SCATTERING BY A BURIED OBJECT

This chapter presents a model problem for scattering by a buried object. The ground is modeled by a two-layered medium (the air and the earth) with a planar interface. For the two-layered medium, it is possible to derive the dyadic Green’s function using Hertz potentials as in Sommerfeld’s book. This Green’s function can then be used to implement a finite element method for the scattering problem using the method of Hazard and Lenoir. In particular, the scatterer is surrounded by an artificial boundary (not necessarily a sphere). Inside the artificial boundary, finite elements are used to represent the solution. Outside the scatterer, the Stratton-Chu formula provides a representation in terms of unknown fields on the surface of the scatterer. This representation is then used to provide a boundary condition on the artificial boundary. The resulting method has great flexibility in the choice of the artificial boundary. The applications of this method to a bounded scatterer in half-space with perfectly conducting boundary, and to scattering by a bounded scatterer in an infinite inhomogeneous background are discussed. Error estimates are proven.