| 一类非均匀介质中电磁场的延拓 |
| |
| 引用本文： | 栾文贵.一类非均匀介质中电磁场的延拓[J].地球物理学报,1988,31(6):695-707. |
| |
| 作者姓名： | 栾文贵 |
| |
| 作者单位： | 中国科学院计算中心 北京 |
| |
| 基金项目： | 国家自然科学基金，地震学联合科学基金 |
| |
| 摘 要： | 本文讨论具垂向光滑变化的非均匀介质中电磁场延拓的数学物理问题及稳定化的算法原理。首先从电磁场的基本方程出发,导出了垂向非均匀介质下磁场的垂直分量所满足的二阶偏微分方程,并且依照实际背景将场的延拓问题化归为解相应二阶椭圆型方程的Cauchy问题。接着利用Fourier变换方法得到了场延拓的形式表达式,然后给出了几种特殊垂向非均匀介质下场延拓的精确解析公式。最后,应用正则化方法建立了场延拓的稳定化的公式,给出了所得公式的离散化形式,同时指出了相应正则化参数的选择原则。
|
| 关 键 词： | 电磁场 非均匀介质 正则化方法 |
| 收稿时间： | 1985-04-09 |
THE CONTINUATION OF ELECTROMAGNETIC FIELDS IN A CLASS OF NON-HOMOGENEOUS MEDIUM |
| |
| LUAN WEN-GUI.THE CONTINUATION OF ELECTROMAGNETIC FIELDS IN A CLASS OF NON-HOMOGENEOUS MEDIUM[J].Chinese Journal of Geophysics,1988,31(6):695-707. |
| |
| Authors: | LUAN WEN-GUI |
| |
| Institution: | Computing Center, Acadcmla Sinica, Beijing |
| |
| Abstract: | In this paper, we discuss some mathematical physics problems and stabilized algorithm principle on the continuation of electromagnetic fields in non-homogeneous medium with vertical smoothing variance. At first, a partial differential equation of the second order satisfying the vertical component of the magnetic field under the vertical non-homogeneous medium is derived, starting off with fundamental equation of electromagnetic fields, and the continuation problem of the field is reduced to solving the Cauchy problem for the corresponding elliptic equation of the second order, according to practical background. Then the formal expression for the field continuation is obtained by the method of the Fourier transform, and the precise analytic formulas for the field continuation under a number of special non-homogeneous medium are given. Finally, using the regularization method, the stabilizated formula for the field continuation is established, the discretization form of resulting formula is given, and the selected principles of the corresponding regularization parameter are shown. |
| |
| Keywords: | Electromagnetic field Non-homogeneous medium Regularization method |
| 本文献已被 CNKI 等数据库收录！ |
| 点击此处可从《地球物理学报》浏览原始摘要信息 |
| 点击此处可从《地球物理学报》下载免费的PDF全文 |
|
