An Improved and Novel Approach for Frequency Domain Forward Modeling of GPR Data Using the Finite Difference Staggered Grid Technique

Abstract

Forward modeling of ground penetrating radar (GPR) data is important for understanding relationships between dielectric layers. For the inversion of GPR data, an effective and advanced forward modeling scheme is always desirable. Here, staggered grid formulations for the finite difference frequency domain (FDFD) method have been developed and modified for the forward modeling of GPR data. The forward problem is first solved using a nine-point regular staggered grid that basically approximates and discretizes the Laplacian operator. In the case of transverse electric mode FDFD method, the implementation of a perfectly matched layer (PML) has been shown to be effective. Among the several PML techniques, the complex frequency shifted perfectly matched layer method has proven to be most useful for absorbing evanescent waves. In this paper, a new and improved nine-point mixed staggered grid formulation is proposed by considering the combination of a five-point Cartesian and nine-point rotated staggered grid. The derived stencils are compared after estimating the reflection errors from the computed simulated wavefields ( $${E}_{y}$$ ) of the homogeneous subsurface model. This newly developed technique exhibits less error than the regular and unstaggered mixed stencils. Lastly, this better and less-time consuming grid is used to extract GPR data from realistic sedimentary models with a surface acquisition setup.