Calculation of reflection and transmission coefficients of a ground penetrating radar signal in MATRIX PRO software

The results of Ground Penetrating Radar (GPR) are usually presented in the amplitude-phase representation with a color scale, which is selected manually and serves only for easier visual perception of radargrams. Individual layers are highlighted along the isophase lines. The specified representation is not informative for geological and geotechnical engineers. A simpler and at the same time informative representation of the results in the form of sections from engineering-geological elements is needed, so new models of data representation are required. To solve the problem of increasing the information content of GPR results, new models and algorithms for processing the initial data are being developed. As one of the directions of development in this work, the possibility of extracting information on the reflection and transmission coefficients at the interfaces of the media is considered. The purpose of the work is to determine the possibility of calculating the reflection and transmission coefficients from GPR data based on in-situ data, to identify the relationship with the attenuation coefficient and to develop an algorithm for their evaluation when processing GPR data, in order to increase the information content of the presentation of GPR results and to develop new models for data presentation in the form of sections from engineering-geological elements. For this purpose, in the summer of 2024, a lake was surveyed in the Moscow region using the ECHO SPHERE ground penetrating radar. The antenna length was 1 m, the frequency was 150 MHz, the transmitter output power was 200 kW (5 kV), and the recording sampling period was 1 ns. Part of the survey was carried out along the shore of the lake, and another part was from the water surface. The depth of the lake is about 1 m. The bottom is sandy and pebbly. A model based on the relationship between the signal reflection coefficient and attenuation coefficient was used to process the data. The attenuation coefficient describes the reduction in wave amplitude during propagation through a medium due to energy dissipation, absorption, and other factors leading to energy loss. It influences the overall energy level of the wave, whereas reflection and transmission coefficients describe how energy is distributed between reflected and transmitted waves at the boundary between different media. Significant attenuation causes substantial energy loss over distance, affecting the remaining energy even if there is not full reflection at the boundaries. Total energy passing through the medium depends on both the transmission coefficient and the attenuation coefficient. This comprehensive view can be represented by the complex refractive index, combining refraction effects and wave attenuation within the medium. In an inhomogeneous medium, the attenuation coefficient for the recorded reflected signal will be variable, so we can represent the change in the attenuation degree as a function of the change in the signal attenuation coefficient in time, which has bursts of arrival of the reflected wave. Consider an incident wave with amplitude A0. Upon reflection, the reflected wave's amplitude becomes AR = RA0, where R represents the reflection coefficient. The attenuation plot exhibits spikes proportional to changes in amplitude, reflecting the influence of R. We approximate the signal as a summation of delayed reflections, assuming the logarithm of this sum follows a linear relation with the attenuation coefficient. Taking the natural logarithm yields a near-linear function correlating with the reflection coefficient. The derivative of the attenuation coefficient measures how quickly the reflection coefficient changes over time, indicating shifts in the medium’s absorption efficiency across interfaces. Linear plots of attenuation coefficient changes reveal abrupt jumps corresponding to reflected signal arrivals, signifying boundaries between media. Changes in the absorption coefficient suggest alterations in material properties. Based on this model, a special algorithm was proposed to estimate reflection and transmission coefficients from GPR data. The proposed algorithm was implemented in the MATRIX PRO program of our own develop. The possibility of estimating reflection and transmission coefficients from GPR data was proved using in-situ data. The proposed model and algorithm for processing and presenting GPR data showed adequate results, which clearly highlight the water layer and the boundary of the lake bottom. Practical significance of the results is the proposed method can be further adapted to identify attenuation coefficients and have the ability to relate them to the specific conductivity of soils. The proposed method can be adapted to create new models for representing GPR data for use in the results of engineering geophysical studies.