三维地形频率域井筒电磁场区域积分方程法模拟

Domain decomposition based integral equation modeling of 3-dimensional topography in frequency domain for well electromagnetic field

井筒电磁法作为一种高效的地球物理勘探技术特别适合我国地形复杂地区(沙漠、高山等)的油气资源勘探.地形起伏区域对井筒电磁响应的观测具有严重影响,但到目前为止人们对三维井筒电磁地形效应特征的研究十分有限.本文提出基于区域划分的积分方程法模拟带地形频率域井筒电磁系统响应,与基于偏微分方程的有限差分、有限单元法相比,该方法能更高效地模拟地形响应.首先根据地形起伏情况定义感应数,将地形条件下目标体的井筒电磁场模拟区域划分为参考模型、背景介质及目标体介质分布子区域,针对各子区域的模拟计算特点,配置Anderson算法、稳定型双共轭梯度-快速傅里叶积分方程算法,从而获得三维地形频率域井筒电磁场响应.通过将计算结果与半空间模型的Anderson算法解析解、带山谷地形模型的其他已发表的三维边界积分方程结果进行对比,检验了本文算法的精度及高效性.最后,系统分析了山谷地形对井筒电磁地井观测系统电磁场响应的影响特征.本文研究结果对三维井筒电磁地形效应的识别和校正具有指导意义.

As an efficient geophysical exploration technology, well electromagnetic method is particularly applicable to oil and gas exploration in China’s complex terrain areas(deserts, mountains, etc.). A serious influence of topographic relief area on the electromagnetic response of well is inevitable but challenging. To the best of our knowledge, there is no literature on modeling the electromagnetic response of three-dimensional(3D)topography with well electromagnetic method. Based on the domain decomposition, an integral equation method is presented to simulate the electromagnetic response of 3D topography in frequency domain via the well electromagnetic method. Compared with the finite difference and finite element method based on partial differential equation, this method is very efficient in simulating topographic response without huge computation or truncation boundary error accumulation or special boundary condition requirements. Firstly, an induction coefficient is defined according to the topographic relief situation. Then the computational domain consisting of the target body, background medium and 3D topography is divided into reference model, background medium and the distribution of target body medium area. According to the characteristics of each sub-region, Anderson algorithm is an analytic solution based on Gaussian filtering, which is used to provide the primary field from the excited sources in surface. And then, the stable double conjugate gradient-fast Fourier transform is incorporated into integral equation algorithm to obtain the fast 3D terrain shaft frequency domain electromagnetic responses. By comparing the calculation results using the new algorithm presented in this paper with the analytical solutions of Anderson algorithm for half-space model with surface electromagnetic method,the precision and the efficiency of this new algorithm are demonstrated. And the ability to model the electromagnetic responses of 3D topography is shown by comparing with the published results of 3D boundary integral equation. Thus, the high accuracy and high efficiency of the new algorithm presented in this paper are validated. Finally, the influence of 3D valley topography on electromagnetic field response of surface to borehole electromagnetic(SBEM) observation system is presented and analyzed. It is observed that the response of SBEM is seriously disturbed by the field of 3D valley topography which is necessarily removed. The research results presented in this paper are of significance for guiding the identification and correction of electromagnetic topographic effect from 3D SBEM.