Adaptive Quantum Genetic Inversion Algorithm for One-Dimensional Magnetotelluric Inverse Problem
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摘要: 将量子遗传算法引入到层状介质大地电磁数据的反演, 得到了层状介质的大地电磁量子遗传反演法.数值试验结果发现该算法仍然存在较严重的早熟收敛现象.为此, 将自适应思想引入到量子遗传算法中来, 通过动态调整量子遗传算法的模型搜索空间, 建立了一种新的改进型量子遗传算法——自适应量子遗传算法, 使算法在迭代过程中能自适应地寻找模型最优值.通过典型测试函数和层状介质大地电磁模型数值试验, 结果表明, 改进算法有效压制了常规量子遗传算法的早熟收敛性, 提高了算法的搜索效率和反演效果.采用该算法对实际的大地电磁资料进行了处理, 取得了较好的地质效果.Abstract: This paper applied the conventional quantum genetic algorithm (QGA) to solve the nonlinear magnetotelluric inverse problem of layered model.However, the conventional QGA shows a premature convergence problem throughout our numerical experiments.In order to overcome the shortcoming of premature convergence, we improved the conventional QGA with automatically adjusting the size of model space with different scales, and eventually developed a novel method, referred as to adaptive quantum genetic algorithm (AQGA), for the inversion of magnetotelluric data.The validity of AQGA method is demonstrated by some optimization test functions and synthetic magnetotelluric models.The results show that AQGA mitigate the premature convergence and improve the efficiency and accuracy of inverted models.The obtained models using AQGA for magnetotelluric field data are well agreed with geological structure, which inferred that the improved AQGA method is powerful for the nonlinear optimization problem.
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Key words:
- adaptive /
- quantum genetic algorithm /
- MT /
- inversion /
- nonlinear optimization /
- geophysical prospecting.
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图 3 常规量子遗传算法(QGA)和自适应量子遗传算法(AQGA)反演结果及拟合度曲线
Fig. 3. Inversion results and fitness curves using QGA and AQGA methods
图 4 不同高斯随机噪声水平情况下两层D型模型AQGA法的反演结果
a.0%噪声; b.5%噪声; c.10%噪声; d.20%噪声
Fig. 4. Inversion results for different random noise level data for two-layer model (D-type) using AQGA method
图 5 AQGA法的反演结果曲线对比(a) 及误差曲线(b)
Fig. 5. Inversion results (a) and error curve (b) using AQGA method for four-layer model (HK-type)
表 1 搜索函数
Table 1. The value of optimizing search function
表 2 两层D型层状介质的模型空间和分辨率
Table 2. Model space and resolution for two-layer (D-type) model
表 3 两层D型模型的QGA和AQGA方法的反演结果
Table 3. Inversion results using QGA and AQGA for two-layer (D-type) model
表 4 两层D型模型的加噪数据AQGA法反演结果
Table 4. Inversion results for random gauss noised data of two-layer model (D-type) using AQGA method
表 5 四层HK型层状介质的模型空间和分辨率
Table 5. Model space and resolution for four-layer model (HK-type)
表 6 四层HK型层状介质的AQGA法反演结果
Table 6. Inversion results for four-layer model (HK-type) using AQGA method
表 7 实测数据的AQGA法反演结果
Table 7. Inversion results of observed MT data using AQGA method
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