Computational Methods for One-Dimensional Scattering in Non-Smooth Media

This thesis implements various numerical algorithms used for acoustic imaging of layered media: the scattering-based algorithm, the classical Born approximation, the refined impedance transform and the echoes-to-impedance transform. The last three are inverse scattering algorithms that numerically convert data in the time domain to an impedance in the spatial domain; however, the simplicity, speed and accuracy can differ greatly among them. In place of physical recordings, the scattering-based algorithm is used to generate accurate synthetic data. Numerical experiments and error analyses reveal significant differences among the three. The principal conclusion is that the method based on the most sophisticated mathematical ideas, namely the echoes-to-impedance transform, is far superior.