基于重力梯度信号的地下隧道探测方法研究

Research on Underground Tunnel Detection Based on Gravity Gradient Signal

首先利用水平半圆柱体模型来对隧道对象进行建模,采用水平线元法对其产生的重力梯度信号进行正演计算。通过水平线元法和正常三重积分法对水平半圆柱体上方重力梯度张量计算结果进行对比,结果表明:水平线元法相对于三重积分法计算结果平均误差小于0.017E,相对误差小于2.6%,验证了水平线元法精度的可靠性。然后利用全张量重力梯度信号对隧道横截面半径和底面埋深进行反演,结果表明:横截面半径反演结果的相对误差小于1.5%,底面埋深反演结果的相对误差小于0.4%,验证了此反演算法的有效性。

This study adopts a horizontal half cylinder to model the tunnel object,and the horizontal line element method is used to forward calculation of the gravity gradient signal generated by the horizontal half cylinder.Comparing the calculation results from the horizontal line element method and the normal triple integration method,the results show that the average error of the horizontal line element method is smaller than 0.017E,and the relative error is smaller than 2.6%,which verifies the reliability of the accuracy of the horizontal line element method.Furthermore,this paper also inverts the tunnel cross-sectional radius and bottom buried depth using the full tensor gravity gradient signal.A numerical test was conducted and the results show that the relative errors of the buried depth and the cross-sectional radius inversion results are smaller than 0.4%and 1.5%respectively,which verifies the effectiveness of the related algorithm.