One-Dimensional Acoustic Scattering: the Direct and Inverse Problems Under Realistic Conditions.

In the first part of this thesis, computer simulation is used to analyze the efficacy of two acoustic impedance reconstruction algorithms. The algorithms are tested under conditions of broad-band acoustic noise and limited transducer bandwidth. We show that the reconstruction algorithms are quite insensitive to noise, especially for media with a relatively small overall impedance changes. The distorting effect of the limited transducer bandwidth is serious, however, but our results show that the distortion can be adequately compensated for by deconvolution in the form of inverse filtering, even in the presence of noise. Consequently, such measurement conditions do not present a serious problem in actual impedance profile reconstructions. In the second part of the thesis, algorithms for both the direct and the inverse lossy scattering problems are presented. The problems are formulated on the basis of losses produced by relaxation processes, and the algorithms developed are tested using computer simulations. Two solution forms are obtained for the direct problem, one using a transmission matrix method and the other using the Impediography formula. The results from both algorithms turn out to be similar when the impedance variation of the inhomogeneous medium is small. The inverse problem is developed under the assumption of small impedance variation using certain linearization techniques. The inverse algorithm allows the reconstruction of both the impedance and absorption profiles when the velocity profile is constant and the frequency dependence of the loss mechanism is known. In order to determine the accuracy of the algorithm, we analyze the error caused by the linearization technique. Finally, the sensitivity of the algorithm to noise is tested.