Borehole Magnetic Gradient Method Based on Detection of Deep Underground Pipeline
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摘要: 目前, 井中磁梯度方法是深埋金属管线常用的探测方法之一, 但是存在理论不够完善及缺乏定量分析方法等问题.研究内容包括3个方面: (1)从无限长水平圆柱体的磁场强度入手, 通过坐标系的转换, 推导出地面探测和井中探测的磁场水平分量、垂直分量的关系, 进一步推导出管线的井中磁梯度公式; (2)根据磁梯度公式模拟出梯度值随有效磁化倾角及孔位的变化情况; (3)通过对模型正演数据的统计分析确定了3种关系式: 极值比与有效磁化倾角之间的关系式、管线的水平位置和磁梯度极值间的孔深距离与有效磁化倾角的关系式、磁梯度极值的绝对值较大者和管线埋深之间的距离与极值距间的比值和有效磁化倾角的关系式.这3种关系式组成了管线埋深及水平位置的估算公式.最后, 通过实例来估算了管线的埋深和平面位置, 根据估算结果进行的正演结果表明了该方法的可行性.Abstract: At present, borehole magnetic gradient is one of the commonly used methods for the detection of deeply buried metal pipelines, which is controversial due to its unsystematic theoretic basis and absence of quantitative analysis. In view of these challenges, this paper aims to present our study involving the following three aspects. (1) The relationships of the vertical component, horizontal component between the magnetic fields of surface and boreholes were derived, and the borehole magnetic gradient formula of deep underground pipeline was deduced, starting from the strength of the magnetic field of infinite horizontal cylinder and the transformation of coordinate system. (2) The relationship of the magnetic gradient changes with the inclination of effective magnetization and the position of hole was simulated according to the formula of magnetic gradient. (3) Three kinds of relationship were determined based on the statistical analysis of the forward modeling data, namely, (a) the relationship between maximum ratio of magnetic gradient and the inclination of magnetic gradient, (b) the relationship of the horizontal position of deep underground pipelines, the extreme distance of magnetic gradient and the inclination of magnetic gradient, (c) the relationship of the ratio of distance between the depth of deep underground pipelines, the depth corresponding to the maximum absolute value of magnetic gradient, the extreme distance of magnetic gradient with the inclination of magnetic gradient. These relationships constitute the estimation formula to estimate the depth and horizontal position of deep underground pipelines. Finally, an example of estimating the depth and horizontal position of deep underground pipeline is given. The feasibility of the method is shown by the results of forward modeling based on the estimation results.
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图 2 管线井中磁梯度随磁化倾角变化的曲线
Fig. 2. Borehole magnetic gradient curve of pipeline changing with magnetic inclination
图 3 管线井中磁梯度随水平距离变化的曲线
Fig. 3. Borehole magnetic gradient curve of pipeline changing with horizontal distance
图 7 钻孔位置(编号为K1、K2与K3)
点划线表示推断的管线水平位置
Fig. 7. The borehole locations (numbers for K1, K2 and K3)
表 1 |ZT, min/ZT, max|与is之间的关系
Table 1. Relationship between|ZT, min/ZT, max| and is
is |L|=0.7 m |L|=0.8 m |L|=1.3 m |L|=1.8 m |L|=2.3 m 0° 1.000 1.000 1.000 1.000 1.000 15° 0.800 0.810 0.805 0.805 0.804 30° 0.647 0.646 0.647 0.645 0.641 45° 0.522 0.516 0.518 0.518 0.520 60° 0.406 0.410 0.411 0.411 0.410 75° 0.330 0.329 0.321 0.322 0.323 90° 0.250 0.250 0.250 0.250 0.250 105° 0.330 0.329 0.321 0.322 0.323 120° 0.406 0.410 0.411 0.411 0.410 135° 0.522 0.516 0.518 0.518 0.520 150° 0.647 0.646 0.647 0.645 0.641 165° 0.800 0.810 0.805 0.805 0.804 180° 1.000 1.000 1.000 1.000 1.000 195° 0.800 0.810 0.805 0.805 0.804 210° 0.647 0.646 0.647 0.645 0.641 225° 0.522 0.516 0.518 0.518 0.520 240° 0.406 0.410 0.411 0.411 0.410 255° 0.330 0.329 0.321 0.322 0.323 270° 0.250 0.250 0.250 0.250 0.250 285° 0.330 0.329 0.321 0.322 0.323 300° 0.406 0.410 0.411 0.411 0.410 315° 0.522 0.516 0.518 0.518 0.520 330° 0.647 0.646 0.647 0.645 0.641 345° 0.800 0.810 0.805 0.805 0.804 360° 1.000 1.000 1.000 1.000 1.000 
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表 2 ED随is及|L|的变化
Table 2. ED changing with is and |L|
is |L|=0.7 m |L|=0.8 m |L|=1.3 m |L|=1.8 m |L|=2.3 m ED (m) ED/|L| ED (m) ED/|L| ED (m) ED/|L| ED (m) ED/|L| ED (m) ED/|L| 0° 0.6 0.86 0.6 0.75 1.0 0.77 1.4 0.78 2.0 0.87 15° 0.5 0.71 0.7 0.88 1.0 0.77 1.5 0.83 1.9 0.83 30° 0.6 0.86 0.7 0.88 1.1 0.85 1.5 0.83 2.1 0.91 45° 0.6 0.86 0.7 0.88 1.2 0.92 1.6 0.89 2.0 0.87 60° 0.6 0.86 0.7 0.88 1.2 0.92 1.6 0.89 2.1 0.91 75° 0.6 0.86 0.8 1.00 1.2 0.92 1.7 0.94 2.2 0.96 90° 0.7 1.00 0.8 1.00 1.3 1.00 1.8 1.00 2.3 1.00 105° 0.6 0.86 0.8 1.00 1.2 0.92 1.7 0.94 2.2 0.96 120° 0.6 0.86 0.7 0.88 1.2 0.92 1.6 0.89 2.1 0.91 135° 0.6 0.86 0.7 0.88 1.2 0.92 1.6 0.89 2.0 0.87 150° 0.6 0.86 0.7 0.88 1.1 0.85 1.5 0.83 2.1 0.91 165° 0.5 0.71 0.7 0.88 1.0 0.77 1.5 0.83 1.9 0.83 180° 0.6 0.86 0.6 0.75 1.0 0.77 1.4 0.78 2.0 0.87 195° 0.5 0.71 0.7 0.88 1.0 0.77 1.5 0.83 1.9 0.83 210° 0.6 0.86 0.7 0.88 1.1 0.85 1.5 0.83 2.1 0.91 225° 0.6 0.86 0.7 0.88 1.2 0.92 1.6 0.89 2.0 0.87 240° 0.6 0.86 0.7 0.88 1.2 0.92 1.6 0.89 2.1 0.91 255° 0.6 0.86 0.8 1.00 1.2 0.92 1.7 0.94 2.2 0.96 270° 0.7 1.00 0.8 1.00 1.3 1.00 1.8 1.00 2.3 1.00 285° 0.6 0.86 0.8 1.00 1.2 0.92 1.7 0.94 2.2 0.96 300° 0.6 0.86 0.7 0.88 1.2 0.92 1.6 0.89 2.1 0.91 315° 0.6 0.86 0.7 0.88 1.2 0.92 1.6 0.89 2.0 0.87 330° 0.6 0.86 0.7 0.88 1.1 0.85 1.5 0.83 2.1 0.91 345° 0.5 0.71 0.7 0.88 1.0 0.77 1.5 0.83 1.9 0.83 360° 0.6 0.86 0.6 0.75 1.0 0.77 1.4 0.78 2.0 0.87
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表 3 2|zm-z0|/ED与is之间的关系
Table 3. Relationship between 2|zm-z0|/ED and is
is |L|=0.7 m |L|=0.8 m |L|=1.3 m |L|=1.8 m |L|=2.3 m 0° 1.000 1.000 1.000 1.000 1.000 15° 0.800 0.857 0.800 0.800 0.842 30° 0.667 0.571 0.545 0.667 0.571 45° 0.333 0.571 0.500 0.500 0.500 60° 0.333 0.286 0.333 0.250 0.286 75° 0.000 0.250 0.167 0.118 0.182 90° 0.000 0.000 0.000 0.000 0.000 105° 0.000 0.250 0.167 0.118 0.182 120° 0.333 0.286 0.333 0.250 0.286 135° 0.333 0.571 0.500 0.500 0.500 150° 0.667 0.571 0.545 0.667 0.571 165° 0.800 0.857 0.800 0.800 0.842 180° 1.000 1.000 1.000 1.000 1.000 195° 0.800 0.857 0.800 0.800 0.842 210° 0.667 0.571 0.545 0.667 0.571 225° 0.333 0.571 0.500 0.500 0.500 240° 0.333 0.286 0.333 0.250 0.286 255° 0.000 0.250 0.167 0.118 0.182 270° 0.000 0.000 0.000 0.000 0.000 285° 0.000 0.250 0.167 0.118 0.182 300° 0.333 0.286 0.333 0.250 0.286 315° 0.333 0.571 0.500 0.500 0.500 330° 0.667 0.571 0.545 0.667 0.571 345° 0.800 0.857 0.800 0.800 0.842 360° 1.000 1.000 1.000 1.000 1.000
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表 4 估算结果及误差平均值
Table 4. Estimation results and its average error
is |L|=0.7 m |L|=0.8 m |L|=1.3 m |L|=1.8 m |L|=2.3 m Z0 (m) |L| Z0 (m) |L| Z0 (m) |L| Z0 (m) |L| Z0 (m) |L| 0° 4.996 0.768 4.996 0.768 4.990 1.280 5.014 1.793 4.980 2.561 15° 4.969 0.748 4.984 0.881 5.003 1.258 5.005 1.887 4.964 2.390 30° 5.007 0.721 5.022 0.840 5.053 1.322 4.979 1.801 5.008 2.284 45° 5.053 0.684 4.970 0.797 4.991 1.365 4.987 1.820 4.983 2.273 60° 5.005 0.646 5.014 0.755 4.996 1.294 5.061 1.726 5.039 2.263 75° 4.946 0.624 4.970 0.832 4.996 1.244 5.038 1.763 4.980 2.282 90° 4.990 0.715 4.989 0.817 4.982 1.328 4.976 1.839 4.969 2.350 105° 5.047 0.621 5.039 0.828 5.018 1.239 4.982 1.755 5.045 2.272 120° 4.990 0.641 4.993 0.749 5.016 1.286 4.954 1.715 4.981 2.248 135° 5.042 0.678 5.036 0.791 5.020 1.354 5.027 1.806 5.036 2.255 150° 4.988 0.716 4.983 0.833 4.956 1.313 5.032 1.790 5.006 2.387 165° 4.997 0.626 5.021 0.878 5.004 1.252 5.006 1.875 5.049 2.379 180° 4.993 0.768 4.993 0.768 4.988 1.280 4.983 1.793 4.976 2.561 195° 5.001 0.628 4.982 0.881 5.000 1.258 5.000 1.886 4.960 2.389 210° 5.009 0.721 5.020 0.840 5.050 1.323 4.976 1.802 5.003 2.283 225° 4.955 0.684 4.968 0.797 4.987 1.365 4.983 1.820 4.977 2.274 240° 5.006 0.646 5.012 0.755 4.993 1.295 5.057 1.727 5.035 2.265 255° 4.948 0.624 4.969 0.832 4.993 1.245 5.034 1.764 4.975 2.283 270° 4.990 0.715 4.988 0.817 4.981 1.328 4.973 1.839 4.966 2.349 285° 5.057 0.614 5.026 0.832 4.998 1.244 4.954 1.763 5.009 2.282 300° 4.998 0.645 4.983 0.755 4.998 1.294 4.930 1.726 4.949 2.264 315° 5.050 0.683 5.026 0.796 5.003 1.364 5.005 1.819 5.007 2.274 330° 4.996 0.721 4.974 0.839 4.941 1.322 5.013 1.801 4.982 2.282 345° 5.003 0.628 5.013 0.881 4.992 1.257 4.988 1.886 5.025 2.389 360° 5.002 0.768 5.002 0.768 5.004 1.280 5.005 1.793 5.008 2.561 中误差 0.021 0.038 0.015 0.031 0.016 0.029 0.022 0.035 0.02 0.072
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