Optimized constraints for the linearized geoacoustic inverse problem

This work is concerned with developing inverse methods to estimate sound speed profiles of the water column and seabed in the shallow-water environment. The approaches are based on a perturbative technique which uses estimates of horizontal wave numbers to determine sound speed profiles. This technique is appropriate for the highly variable shallow-water environment as horizontal wave numbers can be measured semi-locally (1-2 km aperture) and their values are a direct measurement of the local environmental properties. In all previous applications of this technique, this inversion scheme has been used to estimate sound speed in the seabed at a number of discrete depths while assuming water column properties are known.;Compared to past applications of perturbative inversion, the accuracy of the solution is improved by implementing more suitable constraints to address issues of stability and uniqueness associated with solving the ill-posed inverse problem. One such improvement uses qualitative regularization which allows for discontinuities in the sediment sound speed profile to be resolved. The resulting solution is a more accurate representation of the layered structure of the seabed. Another advancement makes reliable inversion for water column properties possible. This is accomplished using approximate equality constraints to address the solution's instability in portions of the waveguide for which the wave number data are insensitive. A further enhancement uses a synthesis of qualitative regularization and approximate equality constraints to provide a mechanism to efficiently invert for sediment and water column sound speed profiles simultaneously. This technique allows for rapid assessment of the water column and the seabed properties in a single step.