Ground Penetrating Radar Detection And Parameter Inversion In Stochastic Effective Medium

Ground penetrating radar (GPR), as an important geophysical explorationmethod, has been widely applied in the near-surface geophysics, hydrology, glaciers,polar exploration and the lunar probe. It is based on the difference of mediumelectrical parameters which includes dielectric constant and conductivity to detect thetarget’s shape, postion, distribution and other characteristic information. As thedevelopment of GPR and other geophysical method, more and more people focus ondetecting target medium composition, distribution characteristics and geologicalproperties parameters such as water content, porosity, permeability, etc. Thetraditional medium electrical parameters of the model are too simple to express therelationship between the electrical parameters and geological parameters. Building thestochastic media model which expresses the complex dielectric constant of complexmedia accurately can not only reflect the micro medium change but also can reflectthe nature of the macro, and is closely linked to the geological property. On this basis,study of GPR detection and parameter inversion based on the stochastic effectivemedia is the key research work to improving the interpretation precision of GPRmethod and expanding its application.In this paper, firstly, we use the hybrid autocorrelation function to join the localrandom ellipse interference and Bruggeman-Hanai and Garnett-Maxwell equations tobuild the multiscale3D stochastic media and multiple parameter stochastic couplingmedia model, respectively. We can obtain the dielectric constant and conductivitymedia model according to the coupling relationship between dielectric constant,conductivity parameters and the hydrogeological parameters, such as moisture contentand porosity. We study the distribution features and describe the complex randomproperty of the random media from the perspective of multi-scale heterogeneity andmultiple parameters coupling relationship.Based on this, we have carried out stochastic media model numerical simulationwith high-accuracy finite difference time domain (FDTD) method. Two types ofFDTD methods are introduced.1) The first one is the3D high order FDTD withCFS-RIPML boundary. Compared with perfectly matched layer (PML) and UPMLboundary, the CFS-RIPML boundary can absorb the evanescent wave, night timereflection and low frequency wave effectively. Besides, the recursive integral (RI)technology does not need spilt electromagnetic component, and thus can effectivelyreduce the complex frequency shift (CFS) technology intermediate variable, save memory and improve the computational efficiency. In addition, the high order finitedifference (FD) grid has higher accuracy than the traditional two order FD.2) Thesecond method is the Transform Optics FDTD (TO-FDTD) method. The main idea ofthis method is to use the coordinate to transform the thoughts, and change theelectromagnetic field under rectangular coordinate system by grid distribution to anon-orthogonal grid pattern. In this way we can expand virtual target grid nodenumber of the body, and do not need to increase the number of grid of whole modeldomain. It can improve the simulation accuracy of the goal and ensure the calculationefficiency without increasing the overall number of grid. It can decrease the grid scaleand minimize numerical calculation error. At the same time, we also compared thismethod with the standard FDTD, non-uniform FDTD, adaptive mesh refinement(AMR) FDTD with different test model.The traditional GPR uses active source detection mode. Here, we apply thepassive interferometry source technology into GPR detection. The main idea of thismethod is to use the noise source in the air or subsurface for long-time signalacquisition, and then extract the observation data by cross-correlation (CC) ormultidimensional deconvolution (MDD) methods. In this paper, we mainly carry outpassive interferometry source GPR numerical simulation. It can obtain high resolutionimaging result in multi-scale random media model with the passive interferometryGPR method.The geophysics invesion can obtain only the target’s indirect parameters, such asthe dielectric constant and conductivity. During data interpretation, we pay moreattention to the hydrology and geology parameter. The geophysics method is only as atool to service the other work. How to evaluate and assess object’s intrinsic physicalparameters is the purpose of geophysics inversion research work. In order to providesteady effective inversion parameters of underground random media, we presented theband-limited impedance inversion and stochastic inversion based on Monte Carlosampling algorithm and applied them in surface GPR and bore-hole radar parameterinversion with synthetic data and real measured data. For stochastic media, theconventional LSQR inversion method has high smooth degree, low resolution and it isunable to distinguish local details of target. The stochastic inversion method hashigher resolution and reflects the detailed information and the inversion error is alsolow. This method is more suitable for random media so as to improve the inversionaccuracy. We can also obtain the high accuracy prosity, water content and otherhydrology and geology parameters according to the Geophysics-hydrogeololgycoupling equations.In conclusion, in this paper, we have built the3D multi-scale random mediamodel and multi-parameter coupling stochastic media model according to the hybridautocorrelation function and Geophysics-hydrogeololgy coupling equations. Then,combining with the high accuracy numerical method, we carry out the active and passive GPR detection modes with different stochastic media models to analyze thedetection feasibility of GPR in complex random media. On this basis, we carry out therandom media inversion and parameter estimation with stochastic inversion method.This article mianly consists of four parts: build stochastic medium model, derive highaccuracy numerical simulation algorithm, study passive interferometry detectionmode and carry out stochastic paprameter inversion methods. The stochastic mediamodel can accurately describe the complex target attributes and establish the couplingrelationship between the target geophysical parameters and the hydrogeologicalparameters. High-accuracy FDTD method has provided accuracy and stablecalculation method for the stochastic media model simulation. Stochastic inversionand impedance inversion method has provided a great technical support for therandom media model parameter estimation and imaging. Through inversion method,we not only obtain the electrical parameters of the geologic body but also reflect theintrinsic geological parameters and distribution. The research results will be able topromote the development of GPR method, improve the detection and interpretationaccuracy of GPR, as well as other geophysical methods. Our research results providescientific methods for other research area, such as target property detection in nearsurface, the deep mine and geothermal exploration, plar region detection and lunarprobe.