Low shear asymptotics for elastic seabeds

This paper deals with the low shear asymptotics of the sound field propagating in a fluid layer with a homogeneous elastic seabed. Using the displacement formulation and applying WKB, we show that although the problem is formally a singular perturbation problem, it can be reduced to a regular one, and we construct a regular expansion for the elastodynamic field in the bottom. The same results come out using alternative formulations, based either on Lamè potentials or on the Love function. The later formulation appears to have independent interest, as it explains why the problem under investigation does not fall in the existing framework of coercive singular perturbations which appear in one-dimensional elasticity.