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.
