Fast simulation of triaxial borehole induction measurements acquired in axially symmetrical and transversely isotropic media
Fast simulation of triaxial borehole induction measurements acquired in axially symmetrical and transversely isotropic media
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DOI：
10.1190/1.3261745
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发表时间：
2009-12
期刊：
影响因子：
3.3
通讯作者：
G. Wang;C. Torres‐Verdín;S. Gianzero
中科院分区：
文献类型：
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作者：
G. Wang;C. Torres‐Verdín;S. Gianzero
我们引入并成功测试了一种有效的方法来模拟在轴对称和横向各向同性 (TI) 介质中获得的三轴钻孔电磁 (EM) 感应测量。该方法使用傅里叶级数展开来表达电磁场和源项的方位角依赖性，从而将本质上的 3D 问题分解为一系列独立的 2D 问题。每个二维问题均采用半解析方法求解，该方法使用归一化贝塞尔函数和归一化汉克尔函数来表达电磁场的径向相关性，从而提高数值稳定性。此外，利用振幅和斜率基函数来描述电磁场的纵向依赖性，以避免水平地层边界附近的网格细化。为了进行验证，我们将新模拟方法与水平和径向分层地层中的两种 1D 分析方法以及包括钻孔和侵入区域的多层地层中的一种 3D 有限差分方法 (3DFD) 进行比较。数值结果表明，与一维方法相比，该方法在高电导率对比度的地层中是准确的，并且在多层地层中比 3DFD 方法的效率高十倍以上。
We introduce and successfully test an efficient method to simulate triaxial borehole electromagnetic (EM) induction measurements acquired in axially symmetrical and transversely isotropic (TI) media. The method uses a Fourier series expansion to express the azimuthal dependence of EM fields and the source term whereby the essentially 3D problem collapses to a series of independent 2D problems. Each 2D problem is solved with a semianalytic method that uses normalized Bessel functions and normalized Hankel functions to express the radial dependence of EM fields, thereby improving numerical stability. In addition, use is made of amplitude and slope basis functions to describe the longitudinal dependence of EM fields to avoid grid refinement in the vicinity of horizontal formation boundaries. For validation, we compare the new simulation method to two 1D analytic methods in horizontally and radially layered formations, and to one 3D finite-difference method (3DFD) in multilayered formations that include borehole and invasion zones. Numerical results indicate that the method is accurate in formations with high conductivity contrasts compared to 1D methods and is more than ten times more efficient than the 3DFD method in multilayer formations.