Direct and inverse problems in wave propagation and applications

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This book is the third volume of a 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 explores recent advancements in wave propagation problem analysis, addressing both forward and inverse problems, particularly in earth sciences. These issues are prevalent in environmental applications like seismic analysis and electromagnetic scattering. Designing efficient numerical methods for the forward problem—calculating scattered fields from known geometric configurations—is complex due to the multiscale nature of these problems. Inverse problems, which involve determining material parameters from measurements, present even greater challenges. The book features review articles on state-of-the-art numerical methods for both problem types, emphasizing efficient computation in wave propagation and scattering, a vital area in numerical mathematics with significant applications in energy and the environment. Key applications include forward wave propagation in heterogeneous media and seismic inversion for subsurface imaging. For instance, modeling radiation absorption and scattering by atmospheric elements aids in interpreting solar and radar measurements, while inverse problems help image subsurface structures. This volume highlights the achievements of Workshop 3, bringing together leading numerical mathematicians and indu