Читать книгу Mathematics in Computational Science and Engineering - Группа авторов - Страница 47

These problems attempt to describe a system of coefficient matrix from observed data, which is used to estimate physical model parameters of the forward numerical models. This coefficient matrix usually represents important properties of the media or of the model that is under study. These properties in the field of geophysics are density, electrical conductivity, heat conductivity, magnetic susceptibility, etc., of the Earth materials. In the process of solving such problems, it is possible to delineate many other details such as the structural intrusions, defects, source of contaminations, location, shape, etc. There is a large number of scientific articles and research publications that have dealt with the ill-posed inverse problems directly or indirectly. Since the theory associated with the inverse problems is relatively new, a shortage of textbooks has been felt in this area. This is due to the fact that the new theories, concepts and approaches have been continuously evolving. Kabanikhin [2] has given a very good and detailed overview of the ill-posed inverse problems. In this review paper, definition of ill-posed inverse problems, its types, and several examples of ill-posed inverse problems are described well.