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物探与化探  2023, Vol. 47 Issue (6): 1467-1478    DOI: 10.11720/wtyht.2023.1239
  方法研究·信息处理·仪器研制 本期目录 | 过刊浏览 | 高级检索 |
基于正余弦算法的瑞利波频散曲线反演
付宇1,2(), 艾寒冰1,2,3, 姚振岸1,2(), 梅竹虚1,2, 苏可嘉1,2,4
1.江西省防震减灾与工程地质灾害探测工程研究中心,江西 南昌 330013
2.东华理工大学 地球物理与测控技术学院,江西 南昌 330013
3.中国地质大学(武汉) 地球物理与空间信息学院,湖北 武汉 430074
4.核工业二七0研究所,江西 南昌 330200
Inversion of the Rayleigh wave dispersion curves based on the sine-cosine algorithm
FU Yu1,2(), AI Han-Bing1,2,3, YAO Zhen-An1,2(), MEI Zhu-Xu1,2, SU Ke-Jia1,2,4
1. Engineering Research Center for Seismic Disaster Prevention and Engineering Geological Disaster Detection of Jiangxi Province(East China University of Technology),Nanchang 330013,China
2. School of Geophysics and Measurement-control Technology,East China University of Technology,Nanchang 330013,China
3. School of Geophysics and Geomatics, China University of Geosciences(Wuhan),Wuhan 430074,China
4. Research Institute No.270,CNNC,Nanchang 330200,China
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摘要 

瑞利波在工程勘察领域应用广泛,通过反演瑞利波频散曲线可有效地获取地层信息,但频散曲线反演中传统全局优化算法存在收敛速度慢、收敛精度低和易早熟的问题。对此,本文引入一种新的全局优化算法——正余弦算法(SCA)进行瑞利波频散曲线反演研究。SCA基于正余弦函数数学性质,应用多个随机参数和自适应变量调整寻优过程中的探索和开发能力,在获得高精度解的同时还保证了收敛速度以及稳定性。首先利用4个不含噪声模型验证了SCA用于频散曲线反演的可行性;随后往模型中加入15%的随机噪声说明了SCA具有较强的抗干扰能力;接着将SCA与粒子群算法(PSO)进行对比,证明了SCA反演频散曲线能得到高精度和高稳定性的解;最后用冰岛Arnarbælidi和美国怀俄明地区的地震数据检验SCA处理实际数据的能力。理论模型试算与实测资料分析的结果表明,SCA具有快速、高精度、稳定、实用性强的特点,可有效地应用于瑞利波频散曲线的定量解释。

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付宇
艾寒冰
姚振岸
梅竹虚
苏可嘉
关键词 ： 瑞利波,  频散曲线反演,  全局优化,  正余弦算法    
Abstract：

Rayleigh wave is widely used in engineering investigation and surveys.The inversion of its dispersion curves allows for effectively obtaining stratigraphic information.However,conventional global optimization algorithms in the dispersion curve inversion have a slow convergence rate and low convergence precision and are prone to prematurity.Therefore,this study introduced a novel global optimization algorithm—the sine cosine algorithm (SCA)—to solve the problems mentioned above.Based on the mathematical properties of sine and cosine functions,the SCA can adjust the exploration and development capabilities during the optimization using multiple random parameters and adaptive variables.As a result,it can ensure a high convergence rate and great stability while obtaining high-accuracy solutions.First,the feasibility of the SCA for the dispersion curve inversion was verified using four noise-free models.Then,the strong anti-interference ability of the SCA was proved by adding 15% of random noise to the models.Afterward,it was verified that SCA can yield high-precision,high-stability solutions in the dispersion curve inversion by comparison with the particle swarm optimization (PSO) approach.Finally,the practicability of the SCA was confirmed using seismic data from Arnarbælidi in Iceland and Wyoming in the USA.As indicated by the calculation results of theoretical models and the analysis of measured data,the SCA has a high processing speed,precision,stability,and practicability and thus allows for effective quantitative interpretation of the Rayleigh wave dispersion curves.

Key words： Rayleigh wave    dispersion curve inversion    global optimization    sine-cosine algorithm
收稿日期: 2022-08-05      修回日期: 2023-09-26      出版日期: 2023-12-20
:  P631.4  
基金资助:江西省教育厅科学技术项目(GJJ200728);江西省自然科学基金项目(20212BAB211003);国家自然科学基金项目(42004113);江西省防震减灾与工程地质灾害探测工程研究中心开放基金项目(SDGD202006)
通讯作者: 姚振岸(1990-),男,博士,讲师,硕士研究生导师,主要从事地震勘探方面的科研与教学工作。Email:an6428060@163.com
作者简介: 付宇(1997-),男,在读硕士研究生,主要从事地震面波勘探方面的学习与研究工作。Email:1635504789@qq.com
引用本文:   
付宇, 艾寒冰, 姚振岸, 梅竹虚, 苏可嘉. 基于正余弦算法的瑞利波频散曲线反演[J]. 物探与化探, 2023, 47(6): 1467-1478.
FU Yu, AI Han-Bing, YAO Zhen-An, MEI Zhu-Xu, SU Ke-Jia. Inversion of the Rayleigh wave dispersion curves based on the sine-cosine algorithm. Geophysical and Geochemical Exploration, 2023, 47(6): 1467-1478.
链接本文:  
https://www.wutanyuhuatan.com/CN/10.11720/wtyht.2023.1239      或      https://www.wutanyuhuatan.com/CN/Y2023/V47/I6/1467
Fig.1  SCA算法流程
模型 层序号 模型参数 搜索范围
vs/(m·s-1) vp/(m·s-1) ρ/(g·cm-3) h/m vs/(m·s-1) h/m
模型A 1 200 780 1.9 5 100~300 2.5~7.5
均匀半空间 350 850 1.9 ∞ 175~525 ∞
模型B 1 200 663 1.9 2 100~300 1~3
2 300 995 1.9 4 150~450 2~6
3 400 1327 1.9 6 200~600 3~9
均匀半空间 500 1658 1.9 ∞ 250~750 ∞
模型C 1 200 663 1.9 2 100~300 1~3
2 160 673 1.9 4 80~240 2~6
3 300 1102 1.9 6 150~450 3~9
均匀半空间 400 1470 1.9 ∞ 200~600 ∞
模型D 1 150 498 1.9 2 75~225 1~3
2 250 829 1.9 4 125~375 2~6
3 200 841 1.9 6 100~300 3~9
均匀半空间 400 1470 1.9 ∞ 200~600 ∞
Table 1  模型参数及反演搜索范围
Fig.2  模型A不含噪声理论数据反演结果
a—反演所得频散曲线;b—反演的横波速度剖面
模型 参数 真实值 不含噪声 含噪声
反演均值 相对误差/% 标准差 反演均值 相对误差/% 标准差
模型A vs1/(m·s-1) 200 199.54 0.23% 1.28 199.69 0.15% 2.71
vs2/(m·s-1) 350 347.90 0.60% 5.98 350.79 0.23% 9.07
H1/m 5 4.76 4.76% 0.18 4.75 5.00% 0.22
模型B vs1/(m·s-1) 200 200.94 0.47% 2.52 200.95 0.47% 3.82
vs2/(m·s-1) 300 300.75 0.25% 7.42 304.07 1.36% 15.60
vs3/(m·s-1) 400 399.19 0.20% 9.34 391.88 2.03% 25.47
vs4/(m·s-1) 500 500.19 0.04% 6.03 499.62 0.08% 6.80
H1/m 2 2.05 2.52% 0.11 2.02 0.83% 0.16
H2/m 4 3.99 0.24% 0.28 3.96 1.12% 0.18
H3/m 6 5.59 6.76% 0.53 5.61 6.54% 0.97
模型C vs1/(m·s-1) 200 197.78 1.11% 9.25 199.90 0.05% 14.71
vs2/(m·s-1) 160 161.15 0.72% 4.52 160.55 0.34% 5.35
vs3/(m·s-1) 300 286.04 4.65% 32.13 285.78 4.74% 22.89
vs4/(m·s-1) 400 397.61 0.60% 13.58 397.19 0.70% 18.96
H1/m 2 1.97 1.57% 0.17 1.91 4.51% 0.23
H2/m 4 3.86 3.58% 0.43 3.85 3.71% 0.30
H3/m 6 5.62 6.28% 1.09 5.51 8.16% 0.43
模型D vs1/(m·s-1) 150 150.58 0.39% 1.03 149.80 0.13% 2.92
vs2/(m·s-1) 250 252.30 0.92% 4.25 251.41 0.56% 7.38
vs3/(m·s-1) 200 199.81 0.09% 3.94 202.01 1.01% 4.41
vs4/(m·s-1) 400 400.90 0.23% 4.80 400.46 0.12% 6.36
H1/m 2 2.03 1.41% 0.07 2.03 1.36% 0.08
H2/m 4 3.93 1.78% 0.14 3.98 0.44% 0.24
H3/m 6 6.09 1.45% 0.23 5.99 0.14% 0.26
Table 2  模型A、B、C、D含噪声与不含噪声反演结果
Fig.3  模型B、C和D不含噪声理论数据反演结果
a1,b1,c1—分别为模型B、C和D反演所得频散曲线;a2,b2,c2—分别为模型B、C和D反演的横波速度剖面
Fig.4  模型A、B、C、D的含噪声理论数据反演结果
a1,b1,c1,d1—分别为模型A、B、C和D反演所得频散曲线;a2,b2,c2,d2—分别为模型A、B、C和D反演的横波速度剖面
Fig.5  模型C多模式数据反演结果
a—反演所得频散曲线;b—反演的横波速度剖面
参数 真实值 基阶数据 多模数据
反演均值 相对误差/% 标准差 反演均值 相对误差/% 标准差
vs1/(m·s-1) 200 197.78 1.11% 9.25 200.18 0.09% 9.75
vs2/(m·s-1) 160 161.15 0.72% 4.52 158.98 0.64% 4.60
vs3/(m·s-1) 300 286.04 4.65% 32.13 308.08 2.93% 21.04
vs4/(m·s-1) 400 397.61 0.60% 13.58 393.26 1.68% 15.64
H1/m 2 1.97 1.57% 0.17 1.99 0.70% 0.23
H2/m 4 3.86 3.58% 0.43 3.99 0.28% 0.30
H3/m 6 5.62 6.28% 1.09 6.08 1.38% 0.43
Table 3  模型C基阶数据和多模式数据反演结果
Fig.6  SCA与PSO在无噪声模型D中反演收敛过程对比
a—放大前的收敛曲线对比;b—放大后的收敛曲线对比
参数 真实值 SCA PSO
反演均值 相对误差/% 标准差 反演均值 相对误差/% 标准差
vs1/(m·s-1) 150 150.58 0.39% 1.03 148.06 1.29% 9.91
vs2/(m·s-1) 250 252.30 0.92% 4.25 242.06 3.18% 23.34
vs3/(m·s-1) 200 199.81 0.09% 3.94 176.28 11.86% 37.69
vs4/(m·s-1) 400 400.90 0.23% 4.80 374.89 6.28% 27.63
H1/m 2 2.03 1.41% 0.07 1.93 3.5% 0.38
H2/m 4 3.93 1.78% 0.14 3.72 6.86% 0.97
H3/m 6 6.09 1.45% 0.23 4.07 32.14% 2.03
Table 4  SCA和PSO反演效果对比
Fig.7  Arnarb?lidi地区地震数据(a)与频散能量图(b)[29]
文献估计层厚 文献S波速度 S波速度搜索范围 厚度搜索范围
/m /(m·s-1) /(m·s-1) /m
0.8 78 60~90 0.1~1.5
0.5 80 70~100 0.1~1.5
0.7 92 80~110 0.1~1.5
1.2 111 100~150 0.5~2.0
1.9 141 120~200 0.5~2.0
3.0 184 150~250 2.0~4.0
4.7 230 200~300 3.0~5.5
7.5 277 250~350 6.0~9.0
5.2 350 300~400 4.0~6.0
∞ 350 320~450 ∞
Table 5  Arnarb?lidi地区前人[29]反演模型参数以及搜索范围[30]
Fig.8  Arnarb?lidi地区瑞雷波相速度反演结果
a—反演所得频散曲线;b—最小目标函数值随迭代次数变化情况;c—反演的横波速度剖面
Fig.9  怀俄明地区地震数据(a)与频散能量(b)[32]
层数 vs/(m·s-1) h/m 泊松比 ρ/(g·cm-3)
1 100~300 1~5 0.38 2.0
2 100~400 1~5 0.38 2.0
3 100~600 1~5 0.35 2.0
4 200~600 1~5 0.35 2.0
5 200~800 均匀半空间 0.30 2.0
Table 6  怀俄明地区前人[32]反演模型参数及搜索范围
Fig.10  怀俄明地区瑞利波相速度反演结果
a—反演所得频散曲线;b—最小目标函数值随迭代次数变化情况;c—测井数据与反演横波速度剖面对比
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