Model of time-distance curve of electromagnetic waves diffracted on a local feature in the georadar study of permafrost zone rock layers

In GPR (georadar) studies, one of the most popular procedures for determining electromagnetic waves propagation velocity in a rock mass is the selection of theoretical hyperbolic time-distance curves and subsequent comparison with the time-distance curve obtained from a GPR measurement. This procedure is based on the model of homogeneous medium, but nowadays the subject of GPR study is often inhomogeneous media, such as horizontally layered media characteristic of loose permafrost zone sediments. The paper presents the findings of studying the formation of hyperbolic time-distance curves of georadar impulses in a horizontally layered medium without taking into account the dispersion and absorption of electromagnetic waves. On the basis of geometrical optics laws, formulas were derived to calculate the shape of the hyperbolic lineup of georadar impulses reflected from a local feature in a multilayer frozen rock mass. On the example of a permafrost zone rock mass containing a layer of unfrozen rocks, the effect of the thicknesses of rock layers and their relative dielectric permittivity on the apparent dielectric permittivity resulting from the calculation of the theoretical hyperbolic time-distance curve was shown. The conditions under which it is impossible to determine the presence of a layer of unfrozen rocks from a hyperbolic time-distance curve are also presented. The established regularities were tested on synthetic georadar radargrams calculated in the gprMax software program. The findings of the theoretical studies were confirmed by the comparison with the results of the analysis of the georadar measurements computer simulation data in the gprMax system (the relative error was less than 0.5%).