Integral Geometry of Tensor Fields - Inverse and Ill-Posed Problems Series (Hardcover, Reprint 2010)

01/07 This title is now available from Walter de Gruyter. Please see www.degruyter.com for more information. Integral geometry can be defined as determining some function or a more general quantity, which is defined on a manifold, given its integrals over submanifolds of a prescribed class. In this book only integral geometry problems are considered for which the submanifolds are one-dimensional. The book deals with integral geometry of symmetric tensor fields. This section of integral geometry can be considered as the mathematical basis for tomography of anisotropic media whose interaction with sounding radiation depends essentially on the direction in which the latter propagates. The main mathematical objects tackled have been given the term ''ray transform'' which refers mainly to optical and seismic rays rather than to X-rays.