基于两步变异差分进化算法的激电测深一维反演

One-dimensional inversion of induced polarization sounding data based on the differential evolution algorithm with two-step mutation

激电测深一维反演是一个多参数非线性优化问题。本文基于改进的两步变异差分进化全局最优化算法实现了激电测深的一维反演。传统的差分进化算法包含变异、交叉和选择操作,变异为单步变异。本文提出的两步变异法分步将最优个体与随机选取的两个个体经变异后产生新个体。加强了最优个体的影响度,提高了全局寻优能力。通过模型试算结果表明,两步变异法比传统方法寻优能力更强。利用等效电阻率法加载极化率参数,通过数字滤波算法可快速正演计算层状模型表面激电测深电阻率曲线,在此基础上应用两步变异差分进化算法不断变异产生新个体,正演计算电阻率与观测值进行拟合,选择适应度值趋近于最大适应度值的个体作为反演结果。本文反演方法操作简便,计算速度快。通过对H型和KH型地电模型进行计算,得出本反演方法有较高的拟合精度。

The one-dimensional inversion of induced polarization(IP)sounding data involves multi-parameter nonlinear optimization.This study achieved the one-dimensional(1D)inversion of IP sounding data based on the improved global optimization algorithm of dif-ferential evolution(DE)with two-step mutation.The conventional DE algorithm includes mutation(single-step),crossover,and se-lection operations.The two-step mutation method proposed in this study can produce new individuals through the mutation of the opti-mal individual and two randomly selected individuals in steps,thus enhancing the influence of the optimal individual and the global op-timization ability.The model test results show that the two-step mutation method has a higher optimization ability than the conventional method.Specifically,the polarizability parameters were loaded using the equivalent resistivity method,and the surface IP sounding re-sistivity curves of a layered model can be quickly calculated through forward modeling using the digital filtering algorithm.Based on this,the DE algorithm with two-step mutation was employed to produce new individuals through continuous mutation.Then,the resis-tivity obtained through forward modeling was fitted with the observed values,and the individuals whose fitness approached the maximum fitness were selected as the inversion results.The inversion method proposed in this study features simple operations and fast calcula-tions.As verified through the calculations of H-and KH-type geoelectric models,the inversion method enjoys high fitting accuracy.