Selecting the frequency of the probing signal of a two-position radar system for sensing the earth’s surface

Abstract

Introduction. Selecting a frequency for remote sensing radar systems is a complex optimization problem. The range of requirements for radar system resolution and subsurface penetration depth is determined by the specific engineering task. Signal propagation conditions also vary: for ground-based ground penetrating radars, the air-to-surface interface does not affect the radar signal, whereas satellite systems must operate in the gigahertz range to minimize ionospheric influence, leading to diffuse scattering and shallow penetration depth. This necessitates a compromise between the physical principles of wave propagation, the required characteristics, and the technical capabilities of the equipment. Materials and Methods. Unlike nadir irradiation, which has a comprehensive theoretical basis, oblique irradiation has been studied much less. A special feature of inclined irradiation is the occurrence of the full refraction (Brewster) effect, which creates additional information opportunities. The analysis utilized mathematical modeling of Fresnel formulas in Matlab. Complex reflection and refraction coefficients were calculated for vertical and horizontal polarizations, taking into account the electrophysical parameters of the media (dielectric constant ε, specific conductivity σ) and signal frequency ω. Penetration depth was estimated using the attenuation coefficient α, determined from the complex propagation coefficient. Resolving power was determined by the geometric dimensions of the first Fresnel zone (reflection ellipse), and the effect of surface irregularities was determined by the Rayleigh criterion. Results and discussion. Modeling for three types of underlying surfaces at frequencies of 200 MHz, 460 MHz, and 2.4 GHz yielded the following patterns. It was found that the position of the Brewster pseudo-angle (minimum absolute value of the reflection coefficient for vertical polarization) and the magnitude of this minimum depend on frequency for high-loss media (clay) and remain stable for low-loss media (wet sand). An inverse dependence of penetration depth on frequency was confirmed. In wet sand, signal attenuation is insignificant even at high frequencies. In clay soils, by contrast, the 2.4 GHz signal attenuates over a distance of less than 0.1 m, while at 200 MHz, the penetration depth can reach several meters for dry clay. Calculations of the reflection ellipse size show that increasing frequency leads to a decrease in the area of the resolution element, increasing detail. However, this tightens the requirements for the permissible height of surface irregularities. Conclusions. With oblique irradiation, frequency selection becomes even more critical than with vertical irradiation, as the reflection parameters become dependent on the angle of incidence, which can be optimized to improve the accuracy of surface property measurements. The conflict between the need for high resolution (high frequencies) and deep penetration (low frequencies) can be resolved by developing multi-band radar systems that combine multiple operating frequencies. Remote sensing with penetration into the ground to a depth of more than 10 cm is possible using low-frequency (decimeter range) aviation (manned or unmanned) or ground-based systems.