Simultaneous reconstruction of geometric parameter and resistivity around borehole in horizontally stratified formation from multiarray induction logging data
Simultaneous reconstruction of geometric parameter and resistivity around borehole in horizontally stratified formation from multiarray induction logging data
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DOI：
10.1109/tgrs.2002.808070
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发表时间：
2003-02
期刊：
影响因子：
--
通讯作者：
Hongnian Wang
中科院分区：
文献类型：
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作者：
Hongnian Wang
新型多阵列感应测井仪由八个不同间距的三线圈阵列组成，工作在三个频率下，测量同相和正交信号，比传统感应测井仪提供更多关于井眼周围电导率分布的信息。地层模型采用水平层状介质，每层侵入剖面呈阶梯状。本文建立了一种正则化迭代反演算法，用于从多阵列感应测井资料中同时反演地层的几何参数和电阻率。在反演过程中，根据微扰原理有效地计算了Frechet导数矩阵对模型参数的影响，并采用麦克斯韦方程和二阶Langrange函数的混合方法确定径向本征模解，进一步提高了Frechet导数矩阵的正演和计算效率。归一化用于将模型向量、测井数据和Frechet矩阵转换为无量纲变量。正则化和指数阻尼因子用于提高反演的稳定性。我们还将分析和减少由输入数据中的噪声和地层厚度误差引起的反演误差。
The new multiarray induction logging tool consists of eight different spacing three-coil arrays, operates at three frequencies, and measures both in-phase and quadrature signals to provide more information on the distribution of conductivity around the borehole than the conventional induction tool. A horizontally layered medium with a step-profile invasion per bed is used to describe the formation model. In this paper, we will establish a regularized iterative inversion algorithm to simultaneously reconstruct geometric parameter and resistivity per bed from the multiarray induction logging data. During the inversion, the Frechet derivative matrix with respect to the model parameters is efficiently calculated in terms of the perturbation principle, and the hybrid approach of Maxwell's equations and the two-order Langrange function is used to determine the eigenmode solution in the radial direction in order to further enhance efficiency of forward modeling and calculation of the Frechet derivative matrix. Normalizations are used to transform the model vector, log data, and the Frechet matrix into dimensionless variables. Regularization and exponential damping factors are used to enhance inversion stability. We will also analyze and reduce the inversion errors originating from the noise in input data and the errors in bed thicknesses.