随钻电磁波测井的高效数值计算理论与方法是近年来油气资源勘探的研究热点。三维各向异性倾斜地层正演数值仿真方法的可靠性已经得到基本认可，但是计算速度慢，无法进行实时地质导向是随钻电磁波测井模拟的发展瓶颈。高阶谱元方法兼具有限元适应任意复杂介质模型的灵活性和谱方法的高精度，而在工程数值模拟计算中备受青睐。本项目将着重研究基于 Gauss–Lobatto–Legendre 多项式的高阶谱元法与数值模式匹配法相结合，快速高效求解三维水平层状非均质各向异性地层中测井响应。主要研究内容有：2.5维高阶谱元法在非均匀介质中快速特征值求解，消除电小问题中出现的低频崩溃现象，谱元数值模式匹配法与传统谱元法相结合的区域分解法等。最终形成系统的随钻电磁波测井问题的快速高精度解法，实现高效可靠的数学计算模型。本项目的基础研究工作成果将有力地提升随钻电磁波测井的计算效率和精度，为油气勘探提供切实可行的理论基础。

The efficient numerical theory and methods for electromagnetic logging while drilling in oil and gas exploration are the research focus in .recent years. The reliability of the three-dimensional simulation method for anisotropic and oblique stratified media has been recognized,.but the computation efficiency is the bottleneck in electromagnetic logging while drilling simulation. The higher-order spectral element .method combines the flexibility of the finite element method and the high accuracy of the spectral method becomes a popular method in .the numerical simulation of engineering application. Here, we will incorporate the accurate spectral element method based on Gauss–Lobatto–Legendre polynomials and numerical mode matching method to develop higher order accuracy and efficient method solving three-dimension logging response with horizontally layered anisotropic formation. The research mainly focuses on the following aspects: higher-order spectral element method for 2.5 dimensional eigenvalue problems with inhomogeneous media; elimination of the low-frequency breakdown problem; domain decomposition method of spectral element numerical mode matching method and the conventional spectral element method. The achievements of this fundamental research should provide a desirable way to improve the precision and efficiency in the calculation of the electromagnetic logging while drilling and practical theoretical basis for oil and gas exploration.