Inverse Problems in Geophysics and Medicine

The geophysical inverse problem deals with the determination of the inner structure of the earth from measurements performed at the earth surface. These measurements can never determine the inner structure in a unique manner, similarly as the geodetic measurements cannot fully and uniquely determine the gravitational field. This implies the relation to improperly posed problems (because for a properly posed problem the three requirements existence, uniqueness, and stability must be satisfied). Many important problems are not properly posed. Not only most inverse problems, from geophysics to medicine and to scientific interference in general, are improperly posed, but even deterministic processes of classical mechanics need not be stable.