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This book presents methods for subsurface soil probing in a vadose zone and mathematical methods for signal processing, enabling the evaluation of the electrical characteristics of soil and objects using the Step-Frequency Continuous Wave Probing Signal based on the Kramers-Kronig theorem and nonlinear singular integral equations for the phase velocity of propagation or the specific attenuation of radio waves in soil. Moisture filtration processes in the vadose zone and their influence on its electrical characteristics are studied using a developed model. A new method for interpreting probing results is presented using the phase structure of signals, which is sensitive to the presence of any inhomogeneities in the subsurface soil structure. Numerous examples of practical probing are given, in particular, the synthesis of an antenna aperture under the soil surface due to the movement of a ground penetrating radar and lateral synthesis for detecting inhomogeneities in airport runways and highways.