多分量感应测井相关理论精准模拟的传输矩阵与积分方程方法研究

Simulation of the multi-component induction well logging (MCIL) responses in tool calibration and complex borehole environments correction is of great importance for tool’s designment and correct interpretation of measurements. In this project, we will form a high-precision method of integral equations to efficient resolve the computational electromagnetics problem encountered in tool’s calibration and complex borehole environments correction. The step-by-step research scheme is described as the following:.Firstly, to formulate respectively the calculating problem of both calibration equipment (including coils, calibration-rings, metallic-mandrel and the earth) and complex borehole environments (composed of inhomogeneous formation, borehole, metallic-mandrel, and coils) with the integral equations and generalized equivalent networks, and to build the relation between tool well logging response and equivalent impedance..Secondly, to select layered anisotropic media as background media of the integral equations and to achieve spatial localized distribution of scatterers in problems of tool’s calibration and complex borehole environments correction，and to translate the volume–surface–wire integral equations into surface–wire integral equations..Thirdly, to simplify propagator matrix calculation of dyadic Green’s function in layered anisotropic media with the low-frequency band of MCIL, and to establish an high-precision numerical integration solution of impedance matrix elements in method of moments..Finally, to study a fast integral equation method in the layered anisotropic media to speed up the solution of matrix equation in methods of moments, and to structure an computing platform with C++Builder OpenGL and CUDA for the tool calibration and complex borehole environments correction. .The successful implementation of this project will not only efficiently solve the computational electromagnetic problem in tool’s calibration and complex borehole environments correction of MCIL, but also can advance the development of the electromagnetic integral equation theory in inhomogeneous medium.

多分量感应测井仪器刻度与井孔环境校正理论精准模拟是仪器设计和应用需解决的重要问题。项目旨在建立用于测井仪器刻度与井孔环境校正基于传输矩阵-积分方程电磁场精准模拟方法，包括：首先，构建描述仪器刻度装置（线圈系-刻度环-芯棒-地面）和井眼环境（线圈系-芯棒-井眼）积分方程广义等效网络模型，建立测井响应和等效阻抗参量直接关系。其次，选择各向异性分层介质作为背景介质实现散射体局域化，简化体面线积分方程为面线积分方程。再次，利用感应低频特性简化分层介质Green函数传输矩阵计算方法，建立高精度阻抗矩阵元计算数值积分方法。最后，研究非均质背景介质条件下矩量法非稀疏矩阵方程的快速求解方法，应用C++Builder-OpenGL-CUDA混合技术构建三维可视化仪器刻度与井孔环境校正理论计算平台。项目将有效解决多分量感应测井仪器刻度和井孔环境校正理论计算难题，也将推动非均质背景中电磁场积分方程理论新发展。

本项目针对多分量感应测井（MCIL）仪器刻度与井孔环境校正响应精准计算难题，开展了传输矩阵和积分方程电磁场精准模拟方法研究。本项目完成主要研究内容和取得成果有：.第一，计算模型和计算方案研究：建立了MCIL响应模拟的广义等效网络模型，将MCIL响应计算问题转化为一个等效网络阻抗参量计算问题，并提出了复杂散射体存在阻抗参量计算的积分方程方法，实现了“化场为路”简化研究思路。.第二，并矢Green函数快速精准算法研究：建立了平面和柱状分层各向异性介质中Green函数精准计算传输矩阵方法，包括均匀单轴各向异性介质电磁场Green函数无坐标形式，平面分层介质电磁场Green函数计算等效边界方法，柱面分层介质电磁场Green函数计算等效边界方法。基于并矢Green函数，建立了MCIL响应函数分析理论，包括单轴各向异性背景介质中MCIL响应函数定义、推导、计算和理论分析。.第三，矩量法矩阵方程迭代算法研究：建立了平面和柱状分层背景介质中矩量法矩阵方程高效的求解方法，包括刻度环散射问题计算简化矩量法，芯棒散射问题计算的简化矩量法，等效阻抗与空间域变换数值积分计算的快速算法，矩阵方程迭代算法的并行运算。.第四，计算平台搭建和验证研究：基于C++和CUDA并行运算架构，搭建了MCIL仪器刻度与井孔环境校正理论计算软件平台；实现基于C++和OpenGL架构三维可视化显示；通过开发的软件平台实现了本项目理论成果推广应用和验证。.通过上述研究，有效地解决了MCIL仪器刻度与井孔环境校正精准计算难题，为我国MCIL仪器自主开发奠定了重要的理论基础并提供了高效的计算工具。同时，本项目提出广义等效网络模型、等效边界法和简化矩量法等方法，对非均质背景中电磁场积分方程理论新发展具有参考价值。