###### Abstract  
This study presents the development of a discrete algorithm for interpreting ground-penetrating radar (GPR) data in vertically inhomogeneous media for the diagnostics of road structures. Experimental data were obtained using an OKO-2 GPR system, followed by primary radargram processing using the CartScan software. This included noise and interference filtering, as well as the initial estimation of the dielectric permittivity of detected layers. The resulting dataset was used to validate numerical algorithms for solving the forward and inverse problems of geolectrics. The proposed approach is based on minimizing a quadratic misfit functional between the calculated and observed values of the horizontal component of the electromagnetic field. The gradient of the functional required for optimization is obtained via the numerical solution of an adjoint problem. A discrete version of this problem was developed, which satisfies the properties of conservativeness and uniformity according to finite difference theory. The inverse problem reconstruction of dielectric permittivity is considered a non-destructive method for radargram interpretation. Assuming a piecewise-continuous medium structure eliminates the need for computing gradients at material interfaces. The proposed methodology enhances the accuracy and reliability of pavement condition assessment and holds practical value for road infrastructure monitoring. caption=true, description=  
* In road diagnostics: identification of voids, structural defects, waterlogged areas, and disruptions in the layered structure [10; 11; 12];
* In archaeology: non-destructive probing of cultural layers, determination of building locations, and identification of burial sites [13; 14; 15]. Additionally, in geological studies, GPR is widely used to investigate active faults without resorting to invasive ground-based methods. Its applications include determining optimal trench locations for paleoseismological studies [16] and characterizing the shallow-depth geometry of active fault systems using both 2D and 3D datasets of GPR data [17]. The primary tool for GPR research is a device that emits electromagnetic pulses into a subsurface medium as it moves along the surface. The OKO-2 series [8] is widely used due to its suitability for non-destructive testing, being specifically designed for non-destructive testing of engineering structures, assessment of road surface conditions, and performance of geotechnical investigations. The OKO-2 complexes feature a modular architecture, which allows for the rapid replacement of antennas operating at frequencies of 400 MHz and 1000 MHz [18]. The 400 MHz antenna configuration offers an optimal trade-off between penetration depth (up to 2-3 m) and spatial resolution (approximately 10 cm), making it particularly effective for the examination of road structures. The signals reflected from the boundary between media are recorded by the receiving antenna, converted into electrical impulses, and stored as a time-domain scan, commonly referred to as a radar image. Each point in the radar profile corresponds to the signal travel time, enabling the reconstruction of the internal structure of the investigated subsurface medium. One of the key tasks in GPR data analysis is the interpretation of radar profiles focused on reconstructing the subsurface structure. In other words, the goal is to determine the geoelectric cross-section of the investigated object based on the recorded electromagnetic response. The development of effective interpretation methods is essential for improving diagnostic accuracy, enhancing the reliability of conclusions, and expanding the application of GPR as a key method in non-destructive testing. Traditional interpretation methods rely on engineering algorithms integrated into the software of GPR systems. An alternative approach focuses on the rigorous mathematical formulation and resolution of coefficient-based inverse problems in electrodynamics.