12. Inversion Procedures
Inverse elastic-wave scattering problems are shown to be ill-posed in general. Standard simplifying assumptions--the first Born approximation, the physical optics approximation, and the stopping power approximation of tomography--are shown to reduce to the same ill-posed mathematical problem, that of inverting a Fourier transform. Practical implications of this fact are illustrated with examples.
Lee, D. A., "Mathematical Principles of Data Inversion" (1980). Proceedings of the DARPA/AFML Review of Progress in Quantitative NDE, July 1978–September 1979. 68.