Επίλυση του ευθέος και αντιστρόφου προβλήματος για υπεδάφιες δομές στην ηλεκτρομαγνητική διασκόπηση υψηλών συχνοτήτων

Abstract

The purpose of this doctoral thesis is the development of a new analytical method for the solution of the inverse 1-D electromagnetic scattering problem. The method is based on a study of frequency response of the plane wave reflection coefficient, for normal incidence on stratified media. The structure of the thesis is as follows. Chapter one provides a literature review on the analytical and numerical methods (with emphasis on the former) developed in the past, to solve the 1-D inverse scattering problem. In chapter two, the basic principles of electromagnetic wave propagation in lossy media and T.E.M. wave propagation in transmission lines, are described. The forward problem is formulated according to transmission line analogy. The input impedance at the interface between the stratified media and air comes up as a linear expression of a hyperbolic tangent. Its argument contains the physical and geometrical characteristics of the Ν - layered half- space. The third chapter sets out the proposed method for the solution of the inverse 1-D electromagnetic scattering problem. The procedure requires the measurement of the complex reflection coefficient in two adjacent frequencies where the real part of the input impedance takes maximum or minimum value. From these two single measurements, all the dielectric and geometric parameters of two - layered media can be found. Simulated examples are presented using ideal (without noise) and noisy data. A discussion follows, on the results of the statistical processing of data, produced by Monte - Carlo simulation. Chapter four seeks to extend the proposed method to cases of three and Ν-layered media. A procedure is proposed, which combines the technique developed for two - layered half - spaces, with measurements of the reflection coefficient at the subjacent interfaces of the stratified dielectric profile. The chapter presents some simulated examples and discusses the method's advantages and drawbacks. Chapter five considers a number of applications in Hydrology and Environmental Geology problems. Simulated models are created by experimental measurements of complex permittivities as found in literature. Monte - Carlo simulation is used to test the method's validity. Chapter six draws the conclusions that flow from the foregoing chapters and discusses the contribution of this doctoral thesis. It also suggests some ideas for further development of the method, in order to extend its applicability.