2.5-D forward modeling of the frequency-domain ground-airborne electromagnetic response in areas with topographic relief
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摘要:
频率域地空电磁探测方法是指在地面布设人工场源，在空中测量电磁场的一种高效的地球物理勘探技术.该方法具有大范围、高通过性、快速测量的优势，尤其适合崎岖山地、沙漠、沼泽、海陆交互带等复杂地貌区域的资源勘查.但是这些地区的地形起伏通常较大，因此分析地形对地空电磁响应的影响具有重要意义.本文利用有限元法对频率域地空电磁响应进行了正演计算，分析了起伏地表条件下的频率域地空电磁响应特征.首先利用傅里叶变换将2.5维问题转化成二维问题，利用伽辽金加权余量法推导了相应的离散有限元方程组.采用任意四边形单元对区域进行不均匀网格剖分，源和异常体附近网格加密处理，保证计算精度，远离目标区域网格逐渐稀疏，模拟无穷远边界，降低对计算资源的要求.在单元内进行插值，将有限元方程组变换为线性方程组，采用总场算法，利用具有一定面积的伪δ函数表达源电流分布，源项近似为分布在以电偶极源为中心的25个节点上.通过求解线性方程组得到波数域电磁响应，再对波数域电磁场响应进行反傅里叶变换从而获得空间域2.5维频率域电磁场值.通过对比2.5维正演结果与均匀半空间解析解，验证了本文算法的精度，同时本文还对地空电磁场与地面电磁场的响应特性进行了对比.
Abstract:Ground-airborne frequency-domain electromagnetic method is an effective and efficient geophysical prospecting method. It usually places the controlled source on the ground and measure the electromagnetic field in the air. This method can achieve fast measurement in large scale, is especially suitable for resource exploration in rugged mountains, deserts, swamps, sea-land interaction zones and other areas with complex topography relief. However, in these areas, the topography relief is serious, so the study of the topographic effect on ground-airborne electromagnetic response is meaningful. In this paper, the 2.5D frequency domain ground-airborne electromagnetic response of topography earth model was calculated based on the finite element method and the response characteristic is analyzed. Fourier transform was applied to the Maxwell's equations to transform a 2.5D problem into a 2D problem, and then the discrete finite element equation was deduced using the Galerkin weighted residual method. The surveyed region is subdivided into many arbitrary quadrilateral elements with different sizes, the ones region near the source and the target have smaller size to ensure the accuracy of numerical calculation, the ones away from the target region have bigger size to simulate infinite boundary and reduce the requirements for computing resource. Interpolation is conducted in the element to transform the finite element equations to the linear system of equations. Using the total field algorithm, the pseudo-delta function with a certain area is employed to approximate the distribution of the source current, the source terms are approximately distributed at 25 nodes centered on the electric dipole source. By solving the equation, the solution of electromagnetic field in wavenumber domain was obtained, then the solution of electromagnetic field in spatial domain can be calculated by the Invers Fourier Transformation. The accuracy of our algorithm was verified by the comparison of our 2.5D forward modeling results and the analytical results. We also compared the electromagnetic field response characteristics measured in the air and on the ground.
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图 2
单元编号和坐标变换关系示意图
Figure 2.
Schematic diagram of cell numbering and coordinate conversion
图 5
无地形异常体模型电磁场响应曲线
Figure 5.
Electromagnetic response curves of target earth model without topography
图 8
带地形无异常体模型，地面测量时的电磁场响应曲线
Figure 8.
Electromagnetic response curves of topography earth model without target when measured on ground surface
图 9
带地形无异常体模型，空中随地形测量时的电磁场响应曲线
Figure 9.
Electromagnetic response curves of topography earth model without target when measured in the air along topography
图 10
带地形无异常体模型，空中同一高度测量时的电磁场响应曲线
Figure 10.
Electromagnetic response curves of topography earth model without target when measured in the air at constant height
图 12
地面测量时，凸地形异常体模型的电磁场响应曲线
Figure 12.
Electromagnetic response curves of convex topography target earth model when measured on ground surface
图 13
地面测量时，凹地形异常体模型的电磁场响应曲线
Figure 13.
Electromagnetic response curves of concave topography target earth model when measured on ground surface
图 14
空中随地形测量时，带地形异常体模型的磁场响应曲线
Figure 14.
Magnetic field curves of topography target earth model when measured in the air along the topography
图 15
空中同一高度测量时，带地形异常体模型的磁场响应曲线
Figure 15.
Magnetic field curves of topography target earth model when measured in the air at constant height
表 1
异常体模型参数
Table 1.
Parameters of target earth model
模型参数 背景电阻率/Ωm 异常体电阻率/Ωm 异常体埋深/m 异常体横向位置x/m 异常体纵向位置z/m 高阻体模型 100 10000 183 7915~8415 -183~-433 低阻体模型 100 50 183 7915~8415 -183~-433 
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表 2
带地形无异常体模型参数
Table 2.
Parameters of topography earth model without target
模型参数 异常体横向位置x/m 异常体纵向位置z/m 凹地形模型 7665~8665 -50~0 凸地形模型 7665~8665 0 ~50
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