3-D Modeling and Analysis of Small-Loop Source TDEM Method Based on CFS-PML-CN-FDTD Method

The small-loop time-domain electromagnetic (TDEM) method has been widely used in urban underground space detection in recent years due to the small workspace requirements. Due to the small side length of the transmitting coil of the small-loop electromagnetic method, more difficulties have been introduced in modeling and instrument development. The traditional modeling method cannot include source calculation, and the error becomes significantly large when calculating the initial field of the small-loop, and the cross iteration of electric and magnetic fields also increases the modeling error of the small-loop. Therefore, a high-precision 3-D small-loop source TDEM modeling method need to be proposed to provide the theoretical basis for feature analysis, inversion, and instrument parameter design. In this article, the electromagnetic wave equations are adopted as the controlling equations and discretized based on the Crank-Nicolson finite-difference time-domain (CN-FDTD) method. The entire computational space, including air and ground, is subdivided into sources to support 3-D small-loop TDEM modeling for shallow anomalous body conditions. Furthermore, the iterative formulas of the electromagnetic wave equations in the complex frequency-shifted perfect match layer (CFS-PML) are derived, the reflection errors are largely suppressed, and the modeling accuracy is significantly improved. Finally, the effectiveness of the improved method is verified by homogeneous models, layered models, and complex anomaly models. In addition, analyzing the propagation characteristics of the small-loop can guide the setting of the receiver sampling rate and improve the accuracy of detection. The results show that the improved method can achieve stable, low-memory, and high-precision 3-D small-loop source TDEM modeling, which can provide theoretical support for the application of the TDEM method in urban and shallow detection.