GPR signal phase structure aplication for estimation of distribution of soil electrical properties on depth

The mathematical algorithms for reconstruction of the soil layers electrical characteristics using the estimated dependency of radio waves attenuation per unit length on frequency or similar dependency on phase velocity are described in [1, 2]. To perform this reconstruction we used a well known Kramer-Kronig equation, which is then lead to a nonlinear singular integral equation for the unknown functional dependence of the soil conductivity on the frequency. Then the equation is solved by a numerical iterative method, with evaluated dependencies of conductivity and permittivity on the frequency in a range of probing signal carrier frequency as a result. The main difficulty here is an attempt to assess the functional dependence of attenuation per unit length or the phase velocity on frequency. The first method uses filtering of signal that corresponds to specific soil layer on the output of georadar receiver phase detector. Then the frequency dependence of the phase velocity of radio waves in this layer is estimated using the displacement of the object image in depth when using low-frequency and high frequency parts of the probe signal spectrum. Both the first and second algorithms do not allow obtaining highly accurately estimated electrical characteristics, so it is impossible to estimate accurately the frequency dependence of attenuation per unit length or the phase velocity of radio waves propagation in the layers of the soil.