Bathymetry inversion using constituent Boussinesq equations

The phenomenon of ocean wave-shoaling, and the associated reduction of ocean wave phase speed with decreased water depth, provides useful information for inferring water depth D (bathymetry) in coastal environments. One strategy for relating D to phase speed C and wave-vector k, of long wave length ocean waves, involves using the 1-dimensional, linear (gravity wave) dispersion relationship C=(g*tanh(kD)/k)^1/2. In principle, this approach has limitations, because the approach is based on a WKB approximation. Thus, it cannot be applied when D varies appreciably over the wavelength of a shoaling-wave. Also, the approach is restricted to waves that have small wave-height. In the present paper, The authors use a set of marine radar image sequences and apply the linear approximation, via a 3D FFT analysis to the sequences. The authors show that for low to moderate wave heights, the approach does retrieve approximately the correct depth. However, an increase in the RMS wave-height from 1 m to 3.5 m produced a much poorer depth estimate, proving the need for an application of a non-linear wave model to the problem, with an associated new retrieval approach. They outline a new procedure for extracting bathymetry that uses the recently developed constituent Boussinesq (CB) equations. The inversion procedure is accomplished using a standard (Levenberg-Marquardt-like), 1-dimensional, cost function minimization procedure