TWO-AND-HALF DIMENSIONAL RECONSTRUCTION OF BURIED TUNNEL AND PIPES FROM CROSS-BOREHOLE AND REFLECTION MEASUREMENTS BY USING A GENETIC AND LEVENBURG-MARQUARDT HYBRID ALGORITHM

Abstract

It is shown that the distribution of the permittivity and the conductivity of the scattering object is obtained from its scattered fields by the iterative inversion in the spectral domain. Analytic formulation shows that the ill-posedness is caused by the evanescent modes of the measured scattered fields that amplify exponentially its measurement errors in the back-propagation process and filtering out all the evanescent modes in the spectral domain cost functional regularizes the ill-posedness of the inversion at the expense of the resolution. The resolution of reconstruction obtained by keeping all the propagating modes and filtering out the evanescent modes for the regularization becomes half a wavelength. The condition for assuring the single global minimum of the cost functional is shown in terms of the number of the measured data points and the hybrid algorithm combining the genetic and the Levenberg-Marquardt algorithms find its global minimum effectively. This iterative inversion with the hybrid algorithm is shown to locate and identify the deep air tunnel and two closely located circular pipes of conducting and dielectric by finding up to 12 physical parameters of the complex dielectric constants, sizes, positions of the object, and the complex dielectric constants of the background earth medium.