Simulation And Inversion Study Of Electromagnetic Response Of Electromagnetic Detection In Wide Frequency Band In 1-D Dispersive Media

The wideband GPR method is the one represent of the high-frequency electromagnetic technique and it uses high-frequency radio wave to determine the distribution of the material in the medium. It was used widely in shallow exploration by its advantages of high precision, lossless and convenient. Because of transmitting frequency of the traditional GPR is usually very high( Hz), the detecting depth of the GPR is shallow and sometimes is about a few to more than ten meters. So the shallow detecting depth is always the one limiting factor to the high-frequency electromagnetic technique and on many situations it can't meet the widely requirement of the detection. By the new research, we hope we can ensure the high detection accuracy and at the same time we also can make deep detection. So more and more people pay more attention to the study and the application of the medium and high frequency bands electromagnetic field. In this paper we choose the response of GPR electromagnetic field which frequency scope is about hundreds KHz to hundreds MHz as the research object to research the simulation and inversion of electromagnetic response of electromagnetic detection in wide frequency band in 1D media. The reason that we choose the GPR as the 10 6? 109 research object is mainly because of the GPR can satisfy us frequency band requirement, and it has the more wide frequency band and the high resolution and also it is the commonly used shallow exploration method and has the widely development prospect.On the other hand, in the practical application of this frequency band, the media which detected by the GPR is always has the dispersion property, so it can cause the changes of electrical parameters, such as the conductivity or the permittivity, and so on when the GPR waves penetrated in the media. And these changes can cause the pulse wavelet wide, the distortion of the waveform or the serious attenuation. These can influence the precision of the response and also make the interpretation is very difficulty. So we can't neglect the influence of the dispersion and in the research of this paper, we must consider the dispersion. Therefore the calculation of this paper need the expression which can embody the electrical parameter is the function of the frequency. Because of the GPR is mainly detect the medium permittivity, I choose the permittivity model of dispersion to make the simulation. When we simulated the response in the different mediums, we use the different models as follows:①Debye function;②Cole-Cole model;③Jonscher model.In the simulation, because of the high frequency of traditional GPR, we usually only consider the displacement current and neglect the transmission current. But in this paper, the frequency is lower than traditional GPR's, so both the current should be considered together. By this reason we deduced the electric field equation of GPR anew as follows: So we can see, the core problem of the electric field response simulation of 1D layered medium is the calculation of the Hankel transforms which contain the Bessal function in the analytical expression. The calculation method is various, such as linear filter method, numerical integration algorithm, Chebyshev polynomial method, a contour integral method, and so on. Because the Hankel transform which is between 0 to infinite interval can be equivalent the integral summation between the the zero points of Bessal function ,so we can calculate the electric field equation by calculating the integral summation between the zero points of Bessal function. There we use the Guass numerical integration algorithm of Alan D.Chave. Although speed of this method is lower than linear filter method, it has higher precision in the frequency field and also it can make up the large error caused by the kernel function oscillation in the high frequency. Moreover because of the Bessal function oscillation, the series forms changed too and the result may be very slowly convergent and even will diverge. So we use continued fraction algorithm which can compensate the slowness of the integration algorithm.By the simulation calculation we can conform that when we didn't consider the dispersive case no matter we use which permittivity model, the reflected wave and refracted wave from every reflection interface can be distinguish very clearly; But when we considered the dispersion, the wavelet became board gradually and amplitude of the reflected waves decayed very seriously even no response along with the offset increase, and the waveform seriously distorted that caused the resolution reduced. All above the cases embody the dispersive effect to the electric field response very well.In the inversion, we used Marquette damped least square method to inverse the resistivity , the permittivity and the depth of the subsurface. In order to improve the inversion efficiency, we introduced Guass numerical integration algorithm of Alan D.Chave to the inversion response calculation. To the Cole-Cole model case in the simulation, the main inversion parameters are media resistivity(nondispersion), optical dielectric constantsε∞, static dielectric constantεsand the media thickness. We applied inversion to homogeneous half-space, two-layer and three-layer media mode. The frequency range was from 0.5 to 250MHz. There were 129 frequency points distributed in the frequency band symmetrically. We use the simulation data which calculated by the Guass numerical integration algorithm of Alan D.Chave as the observation data and use the aboved Marquette damped least square inversion method to inverse the parameters. In addition, in this paper we also did the inversion to electric field response which simulated by the Debye model and the Jonscher model.Form the result of the inversion we can see, the simulation of this paper is correct and the inversion is feasible. The inversion is not only the verification to the simulation method, but also these inversion results will provide the basic for high accuracy engineering and environmental geophysical exploration. In the inversion, because of the lacking information ,some inversed parameters were large and this can be solved by increasing the transceiver distance or increasing the information by extending the range of the frequency.Full of all, this paper provide basic research for the simulation and inversion of GPR electromagnetic field in the dispersive condition which the frequency is from 0.5MHz to 250MHz and aslo for the lower frequency and high accuracy GPR exploration.