地震波传播的褶积微分算子法数值模拟

李信富; 李小凡

地震波传播的褶积微分算子法数值模拟

李信富^{1, 2, 3, 4},
李小凡⁴

1.
中国地质大学地质过程与矿产资源国家重点实验室, 北京 100083
2.
中国地质大学地下信息探测技术与仪器教育部重点实验室, 北京 100083
3.
中国地质大学地球物理与信息技术学院, 北京 100083
4.
中国科学院地质与地球物理研究所岩石圈演化国家重点实验室, 北京 100029

基金项目:

中国地质大学地质过程与矿产资源国家重点实验室开放课题 GPMR0750

详细信息

中图分类号: P315.2
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- 被引次数: 0
出版历程
- 刊出日期: 2008-11-25

Numerical Simulation of Seismic Wave Propagation Using Convolutional Differentiator

LI Xin-fu^{1, 2, 3, 4},
LI Xiao-fan⁴

1.
State Key Laboratory of Geological Process and Mineral Resources, China University of Geosciences, Beijing 100083, China
2.
Key Laboratory of Geo-detection of Ministry of Education, China University of Geosciences, Beijing 100083, China
3.
School of Geophysics and In formation Technology, China University of Geosciences, Beijing 100083, China
4.
State Key Laboratory of Lithospheric Evolution, Institute ofGeology and Geophysics, Chinese Academy ofSciences, Beijing 100029, China

摘要

摘要: 为了解决地震波场数值模拟中的速度与精度的匹配及局部信息与全局信息的耦合等问题, 该文借助新推出的基于Forsyte广义正交多项式的褶积微分算子, 将计算数学中的Forsyte多项式褶积微分算子应用到地震波传播的数值模拟中.复杂非均匀介质模型数值模拟结果说明了该方法的可行性和优越性.该方法同时具有广义正交多项式褶积微分算子的高精度和有限差分短算子算法的高速度.通过对算子长度的调节及算子系数的优化, 可同时兼顾波场解的全局信息与局部信息.
- 佛尔塞正交多项式 /
- 褶积微分算子 /
- 地震波 /
- 数值模拟
Abstract: To improve the accuracy and the efficiency of seismic wave simulation and to couple the local and global information better, this paper develops a novel modeling approach referring to the convolutional differentiator based on generalized Forsyte orthogonal polynomial, which applies optimal convolutional operators for spatial differentiation in wave equation. The numerical experiment of complex heterogeneous model demonstrates that the algorithm can bring reliable results with high precision and can be extended to seismic wave simulation in anisotropic media. This method is highly precise in generalized orthogonal polynomial convolutional differentiator and also highly efficient in finite difference short operator method. The local and global information can be considered at the same time by optimizing the coefficients of the operator and adjusting the operator length.
- Forsyte orthogonal polynomial /
- convolutional differentiator /
- seismic waves /
- numerical simulation

HTML全文

图 1 9点褶积微分算子振幅随采样点的变化曲线

Fig. 1. Amplitude versus sampling point for nine point convolutional differentiator

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图 2 求导精度对比数值试验

Fig. 2. Numerical test for differentiation accuracy comparison

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图 3 Marmousi速度模型及500 ms时的波场快照

a.速度模型; b.x分量; c.z分量

Fig. 3. Snapshots for the Marmousi velocity model at the time of 500 ms

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图 4 试验模型的几何结构

Fig. 4. The geometrical structure of the testing model

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图 5 Forsyte褶积微分算子法波场快照

a.x分量; b.z分量

Fig. 5. Snapshots obtained by Forsyte convolutional differentiator method

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图 6 伪谱法波场快照

a.x分量; b.z分量

Fig. 6. Snapshots obtained by pseudospectral method

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参考文献(22)

[1]	Alterman, Z., Karal, C., 1968. Propagation of seismic waves in layered media by finite difference methods. Bull. Seism. Soc. Am. , 58(1): 367-398.
[2]	Cerjan, C., Kosloff, D., Kosloff, R., et al., 1985. A nonreflecting boundary condition for discrete acoustic and elastic wave equations. Geophysics, 50(4): 705-708. doi: 10.1190/1.1441945
[3]	Dai, Z.Y., Sun, J.G., Zha, X.J., 2005. Seismic wave modeling with hybrid order convolution differentiator. Computing Techniques for Geophysical and Geochemical Exploration, 27(2): 111-114(in Chinese with English abstract).
[4]	Graves, R.W., 1996. Simulating seismic wave propagation in 3D elastic media using staggered grid finite difference. Bull. Seism. Soc. Am. , 86(4): 1091-1106.
[5]	Komatitsch, D., Tromp, J., 1999. Introduction to the spectral-element method for 3-D seismic wave propagation. Geophys. J. Int. , 139: 806-822. doi: 10.1046/j.1365-246x.1999.00967.x
[6]	Kosloff, D., Baysal, E., 1982. Forward modeling by a Fourier method. Geophysics, 47(10): 1402-1412. doi: 10.1190/1.1441288
[7]	Kosloff, D., Reshef, M., Loewenthal, D., 1984. Elastic wave calculation by the Fourier method. Bull. Seism. Soc. Am. , 74(3): 875-891. doi: 10.1785/BSSA0740030875
[8]	Lin, S.H., Zhao, L.Y., 2007. High precision time domain forward modeling for crosshole electromagnetic tomography. Journal of China University of Geosciences, 18 (4): 320-325. doi: 10.1016/S1002-0705(08)60012-6
[9]	Magnier, S., Mora, P., Tarantola, A., 1994. Finite difference on minimal grids. Geophysics, 59(9): 1435-1443. doi: 10.1190/1.1443700
[10]	Teng, J.W., Zhang, Z.J., Yang, D.H., et al., 1995. Digital simulation of tricomponent seismic data in anisotropic media through convolution differential operator. Geophysical Prospecting for Petroleum, 34(3): 14-22(in Chinese with English abstract).
[11]	Xie, J., 1981. Methematical methods for the data processing of geophysical prospecting. Geological Publishing Press, Beijing, 97-104(in Chinese).
[12]	Yu, S.P., 1996. Wide-band Ricker wavelet. Oil Geophysical Prospecting, 31(5): 605-615(in Chinese with English abstract).
[13]	Zhang, Z.J., Teng, J.W., Yang, D.H., 1996. Simulations of the acoustic and elastic wavefield by convolutional differentiator. Acta Seismologica Sinica, 18(1): 63-69 (in Chinese).
[14]	Zhou, B., Greenhalgh, S.A., 1992. Seismic scalar wave equation modeling by a convolutional differentiator. Bull. Seism. Soc. Am. , 82(1): 289-303.
[15]	Zhou, B., Greenhalgh, S.A., Zhe, J., 1993. Numerical seismogram computations for inhomogeneous media using a short, variable length convolutional differentiator. Geophysical Prospecting, 41: 751-766. doi: 10.1111/j.1365-2478.1993.tb00882.x
[16]	Zhou, H., Xu, S.Z., Liu, B., et al., 1997. Modeling of wave equations in anisotropic media using finite element method and its stability condition. Chinese Journal of Geophysics, 40(6): 833-841(in Chinese with English abstract).
[17]	戴志阳, 孙建国, 查显杰, 2005. 地震波混合阶褶积算法模拟. 物探化探计算技术, 27(2): 111-114. https://www.cnki.com.cn/Article/CJFDTOTAL-WTHT200502004.htm
[18]	滕吉文, 张中杰, 杨顶辉, 等, 1995. 各向异性介质中褶积微分算子法三维地震资料的数字仿真. 石油物探, 34(3): 14 -22. https://www.cnki.com.cn/Article/CJFDTOTAL-SYWT199503001.htm
[19]	谢靖, 1981. 物探数据处理的数学方法. 北京: 地质出版社, 97 -104.
[20]	俞寿朋, 1996. 宽带Ricker子波. 石油地球物理勘探, 31(5): 605-615. https://www.cnki.com.cn/Article/CJFDTOTAL-SYDQ199605000.htm
[21]	张中杰, 滕吉文, 杨顶辉, 1996. 声波与弹性波场数值模拟中的褶积微分算子法. 地震学报, 18(1): 63-69. https://www.cnki.com.cn/Article/CJFDTOTAL-DZXB601.008.htm
[22]	周辉, 徐世浙, 刘斌, 等, 1997. 各向异性介质中波动方程有限元法模拟及其稳定性. 地球物理学报, 40(6): 833-841. doi: 10.3321/j.issn:0001-5733.1997.06.012