Inversion of Rayleigh wave dispersion curves based on antlion optimizer
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摘要:
反演瑞雷波频散曲线获得横波速度剖面, 是近地表瑞雷波勘探中最重要的步骤之一; 瑞雷波频散曲线反演是一个多极值、高度非线性问题, 为此引入蚁狮优化算法求解该类问题。蚁狮优化算法是一种群智能算法, 是模仿蚁狮设置陷阱捕食的行为建立的全局优化算法, 该算法收敛速度较快且降低了不同的参数设置对结果产生的影响。通过使用蚁狮优化算法对典型的理论地质模型进行了频散曲线反演, 反演结果表明蚁狮优化算法能够运用在瑞雷波频散曲线反演中且精度较高, 在实测资料中与传统非线性方法进行了对比, 验证了基于蚁狮优化算法频散曲线反演的优势与实用性。
Abstract:Inverting Rayleigh wave dispersion curves to obtain S-wave velocity profiles is one of the most important steps in near-surface Rayleigh wave exploration. Rayleigh wave inversion is a multi-extremum, nonlinear problem, and this paper introduces the antlion optimizer to solve this type of problem. The antlion optimizer is a swarm intelligence algorithm, which is a global optimizer that imitates the behavior of the antlion setting trap predation, which converges faster and reduces the effect of different parameter settings on the result. By using the antlion optimizer to invert the dispersion curve of the typical theoretical geological model, the inversion results show that the antlion optimizer can be applied to the inversion of the dispersion curve with high accuracy, and the advantages and practicality of the dispersion curve inversion based on the antlion optimizer are verified in the measured data compared with the traditional nonlinear methods.
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Key words:
- Rayleigh wave /
- dispersion curve /
- nonlinear algorithm /
- antlion optimizer
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图 1 模型1的反演结果
a.基阶反演频散曲线对比图；b.迭代收敛曲线图；c.横波速度剖面对比
Figure 1. Inversion results of Model 1
图 2 模型2的反演结果
a.基阶反演频散曲线对比图；b.迭代收敛曲线图; c.横波速度剖面对比
Figure 2. Inversion results of Model 2
图 3 模型3的反演结果
a.基阶反演频散曲线对比图；b.迭代收敛曲线图; c.横波速度剖面对比
Figure 3. Inversion results of Model 3
图 4 实测资料及其反演
a.实测地震记录；b.实测频散能量图; c.横波速度剖面; d.反演实测对比; e.横波速度迭代曲线; f.层厚度迭代曲线; g.迭代收敛曲线对比; h.实测资料与反演结果对比
Figure 4. Field dataset and inversion results
表 1 模型1参数及反演搜索范围
Table 1. Parameters of Model 1 and search space in the inversion
层号 理论模型 搜索范围 横波速度/(m·s-1) 纵波速度/(m·s-1) 密度/(g·cm-3) 层厚度/m 横波速度/(m·s-1) 层厚度/m 1 200 663 1.9 4 100~300 2~6 2 300 1 149 1.9 2 150~450 1~3 3 400 1 774 1.9 6 200~600 3~9 4 500 2 030 1.9 半空间 250~750 半空间 
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表 2 模型1反演结果统计
Table 2. Statistics of Model 1 inversion results
模型参数 理论值 统计结果 反演结果 相对误差/% 总误差/% Vs1/(m·s-1) 200 200.14 0.07 2.95 Vs2/(m·s-1) 300 307.59 2.53 Vs3/(m·s-1) 400 390.91 2.27 Vs4/(m·s-1) 500 499.31 0.14 H1/m 4 3.96 1.00 H2/m 2 2.15 7.50 H3/m 6 5.57 7.17
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表 3 模型2参数及反演搜索范围
Table 3. Parameters of Model 2 and search space in the inversion
层号 理论模型 搜索范围 横波速度/(m·s-1) 纵波速度/(m·s-1) 密度/(g·cm-3) 层厚度/m 横波速度/(m·s-1) 层厚度/m 1 200 663 1.8 4 100~300 2~6 2 150 497 1.8 2 100~300 1~3 3 300 994 1.8 6 150~450 3~9 4 400 1 326 1.8 半空间 200~600 半空间
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表 4 模型2反演结果统计
Table 4. Statistics of Model 2 inversion results
模型参数 理论值 统计结果 反演结果 相对误差/% 总误差/% Vs1/(m·s-1) 200 200.60 0.30 3.27 Vs2/(m·s-1) 150 147.98 1.34 Vs3/(m·s-1) 300 308.96 2.99 Vs4/(m·s-1) 400 397.25 0.68 H1/m 4 4.20 5.00 H2/m 2 1.93 3.50 H3/m 6 5.50 8.33
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表 5 模型3参数及反演搜索范围
Table 5. Parameters of Model 3 and search space in the inversion
层号 理论模型 搜索范围 横波速度/(m·s-1) 纵波速度/(m·s-1) 密度/(g·cm-3) 层厚度/m 横波速度/(m·s-1) 层厚度/m 1 150 497 1.8 4 50~250 2~6 2 250 829 1.8 2 100~400 1~3 3 200 663 1.8 3 100~400 1.5~4.5 4 400 1 327 1.8 半空间 200~600 半空间
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表 6 模型3反演结果统计
Table 6. Statistics of Model 3 inversion results
模型参数 理论值 统计结果 反演结果 相对误差/% 总误差/% Vs1/(m·s-1) 150 151.33 0.88 3.60 Vs2/(m·s-1) 250 249.31 0.28 Vs3/(m·s-1) 200 217.65 8.82 Vs4/(m·s-1) 400 399.15 0.21 H1/m 4 4.23 5.75 H2/m 2 2.14 7.00 H3/m 3 2.95 1.67
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