Mathematical and numerical methods in inverse acoustic scattering theory

A survey is given of the inverse acoustic scattering problem of determining the support of an inhomogeneous obstacle from a knowledge of the incident and scattered tune-harmonic fields where the obstacle is situated in a homogeneous or piecewise homogeneous medium. Numerical examples are given for the determination of the support of buried obstacles in the lower half-space from near field data on a bounded region in the upper half-space.