频谱反演法在探地雷达隧道衬砌检测中的应用研究

Application of spectrum inversion method in GPR signal processing for tunnel lining detection

隧道衬砌模型的空间结构属于典型的层状分布,采用探地雷达进行隧道二衬检测时,往往很难识别高度小于调谐厚度的脱空。通过建立含有脱空薄层的隧道二衬层状几何模型,结合电磁波在隧道衬砌中的传播规律,给出了隧道衬砌检测时电磁波的反射模型,并推导了其广义反射系数谱域表达式,从而提出一种根据反射系数序列频谱估算隧道二衬厚度及脱空高度的反演方法。通过分析反射系数序列的幅度谱属性,进一步提出一种估计脱空层高度的快速方法,即根据幅度谱凹陷周期确定脱空层双程走时,进而估算脱空层高度。最后,利用1st Opt数学优化分析软件进行全局优化,并反演求解各参数。物理模型实验及现场应用实例的处理结果表明,当脱空厚度小于1/4波长时,本文所述的频谱反演法仍能准确反演出二衬厚度及脱空层高度,从而提高了探地雷达资料的垂直分辨率。

The spatial structure of tunnel lining model is a typical stratiform distribution, so it is difficult to identify the void area if its height is less than tuning thickness when using ground penetrating radar(GPR) to detect the second lining of tunnel. In this paper, by establishing a geometrical model for the second lining layer of tunnel including void area and considering the spreading law of electromagnetic waves in tunnel lining, a reflection model for electromagnetic waves in tunnel lining detection is obtained, and the generalized reflection coefficient in spectrum expression is deduced as well as an inversion method to further estimate the lining thickness of tunnel and the height of void area according to the reflection coefficient sequence spectrum. By analyzing the amplitude spectrum properties of the reflection coefficient sequence, a quick method to estimate the height of void area is proposed, namely determining the two-way travel time of void area and leading to the height of void area according to the depressing period of the amplitude spectra. Finally, 1stopt mathematical optimization analysis software is adopted for the global optimization and calculation of parameters. The results of physical model experiments and field tests indicate that the spectrum inversion method can also estimate the lining thickness of tunnel and the height of void area accurately when the height of void area is less than 1/4 wavelength, consequently enhancing the vertical resolution of GPR data.