隧道空间对高密度电法在掌子面及侧壁富水构造探测中的影响研究

Study on the Influence of Tunnel Space on the Detection of Water-rich Structures in Face and Side Wall by High Density Electrical Method

在隧道中进行高密度电法探测时,由于全三维正反演算法计算量大,建模较为困难,通常采用半空间假设的二维正反演算法进行计算,而实际隧道更接近于三维全空间模型,因此半空间假设会给视电阻率计算和反演结果带来误差。为研究高密度电法在隧道富水结构探测时采用半空间假设计算视电阻率带来的误差水平,以及对反演结果的影响,本文首先建立隧道三维模型,然后采用数值计算方法计算了三维隧道模型的准确视电阻率值,并将三维模型计算的装置系数带入反演的正演迭代过程,定量分析了半空间假设时对视电阻率和反演结果带来的影响。结果表明,在掌子面探测时,真实视电阻率是半空间假设计算结果的0.66~1.0倍;而在隧道侧壁探测时,该比值在0.9~1.6范围内。但半空间假设计算的视电阻率值的空间特征与真实值基本一致,而且误差较大的视电阻率值大多位于高密度电法的低分辨率区域内,对反演结果的影响较小。模拟结果表明了基于半空间假设的反演算法在隧道探测中的反演误差可以忽略,为实际工程应用提供了理论依据。

When high density electrical detection is carried out in tunnels,full-three-dimensional forward and inversion algorithm is difficult to model due to the large amount of calculation.Two-dimensional forward and inversion algorithm based on half-space hypothesis is usually used for calculation,while the actual tunnel is closer to the three-dimensional full-space model.The half-space hypothesis tends to bring errors to the calculation and inversion results of apparent resistivity.In order to study the error level caused by the apparent resistivity and its influence on the inversion results,the half-space hypothesis is proposed to calculate the error level caused by the apparent resistivity,applying the high-density electrical method to detect water-rich structures in tunnels,In this paper,a 3 D tunnel model is established,and the accurate apparent resistivity of the 3 D tunnel model is calculated by numerical method.Meanwhile,the device coefficients calculated by the 3 D model are brought into the forward iterative process of inversion,and the influence of the half-space assumption on the apparent resistivity and inversion results is quantitatively analyzed.The results show that the true apparent resistivity is 0.66~1.0 times of the calculated results of half-space hypothesis in the palm-surface detection,while the ratio is in the range of 0.9~1.6 in the tunnel sidewall detection.However,the spatial characteristics of the calculated apparent resistivity values based on the half-space hypothesis are basically consistent with the real values,and the apparent resistivity values with large errors are mostly located in the low-resolution region of high-density electrical method,which has little influence on the inversion results.The simulation results show that the inversion error of the algorithm based on the half-space hypothesis can be ignored in tunnel detection,which provides a theoretical basis for practical engineering applications.