The absorbing boundary is the key in numerical simulation of borehole radar.Perfect match layer(PML) was chosen as the absorbing boundary in numerical simulation of GPR.But CPML(convolutional perfect match layer) appr...The absorbing boundary is the key in numerical simulation of borehole radar.Perfect match layer(PML) was chosen as the absorbing boundary in numerical simulation of GPR.But CPML(convolutional perfect match layer) approach that we have chosen has the advantage of being media independent.Beginning with the Maxwell equations in a two-dimensional structure,numerical formulas of finite-difference time-domain(FDTD) method with CPML boundary condition for transverse electric(TE) or transverse magnetic(TM) wave are presented in details.Also,there are three models for borehole-GPR simulation.By analyzing the simulation results,the features of targets in GPR are obtained,which can provide a better interpretation of real radar data.The results show that CPML is well suited for the simulation of borehole-GPR.展开更多
As a highly efficient absorbing boundary condition, Perfectly Matched Layer (PML) has been widely used in Finite Difference Time Domain (FDTD) simulation of Ground Penetrating Radar (GPR) based on the first order elec...As a highly efficient absorbing boundary condition, Perfectly Matched Layer (PML) has been widely used in Finite Difference Time Domain (FDTD) simulation of Ground Penetrating Radar (GPR) based on the first order electromagnetic wave equation. However, the PML boundary condition is difficult to apply in GPR Finite Element Time Domain (FETD) simulation based on the second order electromagnetic wave equation. This paper developed a non-split perfectly matched layer (NPML) boundary condition for GPR FETD simulation based on the second order electromagnetic wave equation. Taking two-dimensional TM wave equation as an example, the second order frequency domain equation of GPR was derived according to the definition of complex extending coordinate transformation. Then it transformed into time domain by means of auxiliary differential equation method, and its FETD equation is derived based on Galerkin method. On this basis, a GPR FETD forward program based on NPML boundary condition is developed. The merits of NPML boundary condition are certified by compared with wave field snapshots, signal and reflection errors of homogeneous medium model with split and non-split PML boundary conditions. The comparison demonstrated that the NPML algorithm can reduce memory occupation and improve calculation efficiency. Furthermore, numerical simulation of a complex model verifies the good absorption effects of the NPML boundary condition in complex structures.展开更多
基金Project(41174061) supported by the National Natural Science Foundation of ChinaProject(2011QNZT011) supported by the Free Exploration Program of Central South University,China
文摘The absorbing boundary is the key in numerical simulation of borehole radar.Perfect match layer(PML) was chosen as the absorbing boundary in numerical simulation of GPR.But CPML(convolutional perfect match layer) approach that we have chosen has the advantage of being media independent.Beginning with the Maxwell equations in a two-dimensional structure,numerical formulas of finite-difference time-domain(FDTD) method with CPML boundary condition for transverse electric(TE) or transverse magnetic(TM) wave are presented in details.Also,there are three models for borehole-GPR simulation.By analyzing the simulation results,the features of targets in GPR are obtained,which can provide a better interpretation of real radar data.The results show that CPML is well suited for the simulation of borehole-GPR.
文摘As a highly efficient absorbing boundary condition, Perfectly Matched Layer (PML) has been widely used in Finite Difference Time Domain (FDTD) simulation of Ground Penetrating Radar (GPR) based on the first order electromagnetic wave equation. However, the PML boundary condition is difficult to apply in GPR Finite Element Time Domain (FETD) simulation based on the second order electromagnetic wave equation. This paper developed a non-split perfectly matched layer (NPML) boundary condition for GPR FETD simulation based on the second order electromagnetic wave equation. Taking two-dimensional TM wave equation as an example, the second order frequency domain equation of GPR was derived according to the definition of complex extending coordinate transformation. Then it transformed into time domain by means of auxiliary differential equation method, and its FETD equation is derived based on Galerkin method. On this basis, a GPR FETD forward program based on NPML boundary condition is developed. The merits of NPML boundary condition are certified by compared with wave field snapshots, signal and reflection errors of homogeneous medium model with split and non-split PML boundary conditions. The comparison demonstrated that the NPML algorithm can reduce memory occupation and improve calculation efficiency. Furthermore, numerical simulation of a complex model verifies the good absorption effects of the NPML boundary condition in complex structures.
