(1. 中南大学 地球科学与信息物理学院，长沙 410083；
2. 中南大学 有色金属成矿预测教育部重点实验室，长沙 410083；
3. 中南大学 资源勘查与环境地质研究院，长沙 410083)
摘 要: 以旋转交错网格(RSG)差分为基础，实现探地雷达(GPR)在非均匀突变介质中的正演数值模拟。通过利用旋转交错差分算子，将雷达波场各场分量设置在非均匀突变介质的基本单元中，单元内同一物性参数定义在同一位置，将对角线方向上物性参数差分值的线性组合来计算坐标轴方向上的物性参数差分值，针对非均匀特征变化剧烈的网格区域，算法中的单元网格形式不再需要进行插值，扩宽了数值稳定性条件的限制。推导了适合于探地雷达的旋转交错网格差分格式及TMy极化模式下的更新方程组，实现了均匀介质和非均匀突变介质中的TMy雷达波场的数值模拟，并分别从解析解、模拟剖面和波场快照的角度，与标准交错网格差分算法进行了对比。结果表明，在模拟非均匀特征明显的介质时，旋转交错网格算法可以选取更大的时间步长，数值色散程度控制更好，提高了模拟效率和成像精度，可更有效地指导非均匀突变介质中探地雷达数据的解译。
关键字: 旋转交错网格；标准交错网格；探地雷达；正演模拟；数值色散
（1. School of Geosciences and Info-Physics, Central South University, Changsha 410083, China;
2. Key Laboratory of Metallogenic Prediction of Nonferrous Metals, Ministry of Education,
Central South University, Changsha 410083, China;
3. Institute of Resources exploration and Environmental Geology, Central South University, Changsha 410083, China）
Abstract:Based on the rotated staggered grid finite-difference, forward simulation in inhomogeneous media with strong discontinuities for ground penetrating radar (GPR) was implemented. By using the rotating staggered difference operator, the GPR wave field components and other physical parameters were distributed in the elementary cells of RSG, in which all field components of one physical property were located at one elementary unit in computational domain, then the difference of field components and physical parameters along the coordinate axes were calculated by using the linear combination value of them across the diagonal coordinate axes, no averaging of elementary cell was needed even in grids-domain with strong heterogeneities, which relax the limitation of the numerical stability condition. The rotated staggered grid finite difference scheme for GPR and the corresponding update equations was deduced in TMy polarization mode, then the numerical simulation of GPR wave field in TMy polarization mode was implemented, in addition, the comparation between the standard staggered grid and RSG was presented from three respects of the analytic solutions, the simulated sections and the field snapshots. The results show that with the more relaxed limitation of the numerical stability condition and the better controlling of numerical dispersion degree, the RSG difference algorithm improves the efficiency and accuracy of simulation, which can effectively guide the GPR data inversion and interpretation in the inhomogeneous media with strong heterogeneities.
Key words: rotated staggered grid; standard staggered grid; ground penetrating radar; forward modeling; numerical dispersion
