Simultaneous inversion of compressibility and density in the acoustic inverse problem

The nonlinear acoustic inverse scattering problem with both variable compressibility and variable density is formulated and solved via the Born iterative method. This is equivalent to the simultaneous electromagnetic inversion of permittivity and permeability in the E_z- or H _z-polarized problem. The solution to the E_z-polarized case for variable permittivity has been studied in detail previously. The results presented here for the H_z-polarized case and those for the simultaneous inversion (or acoustic) problem are new. Two volume integrals are used to represent the scattered field. The unknowns are found by performing Born-type iterations on the resulting integral equation. At each iteration, the unknowns are found through a double-criterion optimization. Several results are presented for both the H_z-polarized and the simultaneous (acoustic) inverse problems. In this case, even though the resolution is subwavelength, it is found that compared to the E_z-polarized case, the resolution is lower.