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| One-dimensional inversion of induced polarization sounding data based on the differential evolution algorithm with two-step mutation |
DING Zhi-Jun1( ), LUO Wei-Bin2(), LIAN Wei-Zhang1, ZHANG Xing1, HE Hai-Pin2 |
1. Gansu Nonferrous Geological Survey Institute, Lanzhou 730000, China
2. Lanzhou Resources and Environment Vocational and Technical University, College of Geology and Jewelry, Lanzhou 730021, China |
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Abstract 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 differential evolution (DE) with two-step mutation. The conventional DE algorithm includes mutation (single-step), crossover, and selection operations. The two-step mutation method proposed in this study can produce new individuals through the mutation of the optimal individual and two randomly selected individuals in steps, thus enhancing the influence of the optimal individual and the global optimization 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 resistivity 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 resistivity 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 calculations. As verified through the calculations of H- and KH-type geoelectric models, the inversion method enjoys high fitting accuracy.
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Received: 15 February 2023
Published: 11 October 2023
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Flow chart of differential evolution
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Flow chart of two-step variation method
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| 模型参数 | 真值 | 取值范围 | 反演次数 | 均值 | 误差/% | | 1 | 2 | 3 | 4 | 5 | | ρ1/(Ω·m) | 100 | [10,300] | 99.72 | 99.50 | 99.78 | 99.50 | 100.32 | 99.76 | -0.24 | | ρ2/(Ω·m) | 30 | [10,150] | 31.15 | 29.93 | 31.80 | 30.09 | 30.31 | 30.66 | 2.19 | | ρ3/(Ω·m) | 110 | [10,300] | 110.56 | 110.56 | 107.63 | 107.27 | 107.34 | 108.67 | -1.21 | | d1/m | 180 | [10,300] | 180.00 | 180.00 | 180.00 | 180.00 | 180.00 | 180.00 | 0.00 | | d2/m | 60 | [10,300] | 59.99 | 60.01 | 59.99 | 60.01 | 60.00 | 60.00 | 0.00 | | η1/m | 0.5 | [0.1, 1] | 0.78 | 1.00 | 0.72 | 1.00 | 0.18 | 0.74 | 0.24 | | η2/m | 8.5 | [3, 11] | 4.97 | 8.72 | 3.00 | 8.24 | 7.56 | 6.50 | -2.00 | | η3/m | 1 | [0.5, 3.5] | 0.50 | 0.50 | 3.13 | 3.46 | 3.40 | 2.20 | 1.20 |
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Parameters and inversion results of H-type earth resistivity model
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Performance comparison between traditional differential evolution and two-step mutation differential evolution
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Comparison of resistivity sounding results between real model and inversion results of H-type model
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| 模型参数 | 真值 | 取值范围 | 反演次数 | 均值 | 误差/% | | 1 | 2 | 3 | 4 | 5 | | ρ1/(Ω·m) | 120 | [10,300] | 119.52 | 120.24 | 120.39 | 120.48 | 120.47 | 120.22 | 0.18 | | ρ2/(Ω·m) | 560 | [100,800] | 557.21 | 557.26 | 559.88 | 559.71 | 557.59 | 558.33 | -0.30 | | ρ3/(Ω·m) | 25 | [10,100] | 26.04 | 26.85 | 26.10 | 24.37 | 24.32 | 25.53 | 2.14 | | ρ4/(Ω·m) | 310 | [50,500] | 310.58 | 306.77 | 303.68 | 304.13 | 310.54 | 307.14 | -0.92 | | d1/m | 110 | [50,300] | 110.00 | 110.00 | 110.04 | 110.00 | 110.00 | 110.01 | 0.01 | | d2/m | 120 | [50,300] | 120.00 | 119.98 | 119.20 | 119.98 | 120.02 | 119.83 | -0.14 | | d3/m | 150 | [50,300] | 150.03 | 150.29 | 160.59 | 150.31 | 149.68 | 152.18 | 1.45 | | η1/m | 0.6 | [0.2,1] | 1.00 | 0.40 | 0.28 | 0.20 | 0.21 | 0.42 | -0.18 | | η2/m | 0.3 | [0.1,0.8] | 0.80 | 0.80 | 0.65 | 0.36 | 0.72 | 0.67 | 0.37 | | η3/m | 9.5 | [3,12] | 5.76 | 3.00 | 11.59 | 11.95 | 11.80 | 8.82 | -0.68 | | η4/m | 1 | [0.8,3.5] | 0.81 | 2.03 | 3.08 | 2.88 | 0.82 | 1.93 | 0.93 |
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Parameters and inversion results of KH-type earth resistivity model
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Comparison of resistivity sounding results between real model and inversion results of KH-type model
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