This investigation is concerned with the 2D acoustic scattering problem
of a plane wave propagating in a non-lossy, isotropic, homogeneous fluid
host and soliciting a linear, isotropic, macroscopically-homogeneous,
generally-lossy, flat-plane layer in which the mass density and wavespeed
are different from those of the host. The focus is on the inverse problem
of the retrieval of the layer mass density. The data is the transmitted
pressure field, obtained by simulation (resolution of the forward
problem) in exact, explicit form via the domain integral form of the
Bergman wave equation. This solution is exact and more explicit in terms
of the mass-density contrast (between the host and layer) than the
classical solution obtained by separation of variables. A perturbation
technique enables the solution (in its form obtained by the domain
integral method) to be cast as a series of powers of the mass density
contrast, the first three terms of which are employed as the trial models
in the treatment of the inverse problem. The aptitude of these models to
retrieve the mass density contrast is demonstrated both theoretically
and numerically.
Retrieval of the piecewise-constant mass density in the Bergman wave equation
