无限元法在三维电测井计算中的应用

APPLICATION OF INFINITE ELEMENT METHOD(IEM) TO 3D ELECTRIC LOGGING CALCULATION

为了更有效地计算三维电测井资料的响应,在三维数值模式匹配法的基础上引入了一种无限元法。该方法把每层待求解的无限大区域划分为两部分:内部有限区域和外部无限区域。对内部区域,形成传统的矩阵;对外部区域,引入几何中的Kelvin变换,对变换后的场域形成另一个矩阵。内外区域的矩阵在公共边界上耦合,形成三维数值模式匹配法广义特征值矩阵。与原来的三维数值模式匹配法比较,这种新方法减少了形成的广义特征值矩阵维数。结果表明,改进后方法的计算速度比原方法快7倍,而使用内存仅为原方法的1/3,可广泛用于电缆和随钻三维电阻率测井的正反演计算。

Infinite element method(IEM) is introduced to the 3D numerical mode-matching(NMM) method to solve the 3D electric logging problem.This method divides the infinite field domain of each layer into inner and outer field domains,the matrices are formed by standard finite element method(FEM) in both inner and outer domain,the Kelvin transformation is introduced and the matrices are formed by a new infinite element format.Matrices of two different parts are coupled in the domains' common interface to form the final matrices of the original problem.This method generates smaller size of generalized matrices than the original 3D NMM method.Results show that the new method spends only 1/7 CPU time and uses only 1/3 memory of the original method.This new method can be widely applied to calculate electromagnetic logging responses.