Analysis of a Whole-Space Transient Electromagnetic Field in 2.5-Dimensional FDTD Geoelectric Modeling

Mine water inrush poses a serious threat to the safe production of coal mines in China. The transient electromagnetic method (TEM) on the ground has been applied to explore water-bearing structures, but the resolution is low. Therefore, some geophysicists in China moved the TEM onto underground coal mine roadways and obtained good results at the end of the last century. Although the TEM has been applied in mining for many years, there are so few theoretical studies that the data interpretation is not accurate. It is necessary to study the transient electromagnetic field diffusion in the entire space with physical or numerical simulation methods. First, based on the diffusion equations, we deduced the wave number domain equations, whose whole-space electromagnetic field is excited by a 3-D source in a 2-D geoelectric model; then, we derived the 2.5-D finite-difference time domain equations. At the beginning of the calculation, we gave the grid nodes near the source the initial values with the cosine filtering method. To improve the calculating efficiency, the time intervals gradually increased with time. At the end of the calculation, we transformed the calculating results from the wave number domain to the space domain by fitting the segmented exponential function. Compared with the analytical solutions, the numerical solutions are accurate, and the algorithm is reliable and efficient. The simulation results of a collapse-column model show that the transient electromagnetic field diffusion in the entire space is dominated by low-resistivity bodies.