The Study Of GPR Response Modeling In Dispersive Medium

As a high-resolution geophysical exploration method, GPR has been widely applied in engineering problems. Ground-penetrating radar electromagnetic wave is transmitting in the ground lossy medium, so there is a high frequency attenuation and dispersion phenomena. There are certain relationships between media electrical parameters and frequency. It indicates that physical characters change with the frequency. It is a more important issue in ground-penetrating radar application. In this paper, we analyzed the relationships between medium electric characters and frequency of the external field, including media polarization, dielectric relaxation and medium frequency dispersion. In external electric field, the polar molecules turn along the direction of electric field. Due to the large inertia, it takes a long time to build around for dipole's turn. In particular, the role of high-frequency electric field, the orientation of electric field poling lag behind changes in polarization process is slow; it is generally believed that it caused frequent casual factors. In previous studies, we can not consider the dispersion in the frequency range of 100-500MHz. But with the development of ground-penetrating radar and application in the lower frequency, the frequency dispersion phenomenon will be considered.In the past, some scholars put forward ideas to resolve the problem of dispersion, which is actually not a problem in seismic exploration. However, the elastic wave and electromagnetic waves have different characters, so the solution of electromagnetic wave frequency dispersion is very difficult. Radar and seismic wave are similar, now the radar data processing are mostly used seismic processing tools, including filtering, stacking technology. However, radar and seismic wave, in essence, is a distinction, which reflects the radar exploration process, the attenuation of high-frequency components is very serious. With the spread of time, the dispersion is also becoming very significant. On the images showed that with the increase of depth, follow-up wavelet progressively wider range decreases and images become blurred, resolution becoming decline. The existence of dispersion not only affects the interpretation, but also has great constraints for other steps.The high frequency electromagnetic wave will be significantly weakened in dispersive medium. In order to simulate the electrical medium properties with frequency changes in the frequency dispersion characteristics, predecessors made many media characterization of the nature of this dispersion model, Cole-Cole model of complex resistivity method has been widely used for the low-frequency rock mineral exploration. In high frequency, we apply the complex permittivity formula on the one-dimensional simulation using Cole-Cole model. Cole-Cole formula is based mainly on character between the complex permittivity and the angular frequencies of electric field. The high-density sampling filter, mainly by adjusting parameters and select sampling intervals calculated filter coefficient to achieve rapid Hankel transform for the electric dipole response. Selection criteria meet the fast calculation speed and high precision. In the traditional electromagnetic sounding theory, the sampling interval is ln10/10; this can not meet the radar frequency range of precision. By adjusting parameters M and setting sampling interval to ln10/100, below 300MHz frequency, it belongs to the scope of the low frequency radar scope. The layered one-dimensional simulation and Xiong and Tripp's result are similar. The results are better. Meanwhile, the model of simulated soil water content also reflects the medium frequency dispersion effects.Two-dimensional simulation based on Debye equation finite difference time domain algorithm. Debye equation provides a dielectric permittivity of the frequency change with the changing macroeconomic trends. It is not only the realized the complex permittivity on the mathematical expression of the real and imaginary parts in the frequency domain decomposition, under a qualitative, but also demonstrated their respective contributions under the very high frequency and static dielectric constant in the external alternating electric field.(Finite Difference Time Domain: FDTD) is a method directly solving the Maxwell rotation equation computer simulation, bring by K.S.Yee in the middle of 1960. It is suitable for analyzing transient response, also need small amount of memory and less computing time. FDTD simulation of the electromagnetic nature is that the space is based on the parameters of space given to the grid, only to the corresponding point of media space parameters; we can simulate the electromagnetic complex structure. This paper presents a solution to the loss FDTD formula, using perfectly matched boundary conditions, from single relaxation time of Debye formula. We made a soil rectangular hollow rotundity model with numerical simulation and extraction of single-channel model in the cent results, and studied the soil attenuation of electromagnetic waves in Debye equation. Combining 2-D images, the results reflect the medium dispersion effect on the attenuation of electromagnetic wave.Ground-penetrating radar has high detecting resolution. But high-frequency electromagnetic wave attenuation limited the detecting depth. To increase the depth detection, the development and application of low frequency ground penetrating radar will become important. Because of the lower and broadband frequencies, the medium frequency dispersion effects will be greatly influenced the results and the accuracy of detection, so we have to consider it. In this paper the numerical simulation technology for the research direction is referenced. This algorithm is to be extended to two-dimensional and three-dimensional simulation of the space. It will be the future work, and also associated with the anti-test algorithm and a complete numerical calculation procedure, and other studies.