Several dielectric as well as conducting pipes mixed and buried in the lossy half ground are reconstructed from the scattered fields measured along the air-earth interface. Parameters such as the positions, the sizes and the medium parameters, i.e. relative dielectric constants and conductivities, of the buried objects as well as the medium parameters of the background lossy half ground are obtained from the scattered fields by iterative multi-parameter optimization method.
One may define the cost functional as the squared summation of the differences between the spatial spectrum of the measured and the calculated fields. Spatial spectrum of the measured fields is obtained by taking its discrete Fourier transform of the numerically calculated fields along the receiving points above the lossy half space in order to regularize the illposedness of the inversion by filtering out the evanescent modes. One may use boundary element method and half space Green`s function to calculate fields scattered from cylinders of dielectric and conductor in lossy half space.
By using optimization algorithm, one may minimize the cost functional iteratively by choosing the various parameters of the cylinders and background medium. One may find the global minimum of the cost functional by using the hybrid optimization algorithm combining the Levenberg-Marquardt and the genetic algorithm. After reaching the global minimum of the cost functional, one may find unknown parameters of cylinders and background medium. Scattered fields at 61 points in the air medium along the air-earth interface are numerically calculated and its discrete Fourier transform gives 25 propagating modes as the measured spectrum of the scattered fields.
From this, 12 physical parameter, such as relative permittivities and conductivities of the background medium(2) and two cylinders(4), and the radii of the cylinders(2) and their center positions(4) are obtained when the measurement error(noise) in the scattered field is assumed to be 0 % and 10 %, respectively. The parameter values are quite close to the original values except the values of permittivity and conductivity of the conducting cylinder which are very large and easily identifiable as a conductor.