基于快速非支配排序遗传算法的VTI介质多分量叠前联合反演

刘炜, 王彦春, 谢玮. 2019. 基于快速非支配排序遗传算法的VTI介质多分量叠前联合反演. 地球物理学报, 62(4): 1453-1470, doi: 10.6038/cjg2019L0641
引用本文: 刘炜, 王彦春, 谢玮. 2019. 基于快速非支配排序遗传算法的VTI介质多分量叠前联合反演. 地球物理学报, 62(4): 1453-1470, doi: 10.6038/cjg2019L0641
LIU Wei, WANG YanChun, XIE Wei. 2019. Multicomponent prestack joint inversion for VTI media based on a fast nondominated sorting genetic algorithm. Chinese Journal of Geophysics (in Chinese), 62(4): 1453-1470, doi: 10.6038/cjg2019L0641
Citation: LIU Wei, WANG YanChun, XIE Wei. 2019. Multicomponent prestack joint inversion for VTI media based on a fast nondominated sorting genetic algorithm. Chinese Journal of Geophysics (in Chinese), 62(4): 1453-1470, doi: 10.6038/cjg2019L0641

基于快速非支配排序遗传算法的VTI介质多分量叠前联合反演

  • 基金项目:

    国家科技重大专项(2016ZX05003-003)资助

详细信息
    作者简介:

    刘炜, 男, 1991年生, 在读博士生, 主要从事多分量叠前联合反演研究.E-mail:lwqhsy123@163.com

    通讯作者: 王彦春, 男, 1959年生, 教授, 博士生导师, 主要从事地震勘探与信息处理方面研究.E-mail:wangyc1109@163.com
  • 中图分类号: P631

Multicomponent prestack joint inversion for VTI media based on a fast nondominated sorting genetic algorithm

More Information
  • 在VTI介质中,由于引入了各向异性参数使得多分量多参数地震反演问题的非线性程度显著增加,因此采用传统的权重加权法构建单目标函数进行反演得到的反演结果往往并不理想.本文以反射率法为基础,结合快速非支配排序遗传算法研究了一种VTI介质的多分量叠前联合反演方法.该方法以反射率法为正演方程,应用互相关原理构建PP波和PSV波的多目标函数,进而采用快速非支配排序遗传算法全局寻优获得VTI介质的厚度、纵横波速度、密度和各向异性参数等多个参数.在正演的过程中,反射率法可以考虑几何扩散、吸收衰减、透射损失、多次波以及纵横波旅行时不匹配等地震波传播效应,更能精确地描述地震波在地下地层中的真实传播情况;在反演的过程中,快速非支配排序遗传算法可以在不引入权重系数的条件下同时优化多个目标函数,获得联合反演问题的Pareto最优解,既不添加权重系数影响又充分利用多分量地震数据.模型测试结果验证了该反演方法的有效性和可行性.

  • 加载中
  • 图 1 

    NSGA Ⅱ多目标函数反演方法流程图

    Figure 1. 

    The workflow of NSGA Ⅱ inversion method

    图 2 

    模型A的τ-p域合成地震记录

    Figure 2. 

    Synthetic seismic records of model A in τ-p domain

    图 3 

    模型A的厚度搜索窗

    Figure 3. 

    Search windows of thickness for model A

    图 4 

    基于传统单目标函数反演方法的模型A各参数反演结果

    Figure 4. 

    Inversion results of model A based on the conventional single-objective function inversion method

    图 5 

    优化搜索窗时基于NSGA Ⅱ反演方法的模型A各参数反演结果

    Figure 5. 

    Inversion results of model A using optimized search window based on the NSGA Ⅱ inversion method

    图 6 

    垂直搜索窗时基于NSGA Ⅱ反演方法的模型A各参数反演结果

    Figure 6. 

    Inversion results of model A using vertical search window based on the NSGA Ⅱ inversion method

    图 7 

    不同情形下模型A的目标函数变化曲线

    Figure 7. 

    Convergence curves of the multi-objective function of model A in different cases

    图 8 

    不同情形下模型A最后一代的种群分布图

    Figure 8. 

    Population distributions of model A at final generation in different cases

    图 9 

    基于实际测井数据建立的一维多层VTI介质模型(模型B)

    Figure 9. 

    1D multilayer VTI model (Model B) generated from a real log

    图 10 

    一维多层VTI介质模型(模型B)的τ-p域合成地震记录

    Figure 10. 

    Synthetic seismic records of 1D multilayer VTI model (Model B) in τ-p domain

    图 11 

    未含噪声时使用搜索窗A模型B的反演结果

    Figure 11. 

    Inversion results without noise of model B using search window A

    图 12 

    含噪声时使用搜索窗A模型B的反演结果(SNR=2)

    Figure 12. 

    Inversion results with noise of model B using search window A (SNR=2)

    图 13 

    未含噪声时使用搜索窗B模型B的反演结果

    Figure 13. 

    Inversion results without noise of model B using search window B

    图 14 

    含噪声时使用搜索窗B模型B的反演结果(SNR=2)

    Figure 14. 

    Inversion results with noise of model B using search window B (SNR=2)

    图 15 

    未含噪声且地层厚度未知的情形下使用搜索窗A时模型B的种群演化图

    Figure 15. 

    Evolution map of the population of model B using search window A under the conditions of unknown thickness and non-noise

    图 16 

    未含噪声情形下使用搜索窗A时模型B最后一代的种群分布图

    Figure 16. 

    Population distributions of model B at final generation without noise using search window A

    图 A1 

    个体i的拥挤距离

    Figure A1. 

    Crowding distance of individual i

    表 1 

    模型A的模型参数

    Table 1. 

    Model parameters of model A

    层数 T
    (m)
    VP
    (m·s-1)
    VS
    (m·s-1)
    ρ
    (g·cm-3)
    ε δ
    1 100 3300 2074 2.25 0.05 0
    2 70 3600 2333 2.4 0.18 0.15
    3 50 3000 1700 2.1 0.1 -0.05
    4 5 4000 2650 2.55 0.2 0.2
    5 60 2800 1500 2.0 0 -0.1
    6 35 3500 2250 2.3 0.14 0.1
    7 120 3300 2074 2.25 0.05 0
    下载: 导出CSV

    表 2 

    基于传统单目标函数反演方法的模型A反演结果的平均误差统计表

    Table 2. 

    The error statistics of inversion results using the conventional single-objective function inversion method for model A

    参数 ΔVP(m·s-1) ΔVS(m·s-1) Δρ(g·cm-3) Δε Δδ
    绝对误差 相对误差
    (%)
    绝对误差 相对误差
    (%)
    绝对误差 相对误差
    (%)
    绝对误差 相对误差
    (%)
    绝对误差 相对误差
    (%)
    不含噪声 146.77 4.53 161.13 8.26 0.0934 4.22 0.0438 21.90 0.0488 24.41
    SNR=2 243.73 7.51 240.43 12.33 0.1799 8.14 0.0954 47.68 0.0996 49.81
    下载: 导出CSV

    表 3 

    优化搜索窗时模型A厚度反演结果的统计表

    Table 3. 

    Inversion results and statistics of thickness using optimized search window for model A

    层数 真实值 SNR=2 SNR=4 SNR=6 SNR=8 未含噪声
    反演值 误差 反演值 误差 反演值 误差 反演值 误差 反演值 误差
    1 100 96.4751 3.5249 97.4977 2.5023 98.5485 1.4515 99.1348 0.8652 99.7843 0.2157
    2 70 72.3935 2.3935 68.5692 1.4308 71.4877 1.4877 71.0522 1.0522 70.6714 0.6714
    3 50 44.3912 5.6088 46.8861 3.1139 48.5143 1.4857 47.1843 2.8157 48.8033 1.1967
    4 5 10.5584 5.5584 8.8523 3.8523 8.6427 3.6427 7.0256 2.0256 6.9654 1.1954
    5 60 56.7170 3.2830 55.1456 4.8544 56.7632 3.2368 61.1941 1.1941 58.5397 1.4603
    6 35 39.0769 4.0769 39.0029 4.0029 38.3480 3.3480 37.9910 2.9910 37.9192 2.9192
    7 120 115.7488 4.2512 118.5870 1.4130 122.1963 2.1963 118.1382 1.8618 119.6795 0.3205
    下载: 导出CSV

    表 4 

    优化搜索窗时模型A各参数反演结果的平均误差统计表

    Table 4. 

    The error statistics of inversion results using optimized search window for model A

    参数 ΔT(m) ΔVP(m·s-1) ΔVS(m·s-1) Δρ(g·cm-3) Δε Δδ
    绝对误差 相对误差
    (%)
    绝对误差 相对误差
    (%)
    绝对误差 相对误差
    (%)
    绝对误差 相对误差
    (%)
    绝对误差 相对误差
    (%)
    绝对误差 相对误差
    (%)
    不含噪声 1.2499 7.70 43.59 1.26 45.24 1.89 0.0289 1.22 0.0154 7.72 0.0122 6.11
    SNR=8 1.8294 8.66 96.18 2.73 76.76 3.86 0.0473 2.08 0.0159 7.96 0.0249 12.45
    SNR=6 2.4070 13.74 112.18 3.42 85.81 4.18 0.0662 2.90 0.0175 8.75 0.0355 17.73
    SNR=4 3.0242 15.50 105.02 3.28 99.39 4.48 0.0895 3.73 0.0293 14.66 0.0381 19.04
    SNR=2 4.0995 21.43 104.58 4.02 115.26 5.06 0.1218 5.31 0.0474 23.71 0.0553 27.67
    下载: 导出CSV

    表 5 

    垂直搜索窗时模型A厚度反演结果的统计表

    Table 5. 

    Inversion results and statistics of thickness using vertical search window for model A

    层数 真实值 SNR=2 SNR=4 SNR=6 SNR=8 未含噪声
    反演值 误差 反演值 误差 反演值 误差 反演值 误差 反演值 误差
    1 100 91.8091 8.1909 92.6150 7.3850 93.6278 6.3722 95.1311 4.8689 96.6314 3.3686
    2 70 75.7067 5.7067 74.2826 4.2826 72.8785 2.8785 68.6674 1.3326 71.4869 1.4869
    3 50 40.1576 9.8424 42.7694 7.2306 44.1089 5.8911 46.5828 3.4172 52.3133 2.3113
    4 5 15.9680 10.9680 14.4776 9.4776 13.4524 8.4524 12.3459 7.3459 10.1241 5.1241
    5 60 52.1102 7.8898 54.8431 5.1569 56.3566 3.6434 62.8992 2.8992 57.5539 2.4461
    6 35 26.3566 8.6434 29.0742 5.9258 31.8992 3.1008 36.6423 1.6423 34.0441 0.9559
    7 120 111.3116 8.6884 112.9715 7.0285 114.0692 5.9308 115.3664 4.6336 123.9272 3.9272
    下载: 导出CSV

    表 6 

    垂直搜索窗时模型A各参数反演结果的平均误差统计表

    Table 6. 

    The error statistics of inversion results using vertical search window for model A

    参数 ΔT(m) ΔVP(m·s-1) ΔVS(m·s-1) Δρ(g·cm-3) Δε Δδ
    绝对误差 相对误差
    (%)
    绝对误差 相对误差
    (%)
    绝对误差 相对误差
    (%)
    绝对误差 相对误差
    (%)
    绝对误差 相对误差
    (%)
    绝对误差 相对误差
    (%)
    不含噪声 2.8032 17.53 72.82 2.18 35.97 1.88 0.0382 1.71 0.0125 6.25 0.0218 10.89
    SNR=8 3.7342 24.84 124.90 3.70 77.41 3.73 0.1142 5.01 0.0228 11.42 0.0267 13.34
    SNR=6 5.1813 30.17 160.72 4.62 151.17 6.87 0.1257 5.53 0.0239 11.97 0.0263 13.14
    SNR=4 6.6410 35.56 197.81 5.64 170.78 8.05 0.1425 6.24 0.0337 16.84 0.0431 21.53
    SNR=2 8.5614 42.92 219.10 6.43 186.87 8.80 0.1714 7.43 0.0377 18.85 0.0611 30.54
    下载: 导出CSV
  •  

    Auld B A. 1973. Acoustic resonators.//Acoustic Fields and Waves in Solids. 2nd ed. New York: John Willey and Sons.

     

    Banik N C. 1987. An effective anisotropy parameter in transversely isotropic media. Geophysics, 52(12):1654-1664. doi: 10.1190/1.1442282

     

    Daley P F, Hron F. 1977. Reflection and transmission coefficients for transversely isotropic media. Bulletin of the Seismological Society of America, 67(3):661-675. http://d.old.wanfangdata.com.cn/NSTLQK/NSTL_QKJJ026959514/

     

    Deb K, Agrawal R B. 1995. Simulated binary crossover for continuous search space. Complex Systems, 9(3):115-148.

     

    Deb K, Agrawal S. 1999. A niched-penalty approach for constraint handling in genetic algorithms.//Artificial Neural Nets and Genetic Algorithms. Vienna:Springer, 235-243.

     

    Deb K, Pratap A, Agarwal S, et al. 2002. A fast and elitist multiobjective genetic algorithm:NSGA-Ⅱ. IEEE Transactions on Evolutionary Computation, 6(2):182-197. doi: 10.1109/4235.996017

     

    Du B Y, Yang W Y, Wang E L, et al. 2016. Joint pre-stack inversion of multiple waves based on Russell approximation. Chinese Journal of Geophysics (in Chinese), 59(8):3016-3024, doi:10.6038/cjg20160824.

     

    Fatti J L, Smith G C, Vail P J, et al. 1994. Detection of gas in sandstone reservoirs using AVO analysis:A 3-D seismic case history using the geostack technique.Geophysics, 59(9):1362-1376. doi: 10.1190/1.1443695

     

    Fryer G J, Frazer L N. 1984. Seismic waves in stratified anisotropic media. Geophysical Journal of the Royal Astronomical Society, 78(3):691-710. doi: 10.1111/j.1365-246X.1984.tb05065.x

     

    Goldberg D E. 1989. Genetic Algorithms in Search, Optimization, and Machine Learning. Boston: Addison-Wesley Professional.

     

    Graebner M. 1992. Plane-wave reflection and transmission coefficients for a transversely isotropic solid.Geophysics, 57(11):1512-1519. doi: 10.1190/1.1443219

     

    Heyburn R, Fox B. 2010. Multi-objective analysis of body and surface waves from the Market Rasen (UK) earthquake. Geophysical Journal International, 181(1):532-544. doi: 10.1111/gji.2010.181.issue-1

     

    Hou D J, Liu Y, Hu G Q, et al. 2014a. Prestack multiwave joint inversion for elastic moduli based on Bayesian theory. Chinese Journal of Geophysics (in Chinese), 57(4):1251-1264, doi:10.6038/cjg20140422.

     

    Hou D J, Liu Y, Ren Z M, et al. 2014b. Multi-wave prestack joint inversion in VTI media based on Bayesian theory. Geophysical Prospecting for Petroleum (in Chinese), 53(3):294-303. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=sywt201403007

     

    Kennett B L N. 1983. Seismic Wave Propagation in Stratified Media. Cambridge: Cambridge University Press.

     

    Kozlovskaya E, Vecsey L, Plomerová J, et al. 2007. Joint inversion of multiple data types with the use of multiobjective optimization:Problem formulation and application to the seismic anisotropy investigations. Geophysical Journal International, 171(2):761-779. doi: 10.1111/gji.2007.171.issue-2

     

    Li Q, Li Q C, Zhang L. 2014. Anisotropic parameter analysis of multi-component data in VTI media. Oil Geophysical Prospecting (in Chinese), 49(3):503-507.

     

    Li T, Mallick S. 2015. Multicomponent, multi-azimuth pre-stack seismic waveform inversion for azimuthally anisotropic media using a parallel and computationally efficient non-dominated sorting genetic algorithm. Geophysical Journal International, 200(2):1134-1152. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=70cde06b79be7e9fb8440b3f434df5ff

     

    Liu Y Z, Wang G Y, Dong L G, et al. 2014. Joint inversion of VTI parameters using nonlinear traveltime tomography. Chinese Journal of Geophysics (in Chinese), 57(10):3402-3410, doi:10.6038/cjg20141026.

     

    Liu Y Z, Wang G Y, Yang J Z, et al. 2015. Multi-parameter full-waveform inversion for VTI media based on Born sensitivity kernels. Chinese Journal of Geophysics (in Chinese), 58(4):1305-1316, doi:10.6038/cjg20150418.

     

    Mallick S, Frazer L N. 1987. Practical aspects of reflectivity modeling.Geophysics, 52(10):1355-1364. doi: 10.1190/1.1442248

     

    Ostrander W J. 1984. Plane-wave reflection coefficients for gas sands at non-normal angles of incidence.Geophysics, 49(10):1637-1648. doi: 10.1190/1.1441571

     

    Padhi A, Mallick S. 2013. Accurate estimation of density from the inversion of multicomponent pre-stack seismic waveform data using a nondominated sorting genetic algorithm. The Leading Edge, 32(1):94-98. doi: 10.1190/tle32010094.1

     

    Padhi A, Mallick S. 2014. Multicomponent pre-stack seismic waveform inversion in transversely isotropic media using a non-dominated sorting genetic algorithm. Geophysical Journal International, 196(3):1600-1618. doi: 10.1093/gji/ggt460

     

    Rüger A. 1997. P-wave reflection coefficients for transversely isotropic models with vertical and horizontal axis of symmetry.Geophysics, 62(3):713-722. doi: 10.1190/1.1444181

     

    Rüger A. 1998. Variation of P-wave reflectivity with offset and azimuth in anisotropic media.Geophysics, 63(3):935-947.

     

    Singh V P, Duquet B, Léger M, et al. 2008. Automatic wave-equation migration velocity inversion using multiobjective evolutionary algorithms.Geophysics, 73(5):VE61-VE73. doi: 10.1190/1.2966008

     

    Stewart R R. 1990. Joint P and P-SV inversion. The CREWES Project Research Report. Calgary:The University of Calgary, 2:112-115. http://d.old.wanfangdata.com.cn/Periodical/sydxxb200601007

     

    Thomsen L. 1986. Weak elastic anisotropy.Geophysics, 51(10):1954-1966. doi: 10.1190/1.1442051

     

    Veire H H, Landrø M. 2006. Simultaneous inversion of PP and PS seismic data.Geophysics, 71(3):R1-R10. doi: 10.1190/1.2194533

     

    Wang M C. 2007. Method and application of multiwave prestack joint inversion lithologic parameters in VTI media[Master's thesis] (in Chinese). Chengdu: Chengdu University of Technology.

     

    Wang Y, Dong L G. 2015. Multi-parameter full waveform inversion for acoustic VTI media using the truncated Newton method. Chinese Journal of Geophysics (in Chinese), 58(8):2873-2885, doi:10.6038/cjg20150821.

     

    Xun H, Dong M Y, Mou Y G. 1997. Wave field simulation using reflectivity method and body-wave radiation patterns in anisotropic media. Oil Geophysical Prospecting (in Chinese), 32(5):605-614. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=QK199700526972

     

    Zhang G Z, Du B Y, Li H S, et al. 2014. The method of joint pre-stack inversion of PP and P-SV waves in shale gas reservoirs. Chinese Journal of Geophysics (in Chinese), 57(12):4141-4149, doi:10.6038/cjg20141225.

     

    Zhong Z, Li L M, Shi Y H. 2011. Pre-stack AVA lithologic parameters inversion and its precision. Geophysical Prospecting for Petroleum (in Chinese), 50(3):225-233. http://d.old.wanfangdata.com.cn/Periodical/sywt201103003

     

    杜炳毅, 杨午阳, 王恩利等. 2016.基于Russell近似的纵横波联合反演方法研究.地球物理学报, 59(8):3016-3024, doi:10.6038/cjg20160824. http://www.geophy.cn//CN/abstract/abstract13019.shtml

     

    侯栋甲, 刘洋, 胡国庆等. 2014a.基于贝叶斯理论的叠前多波联合反演弹性模量方法.地球物理学报, 57(4):1251-1264, doi:10.6038/cjg20140422. http://www.geophy.cn//CN/abstract/abstract10305.shtml

     

    侯栋甲, 刘洋, 任志明等. 2014b.基于贝叶斯理论的VTI介质多波叠前联合反演.石油物探, 53(3):294-303. http://d.old.wanfangdata.com.cn/Periodical/sywt201403007

     

    李勤, 李庆春, 张林. 2014. VTI介质多波各向异性参数分析.石油地球物理勘探, 49(3):503-507. http://d.old.wanfangdata.com.cn/Conference/7627668

     

    刘玉柱, 王光银, 董良国等. 2014. VTI介质多参数联合走时层析成像方法.地球物理学报, 57(10):3402-3410, doi:10.6038/cjg20141026. http://www.geophy.cn//CN/abstract/abstract10890.shtml

     

    刘玉柱, 王光银, 杨积忠等. 2015.基于Born敏感核函数的VTI介质多参数全波形反演.地球物理学报, 58(4):1305-1316, doi:10.6038/cjg20150418. http://www.geophy.cn//CN/abstract/abstract11393.shtml

     

    王明春. 2007. VTI介质多波叠前联合反演岩性参数方法及应用[硕士论文].成都: 成都理工大学.

     

    王义, 董良国. 2015.基于截断牛顿法的VTI介质声波多参数全波形反演.地球物理学报, 58(8):2873-2885, doi:10.6038/cjg20150821. http://www.geophy.cn//CN/abstract/abstract11740.shtml

     

    寻浩, 董敏煜, 牟永光. 1997.各向异性介质中反射率法波场模拟及体波辐射图案.石油地球物理勘探, 32(5):605-614. doi: 10.3321/j.issn:1000-7210.1997.05.001

     

    张广智, 杜炳毅, 李海山等. 2014.页岩气储层纵横波叠前联合反演方法.地球物理学报:57(12):4141-4149, doi:10.6038/cjg20141225. http://www.geophy.cn//CN/abstract/abstract11042.shtml

     

    钟峙, 李录明, 史运华. 2011.叠前AVA岩性参数反演方法及精度分析.石油物探, 50(3):225-233. doi: 10.3969/j.issn.1000-1441.2011.03.003

  • 加载中

(17)

(6)

计量
  • 文章访问数:  509
  • PDF下载数:  290
  • 施引文献:  0
出版历程
收稿日期:  2018-04-13
修回日期:  2018-08-06
上线日期:  2019-04-05

目录