###### Abstract
Such methods are designed to reconstruct the spatial distribution of physical properties, such as the dielectric permittivity, by analyzing recorded data regarding the propagation of electromagnetic waves at observation points. The works of [PERSON] and [PERSON] [19; 20], as well as the study [21], have made a significant contribution to the development of theoretical methods for interpreting radar-grams. These contributions focus on the construction of optimization algorithms for solving inverse coefficient problems in geoelectrics, particularly in layered and vertically inhomogeneous media, along with establishing the correctness and stability of the obtained solutions. These investigations have laid the foundation for modern high-precision and adaptive algorithms for processing GPR data, which are especially valuable for assessing complex engineering and geological structures and detecting subsurface defects. The theoretical foundations and numerical methods for addressing inverse problems in geoelectrics, including proofs of the existence and uniqueness of solutions, are comprehensively detailed in the monograph by [PERSON] and [PERSON] [22]. This work serves as a cornerstone for subsequent research in the field of geophysical inversion problems. A comparison of different methods for solving various inverse coefficient problems is presented in the work of the authors [23]. A number of studies [24; 25] have devoted significant attention to the preprocessing of GPR data with the goal of enhancing interpretation quality. Specifically, various noise suppression techniques are employed, including wavelet transformations (e.g., fourth-order Haar and Daubechies wavelets), frequency filtering, sliding averaging, amplitude correction, Butterworth filters, and Levinson-Durbin algorithms. Additionally, Fourier transforms are specifically utilized to extract the key characteristics of the electromagnetic wave field. A key area of research involves the development of numerical algorithms for solving the inverse problem at the discrete level. In other words, this approach yields a difference scheme with the property of conservation, ensuring energy conservation at the discrete level. The effectiveness of this approach is demonstrated in the studies by [PERSON] et al. [26; 27] and in the work by [PERSON] [28], where a comparative analysis of traditional and discrete approaches is conducted based on numerical examples. In contrast to existing approaches, the proposed discrete algorithm conserves fundamental physical principles, is specifically tailored for vertically inhomogeneous media, and ensures numerical stability. Modern research in geoelectrics highlights the growing adoption of machine learning methods for automating data analysis and enhancing geophysical interpretation. One promising area is the application of unsupervised learning, such as clustering (e.g., the K-Means algorithm), for comprehensive analysis of geoelectric tomography data. In [29], an approach was proposed for identifying areas of filtrate contamination with high reliability and minimal interpretative subjectivity based on resistivity, chargeability, and their ratio. In addition, deep learning methods have been actively applied in flaw detection tasks, such as in the analysis of GPR data. In [30], a study presents an algorithm designed for the automatic detection of hidden defects beneath the lining of railway tunnels using a modified YOLOP architecture. This approach demonstrated high performance, achieving up to 80.6% accuracy with a processing time of less than 0.02 s per image. The integration of geophysical methods with machine learning algorithms enables automation, enhances result reliability, and minimizes expert reliance on complex engineering and geological tasks. This study examines algorithms for GPR sensing based on numerical modeling of the propagation of electromagnetic waves in inhomogeneous media governed by Maxwell's equations.