<i>L</i>1-<i>L</i>2范数联合约束稀疏脉冲反演的应用

王宇; 韩立国; 周家雄; 李海鹏

L1-L2范数联合约束稀疏脉冲反演的应用

1.
中海石油(中国) 有限公司湛江分公司, 广东湛江 524057
2.
吉林大学地球探测科学与技术学院, 吉林长春 130026

基金项目:

国家重大科技专项 2008ZX05023-004

详细信息

作者简介:
王宇( 1982-) , 工程师, 从事地球物理技术在储层描述中的应用研究.E-mail:wangyu1@cnooc.com.cn

中图分类号: P315
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出版历程
- 收稿日期: 2009-01-23
- 刊出日期: 2009-09-25

Application of Combined Norm Constrained Sparseness Spike Inverse

1.
China National Of f shore Oil Company Ltd-Zhan jiang, Zhan jiang 524057, China
2.
College of Geoex ploration Science and Technology, Jilin University, Chang chun 130026, China

摘要

摘要: 稀疏脉冲反演实际上就是利用反褶积原理, 从带有噪声的地震道中计算出具有稀疏分布特征的反射系数的振幅和时间.稀疏脉冲反演是非线性优化问题, 通常都是把非线性优化问题转化为线性优化问题, 然后用线性优化算法求解.以范数约束为基础, 提出L1-L2范数联合约束求解的方法.该算法采用了目前国际流行的内点算法, 与传统的优化算法相比, 这种算法具有精度高, 速度快的优点.通过研究人工模型和南海某油田实际数据, 表明该算法的计算结果和测井记录吻合好, 提高了地震分辨率, 目的层段分辨率优于8m.利用反射系数剖面预测的储层厚度和开发井吻合很好, 大大地降低了资源量计算的风险和油田开发的不确定性.
- 反射系数反演 /
- 稀疏约束反演 /
- 内点算法 /
- 范数
Abstract: Sparse-spike deconvolution is an inverse issue which estimates the time and the amplitudes of the sparseness reflectivity (spikes) from the noisy seismic traces.Sparseness spike inverse is highly non-linear optimization problem that can be solved using the L1-L2 norm constrained method introduced in this paper.This method is characterized with its application of the log-barrier interior point to solve the sparseness inverse problem which is higher in terms of resolution and faster than conventional optimization methods.Resultsfrom the synthetic and real 3D data show that the physically meaningful high-resolution sparse-spike profile can be derived from the band-limited noisy data.Real data show that the method improves seismic resolution and estimates the thickness of thin bed which can reduce the uncertainty of resource estimation and oil field production.
- reflection coefficient inverse /
- sparse-constrained inverse /
- interior point algorithm /
- norm

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图 1 不同噪声水平下楔状模型反演精度测试

1.真实模型厚度; 2.地震视厚度; 3.反演的厚度; a.模拟地震道, 30 Hz雷克子波和楔状模型褶积生成; b.模拟地震道的最大振幅图; c.没有噪声情况下的反演果; d.加了均值为0、±0.005区间正态分布的噪声的反演结果; e.加了均值为0、±0.025区间正态分布的噪声的反演结果; f.加了均值为0、±0.010区间正态分布的噪声的反演结果

Fig. 1. Wedge model inversion test with various noise standard

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图 2 多层反射系数序列的反演结果比较

a.随机反射序数序列; b.主频为30 Hz的雷克子波的反演结果; c.主频为40 Hz雷克子波的反演结果; d.主频为40 Hz雷克子波, 加入了均值为0、±0.01区间正态分布噪声的反演结果

Fig. 2. Multi-layer model inverse test

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图 3 测井数据.地震资料和反演结果对比

测井数据包括声波阻抗、自然伽马和电阻率: 地震资料和反射系数中的红竖线是井点位置

Fig. 3. Comparison between logging data, original seismic data and inverted reflective ceofficients

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图 4 原始地震剖面(a)和反射系数剖面(b)对比

地震资料的主频在45 Hz左右, 受到地震子波的滤波左右.高频成分弱, 地层细节信息基本丢失.反演的反射系数剖面; 反演算法去除了地震子波的滤波作用，有效恢复了地震资料的高频成分, 地层细节信息更加丰富、准确

Fig. 4. Comparison between original seismic data and inverted reflective cofficients

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图 5 地震视厚度图(a)和反演的厚度图(b)对比

Fig. 5. Comparison between seismic apparent thickness map and predicted thickness map from inversion

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表 1 反演的毛厚度和地震视厚度的对比(m)

Table 1. Comparison between seismic apparent thickness and predicted thickness from inversion

参考文献(15)

Debeye, H. W. J., Van Riel, P., 1990. Lpnorm deconvolution. Geophysical Prospecting, 38 (4): 381-403. doi: 10.1111/j.1365-2478.1990.tb01852.x
Gill, P. E., Murray, W., Ponceleon, D. B., et al., 1991. Solving reduced KKT systems in barrier methods for linearand quadratic programming. Techniccal Report SOL91-7, Stanford University, U. S. A. .
Huang, H. X., Han, X. Y., 2006. Mathematic programming. Qinghua University Press (in Chinese).
Kormylo, J., Mendel, J., 1978. On maximum-likelihood detection and estimation of reflection coefficients. 48th Annual International Meeting, SEG Expanded Abstracts, Tulsa, U. S. A., 45-46.
Roos, C., Terlaky, T., Vial, J. P., 1997. Theory and algorithms for linear optimization: An interior point approach. Wiley, Chichester, UK.
Sacchi, M. D., Velis, D. R., Comínguez, A. H., 1994. Mini-mumentropy deconvolution with frequency domain constraints. Geophysics, 59 (6): 938-945. doi: 10.1190/1.1443653
Veeken, P. C. H., Da Silva, M., 2004. Seismic inversion methods and some of their constraints. First Break, 22: 47-72.
Velis, D. R., 2006. Parametric sparse-spike deconvolutionand the recovery of the acoustic impedance. 76th Annual International Meeting, SEG Expanded Abstracts, Tulsa, U. S. A., 2141-2144.
Wang, J., Wang, X., Perz, M., 2006. Structure preserving regularization for sparse deconvolution. 76th Annual International Meeting, SEG Expanded Abstracts, 25: 2072-2076.
Widess, M. B., 1973. Howthinis a thin bed? Geophysics, 38 (6): 1176-1180.
Wright, M. H., 1992. Interior methods for constrained opti-mization. Acta Numeica, 1: 341-407. doi: 10.1017/S0962492900002300
Wright, S. J., 1996. Primaldual interiorpoint method. SI-AM, Philadelphia.
Xu, G. M., 2003. Inverse theory and applications. Seismic Press (in Chinese).
黄红选, 韩续业, 2006. 数学规划. 北京: 清华大学出版社.
徐果明, 2003. 反演理论及其应用. 北京: 地震出版社.