2.5维起伏地表条件下时间域航空电磁正演模拟

时间域航空电磁作为一种高效地球物理勘探技术特别适合我国地形复杂地区(沙漠、高山、湖泊、沼泽等)资源勘查.然而,这些地区地形起伏较大,对航空电磁响应有严重影响,忽略地形影响会给航空电磁数据解释造成很大误差.到目前为止人们对航空电磁地形效应特征研究十分有限.本文提出了基于非结构化网格的有限元法模拟带地形时间域航空电磁系统响应.该方法与基于结构化网格的有限差分相比能更好地模拟地形.首先通过傅里叶变换将2.5维问题转化成二维问题,利用伽辽金方法对二维问题进行离散.通过使用MUMPS求解器,得到波数域电磁响应.利用反傅里叶变换将波数域电磁响应变换到空间域,并利用正弦变换将其变换到时间域,得到2.5维时间域航空电磁响应.通过将本文的计算结果与半空间模型解析解及其他已发表的结果进行对比,检验了本文算法的精度.最后,我们系统分析了山峰和山谷地形对航空响应的影响特征.本文研究结果对航空电磁地形效应的识别和校正具有指导意义.

2.5-D forward modeling of the time-domain airborne EM system in areas with topographic relief

As an effective and efficient geophysical tool, airborne electromagnetic (AEM) has been widely used in many fields such as geological mapping, hydrocarbon and mineral exploration, and environmental and engineering surveys. AEM data interpretation commonly uses a horizontally layered earth model. However,in rugged mountain areas, the topography relief can pose serious effects on AEM survey data, resulting in the distortion of AEM inversion results. The study of the topographic effect on AEM systems has attracted much attention worldwide, but most work has focused on frequency-domain EM systems, little for time-domain airborne EM systems. This paper presents an effort to address this issue. The finite-element (FE) method based on an unstructured grid is used to simulate 2.5-D AEM responses for a topographic earth. We adopt this method, because it can calculate the AEM responses of complex models, while the unstructured grid can very well simulate the topography. To avoid the singularity, we divide the electromagnetic field into a background field and a secondary field. We apply the Fourier transform to Maxwell's equations to transform a 2.5D problem into a 2D problem and solve it in the wavenumber domain. On the outside boundaries, we assume the field vanishes. We use the Galerkin method to discretize the Maxwell equations and solve the final FE equations by the MUMPS solver.To check the accuracy of our algorithm, we compare our results with both analytical results and those from the literature. After that, we calculate the responses of model 1) with only topography; 2) with both topography and one anomaly body; and 3) with both topography and multiple anomaly bodies both in the frequency-domain and time-domain. Finally, we calculate the relative AEM responses of abnormal bodies and topography for both the frequency and time domains to investigate the influence of topography on AEM system responses. Topography has serious effects on the responses of airborne EM systems, especially in the high-frequency range or early time-channels. Numerical experiments show that close to the node points of the topography, AEM responses are demonstrated by sharp changes. Special attention need to be paid to the topographic effect when interpreting AEM survey data over rugged topographic areas. Besides, the topographic effect mainly occurs at the high frequency end and early time-channels, the EM responses of underground conductors mainly occur at low frequencies and later time-channels. These features provide the theoretical basis to identify the responses from the targets and the topography, so that the topographic effect on the AEM system responses can be corrected.