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摘要:
航空电磁系统校准是开展实际测量工作的基础，校准情况直接影响数据处理和解释.传统校准方法通常假设在自由空间中进行，忽略导电大地耦合影响.然而，实际工作中很难找到绝对高阻的校准场地，导电大地对系统校准和观测数据的影响无法忽视.本文以频率域航空电磁系统为例，对导电大地上航电系统校准技术和校准误差改正方法进行研究.我们首先推导了层状导电大地上水平共面和直立共轴线圈系统的校准公式，结果表明导电大地对航电系统校准尤其是水平共面装置的高频信号影响很大.针对校准过程中大地电导率已知的情况，本文采用非线性方程求解技术一次性确定校准线圈位置和Q值；在没有任何辅助信息情况下，也可直接利用实测数据计算校正因子进行迭代求解.测试结果表明该方法快速、准确、有效.考虑到系统相位和增益调整直接影响观测数据，本文提出了航空电磁数据校准误差的改正算法.实测数据误差改正结果表明，导电大地对高频信号影响严重，校准误差改正后的航空电磁数据与实际地质资料更好吻合.
Abstract:Airborne electromagnetic (AEM) calibration is the preliminary work of field exploration,which directly influences the quality of data processing and interpretation. Traditional calibration assumes that the underground at the calibration site is very resistive,so that the induction of the earth can be neglected and the calibrated gain of the AEM system well approximates that when the system is calibrated in the free air space. However,it is sometimes very difficult to find such an ideal site in the production,and the earth influences largely on AEM data,especially when the calibration is conducted on conductive underground.
This paper systematically studied the AEM system calibration above the conductive earth and the data correction of calibration error. We take frequency-domain AEM system as example and derivate the calibration formula for both horizontal coplanar and vertical coaxial systems above the conductive layered earth. The ratio of normalized field from the conductive earth and free-space has been used to evaluate the effect of conductive earth on the EM signal. During the calibration,when a priori information on earth conductivity at the calibration site is available,we will directly obtain the location and Q-value of calibration coil by solving a non-linear equation. Otherwise,an iterative technique has been developed to search the earth conductivity from the AEM measurements over the calibration site. Considering that the calibration of the phase and gain influence all the survey data,we propose an algorithm that uses the ratio of normalized magnetic field in the conductive earth model and in the free-space to calculate a factor for the correction of the calibration error.
The numerical experiments show that the conductive earth largely influence the signal,especially for horizontal coplanar configuration in high frequencies. The iterative results without any auxiliary information show that one can obtain the earth resistivity through several iterations from the survey data (in-phase and quadrate parts) and the correction factor efficiently and accurately. The processing of the survey data shows the effectiveness of calibration method.
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Key words:
- Airborne EM /
- Frequency-domain /
- Calibration /
- Conductive earth /
- Error correction
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图 2
航空电磁系统分别位于导电半空间和自由空间中校准时航空电磁实分量Re和虚分量Im比值随校准场地电阻率变化
Figure 2.
Ratios of the EM fields for the calibration of AEM system over a conductive half-space to those calibrated in the free air-space versus the earth resistivity
图 3
大地导电性对校准信号相位的影响
Figure 3.
Phase shift of the calibration signal resulted from the conductive ground at the calibration site
图 5
校准地大地电阻率迭代计算流程图
Figure 5.
Flowing chart for searching the earth resistivity at the calibration site
图 6
航空电磁实测数据改正结果(左边为原始数据计算的视电阻率，右边为改正后数据计算的视电阻率.数据来自MSE Technology Application Inc.公司)
Figure 6.
Correction of the AEM data (The left column denotes the distributions of apparent resistivity before correcting the calibration error, while the right column shows the corresponding results after the calibration error corrected. Data courtesy of MSE Technology Application INC.)
表 1
校准线圈位置和Q值
Table 1.
Position and Q-value of Q-coil
大地电阻率
/ΩmDIGHEM Standard系统 DIGHEM Resistivity系统 7200 Hz 56 kHz 6200 Hz 25 kHz 101 kHz rQR/m Q rQR/m Q rQR/m Q rQR/m Q rQR/m Q 1.0 1.662 1.033 1.732 0.759 1.956 1.194 1.774 0.784 1.375 0.422 2.0 1.657 1.184 1.829 0.977 1.916 1.225 1.858 1.029 1.582 0.548 3.0 1.640 1.209 1.848 1.096 1.890 1.203 1.865 1.138 1.704 0.677 5.0 1.615 1.193 1.842 1.200 1.861 1.158 1.847 1.213 1.812 0.863 8.0 1.595 1.156 1.820 1.239 1.840 1.117 1.820 1.223 1.857 1.026 10.0 1.587 1.137 1.806 1.239 1.832 1.099 1.806 1.213 1.864 1.091 20.0 1.567 1.084 1.765 1.195 1.815 1.057 1.767 1.157 1.848 1.212 30.0 1.560 1.061 1.744 1.156 1.808 1.041 1.750 1.121 1.824 1.224 40.0 1.556 1.048 1.732 1.130 1.805 1.032 1.740 1.099 1.807 1.214 50.0 1.553 1.039 1.724 1.111 1.803 1.026 1.734 1.083 1.793 1.199 80.0 1.550 1.026 1.711 1.078 1.800 1.017 1.724 1.057 1.768 1.158 100.0 1.548 1.021 1.706 1.065 1.799 1.014 1.720 1.047 1.758 1.138 200.0 1.546 1.011 1.696 1.036 1.797 1.007 1.713 1.026 1.734 1.084 300.0 1.545 1.008 1.693 1.025 1.796 1.005 1.710 1.018 1.725 1.061 500.0 1.544 1.005 1.690 1.016 1.795 1.003 1.708 1.011 1.717 1.039 800.0 1.544 1.003 1.688 1.010 1.795 1.002 1.707 1.007 1.713 1.026 1000.0 1.544 1.002 1.687 1.008 1.795 1.001 1.706 1.006 1.711 1.021 注：除了DIGHEM Standard 7200 Hz线圈系统采用校准线圈同线放置外，其他全部采用旁线.nQ, dQ和LQ分别是校准线圈的匝数、半径和电感.校准信号实虚分量均假设为200 PPM. f=7200 Hz, rTR=7.98 m, nQ=124, dQ=0.23 m, LQ=17 mH; f=56 kHz, rTR=6.32 m, nQ=10, dQ=0.23 m, LQ=0.13 mH; f=6200 Hz, rTR=7.86 m, nQ=124, dQ=0.23 m, LQ=17 mH; f=25 kHz, rTR=7.86 m, nQ=10, dQ=0.23 m, LQ=0.13 mH; f=101 kHz, rTR=7.86 m, nQ=10, dQ=0.23 m, LQ=0.13 mH. 
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表 2
利用迭代算法确定校准场地电阻率
Table 2.
Earth resistivity derived from AEM data using an iterative searching procedure
No. ρ0
/ΩmRe
/PPMIm
/PPMρa1
/ΩmρaN
/Ωm迭代次数 1 1.0 1499.9 393.7 8.10 1.01 5 2 5.0 1424.9 197.7 2.42 5.06 4 3 10.0 1387.1 276.3 5.01 10.11 5 4 50.0 941.7 507.6 41.8 50.38 3 5 100.0 668.8 502.3 91.3 100.6 3 6 500.0 203.9 296.3 490.7 501.5 2 注：DIGHEM Standard系统56 kHz，航电系统飞行观测时高度设为30 m.
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表 3
利用迭代算法确定校准场地电阻率的迭代过程
Table 3.
Iteration procedure for searching the earth resistivity at the calibration site
迭代次数 Re
/PPMIm
/PPMρ
/Ωmfg Re′
/PPMIm′
/PPM1 1499.9 393.7 8.10 1.189 1834.8 184.7 2 1834.8 184.7 1.08 1.323 2042.0 205.6 3 2042.0 205.6 1.01 1.314 2028.1 204.2 4 2028.1 204.2 1.01 1.315 2029.1 204.3 5 2029.1 204.3 1.01 1.315 2029.1 204.3 注：模型为表 2中第一个模型ρ=1 Ωm.Re′和Im′为利用现有大地电阻率对校准误差改正后数据，fg为增益校正因子.
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