Sound scattering from two concentric fluid spheres

The solution to the problem of plane wave and point source scattering by two concentric fluid spheres is derived. The effect of differences in sound speed, density, and absorption coefficient is taken into account. The scattered field is then found in the limit as the outer sphere becomes an infinitely thin shell and compared to the solution for a single fluid sphere for verification. A simulation is then performed using the concentric fluid sphere solution as an approximation to the human head and compared to the solution of a single fluid sphere with the properties of either bone or water. The solutions were found to be similar outside of the spheres but differ significantly inside the spheres.