An Accurate 3-D CFS-PML Based Crank–Nicolson FDTD Method and Its Applications in Low-Frequency Subsurface Sensing

An unsplit-field and accurate Crank-Nicolson cycle-sweep-uniform finite-difference time-domain (CNCSU-FDTD) method based on the complex-frequency-shifted perfectly matched layer (CFS-PML) is proposed. It is applied to 3-D low-frequency subsurface electromagnetic sensing problems. The presented CNCSU-FDTD takes advantage of both CFS-PML and unconditionally stable CN method so that it can attenuate evanescent waves, eliminate late-time reflections, and overcome the stability limits of the FDTD method. The time step intervals in CNCSU-FDTD can be 1000 times larger than that in the regular FDTD for the low-frequency sensing centered at 25 Hz while remaining accurate. Several 3-D numerical examples in the airborne transient electromagnetics system have been demonstrated to validate the proposed method. The CFS-PML-based CNCSU-FDTD method not only attains good accuracy but also saves several dozen times of CPU time as compared with the regular FDTD method.