2.5维直流电法正演中Fourier逆变换离散波数的最优化选取  

Optimized selection of discrete wavenumbers for inverse Fourier transform in 2.5D DC resistivity modeling

作　　者：潘克家[1,2] 汤井田[1] 

机构地区：[1]中南大学有色金属成矿预测教育部重点实验室,地球科学与信息物理学院,湖南长沙410083 [2]中南大学数学与统计学院,湖南长沙410083

出　　处：《中南大学学报（自然科学版）》2013年第7期2819-2826,共8页Journal of Central South University:Science and Technology

基　　金：国家自然科学基金资助项目(41204082);国家科技专项(Sino Probe-03);高等学校博士学科点科研基金资助项目(20120162120036);中国博士后科学基金资助项目(2011M501295)

摘　　要：从优化模型和计算方法 2方面改进点源2.5维直流电法正演中Fourier逆变换离散波数的最优化选取方法。首先利用均匀半空间点源电位的精确解,基于最小二乘法给出计算离散波数的改进非线性最优化问题;然后,利用差分进化(DE)算法进行求解;最后,研究参与计算的电极距数对模拟精度的影响。对具有解析解的典型地电模型,通过与已有文献计算结果进行比较,验证方法的可行性。研究结果表明:增加参与计算的电极距数可有效提高视电阻率曲线近源处的计算精度,并能保证较大电性差异情形下的计算精度;与现有离散波数相比,本文方法得到的波数具有更高的精度和更大的适用范围。The optimized selection method was improved in terms of both the optimization model and computational method for selecting the discrete wavenumbers of inverse Fourier transform,which arise in the 2.5-dimensional direct current resistivity modeling with a point current source.Firstly,with an analytical solution of electric potential produced by a point source in semi-infinite homogeneous medium,an improved nonlinear optimization problem for computing these wavenumbers based on the method of least squares was presented,then it was resolved using the differential evolution（DE） algorithm.Finally,the computational accuracy against the impact of the number of electrode spacings included in the simulation was discussed.For a number of typical geoelectric models with analytical solutions,the method was justified through comparing the computed results to those in literatures.The results show that increasing the number of electrode spacings not only dramatically reduces the error of the apparent resistivity near the point source,but also ensures the computational accuracy for models with a large conductivity contrast.The discrete wavenumbers obtained from the proposed method have a higher accuracy and wider range of applications compared with existing ones.

关 键 词：直流电法 有限单元法 Fourier逆变换 离散波数 差分进化算法 

分 类 号：P631[天文地球—地质矿产勘探]