| Ground penetrating radar (GPR) is an important shallow layer geophysical exploration method which detects the underground structure and the distribution law. The GPR numerical simulation is one of the most significant subjects in the GPR research. The GPR numerical simulation result can help us to work outside and data processing and geologic interpretation of radar data. Currently, the methods of GPR forward simulation are ray tracing method, finite difference time domain method (FDTD) and finite element method (FEM). The finite element method superiority manifests in the simulation of the complex model. So the FEM is used to GPR numerical simulation in this paper.The paper was funded by a joint support of the National Natural Science Fund "The research of GPR' s forward modeling and migration based on finite element of wavelet" (40804027),"The complex GPR element-free method forward simulation and multi-parameter hybrid intelligent optimization inversion"(41074085) and the Hunan province natural fund important project(09JJ3084). The main content of this paper is as follows:1. The FEM wave equation method was derived from the Maxwell system of equations. The process of the derivation about the differential coefficient equation which was solved by the Galerkin method was elaborated, such as how to calculate the mass matrix, the attenuation coefficient matrix, the stiffness matrix, the method of disposing the source, in order to transform the GPR finite element equation to system of linear equations uesing difference to instead of the differential coefficient, etc.2. The method to storage the large-scale sparse matrix was introduced. The Biconjugate Gradient Stabilized (BICGSTAB) algorithm based on the LU incompletely decomposition technology was introduced to solve the large linear systems. The rules of the time step and gridding step which are influence the numerical value stability were given out, discussed the influence of the lumped mass matrix to solve the FEM equation and its advantages and disadvantages.3. The principle of the transmitting boundary condition which is based on transmission mechanism and the Sarma boundary condition which is based on attenuation mechanism were described in this paper. The formula of the two kinds of boundary condition which are used in GPR FEM forward simulation were derivated in detail. Through joined the transitional layer in the Sarma boundary condition to suppress the articicial reflection which is engendered from the interface between the medium area and the damping region. Taking the center electromagnetic pulse source model as example, compared the results of the two kinds of boundary condition.4. Considered the different theoretical mechanism of the transmitting boundary condition and the Sarma boundary condition, a mixed boundary condition which combined with the two kinds of boundary condition was given out in this paper. The main idea is the power of the GPR waves were attenuated by the Sarma boundary condition and then transmitted the residual energy by the transmitting boundary condition. And take the two-dimensional equal model entire wave field snapshot as the example, proved the effect of the mixed boundary condition better than just one kind of boundary condition.5. Compiled the 2D GPR forward simulation program which including the attenuation term or not. Defined the concept and the formula of the attenuation ratio. Through to simulate the attenuation medium and non attenuation medium models, explained the GPR waves transmit in the attenuation medium were absorbed by the medium and the frequency dispersion. Therefore, when the medium is attenuation medium, forward simulation must use the equation which including the attenuation term, obviously conforms to the actual situation of the GPR waves which disseminates in the underground medium. Finally, the results of the typical geoelectric structures can help us to understand the propagation law of GPR waves, so as to guide geologic interpretation of GPR data.
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