随机等效介质探地雷达探测技术和参数反演
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摘要
探地雷达（GPR）作为一种重要的地球物理探测方法，广泛应用于工程地球物理、水文地质探测、冰川探测、极地考察、月球探测等工程与科学研究领域。它以介质的电性参数（主要包括介电常数、电导率和磁导率）差异为基础实现对目标界面和目标体形态、位置等表面特征探测。随着探地雷达以及其它地球物理勘探方法研究的不断深入，探测目标不仅需要获得介质的形态信息，还需要获得介质的内在组分、参数分布以及地质属性参数如含水量、孔隙度，渗透率等本征属性信息。在传统的理论研究中多以均匀介质电性参数为主，但在实际探测中，探测目标以及背景介质往往是随机非均匀分布的，建立描述复杂介质目标属性参数分布的随机介质模型，既能反映介质的微观变化，同时又能体现出宏观性质。在此基础上，将探测目标的物性参数与地质参数联系在一起，开展随机介质探地雷达探测技术和参数反演研究是实现探地雷达属性探测的关键问题。
本文首先建立了基于混合型自相关函数并加入椭圆方程随机干扰的三维多尺度随机介质模型和基于Hanai–Bruggeman和Maxwell–Garnett耦合方程的多参数耦合随机介质模型；根据孔隙度数据推导得到对应耦关系的介电常数和电导率耦合介质模型。两种随机介质模型分别从介质的多尺度非均匀性和多参数耦合性刻画了实际探测目标介质的分布特征。
在此基础上，推导并实现了适合于随机介质模型探地雷达数值模拟计算的高精度有限差分方法。根据随机介质参数的非均匀性和多尺度性，本文提出了以下两种差分计算方法：1）递归积分的复频移完美匹配层吸收边界条件（CFS-RIPML）的三维高阶有限差分方法。该方法对隐失波、晚时反射以及低频波等常规PML, UPML边界无法吸收电磁波有很好的吸收效果。递归积分技术无需场分裂，能有效改善复频移技术中间变量多、内存占用大等问题，提高了计算效率。采用高阶有限差分方法相比常规二阶中心差分有更高的计算精度；2）基于变换光学（Transform Optics）的非均匀网格有限差分方法。该方法的主要思想是基于物质结构参数变化而导致电磁场的传播不变性，在连续与平滑的任意坐标变换之下，Maxwell方程式的形式可以维持不变，而让介电常数与磁导率的表达式变得很复杂。通过这种方式可以虚拟地扩大目标体所占的网格节点数目，并且不增加模型空间的网格数量。这样的网格划分方式可以提高目标的模拟计算精度，同时也保证了计算效率。本文还对比了该方法与常规有限差分，粗细网格交错的亚网格有限差分，渐变非均匀网格有限差分各自的计算效果和适用条件。
除了常规主动源探地雷达探测模式，本文将被动源干涉技术应用到探地雷达探测。该方法的主要思想是利用地下以及空气中的随机电磁噪声源信号进行长时间的记录，然后将得到的数据通过互相关（Cross-correlation）或多维反褶积（Multideconvolution）等方法分离提取目标信号。通过开展地下随机介质目标被动源探地雷达干涉数值模拟计算，实现了被动源目标成像和监测，取得了较好的应用效果。
地球物理反演方法获得的结果只是反映目标属性的间接参数，如介电常数，电导率，波速等。在数据综合解释时，需要参考更多的水文地质资料，地球物理探测技术一直扮演着一种技术手段的角色。如何从探测结果获得更多反映介质本身属性的地质参数是地球物理探测方法研究的关键科学问题。为获得复杂随机介质准确的物性参数，本文开展了有限带宽阻抗反演和蒙特卡洛随机参数反演方法并分别应用于地面探地雷达和井中雷达随机介质模型和实测数据参数反演。对于随机介质，常规反演方法如最小二乘方法存在圆滑程度较高，分辨率低，无法分辨局部细节信息。相对而言，随机反演方法具有更高的目标分辨率，对随机介质目标的细节信息反映更为清晰，反演精度较高，反演误差小。根据耦合方程可以获得高精度的孔隙度，含水量等反映目标本征属性的地质参数。
综上所述，本文在建立随机等效介质模型的基础上，开展高精度有限差分的探地雷达主动源和被动源探测的数值模拟计算，实现了随机介质探地雷达探测和参数反演。随机等效介质模型可以精确描述复杂目标属性，建立目标物性参数与水文地质参数耦合关系。采用CFS-RIPML吸收边界的三维高阶有限差分和变换光学的非均匀有限差分，为随机介质模型计算提供了高精度和高效率数值计算方法。被动源干涉探地雷达探测模式，丰富拓展了探地雷达探测方法技术。随机反演和阻抗反演方法为随机介质目标成像以及参数估计提供了高精度的方法技术。本文从随机介质模型，数值模拟计算，探测模式以及目标参数反演四个方面建立了完整的随机等效介质探地雷达探测研究方法技术。不仅能准确获取目标体的电性参数，还能反演目标的本征地质参数和分布规律，为实现从常规目标形态位置探测到复杂目标介质内在属性探测转变提供了完整的科学技术手段。本文的研究成果在其它科学领域，例如浅地表目标属性分析，深部矿产资源，地热源开发以及极地冰川探测，月球探测等方面都提供了重要的技术手段，具有重要的科学研究价值。
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.
本文首先建立了基于混合型自相关函数并加入椭圆方程随机干扰的三维多尺度随机介质模型和基于Hanai–Bruggeman和Maxwell–Garnett耦合方程的多参数耦合随机介质模型；根据孔隙度数据推导得到对应耦关系的介电常数和电导率耦合介质模型。两种随机介质模型分别从介质的多尺度非均匀性和多参数耦合性刻画了实际探测目标介质的分布特征。
在此基础上，推导并实现了适合于随机介质模型探地雷达数值模拟计算的高精度有限差分方法。根据随机介质参数的非均匀性和多尺度性，本文提出了以下两种差分计算方法：1）递归积分的复频移完美匹配层吸收边界条件（CFS-RIPML）的三维高阶有限差分方法。该方法对隐失波、晚时反射以及低频波等常规PML, UPML边界无法吸收电磁波有很好的吸收效果。递归积分技术无需场分裂，能有效改善复频移技术中间变量多、内存占用大等问题，提高了计算效率。采用高阶有限差分方法相比常规二阶中心差分有更高的计算精度；2）基于变换光学（Transform Optics）的非均匀网格有限差分方法。该方法的主要思想是基于物质结构参数变化而导致电磁场的传播不变性，在连续与平滑的任意坐标变换之下，Maxwell方程式的形式可以维持不变，而让介电常数与磁导率的表达式变得很复杂。通过这种方式可以虚拟地扩大目标体所占的网格节点数目，并且不增加模型空间的网格数量。这样的网格划分方式可以提高目标的模拟计算精度，同时也保证了计算效率。本文还对比了该方法与常规有限差分，粗细网格交错的亚网格有限差分，渐变非均匀网格有限差分各自的计算效果和适用条件。
除了常规主动源探地雷达探测模式，本文将被动源干涉技术应用到探地雷达探测。该方法的主要思想是利用地下以及空气中的随机电磁噪声源信号进行长时间的记录，然后将得到的数据通过互相关（Cross-correlation）或多维反褶积（Multideconvolution）等方法分离提取目标信号。通过开展地下随机介质目标被动源探地雷达干涉数值模拟计算，实现了被动源目标成像和监测，取得了较好的应用效果。
地球物理反演方法获得的结果只是反映目标属性的间接参数，如介电常数，电导率，波速等。在数据综合解释时，需要参考更多的水文地质资料，地球物理探测技术一直扮演着一种技术手段的角色。如何从探测结果获得更多反映介质本身属性的地质参数是地球物理探测方法研究的关键科学问题。为获得复杂随机介质准确的物性参数，本文开展了有限带宽阻抗反演和蒙特卡洛随机参数反演方法并分别应用于地面探地雷达和井中雷达随机介质模型和实测数据参数反演。对于随机介质，常规反演方法如最小二乘方法存在圆滑程度较高，分辨率低，无法分辨局部细节信息。相对而言，随机反演方法具有更高的目标分辨率，对随机介质目标的细节信息反映更为清晰，反演精度较高，反演误差小。根据耦合方程可以获得高精度的孔隙度，含水量等反映目标本征属性的地质参数。
综上所述，本文在建立随机等效介质模型的基础上，开展高精度有限差分的探地雷达主动源和被动源探测的数值模拟计算，实现了随机介质探地雷达探测和参数反演。随机等效介质模型可以精确描述复杂目标属性，建立目标物性参数与水文地质参数耦合关系。采用CFS-RIPML吸收边界的三维高阶有限差分和变换光学的非均匀有限差分，为随机介质模型计算提供了高精度和高效率数值计算方法。被动源干涉探地雷达探测模式，丰富拓展了探地雷达探测方法技术。随机反演和阻抗反演方法为随机介质目标成像以及参数估计提供了高精度的方法技术。本文从随机介质模型，数值模拟计算，探测模式以及目标参数反演四个方面建立了完整的随机等效介质探地雷达探测研究方法技术。不仅能准确获取目标体的电性参数，还能反演目标的本征地质参数和分布规律，为实现从常规目标形态位置探测到复杂目标介质内在属性探测转变提供了完整的科学技术手段。本文的研究成果在其它科学领域，例如浅地表目标属性分析，深部矿产资源，地热源开发以及极地冰川探测，月球探测等方面都提供了重要的技术手段，具有重要的科学研究价值。
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.
引文
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