Compensation-Guided Reverse-Time Migration Jointly Accounting for Relaxation and Ohmic Losses in Ground Penetrating Radar Imaging

Reverse time migration (RTM) is widely used for ground penetrating radar (GPR) data processing, typically formulated assuming non-dispersive wave propagation with frequency-independent feature. However, real subsurface media exhibit dispersion and attenuation, causing GPR waves to suffer significant amplitude, phase, and travel time alterations compared to non-dispersive cases. Conventional RTM neglects frequency-dependent attenuation and velocity dispersion, degrading imaging accuracy and resolution. To provide a feasible solution for achieving high-precision migration imaging of GPR data from high dispersive and attenuating geological structures, as well as from weak deep GPR signals, we address this limitation by proposing a novel GPR RTM algorithm incorporating joint compensation for relaxation and Ohmic losses, based on the time reversal invariance principle. This method employs finite element forward modeling and reverse-time extrapolation on triangular meshes, achieving loss compensation by reversing loss terms in the time-reversed equation to restore temporal symmetry. A zero-time imaging condition is adopted, and a time-varying Butterworth filter suppresses amplified noise for stable extrapolation. Validated through three representative Debye-type dispersive synthetic datasets and in-situ experimental GPR data from wet sand detection, our proposed approach mitigates energy attenuation when compared to conventional RTM and individual loss compensation methods. The results demonstrate superior imaging resolution and enhanced reflectivity amplitudes, while accurately recovering energy losses caused by both Ohmic and relaxation mechanisms.