非均匀介质界面上的偶极层激励响应

The Numerical Computation Technique of Thin-Layer-Potential Response in lnhomogenous Media

以研究具有解析解形式的均匀介质分层结构为基础，提出了克服无限大界面上的激励对收敛性问题影响的数值实现途径。用数值模式匹配方法，求解了非均匀介质中，水平分层界面上的无限大偶极层激励问题。导出了各非均匀分区中的电位表达式。所给公式全部由适合于计算机实现的矩阵形式列出，使得全部求解过程为单纯的矩阵代数运算，无需任何数值积分，从而为求解复杂非均匀地质构造中自然电位测井问题奠定了高效数值模拟的基础。

On the base of finding the analytical solution to a steady-state field problem excited withinfinite-extend thin-layer potentials in the layered homogenous media ,here proposed a powerful numericalcomputation technique to overcome the difficulties resulted from the divergence of the comcerned integrals.As for the problems in inhomogenous media, the numerical mode-matching method is employed to derive theformulas of potentials in each inhomogenous region.As the merits of the present theory, all formulas andarithmetic procedures to get the responses are in matrix forms . Furthermore. there needs on numericalintegration anyway.