Application Of High-order DSC-FDTD Based On CPML Boundary In Ground Penetrating Radar

Ground penetrating radar(GPR)is a technology to detect the distribution shape and characteristics of underground targets.It uses the propagation characteristics of highfrequency pulsed electromagnetic waves in the underground medium and the reflection and Diffraction and other fluctuation laws are used for detection,and the forward modeling technology of ground penetrating radar is part of its theoretical research.The FiniteDifference Time-Domain Method(FDTD)is often the most commonly used research method in the study of ground penetrating radar forward modeling technology.However,FDTD is limited in calculation due to the problem of numerical dispersion error.Due to the grid size,the accuracy cannot be high enough,and the truncation of the boundary conditions of the FDTD algorithm will also cause some reflected waves to affect the calculation results.In this paper,using the high-order FDTD method combined with the absorbing boundary condition,the paper studies and analyzes several models of ground penetrating radar forward modeling.The specific research contents are as follows:1.The difference method,basic principle,meshing and updating process of the FDTD method are introduced,then the stability conditions and numerical dispersion of the FDTD method are discussed,the influence of numerical dispersion on the results is analyzed,and it is proved that the mesh size is too large.lattices can lead to more severe numerical dispersion.The settings of two common excitation sources using FDTD in GPR forward modeling are also introduced.2.The Discrete Singular Convolution(DSC)theory is studied.The DSC method is used to replace the traditional central difference,and the space part of Maxwell’s curl equation is discretized,and the time part remains unchanged.The high-order DSC-FDTD(2,2M)for the derivation of the update equation.The stability conditions and numerical dispersion errors of high-order DSC-FDTD(2,2M)are studied and analyzed,and the stability conditions and numerical dispersion errors of traditional central difference FDTD(2,2)are compared.-FDTD calculation time.3.The advantages and disadvantages of two absorbing boundary conditions,PML and CPML,are analyzed and verified by simulation.Based on the higher-order DSCFDTD(2,2M)theory,combined with the better CPML absorbing boundary condition,the update equation based on the CMPL absorbing boundary condition is derived.This method is combined into the forward modeling of ground penetrating radar,and several common geological models are analyzed,which has a good effect of forward modeling.This paper further combines the CPML absorbing boundary condition with the highorder DSC-FDTD(2,2M)algorithm through in-depth research on the high-order DSCFDTD(2,2M)and absorbing boundary conditions,which is applied to the ground penetrating radar positive In the simulation,the effectiveness of the high-order DSC-FDTD(2,2M)based on CPML boundary conditions in the forward simulation of ground penetrating radar is proved by a simulation example.