地球物理学报  2013, Vol. 56 Issue (3): 1003-1011 PDF

The research on local slope constrained least-squares migration
LIU Yu-Jin, LI Zhen-Chun, WU Dan, HUANG Jian-Ping, WEI Xiao-Qiang
Department of Geophysics, School of Geosciences, China University of Petroleum, Qingdao 266555, China
Abstract: As the difficulty of oil exploration increases, the phenomenon of irregular sampling and missing traces often exits in seismic data, which will introduce imaging noise without special data processing. In order to solve the problem, the conventional method is implementing seismic trace interpolation or data regularization to pre-stack data before imaging with conventional migration. In this paper, seismic imaging is considered as least-squares inverse problem, with constraints of smoothing operator in common image gathers and plane-wave constructor in common offset/angle gathers, to obtain an artifact-reduced seismic image by iteratively minimizing the difference between de-migrated data and input data with preconditioning conjugate gradient method. Experimental results on theoretical model and seismic field data show that the proposed method can suppress the imaging noise introduced by data irregularity thus providing a more accurate image..
Key words: Least-squares migration      Local slope      Plane-wave constructor      Irregular data      High S/N ratio
1 引言

2 方法原理 2.1 Kirchhoff偏移/反偏移的基本原理

 (1)

 (2)

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2.2 LSM基本原理

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2.3 预条件算子的选取

CIGs平滑约束条件的合理性在于:当地表观测数据充足, 或者地下照明充分时, CIGs的能量将沿横向坐标平滑变化.因此, 根据这一特点, 可以在CIGs引入平滑算子对反演结果进行约束.一般采用一阶差分正则化算子作为高通滤波器压制沿偏移距方向变化的高频信息.一阶差分算子的逆为因果积分算子, 而预条件算子和正则化算子互逆, 因此预条件算子为因果积分算子, 为了使得反演结果振幅变化更加均衡, 对因果积分算子进行改进, 加入积分次数作为除数.CIGs平滑算子Pcig定义为以下矩阵的形式:

 (7)

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 (9)

PWC算子是PWD算子的逆, 通过矩阵运算, 对PWC算子进行推导, 推导过程如下:

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3 模型试算与实际资料处理

3.1 凹陷模型测试

 图 1 速度模型及正演数据 (a)模型层速度场; (b)有限差分正演数据; (c)均方根速度场; (d)随机抽除70%后的数据体. Fig. 1 Velocity field and modeling data (a)Interval velocity field; (b)Finite difference modeling data; (c)RMS velocity field; (d)Seismic data after 70% removed randomly.
 图 2 对比常规偏移、平滑约束反演、平滑约束和局部倾角约束反演的成像结果 (a)Kirchhoff偏移成像道集; (b)Kirchhoff偏移叠加成像结果; (c)CIGs平滑约束LSM成像道集; (d)CIGs平滑约束LSM叠加成像结果; (e)CIGs平滑和COGs局部倾角约束LSM成像道集; (f)CIGs平滑和COGs局部倾角约束LSM叠加成像结果. Fig. 2 Comparison of images of conventional migration, CIGs smoothing constrained LSM, CIGs smoothing and COGs local slope constrained LSM (a)Image gathers of Kirchhoff migration; (b)The stacked image of Kirchhoff migration; (c)Image gathers of CIGs smoothing constrained LSM; (d)The stacked image of CIGs smoothing constrained LSM; (e)Image gathers of CIGs smoothing and COGslocal slope constrained LSM; (f)The stacked image of CIGs smoothing and COGs local slope constrained LSM.
 图 3 局部倾角和归一化数据拟合剩余量随迭代次数的变化曲线 (a)局部倾角场; (b)归一化数据拟合剩余量随迭代次数的变化曲线.-o-为cigs平滑约束LSM; -*-为cigs平滑约束和COGs局部倾角约束LSM. Fig. 3 Local slope field and data misfit curve for CIGs smoothing constrained(-o-) and CIGs smoothing & COGs local slope constrained(-*-) LSM (a) Local slope field; (b) Data misfit curve for CIGs smoothing constrained and CIGs.
3.2 实际资料处理

 图 4 常规偏移和LSM叠加成像结果比较. (a)面元归一化后的数据体; (b)叠加速度分析得到的均方根速度场; (c)局部倾角场; (d)Kirchhoff偏移结果; (e)LSM成像结果 Fig. 4 Comparison of image gathers of conventional migration and LSM. (a) Data cube after normalized binning; (b) RMS velocity field after stack velocity analysis; (c) Local slope field; (d) Image gathers of Kirchhoff migraion; (e) Image gathers of LSM
 图 5 常规偏移和LSM叠加成像结果比较 (a)常规偏移的叠加成像结果; (b)LSM的叠加成像结果; (c)常规偏移成像结果局部放大; (d)LSM成像结果局部放大. Fig. 5 Comparison of stacked image of conventional migration and LSM (a) Stacked image of conventional migration; (b) Stacked image of LSM; (c) Close up of conventional migration image; (d) Close up of LSM image.
4 结论与讨论

(1)本文方法的关键之一是偏移与反偏移算子的构建, 这对算子必须互为共轭才能保证迭代反演过程收敛; (2)CIGs平滑约束条件可以有效压制CIGs上的成像噪音, 使得反演后道集内振幅沿偏移距平滑变化, 但是对最终的叠加成像结果没有多少改善; (3)同时加入CIGs平滑约束条件和COGs局部倾角约束条件, 可以从两个不同的方向对反演结果进行优化, 压制CIGs和COGs上的偏移噪音, 并且能够改善最终的反演效果, 提高成像精度; (4)通过加入合适的预条件算子, 可以有效提高反演的收敛速度, 从而在一定程度上降低LSM的计算成本.

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