Three-Dimensional Scattering Equations

2D inverse scattering is the most common model in ground penetrating radar (GPR) data processing. However, recent advances in distributed GPR, coherent GPR, HF GPR, and RF tomography led to an extension of classical 2D work in a more proper 3D scenario. This chapter discusses 3D scattering equations. Specifying the 3D scattering equations, means finding the expressions of Green's functions and (for a given and characterized source) of the incident field. Due to the increased complexity of the 3D dealing, it is useful to generalize the definition of Green's function. In 3D, any Green's function is dyadic and thus can be expressed by means of a general matrix scheme. The chapter discusses retrieval of expressions of the homogeneous Green's functions. The calculation of the homogeneous Green's functions is a preliminary step for the calculation of the half-space Green's functions.