频率域反射波全波形速度反演

成景旺; 顾汉明; 刘春成; 刘志斌

doi:10.3799/dqkx.2013.038

频率域反射波全波形速度反演

doi: 10.3799/dqkx.2013.038

成景旺^{1, 2,},
顾汉明^{1, 2, ,},
刘春成³,
刘志斌³

1.
中国地质大学地球物理与空间信息学院，湖北武汉 430074
2.
中国地质大学构造与油气资源教育部重点实验室，湖北武汉 430074
3.
中海油研究总院，北京 100027

基金项目:

国家重大科技专项 2011ZX05025-001

详细信息

作者简介:
成景旺(1987-)，男，博士，研究方向为石油地震勘探正反演研究.E-mail：chjw2008@126.com

通讯作者:
顾汉明，E-mail：guhanming@263.net

中图分类号: P631.4
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出版历程
- 收稿日期: 2012-04-15
- 刊出日期: 2013-03-01

Full Waveform Inversion for Velocity Structure from Reflected Wave Seismic Data in the Frequency Domain

1.
Institute of Geophysics and Geomatics, China University of Geosciences, Wuhan430074, China
2.
Key Laboratory of Tectonics and Petroleum Resources of Ministry of Education, China University of Geosciences, Wuhan430074, China
3.
CNOOC Research Center, Beijing100027, China

摘要

摘要: 全波形反演不仅利用相位和振幅信息，还利用波形的细节变化，具有刻画模型精确细节的能力.在对稀疏矩阵直接LU分解求解的基础上，采用梯度预处理方法对声波介质速度模型进行了反射波全波形反演.采用误差反向传播算法计算目标函数梯度以及伪Hessian矩阵的对角线元素来做梯度预处理.数值模型的实验结果表明，利用有效的频率段便能反演出分辨率较高的速度结构，用低频反演出的结果作为高频反演的初始模型，减少了解的非唯一性.二维高斯光滑初始模型提供了有利的低频信息，得到较好的反演结果.伪Hessian矩阵的预处理吸收了高斯牛顿法的二次收敛优势，在不增加计算量的前提下，加快收敛速度.
- 全波形反演 /
- 梯度预处理 /
- 误差反向传播算法 /
- 伪Hessian矩阵
Abstract: Full waveform inversion uses not only phase and amplitude information, but also waveform details, revealing precise details of the model. We use the LU factorization technique directly to solve the forward modeling, and show a preconditioned gradient method to inverse the velocity structure using the reflected wave from low-frequency to high-frequency in this study. The numerical structure of the finite difference method and back-propagation algorithm is exploited to develop an algorithm that explicitly calculates the Jacobin matrix utilizing a forward model solution. Furthermore, the diagonal elements of the false Hessian matrix are used as the preconditioned operator. Numerical tests on simple synthetic models find that a good velocity model can be obtained only by several frequency inversions, and the strategy of using low-frequency inversion result as the starting model in the high-frequency inversion can greatly reduce the non-uniqueness of their solutions. The initial model directly affects the imaging result. The smooth two-dimensional Gaussian model provides favorable low-frequency information for a better inversion result. The fast convergence can be achieved by using of the false Hessian matrix without any increase in the premise of computation.
- full waveform inversion /
- preconditioned gradient /
- back-propagation algorithm /
- false Hessian matrix

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图 1 不同频率的反演结果(其中b~i为2~16 Hz的反演结果)

Fig. 1. The inverted model at different frequencies

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图 2 复杂模型

a.理论模型；b.初始模型；c.反演速度模型

Fig. 2. The complex model

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图 3 合成记录对比

a.理论模型合成记录；b.反演结果合成记录；c.两者残差

Fig. 3. Comparison of the synthetic seismograms

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图 4 Marmous模型及反演结果

a.理论模型；b.初始模型；c.未进行预处理反演结果；d.预处理反演结果

Fig. 4. The Marmous model and the inverted velocity model

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图 5 模型合成记录以及残差

a.理论模型合成记录；b.未进行预处理反演结果合成记录；c.预处理反演结果合成记录；d.初始模型合成记；e.记录b和记录a残差；f.记录c和记录a残差

Fig. 5. The synthetic seismograms and the residual

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图 6 横向不同位置速度曲线

a.4 000 m处；b.5 600 m处；c.6 875 m处

Fig. 6. The velocity curves at different horizontal positions

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图 7 迭代误差曲线

a.预条件梯度法迭代曲线；b.未进行预处理迭代曲线

Fig. 7. The relative error as a function of iteration number

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参考文献(24)

Ben-Hadj-Ali, H., Operto, S., Virieux, J., 2008. Velocity Model Building by 3D Frequency-Domain, Full-Waveform Inversion of Wide-Aperture Seismic Data. Geophysics, 73(5): VE101-VE117. doi: 10.1190/ 1.2957948
Bian, A.F., Yu, W.H., 2011. Layer-Stripping Full Waveform Inversion with Damped Seismic Reflection Data. Journal of Earth Science, 22(2): 241-249. doi:10.1007/ s12583-011-0177-6
Hicks, G.J., Pratt, R.G., 2001. Reflection Waveform Inversion Using Local Decent Methods: Estimating Attenuation and Velocity Over a Gas-Sand Deposit. Geophysics, 66(2): 598-612. doi:10.1190/ 1.1444951
Ha, T., Chung, W., Shin, C., 2009. Waveform Inversion Using a Back-Propagation Algorithm and a Huber Function Norm. Geophysics, 74(3): R15-R24. doi:10.1190/ 1.3112572
Long, G.H., Li, X.F., Zhang, M.G., et al., 2009. Visco-Acoustic Transmission Waveform Inversion for Velocity Structure in Space-Frequency Domain. Acta Seismologica Sinica, 31(1): 32-41(in Chinese with English abstract). doi: 10.1007/s11589-009-0045-y
Malinowski, M., Operto, S., 2008. Quantitative Imaging of the Permo-Mesozoic Complex and Its Basement by Frequency Domain Waveform Tomography of Wide-Aperture Seismic Data from the Polish Basin. Geophysical Prospecting, 56: 805-825. doi: 10.1111/ j.1365-2478.2007.00680.x
Pratt, R.G., Shin, C.S., Hicks, G.J., 1998. Guass-Newton and Full Newton Methods in Frequency-Space Seismic Waveform Inversion. Geophysical Journal International, 133(2): 341-362. doi: 10.1046/ j.1365-246X.1998.00498.x
Shin, C., Yoon, K.G., Marfurt, K.J., et al., 2001. Efficient Calculation of a Partial-Derivative Wave Field Using Reciprocity for Seismic Imaging and Inversion. Geophysics, 66(6): 1856-1863. doi: 10.1190/1.1487129
Shin, C., Jang, S., Min, D.J., 2001. Improved Amplitude Preservation for Prestack Depth Migration by Inversion Scattering Theory. Geophysical Prospecting, 49(5): 592-606. doi: 10.1046/ j.1365-2478.2001.00279.x
Sourbier, F., Haidar, A., Giraud, L., et al., 2011. Three-Dimensional Parallel Frequency-Domain Visco-Acoustic Wave Modeling Based on a Hybrid Direct/Iterative Solver. Geophysical Prospecting, 59(5): 834-856. doi: 10.1111/ j.1365-2478.2011.00966.x
Tarantola, A., 1984. Inversion of Seismic Reflection Data in the Acoustic Approximation. Geophysics, 49(8): 1259-1266. doi: 10.1190/ 1.1441754
Wu, G.C., Liang, K., 2005. Quasi P-Wave Forward Modeling in Frequency-Space Domain in VTI Media. OGP, 40(5): 535-545 (in Chinese with English abstract). http://www.researchgate.net/publication/297432449_Quasi_P-wave_forward_modeling_in_frequency-space_domain_in_VTI_media
Wu, G.C., Liang, K., 2005. Combined Boundary Conditions of Quasi P-Wave within Frequency-Space Domain in VTI Media. GPP, 44(4): 301-307(in Chinese with English abstract). http://en.cnki.com.cn/Article_en/CJFDTOTAL-SYWT200504002.htm
Xu, K., Wang, M.Y., 2001. Finite Element Inversion of the Coefficients of Acoustic Equation in Frequency Domain. Chinese Journal of Geophysics, 44(6): 852-864(in Chinese with English abstract). http://en.cnki.com.cn/Article_en/CJFDTOTAL-DQWX200106014.htm
Xu, K., Wang, M.Y., 2004. Frequency-Domain Finite-Element Inversion of Elastic-Wave Velocity Using the Geological Regular-Blocky-Model Method. Chinese Journal of Geophysics, 47(4): 708-717(in Chinese with English abstract). http://www.oalib.com/paper/1567254
Yin, W., Yin, X.Y., Wu, G.C., et al., 2006. The Method of Finite Difference of High Precision Elastic Wave Equation in the Frequency Domain and Wave-Filed Simulation. Chinese Journal of Geophysics, 49(2): 561-568 (in Chinese with English abstract). http://en.cnki.com.cn/Article_en/CJFDTOTAL-DQWX200602031.htm
Zhang, R.Z., Yuan, C., 2009. Application of the Seismic Waveform Inversion Technique. Natural Gas Industry, 29(2): 52-54 (in Chinese with English abstract). http://en.cnki.com.cn/Article_en/CJFDTOTAL-TRQG200902012.htm
龙桂华, 李小凡, 张美根, 等, 2009. 频率域粘弹性声波透射波形速度反演. 地震学报, 31(1): 32-41. doi: 10.3321/j.issn:0253-3782.2009.01.004
吴国忱, 梁锴, 2005. VTI介质频率-空间域准P波正演模拟. 石油地球物理勘探, 40(5): 535-545. doi: 10.3321/j.issn:1000-7210.2005.05.010
吴国忱, 梁锴, 2005. VTI介质准P波频率空间域组合边界条件研究. 石油物探, 44(4): 301-307. doi: 10.3969/j.issn.1000-1441.2005.04.001
许琨, 王妙月, 2001. 声波方程频率域有限元参数反演. 地球物理学报, 44(6): 852-864. doi: 10.3321/j.issn:0001-5733.2001.06.015
许琨, 王妙月, 2004. 利用地质规则块体建模方法的频率域有限元弹性波速度反演. 地球物理学报, 47(4): 708-717. doi: 10.3321/j.issn:0001-5733.2004.04.024
殷文, 印兴耀, 吴国忱, 等, 2006. 高精度频率域弹性波方程有限差分方法及波场模拟. 地球物理学报, 49(2): 561-568. doi: 10.3321/j.issn:0001-5733.2006.02.032
张荣忠, 袁诚, 2009. 地震波形反应技术的应用. 天然气工业, 29(2): 52-54. http://www.cnki.com.cn/Article/CJFDTotal-TRQG200902012.htm