## 1 Introduction  
Tunnel defects are a prominent problem in railway, highway, and underground engineering all over the world, especially the high-speed railway tunnels in China [1]. Due to the influence of various factors, such as geology, climate, design, and construction conditions, a variety of defects appear during the normal operation of tunnels, including water leakage, cavity, crack, and insufficient thickness of tunnel linings [2, 3]. Therefore, tunnel defects are a worldwide hot problem, especially in the mountainous area of southwest China. With the rapid construction of high-speed railway tunnels in China, situations of tunnel defects have been increasing rapidly in recent years, particularly in the last 2 to 3 years. For example, the completed line of the Guiyang section of the Shanghai-Kunming high-speed railway, with a design speed of 250 km/h, is 559.5 km in length [4]. There are 223 tunnels with a total length of 330.3 km, and the tunnel length accounts for 59% of the line length. Based on the investigation results of field survey and ground penetrating radar testing on 59 tunnels of this line, a total of 30,571 defects occurred in these tunnels in less than one year of operation, where the number of water leakages and cavities is as high as 1471 and 941, respectively. The same type of tunnel defects have already been found in many high-speed railway tunnels in operation. If not dealt with in time, it is only a matter of time before serious water leakages and even the collapse of tunnel linings occur, which will cause a great potential danger to the normal service of high-speed railway tunnels. At present, four main problems are raised in the defect detection of high-speed railway tunnels. Firstly, serious defect problems have appeared in the high-speed railway tunnels. Then, more and more long-distance tunnels are being built and planned. Thirdly, high-speed railway tunnels will enter a peak period of maintenance in the next few years. Finally, the current manual detection method is unable to complete such a large detection in the short maintenance time of high-speed railway. According to the maintenance regulation of a high-speed railway tunnel [4; 5], all maintenance work must be completed within a limited time. However, the present tunnel defect detection technology cannot meet all requirements of the rapid maintenance of a high-speed railway tunnel. Therefore, it is urgent to investigate an efficient and rapid detection method to accomplish such a large tunnel defect detection works within a limited maintenance time. The transient electromagnetic method (TEM) is widely used in various fields, such as coal mine and tunnel construction exploration, deep-sea metal mineral exploration, and ground exploration [6; 7]. Based on the identification performance of the low-resistivity body of TEM technology, the vehicle-borne TEM has been preliminarily proposed to rapidly detect tunnel defects behind tunnel linings [3], and the adaptability of this rapid detection method was also investigated [8; 9]. [PERSON] et al. [3] adopted the numerical simulation method to investigate the variation rule of the transient electromagnetic response curve of a low-resistivity water-bearing body at the condition of short-distance and whole-space, and revealed the transient electromagnetic digital characteristic parameters that can reflect the regular physical parameters of a low-resistivity water-bearing body. [PERSON] et al. [8] used the combination of a least square support vector machine and particle swarm optimization algorithm to study the three-dimensional fast inversion of a short-distance low-resistivity water-bearing body, and realized the prediction of physical parameters of a low-resistivity water-bearing body. [PERSON] [9] investigated the whole-space electromagnetic response characteristics under different coil sizes by means of numerical simulation, proposed the most appropriate coil parameters for short-distance detection, and revealed the advantages and limitations of a small-dimension coil.