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GPR numerical simulation of full wave field based on UPML boundary condition of ADI-FDTD

机译：基于ADI-FDTD的UPML边界条件的全波场GPR数值模拟

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摘要

Alternating direction implicit difference scheme (ADI-FDTD) divides a traditional time step into two time steps, with forward difference and backward difference, and integrates both the advantages of unconditional stability of implicit difference scheme and relatively simple calculation of explicit difference scheme, it breaks through the constraint of Courand-Friedrichs-Levy (CFL), and is characterized by unconditional stability. And the boundary condition of uniaxial anisotropic perfectly matched layer (UPML) is anisotropic medium PML applied in absorption edge of FDTD area, with the absorption of wide band, simple iterative formula, and easy programming, without the electric and magnetic field splitting. By discretizing the Maxwell equations in a two dimensional structure, numerical formulas of ADI-FDTD with UPML boundary condition for GPR wave are presented in detail. GPR simulations are carried out for two models. Based on the analysis of numerical results, insights of the radar wave spreading and changing in space are obtained, which can provide a better interpretation of real radar data. The results show that the ADI-FDTD algorithm based on the UPML boundary condition can deploy larger time step and eliminate the strong reflection on the truncated boundaries, lead to an efficient GPR modeling.
机译：交替方向隐式差分方案（ADI-FDTD）将传统时间步分为正向差分和后向差分两个时间步，并且兼具隐式差分方案的无条件稳定性和显式差分方案的相对简单计算的优点，通过Courand-Friedrichs-Levy（CFL）的约束，并且具有无条件稳定性的特点。单轴各向异性完美匹配层（UPML）的边界条件是在FDTD区域的吸收边缘上应用各向异性介质PML，具有宽带吸收，简单的迭代公式和易于编程的特性，且不会产生电场和磁场分裂。通过在二维结构中离散麦克斯韦方程组，给出了具有UPML边界条件的GPR波的ADI-FDTD的数值公式。对两个模型进行了GPR模拟。在对数值结果进行分析的基础上，获得了雷达波在空间中扩展和变化的见解，可以更好地解释实际雷达数据。结果表明，基于UPML边界条件的ADI-FDTD算法可以部署更大的时间步长，并且消除了对截短边界的强烈反射，从而实现了有效的GPR建模。

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