An interpolating scaling functions method with low-storage five-stage fourth-order explicit Runge-Kutta schemes for 3D ground penetrating radar simulation

Abstract

Accurate and efficient 3D simulation is extremely important for both grasping the features of radar wave propagation in realistic models and the high-resolution inversion. In this paper, we propose a new numerical algorithm called the low-storage five-stage fourth-order explicit Runge-Kutta interpolation scaling function method (LSERK-ISFM) and apply it into the 3D simulation of ground penetrating radar (GPR). Firstly, we derive the auxiliary differential equation (ADE) of the 3D Maxwell's equations based on the complex-frequency shifted perfectly matched layer (CFS-PML), discretize the spatial derivative of the Maxwell equation by ISFM, and integrate the temporal dimension through the LSERK scheme. Compared with the traditional finite-difference time-domain (FDTD) method, the LSERK-ISFM algorithm can effectively improve the precision of space-time dispersion of the Maxwell's equations. Specifically, by the homogeneous vacuum medium model, we compare the forward modeling results of the different number of grids per wavelength, the comparison results prove that a smaller number of grids per wavelength can be selected in the LSERK-ISFM scheme, which can greatly contribute to reducing the consumption of memory. Then we build a simple 3D model to properly compare the proposed algorithm with the coarse-mesh FDTD and the fine-mesh FDTD, the results show that, with the same mesh generation, the LSERK-ISFM algorithm outperforms the conventional FDTD algorithms in terms of both accuracy and efficiency. Finally, we test the algorithm on a 3D complex model by a series of 3D forward profiles and the corresponding slices, both simulated reflections and diffractions clearly depict the shape and location of the anomalous bodies, which shows great potential of application in the field of 3D exploration and interpretation for GPR community.