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

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.