核磁共振2D/3D地下水成像方法及其阵列式地面探测系统研究
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摘要
地面核磁共振技术（MRS）在我国北方干旱和半干旱地区寻找地下水以及高效评价层状地下水资源等领域获得了广泛应用，然而，针对西南丘陵和喀斯特地区的裂隙水和岩溶水等复杂地下水探测，该方法仍存在成像精度低、探测分辨率低和工作效率低等问题。因此，发展新型的高精度核磁共振2D/3D地下水成像方法及高效高分辨率的地面MRS探测系统一直是该领域的迫切需求。本文针对国内外现有的同一线圈移动测量模式和分离线圈轮换测量模式的缺陷，首次提出了阵列线圈测量模式，仅用一次测量的结果就可代替分离线圈多次测量的结果，具有高效率，高分辨率和高覆盖率等优势。同时，针对裂隙水和岩溶水等非层状不均匀的复杂地下水，提出了高精度的2D和3D MRS含水量成像方法以及单弛豫和多弛豫时间T_2~*的2D成像方法。基于此，研制了具有多通道采集单元的阵列式地面MRS系统，最后给出了野外实验结果和应用实例。论文主要的研究工作及取得的成果如下：
1、针对1D MRS忽略的线圈方向角度，引入旋转角度矩阵，解决了任意线圈方向角度和地磁场角度变化下的MRS正演计算问题，并仿真分析了线圈方向角度对2D测量信号的影响。
2.针对现有2D MRS测量分辨率低和效率低的问题，提出快速高分辨率和高覆盖率的阵列线圈测量模式，借助奇异值分解（SVD）进行分辨率半径研究，发现阵列线圈一次测量就可实现2D高分辨率探测，长方形发射线圈和半覆盖型接收线圈组合是最优的测量模式。
3.针对目前3D测量效率低和覆盖面积有限的缺点，提出了阵列线圈对角线移动测量模式，探测分辨率显著优于同一线圈，用较少的测量次数可实现较大覆盖面积的高分辨率3D探测。
4.针对目前2D地下水成像方法中均匀网格数量大，成像精度低，以及算法不稳定等问题，提出了以分辨率半径为尺度函数的2D空间非均匀剖分方法，结合差异准则和L曲线的正则化参数双重选择方法，目标函数线性化及非约束空间转换的Jacobain变换方法，实现了基于MRS信号初始振幅的高精度2D含水量成像。
5.通过对2D复杂地下水模型的仿真和初始振幅反演，对比了阵列线圈、分离线圈和同一线圈3种测量模式的成像结果，在较低信噪比情况下，长方形阵列线圈半覆盖型测量模式同样具有较高的分辨率，与2D MRS分辨率理论分析结论一致。
6.针对基于MRS信号包络的QT反演中无法存储多弛豫灵敏度核函数的问题，提出了两种解决方法：一种是简化为单弛豫信号的2D QT反演，实现了含水量和弛豫时间T*2的双参数成像，成像结果更稳定；另一种是基于含水单元的2D Cell反演，实现含水量和多弛豫时间分布的同时成像。
7.针对目前基于均匀网格的3D含水量成像方法精度低和含水量误差大的问题，采用目标体和围岩区域不同密度的非均匀网格剖分，实现了基于MRS信号初始振幅的3D含水量成像方法，通过对仿真的复杂地下水模型和德国Einersberger湖的实测数据，验证了3D成像方法的高精度定位和定量效果。
8.根据现有单通道地面MRS系统的组成结构和问题，研发了适用于阵列线圈测量模式的接收单元和控制软件，通过改进快速消耗电路使死区时间由原来的38ms减小到15ms，改进信号调理电路和采集电路提高数据分辨率，采用一主多从的结构和手拉手的连接方式实现了高精度的同步控制和高速数据传输等关键技术，使阵列式地面MRS系统的技术指标与国际最先进的MRS仪器基本持平。
通过对以上内容的研究，完成了对核磁共振2D/3D地下水成像方法及其阵列式地面探测系统的研究，主要的创新工作在于：
首次提出的阵列线圈测量模式，一次测量可实现2D剖面高分辨率探测，对角线移动测量可以实现3D大覆盖面积的高分辨率探测，解决了传统MRS的测量效率低和分辨率低的问题。
提出了基于分辨率半径的地面MRS探测性能分析方法，对比得到长方形阵列线圈半覆盖型测量模式具有最优的探测分辨率，并根据分辨率半径实现了2D/3D空间的非均匀剖分，为实现地下水高精度成像提供了基础。
提出了差异准则和L曲线双重选择正则化参数，Jacobain变换实现目标函数线性化和非约束空间转换等算法，解决了目前反演算法不稳定、非线性和变量约束等问题，实现了2D/3D地下水高精度的含水量成像，不仅可以判断非层状不均匀含水构造的位置和规模，而且可以精确计算含水总量。
针对MRS信号包络的单弛豫和多弛豫特性，提出了含水量和单弛豫时间双参数成像的2D QT反演，反演结果更稳定；以及基于含水单元概念的Cell反演，实现多孔隙结构的含水构造含水量和多弛豫时间同时成像。
本文研究的地下水成像方法和地面MRS系统已在蒙古国Halatura铁矿地下水源探测、中国辽宁桓仁崔家村堤坝渗漏探测和安徽黄山阳台村滑坡稳定性探测等工程实践中得到应用，取得了理想的探测效果和地下水成像结果，验证了方法和系统的有效性和实用性。本文提出的地下水成像方法和阵列式地面MRS系统，将为我国西南地区及复杂地质环境下的2D/3D地下水探测，提供有力的技术支撑。
Magnetic Resonance Sounding (MRS or Surface NMR) is widely applied in the fielddetecting for groundwater exploration and high efficient evaluation of groundwater resourcesin arid and semi-arid regions of northern China. However, for the groundwater in thecomplicated geological condition, like fissure water in the bedrock and karst water in thesouthwest of China, MRS technology has many problems on low imaging precision, lowdetecting resolution and also low operating efficiency. Therefore, development of newhigh-precision2D/3D imaging method and high-resolution surface detection system has beenthe urgent demand in the field of MRS technology. Due to the defects of existed offsetmeasurement with coincident and separated loop, a new measurement with array loop isproposed in this thesis, which can replace the result of multiple measurements with separatedloops by only one measurement, and has the advantage of high-efficiency, high-resolutionand high-coverage. For the complicated groundwater in non-layered and non-uniform space,high-precision2D and3D imaging methods of water content as well as relaxation timeT*2are presented. On the basis of MRS imaging, array surface MRS system with multi-channelacquisition units is developed, and the results of field experiments and application cases aredescribed. The main research work and achieved results of this thesis are as follows:
1. As1D MRS ignores the direction angle of loop layout, I introduce the rotation anglematrix to solve the MRS forward calculation problem with arbitrary angles of loop directionand the geomagnetic field. Moreover, I analyze the influence of the loop profile directionangel in2D measurements by simulation models.
2. For the low resolution and efficiency of the existed2D measurements, I propose anarray loop configuration to carry out the fast and high-coverage measurement in2D profile.By analyzing the resolution radius, I conclude that array loop configuration can achieve2Dhigh-resolution detection by only one measurement, and the combination of rectangulartransmitter loop and half-over-lapping receiver loops is the optimal configuration.
3. For the low efficiency and limited coverage in3D measurement, I take advantageof the diagonal measurement with array loops, which significantly improves the resolution inrespect to the coincident loop. It can detect a large coverage area of3D groundwater in highresolution with a small number of measurements.
4. To the issues of large number meshes, low precision imaging and instability ofalgorithm, I propose a non-uniform mesh generation mouthed based on the resolution radius,combine with discrepancy principle and L-curve method to select the regularization parameter,and apply Jacobain transform in objective function linearization and non-constraint spaceconversion. Finally, the stability high-precision MRS imaging of2D water content is solvedby the initial value inversion (IVI).
5. By simulating and inverting a complicated groundwater model by IVI, I contrastimaging results of coincident, separated and array loop configurations, and find therectangular array loop in half-over-lapping measurement mode provides a high resolution of2D MRS even in the case of low signal-to-noise (SNR). The conclusion consists with thetheoretical analyses of2D resolution studies.
6. Due to the storage of2D sensitivity kernels with multi-relaxation process in QTinversion using complete envelop data, I offer two solutions. One is to simplify the kernel inmono-relaxation process, and the imaging with two parameters, water content and singlerelaxation time, is inverted. In addition, the inversion results are more stable than IVI. Theother is base on the2D water cell inversion, which can achieve the water content andmulti-relaxation times imaging.
7. For the low precision in the3D imaging based on uniform meshes and high-errorestimation of water volume, I use the non-uniform meshes with different density in the targetand the surrounding regions, and accomplish the3D water content imaging based on IVI. Thesummation and filed data from Einersberger Lake in Germany is tomography inverted inhigh-precision3D image, and the water volume is quantified with high accuracy.
8. According to the composition and defects of existing single-channel surface MRSsystem, I develop multi-channel receiver units and control software for array loopconfiguration. By improving the rapid consumption circuit, the dead time of system reducesfrom38ms to15ms, and the data resolution of acquisition circuit and the signal conditioningcircuit are also improved. The structure of master with multi-client and hand-by-handconnection is used to achieve the high-precision synchronization control and high-speed datatransmission. These key technologies make the new system to catch up the most advantageinstrument in the world. Based on the study of the above contents, I complete the development of2D/3D MRSgroundwater imaging method and its array surface detection system. The main innovation liesas follow:
The array loop configuration I proposed can achieve high-resolution profiledetection by one measurement in2D, and large coverage area detection by diagonaloffset measurement in3D, which solves the low-efficiency and low-resolutionproblem of traditional MRS measurement.
The resolution radius I proposed is useful for the evaluation method of surface MRSdetection, and after the contras, I find the rectangular array loop in half-over-lappingmeasurement mode provides the highest resolution in2D. Based on the resolutionradius, I also general the non-uniform meshes in2D and3D for high-precisionimaging.
I combine the regularization parameter selection methods with discrepancy principleand L-curve method and apply Jacobain transform in objective function linearizationand non-constraint space conversion to realize the stability high-precision MRSimaging of2D and3D water content by the initial value inversion (IVI).
To the single relaxation and multi-relaxation properties of MRS signal envelope, Iimprove the QT inversion and propose Cell inversion to image the water content andalso relaxation timeT*2.
The MRS imaging method and surface MRS system have been applied in engineeringpractice, like the groundwater source detection for Halatura iron ore in Mongolia, the damleakage detection in Huanren, Liaoning province of China, and the landslide stabilitydetection in Yantaicun Landsilde, Anhui province of China. The results of2D groundwaterimaging are consisting with the other geophysics methods, verifying the effectiveness andpracticality of the method and system. It provides a strong technical support for groundwaterexploration in southwest of China and complicated geological environment.
1、针对1D MRS忽略的线圈方向角度，引入旋转角度矩阵，解决了任意线圈方向角度和地磁场角度变化下的MRS正演计算问题，并仿真分析了线圈方向角度对2D测量信号的影响。
2.针对现有2D MRS测量分辨率低和效率低的问题，提出快速高分辨率和高覆盖率的阵列线圈测量模式，借助奇异值分解（SVD）进行分辨率半径研究，发现阵列线圈一次测量就可实现2D高分辨率探测，长方形发射线圈和半覆盖型接收线圈组合是最优的测量模式。
3.针对目前3D测量效率低和覆盖面积有限的缺点，提出了阵列线圈对角线移动测量模式，探测分辨率显著优于同一线圈，用较少的测量次数可实现较大覆盖面积的高分辨率3D探测。
4.针对目前2D地下水成像方法中均匀网格数量大，成像精度低，以及算法不稳定等问题，提出了以分辨率半径为尺度函数的2D空间非均匀剖分方法，结合差异准则和L曲线的正则化参数双重选择方法，目标函数线性化及非约束空间转换的Jacobain变换方法，实现了基于MRS信号初始振幅的高精度2D含水量成像。
5.通过对2D复杂地下水模型的仿真和初始振幅反演，对比了阵列线圈、分离线圈和同一线圈3种测量模式的成像结果，在较低信噪比情况下，长方形阵列线圈半覆盖型测量模式同样具有较高的分辨率，与2D MRS分辨率理论分析结论一致。
6.针对基于MRS信号包络的QT反演中无法存储多弛豫灵敏度核函数的问题，提出了两种解决方法：一种是简化为单弛豫信号的2D QT反演，实现了含水量和弛豫时间T*2的双参数成像，成像结果更稳定；另一种是基于含水单元的2D Cell反演，实现含水量和多弛豫时间分布的同时成像。
7.针对目前基于均匀网格的3D含水量成像方法精度低和含水量误差大的问题，采用目标体和围岩区域不同密度的非均匀网格剖分，实现了基于MRS信号初始振幅的3D含水量成像方法，通过对仿真的复杂地下水模型和德国Einersberger湖的实测数据，验证了3D成像方法的高精度定位和定量效果。
8.根据现有单通道地面MRS系统的组成结构和问题，研发了适用于阵列线圈测量模式的接收单元和控制软件，通过改进快速消耗电路使死区时间由原来的38ms减小到15ms，改进信号调理电路和采集电路提高数据分辨率，采用一主多从的结构和手拉手的连接方式实现了高精度的同步控制和高速数据传输等关键技术，使阵列式地面MRS系统的技术指标与国际最先进的MRS仪器基本持平。
通过对以上内容的研究，完成了对核磁共振2D/3D地下水成像方法及其阵列式地面探测系统的研究，主要的创新工作在于：
首次提出的阵列线圈测量模式，一次测量可实现2D剖面高分辨率探测，对角线移动测量可以实现3D大覆盖面积的高分辨率探测，解决了传统MRS的测量效率低和分辨率低的问题。
提出了基于分辨率半径的地面MRS探测性能分析方法，对比得到长方形阵列线圈半覆盖型测量模式具有最优的探测分辨率，并根据分辨率半径实现了2D/3D空间的非均匀剖分，为实现地下水高精度成像提供了基础。
提出了差异准则和L曲线双重选择正则化参数，Jacobain变换实现目标函数线性化和非约束空间转换等算法，解决了目前反演算法不稳定、非线性和变量约束等问题，实现了2D/3D地下水高精度的含水量成像，不仅可以判断非层状不均匀含水构造的位置和规模，而且可以精确计算含水总量。
针对MRS信号包络的单弛豫和多弛豫特性，提出了含水量和单弛豫时间双参数成像的2D QT反演，反演结果更稳定；以及基于含水单元概念的Cell反演，实现多孔隙结构的含水构造含水量和多弛豫时间同时成像。
本文研究的地下水成像方法和地面MRS系统已在蒙古国Halatura铁矿地下水源探测、中国辽宁桓仁崔家村堤坝渗漏探测和安徽黄山阳台村滑坡稳定性探测等工程实践中得到应用，取得了理想的探测效果和地下水成像结果，验证了方法和系统的有效性和实用性。本文提出的地下水成像方法和阵列式地面MRS系统，将为我国西南地区及复杂地质环境下的2D/3D地下水探测，提供有力的技术支撑。
Magnetic Resonance Sounding (MRS or Surface NMR) is widely applied in the fielddetecting for groundwater exploration and high efficient evaluation of groundwater resourcesin arid and semi-arid regions of northern China. However, for the groundwater in thecomplicated geological condition, like fissure water in the bedrock and karst water in thesouthwest of China, MRS technology has many problems on low imaging precision, lowdetecting resolution and also low operating efficiency. Therefore, development of newhigh-precision2D/3D imaging method and high-resolution surface detection system has beenthe urgent demand in the field of MRS technology. Due to the defects of existed offsetmeasurement with coincident and separated loop, a new measurement with array loop isproposed in this thesis, which can replace the result of multiple measurements with separatedloops by only one measurement, and has the advantage of high-efficiency, high-resolutionand high-coverage. For the complicated groundwater in non-layered and non-uniform space,high-precision2D and3D imaging methods of water content as well as relaxation timeT*2are presented. On the basis of MRS imaging, array surface MRS system with multi-channelacquisition units is developed, and the results of field experiments and application cases aredescribed. The main research work and achieved results of this thesis are as follows:
1. As1D MRS ignores the direction angle of loop layout, I introduce the rotation anglematrix to solve the MRS forward calculation problem with arbitrary angles of loop directionand the geomagnetic field. Moreover, I analyze the influence of the loop profile directionangel in2D measurements by simulation models.
2. For the low resolution and efficiency of the existed2D measurements, I propose anarray loop configuration to carry out the fast and high-coverage measurement in2D profile.By analyzing the resolution radius, I conclude that array loop configuration can achieve2Dhigh-resolution detection by only one measurement, and the combination of rectangulartransmitter loop and half-over-lapping receiver loops is the optimal configuration.
3. For the low efficiency and limited coverage in3D measurement, I take advantageof the diagonal measurement with array loops, which significantly improves the resolution inrespect to the coincident loop. It can detect a large coverage area of3D groundwater in highresolution with a small number of measurements.
4. To the issues of large number meshes, low precision imaging and instability ofalgorithm, I propose a non-uniform mesh generation mouthed based on the resolution radius,combine with discrepancy principle and L-curve method to select the regularization parameter,and apply Jacobain transform in objective function linearization and non-constraint spaceconversion. Finally, the stability high-precision MRS imaging of2D water content is solvedby the initial value inversion (IVI).
5. By simulating and inverting a complicated groundwater model by IVI, I contrastimaging results of coincident, separated and array loop configurations, and find therectangular array loop in half-over-lapping measurement mode provides a high resolution of2D MRS even in the case of low signal-to-noise (SNR). The conclusion consists with thetheoretical analyses of2D resolution studies.
6. Due to the storage of2D sensitivity kernels with multi-relaxation process in QTinversion using complete envelop data, I offer two solutions. One is to simplify the kernel inmono-relaxation process, and the imaging with two parameters, water content and singlerelaxation time, is inverted. In addition, the inversion results are more stable than IVI. Theother is base on the2D water cell inversion, which can achieve the water content andmulti-relaxation times imaging.
7. For the low precision in the3D imaging based on uniform meshes and high-errorestimation of water volume, I use the non-uniform meshes with different density in the targetand the surrounding regions, and accomplish the3D water content imaging based on IVI. Thesummation and filed data from Einersberger Lake in Germany is tomography inverted inhigh-precision3D image, and the water volume is quantified with high accuracy.
8. According to the composition and defects of existing single-channel surface MRSsystem, I develop multi-channel receiver units and control software for array loopconfiguration. By improving the rapid consumption circuit, the dead time of system reducesfrom38ms to15ms, and the data resolution of acquisition circuit and the signal conditioningcircuit are also improved. The structure of master with multi-client and hand-by-handconnection is used to achieve the high-precision synchronization control and high-speed datatransmission. These key technologies make the new system to catch up the most advantageinstrument in the world. Based on the study of the above contents, I complete the development of2D/3D MRSgroundwater imaging method and its array surface detection system. The main innovation liesas follow:
The array loop configuration I proposed can achieve high-resolution profiledetection by one measurement in2D, and large coverage area detection by diagonaloffset measurement in3D, which solves the low-efficiency and low-resolutionproblem of traditional MRS measurement.
The resolution radius I proposed is useful for the evaluation method of surface MRSdetection, and after the contras, I find the rectangular array loop in half-over-lappingmeasurement mode provides the highest resolution in2D. Based on the resolutionradius, I also general the non-uniform meshes in2D and3D for high-precisionimaging.
I combine the regularization parameter selection methods with discrepancy principleand L-curve method and apply Jacobain transform in objective function linearizationand non-constraint space conversion to realize the stability high-precision MRSimaging of2D and3D water content by the initial value inversion (IVI).
To the single relaxation and multi-relaxation properties of MRS signal envelope, Iimprove the QT inversion and propose Cell inversion to image the water content andalso relaxation timeT*2.
The MRS imaging method and surface MRS system have been applied in engineeringpractice, like the groundwater source detection for Halatura iron ore in Mongolia, the damleakage detection in Huanren, Liaoning province of China, and the landslide stabilitydetection in Yantaicun Landsilde, Anhui province of China. The results of2D groundwaterimaging are consisting with the other geophysics methods, verifying the effectiveness andpracticality of the method and system. It provides a strong technical support for groundwaterexploration in southwest of China and complicated geological environment.
引文
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