three-part series documenting the "Radon Special Semester 2011 on Multiscale Simulation & Analysis in Energy and the Environment," held in Linz, Austria, from October 3-7, 2011. It focuses on the mathematical and computational methods essential for large-scale inverse problems and data assimilation in various applications, including weather forecasting, medical tomography, and oil exploration. Regularisation techniques are crucial for ensuring the quality and theoretical soundness of solutions. The volume presents interdisciplinary survey articles on large inverse problems in earth sciences, where operational weather forecasting models can have 10^7 to 10^8 degrees of freedom, reflecting averaged atmospheric properties. Accurate forecasts depend on precise initial conditions, supported by daily satellite data providing 10^6 to 10^7 observations. These measurements, while averaged, differ from model representations. The book discusses how to regularise problems using physically-based models and the process of data assimilation, which involves fitting model trajectories to observations while accounting for errors. It also explores stochastic approaches using ensembles of model trajectories to refine mean values and spreads. The volume highlights the contributions from experts in inverse problem theory and practical applications in earth sciences, documenting the outcomes of Workshop 2 on Large