大地电性源和固定翼航空瞬变电磁系统作为航空瞬变电磁勘探的主要表现形式，是极低频地下电磁探测的重要研究对象。为了高效探测电磁场变化，大幅提高正演数值算法的计算效率，需要突破因求解极低频探测问题而导致的计算量巨大的学术难题。在极低频地下电磁探测实现中，有条件稳定的时域有限差分算法面临高空间和高周期采样密度的问题，导致该算法计算效率急剧下降，变得不切实际。为了克服有条件稳定的限制，本项目拟通过采用分解分裂技术，研究基于无条件稳定的改进型克兰克-尼克尔森时域有限差分法在Z变换技术离散下的新理论和新方法。针对极低频电磁探测问题，分别提出了：（1）系数可修正的克兰克-尼克尔森一致循环扫描法；（2）可并行的克兰克-尼克尔森直接分裂法；（3）高精度可并行的克兰克-尼克尔森近似因子分解法。项目的完成可以显著地提高计算效率和精度，为现场电磁探测节约时间和经济成本。

As the main form of airborne transient electromagnetic system (ATEM), both the grounded electrical-source and fixed-wing ATEMs are important research objects of the extremely low-frequency subsurface sensing. In order to efficiently detect fluctuations of electromagnetic fields and improve computational efficiencies of numerical methods, a very large number of computational burdens due to working under extremely low frequency need overcoming as an academic difficulty. under the implementations of extremely low-frequency subsurface sensing, the conditionally-stable finite-difference time-domain (FDTD) encounters circumstances of high spatial and temporal sampling densities, leading to the drastic deterioration of its computational efficiency and even becoming impractical beyond the tolerance in ATEM applications. To overcome the limitation of conditional stability, this project studies the new theories and methods of modified CN-FDTD with the unconditional stability based on discretization of Z-transform methods by adopting different approximation and splitting schemes. Aiming at solving extremely low-frequency ATEM problems, three modified CN-FDTD are proposed respectively, including (1) the Crank-Nicolson-Cycle-Sweep-Uniform FDTD (CNCSU-FDTD) with coefficient-modification technique for reducing the numerical dispersion; (2) the Crank-Nicolson-Direct-Splitting FDTD (CNDS-FDTD) with parallelizable computation; (3) the higher accuracy Crank-Nicolson-Approximate-Factorization-Splitting FDTD (CNAFS-FDTD) with parallelizable computation. The accomplishment of the project will substantially improve the computational efficiency and accuracy so that more time and economic cost can be saved for the electromagnetic sensing in the spot scene.