中文摘要：

本文根据均匀介质中时间域麦克斯韦方程组,应用伪谱法模拟三维全空间瞬变电磁场的扩散.将电磁场的六分量整理成统一的方程,通过初值条件替代源项将源响应问题转化为初值问题.使用快速傅里叶变换近似空间偏导数,应用切比雪夫多项式近似演化算子来求解方程.通过与全空间均匀介质瞬态线源响应的解析解的比较,验证伪谱法的有效性.计算和分析不同时刻全空间均匀介质中高阻体和低阻体的响应,说明瞬变电磁法对高阻体灵敏度不高,但能较好的分辨低阻体的特点,并反映出时间域伪谱法的优点,即可以连续地计算出电磁场扩散及与低阻体的响应过程.最后讨论伪谱法未来可能应用于矿井瞬变电磁和海底瞬变电磁等领域.

英文摘要：

Based on the 3D Maxwell＇s equation in time domain,the pseudo-spectral method is used to simulate electromagnetic propagation in whole-space in time domain in this paper. The six components of electromagnetic field are transformed to same form.By means of replacing source with initial condition,the problem of respond with source is transformed to the problem with initial condition. Then the fast Fourier transforming is used to compute spatial derivatives and the Chebyshev expansion to approximate evolution operator. To verify the method,the numerical solutions of response of transient line in whole-space are compared with analytical solutions. The numerical solutions of response of a transient electric dipole in whole-space shows that transient electromagnetic method（ TEM） has high resolution to low resistance and low resolution to high resistance. And the advantage of pseudospectral method is that it can simulate electromagnetic propagation and the response of the low resistance continuously. Finaly, it discusses the potential application fields of pseudo-spectral method are mine and seafloor TEM.