有限元直接迭代算法及其在线源频率域电磁响应计算中的应用

DIRECT ITERATIVE FINITE ELEMENT (DIFE) ALGORITHM AND ITS APPLICATION TO ELECTROMAGNETIC RESPONSE MODELING OF LINE CURRENT SOURCE

采用有限元直接迭代算法实现了线源频率域测深电磁响应的二维正演计算 .首先给出了线源正演问题的有限元直接迭代格式 ,然后由迭代法进行求解 .在处理奇异源问题上 ,采用向内递推的组合网格技巧 ,在源点附近可进行局部加密 ,并实现粗细网格的对接 ,从而较好地解决了奇异源附近的计算问题 .还提出一种迭代求取全区视电阻率的方法 ,避免了远近区的划分 .通过对均匀半空间、层状介质和二维模型电磁响应的计算 ,获得了与大地电磁测深相似的视电阻率曲线 ,验证了算法的正确性 ;通过对计算结果的分析 ,在理论上说明了线源频率域近区测深的可行性 .

The Direct Iterative Finite Element algorithm (DIFE) is used to calculate the electromagnetic responses at earth surface excited by a line current source. The direct iterative formulation is deduced first, then iterative method is applied to solve the Finite Element (FE) equations. The compound griding method, including re-interpolation scheme at the adjacent points, has been realized to denser local grids near the source point, thus the precision of field calculation near the source point is assured. An iterative approach has been put forward to obtain the whole range apparent resistivity from the electric field response excited by line current source. This approach has been verified through the calculations of uniform half space model, layered earth model and two dimensional earth models. For all these models, apparent resistivity curves, which are very similar to magnetotelluric responses, are obtained. It shows in theory that the frequency domain sounding in near zone of the line current source is possible.