基于小波变换时能密度法的隧道空洞充填物识别研究

灰岩地区隧道修建过程中，制约安全高效建设的最主要因素是隧道掘进工作面前方的不良地质情况，加之溶洞、断层与破碎带等不良地质具有较强的隐蔽性，如何提高隧道短距离超前地质预报的判释水平显得尤为重要。为便于对地质雷达信号图谱特征进行定量解释，开展了基于时域有限差分法的正演模拟与室内物理模型实验。在小波变换与奇异性检测原理的基础上，构造了与地质雷达发射子波波形相似度高的雷达小波基，添加到小波分析工具箱中，提出了一种新的基于雷达小波基的小波变换时能密度法，将其应用于空洞充填物正演模拟与模型实验地质雷达信号的定量识别，并与波形分析法、Db4小波变换法和雷达小波变换法的识别结果进行比较。研究结果表明，波形分析法虽能有效识别空洞充填物的尺寸大小，但需通过反射系数等先验知识来确定空洞充填物的界面反射位于波峰或波谷;Db4小波变换模极大值法易得到地质雷达信号奇异点，但奇异点的提取位置与不同小波基的时频局部化特征有关，Db4小波变换法识别结果的相对误差约15%;雷达小波变换模极大值法与小波变换时能密度法的识别效果均较好，但小波变换时能密度法的分辨率更高，且不需选择最优尺度。当空洞充填物的尺寸大于电磁波波长时，小波变换时能密度法识别结果的相对误差小于5%。

Research on identification of tunnel cavity fillings by time-energy density analysis based on wavelet transform

In the tunnel construction at limestone area,the unfavorable geological conditions ahead the tunnel face is the most important factor to restrict the safe and efficient construction of the tunnel.In addition,the adverse geological bodies such as karsts,faults and fracture zones have strong concealment.Thus,how to improve the interpretation level of tunnel short-range advanced geological prediction is particularly important.In order to improve the quantitative interpretation of ground penetrating radar (GPR) signals characteristics,a forward modeling based on time domain finite difference method and an experimental study of indoor physical model were carried out.Based on the principle of wavelet transform and singularity detection,a radar wavelet basis with a high similarity to GPR emission wavelet was constructed and added to the wavelet analysis toolbox.Using the radar wavelet basis as a foundation,a new time-energy density analysis based on wavelet transform method (TEDAWT) was proposed.The TEDAWT method was applied to the quantitative identification of the cavity fillings in the GPR forward modeling and physical experiment,and compared with the recognition results of the waveform analysis method,Db4 wavelet transform method and radar wavelet transform method.The results show that the waveform analysis method can effectively identify the size of cavity fillings,but reflection coefficient and other prior knowledge are required to determine the interfacial reflection of cavity fillings which is located in a crest or trough.The Db4 wavelet transform modulus maximum method is easy to obtain the singular points of GPR signals,but the extraction position of singular points is related to the time-frequency localization characteristics of different wavelet bases.The relative error of the recognition results using Db4 wavelet transform method is about 15%.The recognition effect of the radar wavelet transform modulus maxima method and the TEDAWT method are both better,while the TEDAWT method has higher resolution,and does not need to select the optimal scale.When the size of the cavity fillings is larger than the wavelength of the electromagnetic wave,the relative error of the TEDAWT method is less than 5%.