Abstract
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.
Highlights
Numerical modeling of ground penetrating radar (GPR) is an important means to study high-frequency electromagnetic wave detection, which plays a critical role in theoretical research of electromagnetic wave propagation in underground structures and guiding for processing and interpretation of actual data [1]
The Perfectly Matched Layer (PML) boundary condition is difficult to apply in Ground Penetrating Radar (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
Summary
Numerical modeling of ground penetrating radar (GPR) is an important means to study high-frequency electromagnetic wave detection, which plays a critical role in theoretical research of electromagnetic wave propagation in underground structures and guiding for processing and interpretation of actual data [1]. Basu et al [53] [54] proposed a non-split PML boundary condition suitable for second-order elastic wave FETD forward modeling with high calculation accuracy and great improvement in calculation efficiency. The PML boundary condition based on second-order wave equations has been widely used in FETD numerical modeling of acoustic wave [55] [56] [57], elastic wave [50] [52] [58] [59] and surface wave [60], and has been continuously developed [61] [62]. We give the computation format of FETD in time domain by using Galerkin approximation technique and develop the FETD forward modeling algorithm of second-order GPR wave equation based on the non-split PML boundary condition. Letting (∂t + dx ) E z,=2 P x , ∂t + d y E z,=4 P y , the second and fourth equations in Equation (9) can be rewritten as: μσ t
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