Aspects on Reverberation modelling and Inversion with Physical Scattering Kernels

In shallow water, reverberation data can often be used to extract information about bottom properties. A forward model is needed to compute replica traces for given bottom properties, and an inversion algorithm is needed to match measured and modelled data. Emphasis is here given to cases with bottom depths around 250 m and sonar frequencies around 1500 Hz. The forward model needs to be accurate and fast enough. A ray model is chosen, that accommodates back-scattering kernels of empirical Lambert as well as physical SPM (small perturbation theory) types. The accuracy is evaluated by comparisons to a normal-mode reverberation model. Satisfactory agreement is typically obtained, although mismatch for soft bottom cases with energy carried by an isolated surface duct mode is also noted. Lambert’s law is separable as concerns incidence and scattering angle factors, which is important for computational efficiency in connection with inversion. The SPM kernel is not separable, however, but separable approximations are developed. They are accurate at small to moderate grazing angles and enhance computational speed significantly. Scatter plots, showing for each parameter misfit for all forward model runs, are presented for differential evolution inversion examples. As is also apparent from an inspection of the kernel, the SPM parameters for roughness height and correlation length are difficult to determine independently. Rather than exhibiting a wide spread of possible values, however, the scatter plots may get side tracked to erroneous solutions. A more appropriate parameterization is selected to resolve this problem.