Efficacious GPR Implementations of Z-Transform-Based Hybrid LOD-FDTD with Subgridding Scheme: Theoretical Formalism and Numerical Study

Ground penetrating radar (GPR) forward modeling is one of the core geophysical research topics and also primary task simulating ground system. It a process propagation laws characteristics electromagnetic waves in simulated space when distribution internal parameters exploration region known. And finite-difference-time-domain (FDTD) method has space-time transient evolution wave, whose numerical simple easy to program, so it become most extensively utilized methods GPR modeling. generally known that conventional FDTD approach requires finer uniform Yee cell all time produce satisfactory accuracies from simulations GPR. However, smaller temporal incremental be adopted due lower spatial incremental, which would dramatically weaken advantage method. To solve this issue, subgridding-technique-based hybrid local-one-dimensional (LOD-FDTD) applied work classical scenarios. In method, unconditional-stable LOD-FDTD employed fine-grid domain, while traditional used coarse-grid could avoid oversampling problem local domain if scheme adopted. Meanwhile unconditional stability LOD-FDTD, larger step, derived coarse grid satisfies Courant-Friedrichs-Lewy (CFL) condition, whole long-time interpolation circumvented. Additionally, proposed arbitrarily adjusted by means different ratio both coarse- fine-grid, hence holds much higher generality. As compared with auxiliary differential equation (ADE) technique, Z-transform integrated into for multi-pole Debye-based dispersive media resulting more direct implementations fewer computing steps. Finally, three problems are carried out validate efficiencies