Research Article | DOI: https://doi.org/
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Copyright: © 2019 JunLing Bu. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Received: 30 November -0001 | Accepted: 30 November -0001 | Published: 30 November -0001
Keywords: GPR; CPML; symplectic algorithm; simulation model
Complex frequency shift perfectly matched layer has good absorption effect for litter wave and lost wave in long time domain calculation and is widely used in finite difference time domain simulation. In this paper, Convolution perfectly matched layer (CPML) is applied to symplectic algorithm to simulate Ground-penetrating radar (GPR) electromagnetic wave propagation in underground structure. Transverse Magnetic (TM) wave is taken as an example. A symplectic algorithm based on CPML boundary is deduced. A simple example is given to verify that CPML has a good absorption effect. Finally, a two-dimensional GPR profile is obtained by simulating the propagation of GPR electromagnetic wave in a complex geoelectric model. The results show that the symplectic algorithm based on CPML boundary conditions can effectively reduce the boundary reflection error and realize forward simulation of arbitrary complex irregular models.
Ground penetrating radar (GPR) is the most widely used nondestructive testing method for highway, railway and tunnel structures [1]. The detection principle is that the electromagnetic pulse is generated by the transmitting antenna and transmitted to the underground structure. When the electromagnetic wave meets the interface between the underground target and the medium, it scatters, diffracts and reflects. The reflected signal is received by the receiving antenna. Through the inversion analysis of the echo signal, the depth of the underground target and the thickness of the structure layer can be obtained. Accurate and efficient forward numerical model is the key to improve the inversion accuracy and speed.
At present, the forward modeling methods of ground penetrating radar mainly include finite element method [2], ray tracing method [3], finite difference time domain (FDTD) [4], alternating direction implicit FDTD (ADI-FDTD) [5], symplectic algorithm [6]. Although these methods can simulate the propagation of ground penetrating radar electromagnetic waves in underground structures, there are still some shortcomings in the calculation efficiency in practical engineering applications. For example, the finite element method is suitable for solving complex boundary conditions, but its computational program is complex, the solution time is long, and the pseudo-solution phenomenon may occur. FDTD method is the most widely used electromagnetic wave simulation method for ground penetrating radar at present, but its computational efficiency is limited by Courant-Friedrichs-Lewy (CFL) stability conditions, symplectic algorithm is used. Computational efficiency is improved compared with FDTD [7].
In the forward model of ground penetrating radar (GPR), absorbing boundary conditions need to be loaded at the boundary of the computational domain to prevent electromagnetic waves from reflecting at the boundary. In this paper, the CPML boundary suitable for symplectic algorithm is derived, and an accurate and efficient numerical model of ground penetrating radar (GPR) electromagnetic wave propagation in complex lossy underground structures is established. The effectiveness of the algorithm is verified by the numerical model of two-layer pavement structure.
A special Hamilton system can be expressed as:
Figure 1. schematic diagram of the distribution of field component U at different times.
Numerical Simulations
Firstly, the validity and accuracy of the algorithm are verified by the two-layer pavement model shown in Figure 2. The first layer represents asphalt concrete, the second layer represents cement stabilized macadam, all materials are considered nonmagnetic. Specific model size and material parameters are selected as shown in Figure 2. The time step and spatial increment are dt = 0.005 ns and Δx = Δy = 0.25 cm, respectively. In this model, the Ricker wave of 1.0 GHz central frequency (Figure 3) is used to represent the excitation source. Figure 4 is the calculation result of the field value U component at the node (24 cm, 100 cm) simulated by symplectic algorithm based on CPML boundary. The calculation results show that the pavement layers can be clearly seen.
In this paper, a ground penetrating radar wave propagation model in two-dimensional lossy media is established based on CPML boundary symplectic algorithm. The accuracy and validity of CPML-based boundary symplectic algorithm are verified by an example of a damaged pavement model. The results show that the CPML boundary symplectic algorithm can effectively simulate GPR electromagnetic wave propagation in underground structures. The algorithm provides an accurate and efficient forward model for the next two-dimensional inversion.
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