The inverse problem of electrical resistivity surveys (ERS) is difficult because of its nonlinear and ill-posed nature. For this task, traditional linear inversion methods still face challenges such as sub-optimal approximation and initial model selection. Inspired by the remarkable non-linear mapping ability of deep learning approaches, in this paper we propose to build the mapping from apparent resistivity data (input) to resistivity model (output) directly by convolutional neural networks (CNNs). However, the vertically varying characteristic of patterns in the apparent resistivity data may cause ambiguity when using CNNs with the weight sharing and effective receptive field properties. To address the potential issue, we supply an additional tier feature map to CNNs to help it get aware of the relationship between input and output. Based on the prevalent U-Net architecture, we design our network (ERSInvNet) which can be trained endto-end and reach real-time inference during testing. We further introduce depth weighting function and smooth constraint into loss function to improve inversion accuracy for the deep region and suppress false anomalies. Four groups of experiments are considered to demonstrate the feasibility and efficiency of the proposed methods. According to the comprehensive qualitative analysis and quantitative comparison, ERSInvNet with tier feature map, smooth constraints and depth weighting function together achieve the best performance.

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a b s t r a c tDetecting, real-time monitoring and early warning of underground water-bearing structures are critically important issues in prevention and mitigation of water inrush hazards in underground engineering. Direct current (DC) resistivity method is a widely used method for routine detection, advanced detection and real-time monitoring of water-bearing structures, due to its high sensitivity to groundwater. In this study, the DC resistivity method applied to underground engineering is reviewed and discussed, including the observation mode, multiple inversions, and real-time monitoring. It is shown that a priori information constrained inversion is desirable to reduce the non-uniqueness of inversion, with which the accuracy of detection can be significantly improved. The focused resistivity method is prospective for advanced detection; with this method, the flanking interference can be reduced and the detection distance is increased subsequently. The time-lapse resistivity inversion method is suitable for the regions with continuous conductivity changes, and it can be used to monitor water inrush in those regions. Based on above-mentioned features of various methods in terms of benefits and limitations, we propose a three-dimensional (3D) induced polarization method characterized with multi-electrode array, and introduce it into tunnels and mines combining with real-time monitoring with time-lapse inversion and cross-hole resistivity method. At last, the prospective applications of DC resistivity method are discussed as follows: (1) available advanced detection technology and instrument in tunnel excavated by tunnel boring machine (TBM), (2) high-resolution detection method in holes, (3) four-dimensional (4D) monitoring technology for water inrush sources, and (4) estimation of water volume in water-bearing structures.

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