Two-dimensional SNMR imaging based on HED integration under undulating terrain conditions
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摘要:
传统的地面核磁共振（SNMR）方法在正演计算时往往不考虑地形条件，这会影响二维成像的精确性。本研究基于谐变电偶极子（HED）积分方法对地形起伏情况下的SNMR响应信号特征进行分析，发现地形是影响反演结果的关键因素。通过数值模拟建立单斜模型、堤坝模型2类地质模型，对2类地形条件下的SNMR二维信号特征及反演结果进行对比分析。结果表明，考虑地形起伏的SNMR二维反演结果，在含水体位置、形态和含水量方面与预设模型一致性更好，利用HED积分方法能够克服地形因素影响，有效提升地形起伏条件下含水体边界的识别能力和含水层整体的连续性。结合高密度电阻率法（ERT）在贵阳红枫湖进行场地验证，发现考虑地形起伏的HED积分SNMR二维反演可直观表征地下含水分布，并准确划定含水层位置和形态，更能反映含水层横向分布复杂性，提高了反演的精确性。试验结果验证了基于HED积分的方法能够更好地适应复杂的地形环境，为高精度地下水探测提供一定的技术支撑与方法参考。
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关键词:
- 地面核磁共振（SNMR） /
- 谐变电偶极子（HED） /
- 起伏地形 /
- 地下水 /
- 信号特征
Abstract:ObjectiveTraditional surface nuclear magnetic resonance (SNMR) methods often neglect terrain conditions during forward modeling, which affects the accuracy of two-dimensional imaging. If the excitation electromagnetic field is still calculated using traditional SNMR methods under such conditions, the accuracy of two-dimensional imaging will be compromised. This study analyzes the characteristics of SNMR response signals under undulating terrain based on the harmonic electric dipole (HED) integral method, revealing that terrain is a key factor affecting inversion results.
MethodsNumerical simulations were conducted to establish two geological models: Monoclinal and embankment models. And a comparative analysis was performed on SNMR two-dimensional signal characteristics and inversion results under different terrain conditions.
ResultsThe results showed that SNMR two-dimensional inversion incorporating undulating terrain achieved better agreement with preset models in terms of water-bearing body location, geometry, and water content. The HED integral method could overcome the influence of terrain factors, effectively enhancing the identification capability of water-bearing body boundaries and the overall continuity of aquifers under undulating terrain conditions. Field validation at Hongfeng Lake in Guiyang, combined with electrical resistivity tomography (ERT), showed that the HED-based SNMR two-dimensional inversion under undulating terrain clearly visualized subsurface water distribution, accurately delineated aquifer locations and geometries, and better reflected the complexity of aquifer lateral distribution, thereby enhancing inversion accuracy.
ConclusionThe experimental results verify that the HED integral method better adapts to complex terrain conditions and provides technical support as well as methodological reference for high-precision groundwater detection.
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图 1 基于HED积分计算电磁场示意图
A～F. 矩形线圈端点；P. 地下任意点；O. 原点；xyz. 空间坐标系；r1, r2. 点P与点A，B的距离；PE. 电偶极子微元
Figure 1. Schematic diagram of electromagnetic field calculation based on HED integration
图 2 单斜地形下含水体模型及网格剖分图
a. 单斜地形模型；b. 非结构化三角网格剖分。coil 1～coil 7. 线圈编号；x. 水平距离；z. 深度；红色区域表示预设的块状含水体模型；蓝色虚线表示非结构化三角网格剖分的块状含水体模型边界；下同
Figure 2. Water-bearing body model and mesh division diagram under monoclinal terrain
图 3 单斜地形下7组线圈采集的灵敏度核函数示意图
a～g. q=60 A·ms；h～n. q=
15000 A·ms。q. 激发脉冲矩；K. 灵敏度核函数；红色虚线表示预设含水体模型边界；下同Figure 3. Schematic diagram of sensitivity kernel functions of seven coil sets under monoclinal terrain
图 4 7次数据采集初始振幅随脉冲矩变化曲线图
Figure 4. Variation curves of initial amplitude with pulse moment from seven data acquisitions
图 5 单斜地形下块状含水体的SNMR二维反演剖面图
a. 考虑地形起伏；b. 忽略地形起伏。黑色虚线表示预设模型的边界
Figure 5. Two-dimensional SNMR inversion profiles of block-shaped water-bearing body under monoclinal terrain
图 6 堤坝地形下含水体模型及网格剖分图
a. 堤坝地形模型；b. 非结构化三角网格剖分。红色区域表示预设的块状含水体模型；蓝色虚线表示非结构化三角网格剖分的块状含水体模型边界
Figure 6. Water-bearing body model and mesh division diagram under embankment terrain
图 7 堤坝地形下5组线圈采集的灵敏度核函数示意图
Figure 7. Schematic diagram of sensitivity kernel functions of five coil sets under embankment terrain
a～e. q=60 A·ms；f～j. q=
15000 A·ms。黑色虚线表示预设含水体模型边界
图 8 5次数据采集初始振幅随脉冲矩变化曲线图
Figure 8. Variation curves of initial amplitude with pulse moment from five data acquisitions
图 9 堤坝地形下块状含水体的SNMR二维反演剖面图
a. 考虑地形起伏；b. 忽略地形起伏。黑色虚线为预设模型边界
Figure 9. Two-dimensional SNMR inversion profiles of block-shaped water-bearing body under embankment terrain
图 10 研究区的地理位置及测线布置图
Figure 10. Geographic location and survey line arrangement of study area
图 11 高密度电阻率法L1测线反演得到的电阻率剖面图
红色椭圆形虚线表示推测修建堤坝回填的松散堆积层；黑色矩形虚线表示SNMR线圈的布设范围
Figure 11. Resistivity profile inverted from line L1 using electrical resistivity tomography
图 12 SNMR一维反演含水量直方图
a. 倾斜铺设 coil 1；b. 半倾斜铺设 coil 2；c. 半倾斜铺设 coil 3；d. 半倾斜铺设 coil 4
Figure 12. Histograms of water content from one-dimensional SNMR inversion
图 13 SNMR各接收线圈二维灵敏度核函数分布图
a.倾斜铺设 coil 1；b. 半倾斜铺设 coil 2；c. 半倾斜铺设 coil 3；d. 半倾斜铺设 coil 4
Figure 13. Distribution of two-dimensional sensitivity kernel functions of SNMR receiver coils
图 14 实测数据SNMR二维反演结果对比图
a. 考虑地形起伏；b. 忽略地形起伏。紫色线圈表示考虑地形起伏与忽略地形起伏2种反演结果差异显著的位置
Figure 14. Comparison of two-dimensional SNMR inversion results from measured data
表 1 场地试验过程中的地球物理参数
Table 1. Geophysical parameters during the field experiment process
参数 线圈边长/m 线圈数量/个 线圈匝数/匝 线圈类型 地磁倾角/(º) 拉莫尔频率/Hz 脉冲矩/个 叠加次数/次 数值 50 4 1 方形线圈 41.72 2066 16 64 
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