探地雷达三维高阶时域有限差分法模拟研究

探地雷达数值模拟中，时域有限差分法在时间和空间上一般采用二阶精度的中心差分近似(FDTD(2,2))，其形式简单，但数值色散误差较大，在复杂模型模拟时不能很好地反映模型的精细变化.高阶时域有限差分法能很好地改善数值色散带来的误差，提高模拟精度.本文基于三维高阶时域有限差分法的基本原理实现了探地雷达正演模拟，采用单轴各向异性完全匹配层(UPML)作为吸收边界条件，可以有效地吸收外向传播的电磁波，在大大地提高计算效率的同时，也能很好地改善边界的吸收效果.分析对比正演模拟结果，通过三维高阶时域有限差分正演能获得目标体准确电磁响应信息，并能很好的提高模拟精度.

Study of three dimension high-order FDTD simulation for GPR

The finite-difference time-domain (FDTD) method usually uses the second order accuracy central difference approximation (FDTD(2,2)) in time and space in numerical simulation of ground-penetrating radar (GPR). Because of numerical dispersion error, the response of complex model is not very clear, especially for fine structures. The high-order finite-difference time-domain method (HO-FDTD) is efficient in improving accuracy and reducing the error caused by numerical dispersion. We simulate three-dimensional GPR data based on the basic principles of HO-FDTD method using the uniaxial anisotropic perfectly matched layer (UPML) as absorbing boundary. It can effectively absorb the electromagnetic waves reflection at boundary and greatly increase the computational efficiency. Three dimensional HO-FDTD simulation can get accurate electromagnetic response information for target and improve simulation accuracy by analyzing and comparing the results of forward modeling.