Ground penetrating radar inversion in 1-D: an approach for the estimation of electrical conductivity, dielectric permittivity and magnetic permeability

This paper presents a method for inverting ground penetrating radargrams in terms of one-dimensional profiles. We resort to a special type of lineariz ation of the damped E-field wave equation to solve the inverse problem. The numerical algorithm for the inversion is iterative and requires the soluti on of several forward problems, which we evaluate using the matrix propagat ion approach. Analytical expressions for the derivatives with respect to ph ysical properties are obtained using the self-adjoint Green's function meth od. We consider three physical properties of materials; namely dielectrical permittivity, magnetic permeability and electrical conductivity. The inver se problem is solved minimizing the quadratic norm of the residuals using q uadratic programming optimization. In the iterative process to speed up con vergence we use the Levenberg-Mardquardt method. The special type of linear ization is based on an integral equation that involves derivatives of the e lectric field with respect to magnetic permeability, electrical conductivit y and dielectric permittivity; this equation is the result of analyzing the implication of the scaling properties of the electromagnetic field. The gr ound is modeled using thin horizontal layers to approximate general variati ons of the physical properties. We show that standard synthetic radargrams due to dielectric permittivity contrasts can be matched using electrical co nductivity or magnetic permeability variations. The results indicate that i t is impossible to differentiate one property from the other using GPR data . (C) 2000 Elsevier Science B.V. All rights reserved.