基于贴体全交错网格的起伏地表正演模拟影响因素

doi:10.13278/j.cnki.jjuese.201603306

吉林大学学报(地球科学版) ›› 2016, Vol. 46 ›› Issue (3): 920-929.doi: 10.13278/j.cnki.jjuese.201603306

基于贴体全交错网格的起伏地表正演模拟影响因素

李庆洋¹, 李振春¹, 黄建平¹, 李娜², 苏在荣³

1. 中国石油大学(华东)地球科学与技术学院, 山东青岛 266580;
2. 中原油田分公司物探研究院, 河南濮阳 457001;
3. 南通市统计局, 江苏南通 226000

收稿日期:2015-09-01 出版日期:2016-05-26 发布日期:2016-05-26
作者简介:李庆洋(1988),男,博士研究生,主要从事地震波正演及偏移成像工作,E-mail:liqingyang.1988@163.com
基金资助:
国家重点基础研究发展计划（国家“973”计划）（2011CB202402）；国家自然科学基金项目（41274124）；中央高校基本科研业务费专项资金（14CX06072A）

Factor Analysis of Seismic Modeling with Topography Based on a Fully Staggered Body-Fitted Grids

Li Qingyang¹, Li Zhenchun¹, Huang Jianping¹, Li Na², Su Zairong³

1. School of Geoscience, China University of Petroleum(East china), Qingdao 266580, Shangdong, China;
2. Geophysical Exploration Research Institute of Zhongyuan Oilfield Company, Puyang 457001, Henan, China;
3. Nantong Municipal Statistics Bureau, Nantong 226000, Jiangsu, China

Received:2015-09-01 Online:2016-05-26 Published:2016-05-26
Supported by:
Supported by the State Key Development Program for Basic Research of China (2011CB202402), the National Natural Science Foundation of China (41274124) and the Fundamental Research Funds for the Central Universities (14CX06072A)

摘要/Abstract

摘要：

贴体网格有限差分正演模拟算法不仅能够精确模拟任意起伏地形下的波场特征，且计算效率较高，是一种很有应用前景的处理西部复杂地表问题的方法；然而，目前求解波动方程时常用的同位网格和标准交错网格，在处理贴体网格起伏地表正演模拟时存在诸多问题。为此，将全交错网格引入到曲线坐标系下，避免了标准交错网格的插值误差和同位网格中奇偶失联引起的高频振荡现象，提高了模拟精度，减小了算法实现的复杂度。在自由边界条件实施时，采用牵引力镜像法计算速度分量，速度自由边界条件配合紧致交错差分格式更新应力分量，得到了较好的效果。随后，重点研究了贴体全交错网格正演模拟算法的影响因素，考虑了网格正交性、网格间距和网格拼接等的影响，并取得了如下认识：算法对网格的正交性没有过分要求；网格间距的突变会引起虚假反射的产生；不同类型的网格拼接对模拟结果不会造成明显的影响。

关键词: 起伏地表, 贴体网格, 全交错网格, 正演模拟, 影响因素

Abstract:

Finite-difference forward modeling method with body-fitted can accurately simulate wavefields in presence of topography, meanwhile, the computational efficiency is relatively high. Therefore, it is a prospecting method for dealing with the western complex surface. The collocated-grid and standard staggered grid are often used to solve wave equation. However, they show many problems when the above two grids are extend to body-fitted grids. By introducing the fully-staggered grid to curvilinear coordinates, the proposed method can avoid not only the interpolation error when standard staggered grid are used, but also the high-frequency oscillations with the collocated-grid. Thus, it can improve the simulation accuracy and reduce the complexity of the algorithm degrees. To satisfy the free surface boundary condition, we use the traction image method to calculate the velocity components, the method also uses the velocity of free boundary conditions with compact staggered difference format to update the stress components. Model tests show that the proposed method can obtain the good results. And then, we mainly study the influence factors of forward modeling algorithm by a fully staggered body-fitted grids, such as, the orthogonality of grids, the grid spacing change, and the skewness of meshes.Finally, we obtain some conclusions as follows:the algorithm is not sensitive to the orthogonality of grids;the grid spacing changing can lead to false reflection;the result of simulation is not affected by the skewness of different types of grids.

Key words: irregular free surface, body-fitted grid, full staggered-grid, forward modeling, factors

中图分类号:

P631.4

李庆洋, 李振春, 黄建平, 李娜, 苏在荣. 基于贴体全交错网格的起伏地表正演模拟影响因素[J]. 吉林大学学报(地球科学版), 2016, 46(3): 920-929.

Li Qingyang, Li Zhenchun, Huang Jianping, Li Na, Su Zairong. Factor Analysis of Seismic Modeling with Topography Based on a Fully Staggered Body-Fitted Grids[J]. Journal of Jilin University(Earth Science Edition), 2016, 46(3): 920-929.

参考文献

[1] 张华,李振春,韩文功.起伏地表条件下地震波数值模拟方法综述[J].勘探地球物理进展,2007,30(5):334-339. Zhang Hua, Li Zhenchun, Han Wengong. Review of Seismic Wave Numerical Simulation from Irregular Topography[J]. Progress in Exploration Geophysics, 2007, 30(5):334-339.

[2] 孙建国.复杂地表条件下地球物理场数值模拟方法评述[J].世界地质,2007,26(3):345-362. Sun Jianguo. Methods for Numerical Modeling of Geophysical Fields Under Complex Topographical Conditions:A Critical Review[J]. Global Geology, 2007, 26(3):345-362.

[3] 裴正林.任意起伏地表弹性波方程交错网格高阶有限差分法数值模拟[J]. 石油地球物理勘探,2004,39(6):629-634. Pei Zhenglin. Numerical Modeling Using Staggered-Grid High-Order Finite-Difference of Elastic Wave Equation on Arbitrary Relief Surface[J]. Oil Geophysical Prospecting, 2004, 39(6):629-634.

[4] 王雪秋,孙建国.地震波有限差分数值模拟框架下的起伏地表处理方法综述[J]. 地球物理学进展,2008, 23(1):40-48. Wang Xueqiu, Sun Jianguo. The State-of-the-Art in Numerical Modeling Including Surface Topography with Finite-Difference Method[J]. Progress in Geophysics, 2008, 23(1):40-48.

[5] 王秀明,张海澜.用于具有不规则起伏自由表面的介质中弹性波模拟的有限差分算法[J].中国科学:G辑:物理学、力学、天文学, 2004, 34(5):481-493. Wang Xiuming, Zhang Hailan. Modeling the Seismic Wave in the Media with Irregular Free Interface by the Finite-Difference Method[J]. Science in China:Series G:Physica, Mechanica and Astronomica, 2004, 34(5):481-493.

[6] 郭振波,李振春.起伏地表条件下频率-空间域声波介质正演模拟[J].吉林大学学报(地球科学版),2014, 44(2):683-693. Guo Zhenbo, Li Zhenchun. Acoustic Wave Modeling in Frequency-Spatial Domain with Surface Topography[J]. Journal of Jilin University (Earth Science Edition), 2014, 44(2):683-693.

[7] 李振春,李庆洋,黄建平,等. 一种稳定的高精度双变网格正演模拟与逆时偏移方法[J]. 石油物探, 2014, 53(2):127-136. Li Zhenchun,Li Qingyang,Huang Jianping,et al. A Stable and High-Precision Dual-Variable Grid Forward Modeling and Reverse Time Migration Method[J]. Geophysical Prospecting for Petroleum, 2014, 53(2):127-136.

[8] Hestholm S, Ruud B. 2-D Finite-Difference Elastic Wave Modeling Including Surface Topography[J]. Geophysical Prospecting, 1994, 42:371-390.

[9] 董良国,郭晓玲,吴晓丰,等.起伏地表弹性波传播有限差分法数值模拟[J]. 天然气工业,2007, 27(10):38-41. Dong Liangguo, Guo Xiaoling, Wu Xiaofeng,et al. Finite Difference Numerical Simulation for the Elastic Wave Propagation in Rugged Topography[J]. Natural Gas Industry. 2007, 27(10):38-41.

[10] Tarrass I,Giraud L,Thore P.New Curvilinear Scheme for Elastic Wave Propagating in Presence of Curved Topography[J]. Geophysical Prospecting, 2011,59:889-906.

[11] Fornberg B. The Pseudo-Spectral Method:Accurate Repre-sentation in Elastic Wave Calculations[J]. Geophysics, 1988, 53:625-637.

[12] Komatitsch D, Coute F, Mora P. Tensorial Formulation of the Wave Equation for Modelling Curved Interfaces[J]. Geophysical Journal International, 1996, 127:156-168.

[13] Zhang W, Chen X. Traction Image Method for Irregular Free Surface Boundaries in Finite Difference Seismic Wave Simulation[J]. Geophysical Journal International, 2006, 167:337-353.

[14] Zhang W, Shen Y, Zhao L. Three-Dimensional Aniso-tropic Seismic Wave Modelling in Spherical Coordinates by a Collocated-Grid Finite-Difference Method[J]. Geophysical Journal International, 2012, 188:1359-1381.

[15] 祝贺君,张伟,陈晓非.二维各向异性介质中地震波场的高阶同位网格有限差分模拟[J].地球物理学报, 2009, 52(6):1536-1546. Zhu Hejun, Zhang Wei, Chen Xiaofei. Two-Dimensional Seismic Wave Simulation in Anisotropic Media by Non-Staggered Finite-Difference Method[J]. Chinese Journal of Geophysics, 2009, 52(6):1536-1546.

[16] Appelo D, Petersson N A. A Stable Finite Difference Method for the Elastic Wave Equation on Complex Geometries with Free Surfaces[J]. Communications in Computational Physics, 2009, 5:84-107.

[17] 兰海强,刘佳,白志明.VTI介质起伏地表地震波场模拟[J]. 地球物理学报,2011, 54(8):2072-2084. Lan Haiqiang, Liu Jia, Bai Zhiming. Wave-Field Simulation in VTI Media with Irregular Free Surface[J]. Chinese Journal of Geophysics, 2011, 54(8):2072-2084.

[18] 丘磊,田钢,石战结, 等.起伏地表条件下有限差分地震波数值模拟:基于广义正交曲线坐标系[J].浙江大学学报(工学版), 2012,46(10):1923-1930. Qiu Lei, Tian Gang, Shi Zhanjie, et al. Finite-Difference Method for Seismic Wave Numerical Simulation in Presence of Topography:In Generally Orthogonal Curvilinear Coordinate System[J]. Journal of Zhejiang University (Engineering Science), 2012, 46(10):1923-1930.

[19] Rao Y, Wang Y H. Seismic Waveform Simulation with Pseudo-Orthogonal Grids for Irregular Topographic Models[J]. Geophysical Journal International, 2013, 194:1778-1788.

[20] 孙建国,蒋丽丽. 用于起伏地表条件下地球物理场数值模拟的正交曲网格生成技术[J]. 石油地球物理勘探, 2009, 44(4):494-500. Sun Jianguo, Jiang Lili. Orthogonal Curvilinear Grid Generation Technique Used for Numeric Simulation of Geophysical Fields in Undulating Surface Condition[J]. Oil Geophysical Prospecting, 2009, 44(4):494-500.

[21] 蒋丽丽,孙建国. 基于Poisson方程的曲网格生成技术[J].世界地质, 2008, 27(3):298-305. Jiang Lili, Sun Jianguo. Source Terms of Elliptic System in Grid Generation[J]. Global Geology, 2008, 27(3):298-305.

[22] Lisitsa V,Vishnevskiy D.Lebedev Scheme for the Nume-rical Simulation of Wave Propagation in 3D Anisotropic Elasticity Double Dagger[J]. Geophysical Prospecting, 2010, 58:619-635.

[23] 李娜,黄建平,李振春,等. Lebedev网格改进差分系数TTI介质正演模拟方法研究[J]. 地球物理学报,2014, 57(1):261-269. Li Na, Huang Jianping, Li Zhenchun, et al. The Study on Numerical Simulation Method of Lebedev Grid with Dispersion Improvement Coefficients in TTI Media[J]. Chinese Journal of Geophysics, 2014, 57(1):261-269.

[24] 李庆洋,黄建平,李振春,等.起伏地表贴体全交错网格仿真型有限差分正演模拟[J].石油地球物理勘探,2015, 50(4):633-642. Li Qingyang, Huang Jianping, Li Zhenchun, et al. Undulating Surface Body-Fitted Grid Seismic Modeling Based on Fully Staggered-Grid Mimetic Finite Difference[J]. Oil Geophysical Prospecting, 2015, 50(4):633-642.

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基于贴体全交错网格的起伏地表正演模拟影响因素

Factor Analysis of Seismic Modeling with Topography Based on a Fully Staggered Body-Fitted Grids

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