Inversion of geoelectrical resistivity observed with multi-separation of electrodes
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摘要: 地电阻率多极距观测的目的是借助对观测数据的反演获得地下介质中不同层位真电阻率的变化.本文以3层结构为例，对地电阻率多极距观测的一维反演的效果进行了初步地理论研究.首先研究了一维地电阻率结构下观测数据一维反演的模拟效果，得到了各层电阻率值，且与真电阻率值很接近，说明在地下电性结构为一维的情况下，电阻率多极距观测可以区分出不同地层的电阻率变化.其次，考虑到台址下电阻率结构的复杂性，研究了上两层界面存在起伏的情况下，多极距观测数据一维反演的效果，结果显示：当电阻率变化较小时，各层反演得到的电阻率的变化与真电阻率十分符合；当上两层介质的电阻率变化较大时，各层反演得到的电阻率出现畸变，与真实电阻率的变化情况存在一定差别，表明浅层电阻率变化达到一定程度后将会影响对深部电阻率变化情况的正确判断.一般情况下，观测的时间间隔越短，则连续两次观测时段内各层介质的电阻率变化越小，因此缩短多极距观测的时间间隔可能是避免出现上述畸变现象的有效观测手段.Abstract: Preliminary theoretical studies were dealt with in this paper on the efficiency of one-dimensional inversion of apparent resistivity data observed with multi-separation array, for understanding the true resistivity variations with time inside the media. To this end a three-layer model has been taken as an example. Firstly, we did the inversion of the theoretical apparent resistivity data by forward modeling calculation for each layer in one-dimensional resistivity structure. The result shows a good consistency between the true resistivity variations and that obtained with inversion of each layer, suggesting that one-dimensional inversion technology is adequate for recognizing the variations of resistivity in each layer. Secondly, more complex model was taken due to some interface fluctuation, which deviated from one-dimensional model to some extent. The same process of forward-inversion was conducted in the case of the fluctuation of interfaces of the three-layer model, the results showed that good fitting can be found only in the condition of non-large variations of resistivity of the first-and second-layers, otherwise the inverted resistivity of each layer will turn up distortion. Usually the shorter the time interval of observation, the smaller the medium resistivity change during the two consecutive observation. Therefore, to reduce the distortion, it could be available by taking short time interval of observation with multi-separation array.
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图 1 仅第1层电阻率ρ1变化时各层的多极距电阻率一维反演结果(虚线)与真电阻率(实线)的比较
Figure 1. Comparison of the resistivity by inversion with multi-separation array (dashed line) and actual resistivity (solid line) for each layer only when resistivity of the first-layer ρ1 varies with 11:11:47
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图 2 仅第3层电阻率ρ3变化时各层的多极距电阻率一维反演结果(虚线)与真电阻率(实线)的比较
Figure 2. Comparison of the resistivity by inversion with multi-separation array (dashed line) and actual resistivity (solid line) for each layer only when resistivity of the third-layer ρ3 varies with 11:12:03
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图 3 第1，3层电阻率ρ1和ρ3变化，第2层电阻率ρ2不变时各层的多极距电阻率一维反演结果(虚线)与真电阻率(实线)的比较
Figure 3. Comparision of the resistivity by inversion with multi-separation array (dashed line) and the actual resistivity (solid line) for each layer when resistivity of the first-and third-layer ρ1 and ρ3 vary with time, but resistivity of the second-layer ρ2 remains unchanged
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图 4 3层电阻率ρ1，ρ2，ρ3均变化时各层的多极距电阻率的一维反演结果(虚线)与真电阻率(实线)的比较
Figure 4. Comparision of the resistivity by inversion with multi-separation array (dashed line) and the actual resistivity (solid line) for each layer when resistivity of the whole three layers ρ1, ρ2 and ρ3 all vary with 11:13:04
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图 5 用于二维正演方法准确性检验的一维模型
Figure 5. The one-dimensional model for the accuracy test of two-dimensional forward modeling method
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表 1 一维电性结构下多极距观测系统的布极参数
Table 1 The electrodes arrangement parameters of multi-separation array system in one-dimension
AB/m MN/m 30 2 100 16 270 30 500 100 1000 300 
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表 2 二维电性结构下多极距观测系统布极参数和针对图 5所示模型利用一维与二维正演方法计算得到的视电阻率结果对比
Table 2 The electrodes arrangement parameters of multi-separation array in two dimension and the comparision of apparent resistivities calculated from one-dimensional and two-dimensional forward modeling based on the model of Fig. 5
装置编号 AB/m MN/m 一维视电阻率
ρ1D/(Ω·m)二维视电阻率
ρ2D/(Ω·m)相对误差 C1 200 50 38.38 38.20 -0.47% C2 400 150 50.49 50.18 -0.61% C3 600 150 64.24 64.64 0.62% C4 800 250 73.58 74.08 0.68% C5 1000 350 81.46 81.02 -0.32% 注：相对误差=(ρ2D-ρ1D)/ρ1D.
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