Finite element method GPR forward simulation based on mixed boundary condition

Based on Maxwell's equations, this paper deduces the finite element wave equation of Ground Penetrating Radar (GPR). It also describes the principle of the transmitting boundary condition and the Sarma boundary condition, deduces the theoretical formula of these two boundary conditions. By adding a transitional layer into the damping region, the adding method of the Sarma boundary condition is optimized, suppressing the artificial reflection at the interface between the medium zone and the damping region. Considering the different theoretical mechanisms of the transmitting boundary condition and the Sarma boundary condition, it proposes a mixed boundary condition combining the transmitting boundary condition and the Sarma boundary condition, which enables the remained energy of GPR wave to be transmitted through the transmitting boundary condition after it is attenuated and absorbed by Sarma boundary condition, integrating the advantages of the two conditions. In addition, it takes the center pulse excitation source in two-dimensional homogeneous model as an example, compares the processing effects based on the cases with or without boundary conditions, or with different boundary conditions, in a visualized way of snapshots for the full GPR wave field, through the realization of Matlab procedure. The result indicates that the effect of using the mixed boundary condition is superior than using a single boundary condition. In the end, a numerical simulation for two typical GPR earth-electricity models is carried out with the finite element method based on the mixed boundary condition, providing the guidance for GPR data processing and engineering practice.