Inverse scattering problems for acoustic waves in an inhomogeneous medium
Abstract
The inverse scattering problem is considered of determining either the absorption of sound in an inhomogeneous medium or the surface impedance of an obstacle from a knowledge of the far field patterns of the scattered field corresponding to many incident timeharmonic plane waves. First, the inverse problem is studied in the case when the scattering object is an inhomogeneous medium with complex refractive index having compact support. The approach to this problem is the orthogonal projection method of ColtonMonk (1988). After that, the analogue is proven of Karp's Theorem for the scattering of acoustic waves through an inhomogeneous medium with compact support. Some of these results are then generalized to the case when the inhomogeneous medium is no longer of compact support. If the acoustic wave penetrates the inhomogeneous medium by only a small amount then the inverse medium problem leads to the inverse obstacle problem with an impedance boundary condition. The inverse impedance problem is solved of determining the surface impedance of an obstacle of known shape by using both the methods of KirschKress and ColtonMonk (1989).
 Publication:

Ph.D. Thesis
 Pub Date:
 1990
 Bibcode:
 1990PhDT........37K
 Keywords:

 Acoustic Impedance;
 Acoustic Scattering;
 Inhomogeneity;
 Inverse Scattering;
 Sound Waves;
 Boundary Conditions;
 Far Fields;
 Orthogonality;
 Plane Waves;
 Refractivity;
 Surface Properties;
 Acoustics