起伏地表频域/时域航空电磁系统三维正演模拟研究

3D modeling on topographic effect for frequency-/time-domain airborne EM systems

由于航空电磁系统具有工作频率低、时间延迟短等特点,地形对航空电磁响应有很大影响,忽略地形影响会给航空电磁数据解释造成很大误差.本文将基于非结构化网格的矢量有限元法应用于模拟起伏地表条件下频域/时域(FD/TD)三维航空电磁系统响应.该方法由于采用非结构网格,与传统的结构化网格电磁正演算法相比,能更好地拟合地形和地下不规则异常体,提高对不规则地形和地下介质航空电磁响应的计算精度.通过将计算结果与半空间模型的半解析解及已发表的结果进行对比,检验了本文算法的精度.通过对典型山峰和山谷地形航空电磁响应分析对比,总结了地形对航空电磁响应的影响特征.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.

Airborne electromagnetic（AEM）exploration is an effective geophysical tool,especially suitable for survey in ridged mountain areas. Theoretical research shows that topography has serious effect on airborne EM responses.Negligence of this effect may create large errors in AEM interpretations.However,until now little study has been done on 3D topographic effect on frequency-/time-domain（FD/TD）airborne EM systems.Most scholars dealt with this problem using a structured grid that can′t simulate topography accurately.We present analgorithm using edge-based unstructured finite-element method（FEM）.Starting from the frequency-domain Maxwell′s equations,we obtain a vector Helmholtz equation for a stable solution when air is present.We use the Galerkin method to discretize the Helmholtz equation and obtain the final finite-element equations.To accelerate the calculation speed,the source response in a free-space is used as the primary field,while the direct solver is used to deal with the multiple-source problem.After calculating the frequency-domain AEM responses,a Hankel′s transform is applied to obtain the time-domain EM responses.To check the accuracy of the presented algorithm for AEM topographic modeling,we compare our results with both the semi-analytical results and those from published literatures.After that,we calculate the EM responses for 3D models with only topography and with both topography and anomalous targets.From profiled AEM responses,we draw similar conclusions to those of Yin（2015）,while from area AEM responses,we find that：1）for frequency-domain AEM systems,the real part of AEM response contains more information to deep earth than the imaginary part;2）for time-domain AEM system,the magnetic induction dB/dt reveals the underground conductivity distribution better than the B field.These features provide the theoretical basis for identification and correction of topographic effect from the AEM measurements.