Transient electromagnetic method (TEM) inversion is significantly nonlinear. To eliminate the multicollinearity problem faced by the extreme learning machine (ELM) algorithm for TEM inversion, an improved ELM algorithm (F-ELM) based on fractal dimension technology is proposed. By reducing the dimension of the hidden layer output matrix (H) based on fractal dimension theory without losing the main statistical information, the proposed algorithm can not only guarantee the full column rank of the newly produced hidden layer output matrix $\left(H^{\prime }\right)$ but also enhance the training speed of the overall process. To prove the effectiveness of the F-ELM algorithm, a synthetic example and a field example using TEM inversion are established in this study. The experimental results illustrate that compared with the ordinary ELM algorithm and its variants, the proposed algorithm greatly reduces the computing time, improves the inversion accuracy and stability of the algorithm. Furthermore, it is also proven that the F-ELM algorithm is a very effective technique for TEM inversion.

瞬态电磁法 (TEM) 反演是显着非线性的。针对TEM反演极限学习机(ELM)算法面临的多重共线性问题，提出了一种基于分形维数技术的改进ELM算法(F-ELM)。该算法基于分形维数理论对隐藏层输出矩阵（H）进行降维，同时不丢失主要统计信息，不仅可以保证新生成的隐藏层输出矩阵的全列秩$\left(H^{\prime }\right)$还能提升整个过程的训练速度。为了证明 F-ELM 算法的有效性，本研究建立了一个合成实例和一个使用 TEM 反演的场实例。实验结果表明，与普通ELM算法及其变体相比，该算法大大减少了计算时间，提高了算法的反演精度和稳定性。此外，还证明了 F-ELM 算法是一种非常有效的 TEM 反演技术。