### A direct solution for dielectric and geometric parameters of lossy two - layered media - applications in environmental geology

#### Abstract

It is well known that reflectometry offers a simple tool for determining dielectric properties of materials. For homogeneous materials the procedure is simple and only a single measurement of the reflection coefficient is enough. If the material is inhomogeneous or stratified, indirect procedures for calculating the dielectric properties are required. A direct method for determining the characteristics of a lossy two-layered medium is presented. The technique is based on the study of the frequency response of the complex reflection coefficient of a plane wave incident at the interface between the stratified media and the air (Mertzanides et al., 2000, Mertzanides et al., 2001). The input impedance Zin, at the interface between air and the dielectric surface, can be found from R by (Wait, 1985): …..

Our method offers the possibility of direct calculation of the two layer parameters from two single measurements of the reflection coefficient, avoiding the use of any iterative procedure. In summary, the inversion procedure will make the following steps:

• Measurements of the reflection coefficient R versus frequency.

• Calculation of the Zin=A+jB from Eq. (1).

• Derivation of two extreme values of Real(Zin) in two sequential angular frequencies ωΐ and ω2.

• Calculation of tanôj from Eq. (2).

• Calculation of ε from Eq. (3) and 1 from Eq. (4).

• Calculation of ε2 and tanô2 from Eqs. (5) and (6).

The range of applications includes problems in engineering and environmental geology. More specific, the method offers a useful analytical tool for interpreting remote sensing data, concerning identification of pollution in oceans caused by plankton or petroleum, inspection the use of fertilizers in cultivation areas, determination of soil moisture etc. Furthermore, it can be applied in cases like shallow stratigraphy and water table mapping, detection of organic and inorganic contaminants in underground water, checking the distortion of walls, the asphalt of roads and in archaeological prospection. where ε and tan δ, are the dielectric constant and tangential losses of ilh layer, 1, is the depth of the upper

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