Scattering from cylindrical inhomogeneities in a lossy medium


  • Leon Peters Jr.,

  • Jack H. Richmond


Many buried scattering objects of interest take the form of two-dimensional geometries. This includes scattering from utility lines, tunnels, and geological structures such as fault lines. Radar systems used to detect these objects commonly use antennas that are at least comparable in size to the depth of the target. Thus the target and the antenna do not satisfy far zone conditions, and the radar range equation is not applicable. Consequently, the usual separate analyses of range, antenna, and target are not possible. In a previous paper a method was outlined that permitted the antenna properties and the scattering properties of a two-dimensional target to be treated separately for the case of a linear electric or magnetic dipole source parallel to the axis of the two-dimensional scatterer. This involved computing the received voltage for an antenna located at the image position, i.e., at twice the target range, and computing the backscattered fields for an electric or magnetic line source at the position of the transmitting antenna. This model has also been applied approximately to a video pulse radar with an orthogonal dipole antenna system. It would also be applicable to large loop antennas quite commonly used in geophysical explorations, as will be discussed. The primary goal of this paper is to discuss additional scattering analyses that could be used to extend the previous results. The major thrust then is to generate solutions for the scattering attenuation function (SAF) which has the form ES/EI or HS/HI where the EI (or HI) are the electric (or magnetic) fields of an electric (or magnetic) line source at the image position and the ES (or HS) are the respective scattered fields. Eigenfunction solutions have been used to obtain the SAF for circular cylindrical geometries to represent pipes and tunnels. Moment method solutions have been applied to perfectly conducting wires with and without a dielectric sheath. Moment method solutions have been applied to noncircular penetrable bodies using the polarization currents to represent the unknowns. Such solutions were developed for a line source above dikes by Parry and Ward (1971) and Hohman (1975) in the early seventies. Such solutions can be made for frequencies that include several target resonances for potential target identification. These solutions can possibly be extended to include fault lines, joints, etc., provided their electrical properties can be estimated by using some of the concepts involved in the hybrid geometrical theory of diffraction-moment approach. The methods of the modified geometrical optics could also be applied to obtain scattered fields at higher frequencies. These and other potential approaches will be discussed.