In this article, to solve the frequency-domain airborne electromagnetic (EM) modeling problem, we express the electric and magnetic field by the vector magnetic potential and the scalar electric potential and derive the governing equation using the Galerkin weighted residual method under the Coulomb gauge. To avoid the strong singularity of the solution near the transmitting source, we directly solve the relatively slow-changing secondary potential. By introducing the spectral element method (SEM) based on unstructured tetrahedral grids, in which the EM field in each element is characterized by high-order Proriol–Koornwinder–Dubiner (PKD) orthogonal polynomials, we can obtain stable and accurate numerical solutions. By establishing the mapping relationship between the physical domain, the right-angled tetrahedral reference domain, and the orthogonal hexahedral domain, we can easily accomplish the element matrix analysis and calculation. The numerical examples show that, when the SEM is used to simulate the airborne EM response, a high accuracy can be obtained even if a very coarse grid is used. Furthermore, since the tetrahedral grids can easily model the complex boundaries, the SEM based on unstructured grids has significant advantages for simulating complex underground structures.

We develop a new spectral-element method by incorporating a domain-decomposition technique, referred to as the dual-primal spectral-element tearing and interconnecting method (SETI-DP), for high-precision forward simulation of the 3D direct current (DC) resistivity method. To handle the terrain and complex underground structures, we use unstructured tetrahedral meshes to divide the computational domain. These meshes are then partitioned into nonoverlapping subdomains. By applying a continuity condition of the current density to be solved, all subdomains become coupled to each other. Using a Lagrange multiplier, the global equation system for our forward modeling can be simplified into that for the subdomain interfaces, and the continuity conditions on the subdomain interfaces are obtained by solving these subdomain interface equations. Finally, the forward problem for each subdomain is solved independently using these boundary conditions. Numerical experiments indicate that our algorithm can greatly improve computational efficiency and reduce memory consumption without losing accuracy when choosing the appropriate number of subdomains. We further apply our method to the forward simulation of a tunnel detection problem. The numerical results demonstrate that our new SETI-DP method can effectively simulate the tunnel’s complex structures, and the DC resistivity method can detect the adverse geologic bodies in front of the tunnel face.

In the process of tunnel construction and urban underground space development, karst caves and cavities often cause casualties and economic losses. However, due to the influence of complex terrain and buildings on the ground, conventional geophysical detection methods cannot obtain accurate information on hidden geological bodies under buildings and in front of tunnels. The grounded-wire source transient electromagnetic method (TEM) has a relatively simple transmission and reception system and is widely used in the detection of coal mine goafs and karst caves. Therefore, we apply this method to bore-holes and propose a cross-hole grounded-wire source TEM detection method. This method involves deploying grounded-wire transmitting sources and receiving electrodes in different bore-holes to accurately detect concealed geological hazards in urban underground construction processes. In this study, we use the research methods of the TEM field diffusion mechanism of a vertical grounded-wire source, a numerical simulation of a cross-hole and grounded-wire source TEM of different electrical models and an indoor physical experiment in a strong interference environment to analyze the detection ability of a cross-hole grounded-wire source TEM. Differential processing was applied to both the numerical simulation and experimental data. The research results indicated that, owing to the influence of the ground–air boundary, extreme values of the z component of the electric field moved toward deeper regions away from the grounded-wire source. Differential processing effectively increased the detection accuracy of this method, and a higher differential order provided clearer characterization of the boundaries of the target body. Spatial averaging filtering can effectively remove the influence of random noise, enhancing the ability of the cross-hole grounded-wire source TEM to identify anomalous bodies. After difference processing, the cross-hole grounded-wire source TEM data could more precisely capture the boundaries of concealed geological bodies in urban underground spaces.

Seepage is a common hydrogeologic hazard in engineering. Determining the seepage paths is vital for derisking the instability of embankment structures. With the improvement of the acquisition accuracy of magnetic sensors, the magnetometric resistivity method has become an emerging technology for detecting seepage paths through earth-filled dams. This technique is nondestructive and gives prominent signals. However, the resulting magnetic data have seen ambiguity in fully determining the targets. We develop an induced magnetic gradient surveying approach to monitor seepage paths in earth-filled dams. First, we briefly review the electromagnetic theory for the magnetic gradient tensor based on Maxwell’s equations. To match against the measurements, we present an accurate modeling framework using the third-order finite-element method and a novel compact difference scheme. We verify our approach on semianalytical 1D and 3D models. Systematic modeling studies are then carried out to investigate the spatial distribution characteristics and sensitivities of the induced magnetic gradient to the seepage in typical dam scenarios. In addition, we conduct two field experiments in the Zhongmou experimental base and Xixiayuan Reservoir in Henan Province, China, respectively. The induced magnetic field vector and its gradient components are both acquired. Cross-validation with a priori geologic information shows that the seepage path can be spatially identified by the induced magnetic gradient components Byy, Byz, Bzy, and Bzz, whereas the field components failed to locate the seepage pathways. This successful application indicates that our approach could be a promising solution for seepage path discrimination in earth-filled dams with high resolution.

Coal and gas outburst accident is a significant risk in high-gas outburst coal seams, and effective pressure relief gas extraction plays a crucial role in mitigating these hazards. The core challenge lies in understanding the seepage behavior of the coal rock body in the three zones of the overburden during multiple protective layer mining. This study employed a damaged coal rock body seepage test system to conduct repeated loading and unloading seepage tests on coal rock samples from these zones. The results show that the permeability of the broken coal rock body in the caving zone decreases with increasing stress, while it increases with (a) larger particle sizes of the broken coal rock body and (b) with a higher proportion of rock in the sample. The permeability distribution in the goaf follows an “O”-shaped circle pattern and gradually increases from the center outward. Additionally, When the protected layer is located within the fracture zone of the protective layer mining, and the first protective layer mining has already resulted in significant stress relief and permeability improvement, the effect of stress release and permeability enhancement from the second protective layer mining becomes less pronounced. In contrast, if the first protective layer mining does not sufficiently relieve stress or enhance permeability, the second protective layer mining has a more substantial effect. These findings are significant for analyzing the effects of pressure relief enhancement in multi-protective layer mining of high-gas outburst coal seams and for optimizing gas extraction.

To address the challenge of accurately detecting hidden water inrush hazards ahead of working faces, a cross-hole transient electromagnetic (TEM) method utilizing a grounded-wire source is proposed. The technique positions a step-current-driven grounded-wire source within a working-face borehole, while electrode arrays in adjacent boreholes measure secondary electric field responses. This configuration minimizes interference from metal supports or machines, thereby enhancing the signal-to-noise ratio of the TEM signals. A theoretical analysis based on the unstructured finite-element (FE) method is used to investigate the configuration. The collected data are processed using differential techniques, and the results confirm the method’s effectiveness in detecting anomalies. This paper investigates the response of our cross-hole method to anomalies in terms of size, resistivity contrasts, and spatial location, with anomaly boundaries quantitatively delineated via first-order differential analysis. This significantly enhances the capability of TEM detection in identifying anomalies. A comparison between our cross-hole method and the traditional roadway–borehole TEM method, using the trapped column model, demonstrates that the proposed cross-hole device more effectively locates anomalies and improves accuracy. Furthermore, this technique enables the formation of a 3D observation framework by utilizing existing boreholes, presenting promising prospects for future applications.