层状单轴各向异性介质中长导线源电磁响应的快速计算

A fast calculation method for electromagnetic fields generated by finite-length wire sources in stratified uniaxial anisotropic medium

在场源附近,长导线源不能视作电偶极子源。长导线源电磁响应的常用计算方法是对场源进行离散,再对离散电偶极子电磁场进行叠加,这种方法计算简单,但计算效率较低。针对这一问题,提出了有限单元形函数积分算法。该算法从电偶极子场的解析表达式出发,将长导线源进行剖分,通过在每个剖分单元上构造形函数来求解积分表达式。通过模型算例对传统电偶极子叠加算法和形函数积分算法的计算精度及计算效率进行了测试。从测试结果可以看出,无论在场源中远区还是近区,形函数积分算法只需要将长导线源剖分成两个单元就能达到很高精度,而电偶极子叠加算法需要将长导线源离散成大量的电偶极子才能达到相同数值精度,相同数值精度条件下形函数积分算法具有更高的计算效率,且离场源越近计算效率优势越明显。

A finite-length wire source cannot be approximated as a point dipole when the distance between source and receiver is short. Usually, electromagnetic field calculation for finite-length wire sources can be achieved by two steps: discretize the wire into point dipole pieces, and evaluate several integrals to calculate each point dipole contribution. Although this is simple, the summation of point dipole fields entails significant computational cost. In this paper, we propose a fast and accurate calculation method for the electromagnetic response with finite-length wire sources. Based on the analytic solutions of electric dipole, the method solves the integral problem by discretizing the wire and constructing shape function on each element. The calculation accuracy and efficiency for both the proposed shape function integral algorithm and the point dipoles summation solution are shown on model tests. The results show that the shape function integral algorithm can achieve high accuracy even when the wire source is only divided into 2 elements. However, in order to reach the same relative error, the point dipoles summation solution needs many discrete elements. Therefore, we can conclude that shape function integral algorithm is a fast and accurate numerical method, especially when the source-receiver distances are short. © 2016, Editorial Department OIL GEOPHYSICAL PROSPECTING. All right reserved.