基于波动方程叠前偏移的频率优化
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摘要
为了提高叠前偏移的计算效率并保持成像精度,此文以偏移原理为研究对象。在适当减少频率使用可以提高偏移效率的基础上,根据Hessian矩阵是非奇异的,得出了能够避免图像中出现绕射假频的频率采样方法。采样点的选取根据速度、偏移深度和偏移距的不同而不同,不仅减少了频率而且使用了有效的频率集。然后以傅里叶有限差分法为试验方法,用两个数值模型进行偏移试算,通过成像精度及运算时间证明了该频率采样方法的正确性和有效性。
In order to improve the computational efficiency of pre-stack migration and maintain the imaging accuracy, this paper takes the migration principle as the research object. On the basis that migration efficiency can be improved by appropriate reduction of frequency usage, the frequency sampling method which can avoid the wrap-around artefacts in the image is obtained according to Hessian theory that matrix is nonsingular. The sampling points are selected differently according to the velocity, depth of the migration and offset, which not only reduces the frequency but also uses a subset of the effective frequencies. The Fourier finite difference method is used as an experimental method in this paper, in which two numerical models are used for migration trial calculation, and the correctness and validity of this frequency sampling method are proved by imaging accuracy and operation time.
In order to improve the computational efficiency of pre-stack migration and maintain the imaging accuracy, this paper takes the migration principle as the research object. On the basis that migration efficiency can be improved by appropriate reduction of frequency usage, the frequency sampling method which can avoid the wrap-around artefacts in the image is obtained according to Hessian theory that matrix is nonsingular. The sampling points are selected differently according to the velocity, depth of the migration and offset, which not only reduces the frequency but also uses a subset of the effective frequencies. The Fourier finite difference method is used as an experimental method in this paper, in which two numerical models are used for migration trial calculation, and the correctness and validity of this frequency sampling method are proved by imaging accuracy and operation time.
引文
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[5] LOEWENTHAL D,HU L Z.Two methods for computing the imaging condition for common-shot pre-stack migration[J].Geophysics,1991(4):378–381.
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[7] 王东,李文卉,熊登,等.静校正对波动方程叠前深度偏移成像效果的影响[J].石油地球物理勘探,2017(2):76-80.
[8] 匡斌,王华忠,陈世军,等.傅里叶有限差分深度偏移成像方法研究和应用[J].石油地球物理勘探,2001(6):698-704.
[9] GAZDAG J.Modeling of the acoustic wave equation with transform methods[J].Geophysics,1981(6):854-859.
[10] 俞岱,杨飞龙,孙渊,等.井间地震高斯束叠前深度偏移成像方法[J].物探化探计算技术,2018(2):141-149.
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[13] PLESSIX R E,MULDER W A,PRATT R G.Frequency-domain finite-difference migration with only few frequencies?[C].Expanded Abstracts of Annual Internet SEG Mtg,2001.
[14] 匡斌,王华忠,陈世军,等.傅里叶有限差分深度偏移成像方法研究和应用[J].石油地球物理勘探,2001(6):698-704.
[15] 田东升,王云专,李义鹏,等.单程和双程波动方程叠前深度偏移方法[J].东北石油大学学报,2014(4):39-45.
[2] 刘定进,杨勤勇,方伍宝,等.叠前逆时深度偏移成像的实现与应用[J].石油物探,2011(6):545-549.
[3] ALFORD R,KELLY K,BOORE D.Accuracy of finite-difference modeling of the acoustic wave equation[J].Geophysics,1974(6):834-842.
[4] 张宇.从成像到反演:叠前深度偏移的理论、实践与发展[J].石油物探,2018(1):1-23.
[5] LOEWENTHAL D,HU L Z.Two methods for computing the imaging condition for common-shot pre-stack migration[J].Geophysics,1991(4):378–381.
[6] LI Z,LYNN W,CHAMBERS R.Enhancements to pre-stack frequency wave number (f-k) migration[J].Geophysics,2012(1):27-40.
[7] 王东,李文卉,熊登,等.静校正对波动方程叠前深度偏移成像效果的影响[J].石油地球物理勘探,2017(2):76-80.
[8] 匡斌,王华忠,陈世军,等.傅里叶有限差分深度偏移成像方法研究和应用[J].石油地球物理勘探,2001(6):698-704.
[9] GAZDAG J.Modeling of the acoustic wave equation with transform methods[J].Geophysics,1981(6):854-859.
[10] 俞岱,杨飞龙,孙渊,等.井间地震高斯束叠前深度偏移成像方法[J].物探化探计算技术,2018(2):141-149.
[11] SIRGUE L,PRATT R G.Frequency domain waveform inversion:A strategy for choosing frequencies[C].Expanded Abstracts of 63rd Annual Meeting EAGE Eur,2001.
[12] ROMERO L A.Phase encoding of shot records in pre-stack migration[J].Geophysics,2000(2):426-436.
[13] PLESSIX R E,MULDER W A,PRATT R G.Frequency-domain finite-difference migration with only few frequencies?[C].Expanded Abstracts of Annual Internet SEG Mtg,2001.
[14] 匡斌,王华忠,陈世军,等.傅里叶有限差分深度偏移成像方法研究和应用[J].石油地球物理勘探,2001(6):698-704.
[15] 田东升,王云专,李义鹏,等.单程和双程波动方程叠前深度偏移方法[J].东北石油大学学报,2014(4):39-45.