Utilizing fractional time derivative of instantaneous frequency for the evaluation of wedge and thin-layer structures in measured and modelled GPR data

This study proposes a novel approach for evaluating wedge and thin-layer structures in 2-D ground-penetrating radar (GPR) data by computing instantaneous frequency (IF) using fractional time derivatives. The Caputo fractional differential operator is employed as a more suitable alternative to standard IF methods for resolving thin layers and wedge geometries. To demonstrate the method's effectiveness, 2-D forward modelling based on the finite-difference time-domain (FDTD) technique was used to generate synthetic radargrams for various scenarios. Models included thin layers with thicknesses of 5, 7, and 10 cm, and a wedge with thickness varying from 0 to 20 cm, each with distinct relative dielectric permittivity values. Synthetic modelling was conducted using a 300 MHz Ricker wavelet to evaluate fractional instantaneous frequency (FIF) performance under moderate frequency conditions. FIF was computed for each trace in the synthetic radargrams at different derivative orders. The FIF-calculated radargrams of the experimental data revealed enhanced interpretation of the wedge structure, particularly in its thinner regions. To validate these findings, GPR measurements were conducted using a high-frequency 2 GHz antenna on three laboratory models: a distilled-water-filled wedge, a finer-sand wedge, and a thin-layer structure. The FIF-calculated radargrams revealed enhanced interpretation of wedge and thin-layer structures, particularly in thinner regions. Overall, the results demonstrate that FIF analysis significantly improves boundary detection and thickness estimation in both synthetic and real GPR data. This technique offers valuable advantages for non-destructive subsurface evaluation in geological, archaeological, engineering, and environmental applications.