时间域航空电磁法2．5维有限元模拟

摘要

Based on the triangular mesh dissection of the finite element method, this paper presents the 2.5⁃D airborne transient elec⁃tromagnetic method forward modeling. Firstly the time domain electromagnetic partial equations are converted into laplace domain with the numerical time⁃frequency transform algorithm, then the 2.5⁃D expressions are obtained from 3⁃D case by adopting the fourier trans⁃form. The airborne data are acquired from the results of the digital inverse laplace transform of the 2⁃D electric and magnetic compo⁃nents in laplacian domain, which is computed using finite element method. Instead of the conventional algorithm, the anomalous field method is employed throughout the finite element process, so that the source singularity of total field is avoided. the source impact is embodied in the differencial equation by appling the background electromagnetic field item. The computing accuracy and efficiency would be managed rigorously due to the wide dynamic range of the transient singnal, as well as the two⁃time inverse laplace and fourier transforms. Otherwise the accumulative error will soar acceptably. The synthetic model experiments shows that the numeric modeling so⁃lutions match the analytical results of homogeneous and layered erath responses well, which also proves the effectiveness of the algo⁃rithm.%采用三角网格剖分的有限元法，研究了2．5维航空瞬变电磁法正演模拟问题。利用时频变换数值方法将时间域电磁场转换到拉氏域，再利用傅里叶变换将三维问题降维变为2．5维问题，然后由有限元法求解得到拉氏域二维电磁场，逆拉氏变换后得到时间域航空瞬变响应。为了回避正演模拟中总感应磁场在场源处的奇异性问题，采用异常场算法，场源响应通过在微分方程中施加背景电磁场实现。由于瞬变电磁信号具有较大的动态范围，而且需要经过两次正、逆拉氏变换和傅里叶变换，每个环节的计算精度和速度要严格控制在较高的水平上，否则积累误差会非常大。模型计算表明均匀大地和层状大地模型解析解与数值解吻合很好。这证明该算法是正确可行的，可作为研究二维复杂地质体的方法手段。