Geometric and Integral Equation Methods for Scattering in Layered Media
This dissertation is an extension of the Stenger -Johnson-Borup sinc and Fast Fourier Transform (FFT) based integral equation imaging algorithms to the case of a layered ambient medium. This scenario has medical, geophysical and nondestructive testing applications. It is also a first step in the direction of incorporating a geometric point of view in forward and inverse scattering. The construction of layered Green's functions and concomitant inverse scattering algorithms for inhomogeneities residing within a layered medium whose layers are known a priori is carried out. Computer simulations and numerical experiments investigate the ill -posedness of inverse scattering in this context. Both 2 and 3D ambient media are considered and the relationship to the distorted wave Born approximation are discussed. Noise contamination and attenuation in both the layered background medium and the inhomogeneity are included for realism. Global minimization techniques based on homotopy are introduced and generalized. Concepts from Cartan/Kahler differential geometry play a natural role in understanding homotopy methods of global minimization. These minimization methods have application to biomolecular modelling as well as scattering. Exterior Differential Forms provide a natural vehicle for extending results determined here to include shear effects in fully elastic media. It is also shown that the methods developed here can be extended to ambient media with different types of known structure.
- Pub Date:
- GEOMETRIC EQUATION;
- Physics: Acoustics; Mathematics; Engineering: Biomedical