计算层状介质中电磁场的层矩阵法

现有人工源频率域电磁法的研究大多仅针对某种具体的方法，而较少将问题综合起来分析.本文综合多种方法的共同点提出了层矩阵法，它采取了源置于层间的模型进行公式的推导，理论上可以计算任意层状介质中任意位置的任意场源在空间中任意位置产生的场强，可适用于多种电磁法的正演模拟计算.层矩阵法的核心是对空间域的变量x, y, z中的x和y变量进行傅氏变换后转换到波数域k_x和k_y中，在波数域利用边界条件，用层矩阵建立起各层的关系后计算得到各层的波数域电磁场值，然后经过二维反傅氏变换最终得到空间域中任意位置的场值.因为文中定义的层矩阵是建立层关系的关键，所以称此方法为层矩阵法.本文以水平电偶源为例独立推导了层状介质中人工源频率域电磁场解的理论公式.为了验证方法的正确性，文中建立了多种模型，利用自行编排的程序将层矩阵法与现有文献的各种解析公式的解进行了对比，结果表明本文提出的层矩阵法是灵活的、可靠的.

Calculate electromagnetic fields in stratified medium with layer-matrix method

The researches of artificial-source frequency-domain electromagnetic methods are often separated from each other.The layer-matrix method put source in stratified medium, gives frequency domain electromagnetic fields solution for stratified medium, can calculate electromagnetic fields at random position for random source, it is suitable for many kinds of electromagnetic methods. The key of layer-matrix method is establishing equations by using layer matrix in wave number (k_x, k_y, z) domain, then obtains the electromagnetic fields of wave number domain. After inverse Fourier transform, we can get electromagnetic fields at random position in spatial domain. Because layer matrix is the key of establishing equations, so we call it the layer-matrix method. In order to confirm the reliability of layer-matrix method, we compare it with some analytic solutions. The results indicate that the layer-matrix technique is credible and effective.