Inverse Methods

Remote sounding of the atmosphere has proved to be a fruitful method of obtaining global information about the atmospheres of the earth and other planets.

This textbook presents a comprehensive treatment of the theory and implementation of inverse methods in the analysis and interpretation of Earth’s gravity field. By restricting their consideration to a local rather than global level, the authors focus on the use of observations and data that are more sensitive to local mass anomalies. All necessary theoretical aspects are reformulated in terms of a Euclidean framework so that less complex tools from mathematical analysis can be utilized.

This textbook provides a comprehensive and didactic introduction from the basics to the current state of the art in the field of EEG/MEG source reconstruction. Reconstructing the generators or sources of electroencephalographic and magnetoencephalographic (EEG/MEG) signals is an important problem in basic neuroscience as well as clinical research and practice. Over the past few decades, an entire theory, together with a whole collection of algorithms and techniques, has developed.

This book describes the theory and practice of the Hole-Drilling Method for measuring residual stresses in engineering components. Such measurements are important because residual stresses have a "hidden" character because they exist locked-in within a material, independent of any external load. These stresses are typically created during component manufacture, for example, during welding, casting, or forming. Because of their hidden nature, residual stresses are difficult to measure and consequently are often ignored. However, they directly add to loading stresses and can cause catastrophic failure if not properly included during engineering design. Thus, there is an urgent need to be able to identify and measure residual stresses conveniently and reliably.

This textbook is an introduction to the subject of inverse problems with an emphasis on practical solution methods and applications from geophysics. The treatment is mathematically rigorous, relying on calculus and linear algebra only; familiarity with more advanced mathematical theories like functional analysis is not required.

This second edition addresses the question of which finite groups occur as Galois groups over a given field. In particular, this includes the question of the structure and the representations of the absolute Galois group of K, as well as its finite epimorphic images, generally referred to as the inverse problem of Galois theory.

This volume examines some recent advances in inverse problems, new aspects of their mathematical modeling of inverse problems regarding in relation to their applications in physical systems and used the computational methods used.

This book describes unified image-based measurement methods (theories, numerical methods, and algorithms) to determine the important physical quantities of complex flows in engineering and natural systems, including velocity, pressure, temperature, heat transfer, and skin friction. It presents a systematical study of the inverse problems in global flow diagnostics in a unified framework of the variational formulations. The authors further illustrate the main physical quantities in fluid mechanics, including velocity, pressure, skin friction and surface heat flux, extracted from flow visualization images obtained in experiments and observations. The developed methods are applicable in various image-based flow measurements in diverse disciplines ranging from fluid mechanics/aerodynamics to plenary sciences.