3.5 Inverse Scattering for an Obstacle in a Stratified Medium

We consider an inverse acoustic scattering problem for an unknown object in a stratified medium. Suppose a compact obstacle, coinciding with the region ?, is imbedded in a stratified medium. We refer to the medium as being acoustically stratified when the refraction index varies with depth, which is frequently the case for oceans. In many cases this stratification occurs because warmer water is lighter and tends to move to the surface as heavier water sinks due to gravity. Other factors such as salinity also affect the refraction properties of the fluid column. In a stratified medium, sound waves may be trapped by acoustic ducts and caused to propagate horizontally. Therefore, the scattered energy flux does not spread spherically. Instead, there is a free-wave far field and guided-wave far field. Due to the nature of stratified media, some results that are valid for inverse scattering in a homogeneous medium may not hold for a stratified medium. For example, in the shape of a scatterer may be determined uniquely from its far-field patterns. This may not be true for a stratified medium, unless the far field may be detected in a window large enough to contain both free waves and guided waves. In other words, two open sets are needed; one for the free-wave far field and one the for guided-wave far field.