基于双二次插值的探地雷达有限元数值模拟

从探地雷达(GPR)满足的波动方程出发,详细介绍了二维GPR模型单元剖分、二次插值、数值积分和有限元刚度矩阵总体合成的GPR有限元求解过程.为解决数值模拟时截断边界处的超强反射,采用Clay Bout透射边界条件对雷达波进行衰减,进而压制了来自截断边界处的反射波.在满足时间步长与空间网格差分稳定性前提下,采用中心差分法对GPR有限元方程进行离散,并用不完全LU分解预处理的BICGSTAB算法求解系数方程组,然后编制了基于双二次插值的GPR有限元正演模拟matlab程序.运用该程序分别对矩形和"V"字形两个典型地电模型进行正演计算,得到了正演剖面图,将该正演剖面图与基于线性插值的FEM算法的正演剖面图做了对比分析.结果表明基于双二次插值FEM算法相比基于双线性插值FEM算法异常响应更明显,具有更高的模拟精度,更有利于指导雷达剖面的数据解译.

Finite element numerical simulation for GPR based on quadratic interpolation

Started from the GPR wave undulation equation,this article introduced element subdivision,interpolation,integration,general synthesis and GPR finite element wave equation deducing process in details.In order to eliminate the super strong reflection on the interceptive boundary when the FEM was conducting GPR forward simulations,the transmission absorbed boundary condition was adapted to transmit out reflected waves that in the interceptive boundary of GPR wave,and then suppressed the reflected wave from the interceptive boundary.Under the premise of meeting the time step and space grid difference stability,using central difference method to discrete GPR finite element equation and BICGSTAB algorithm to solve the Coefficient equations.Afterwards,establishing the matlab program of GPR finite element forward simulations.Applying this program to conduct FEM forward simulations for two geoelectric model of Rectangular block and "V" shape respectively,we obtained the GPR profiles of FEM forward simulations based on quadratic interpolation.Comparing the profiles based on this forward simulations and the FEM forward simulations profiles based on linear interpolation,the results show that the abnormal response of the FEM based on quadratic interpolation is more significant than that of the FEM based on linear interpolation,it has higher simulation accuracy and more conducive to guide the interpretation of the radar profile data.