Second-order symplectic PRK scheme for ground-penetrating radar simulations in dispersive materials

Abstract

An accurate and effective forward model is helpful in interpreting measured ground-penetrating radar (GPR) data. In this paper, an explicit second-order symplectic partitioned Runge–Kutta scheme (SPRK) with Higdon's absorbing boundary condition is developed to simulate GPR wave propagation in dispersive media. For this purpose, the first-order Debye dispersion model is successfully applied to the second-order SPRK method. A single-layer dispersive medium model and a three-layer pavement structure model are simulated, in order to verify the accuracy and efficiency of the second-order SPRK method, as well as to clarify the effect of dispersion on the GPR echo signal. The numerical simulation results demonstrate that the proposed algorithm not only can maintain the simulation accuracy, but can also save about 19% of the calculation time, when compared with the FDTD algorithm, in a dispersive medium. We also obtain the GPR profile of a pavement structure with a circular cavity disease and an underground pipe structure in a dispersive medium, and the simulation results show that the dispersion characteristics of the materials lead to high absorption of the GPR electromagnetic waves. Finally, field experiment data are used to further verify the applicability of the algorithm. The numerical simulations and experiments indicate that the dispersion of the medium must be considered in GPR numerical simulation, and the authenticity of the simulated image must be ensured.