Optimized constraints for the linearized geoacoustic inverse problem

A geoacoustic inversion scheme to estimate the depth-dependent sound speed characteristics of the shallow-water waveguide is presented. The approach is based on the linearized perturbative technique developed by Rajan et al. [J. Acoust. Soc. Am. 82, 998-1017 (1987)]. This method is applied by assuming a background starting model for the environment that includes both the water column and the seabed. Typically, the water column properties are assumed to be known and held fixed in the inversion. Successful application of the perturbative inverse technique lies in handling issues of stability and uniqueness associated with solving a discrete ill-posed problem. Conventionally, such problems are regularized, a procedure which results in a smooth solution. Past applications of this inverse technique have been restricted to cases for which the water column sound speed profile was known and sound speed in the seabed could be approximated by a smooth profile. In this work, constraints that are better suited to specific aspects of the geoacoustic inverse problem are applied. These techniques expand on the original application of the perturbative inverse technique by including the water column sound speed profile in the solution and by allowing for discontinuities in the seabed sound speed profile.