论文部分内容阅读
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.
In this paper, based on the time-domain Maxwell’s equations in a homogeneous medium, the pseudo-spectral method is used to simulate the diffusion of three-dimensional full-space transient electromagnetic fields. The six components of the electromagnetic field are organized into uniform equations. Value problem is solved by using the Fast Fourier Transform to approximate the partial derivatives of the space and the Chebyshev polynomial evolution operator is used to solve the equation.The comparison between the analytical solutions of the transient source response in a homogeneous medium and the full space verifies the effectiveness of the pseudospectral method The calculation and analysis of the response of high resistance body and low resistance body in homogeneous medium at different time points shows that the transient electromagnetic method is not sensitive to high resistance body but can distinguish the characteristics of low resistance body well and reflect the time Domain pseudospectral method can continuously calculate the electromagnetic field diffusion and the response process with the low resistance body.Finally, it is discussed that the future of the pseudospectral method may be applied to the fields of mine transient electromagnetic field and the seafloor transient electromagnetic field.