基于最小二乘法优化系数的傅里叶有限差分偏移
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摘要
复杂构造油气藏的勘探已经成为当前的重点,也是进行高分辨率地震勘探的瓶颈。为了获得精确的复杂构造成像,一般采用具有高角度、频散小、适应纵横向速度变化的傅里叶有限差分法来实现叠前深度偏移,但该方法对陡倾角成像还存在明显的误差。为此,利用全局优化的非线性多元最小二乘法对傅里叶有限差分算子中的系数进行优化,从而在保持计算效率的前提下,提高了成像角度及陡倾角的成像精度。通过对SEG/EAGE模型进行优化系数的傅里叶有限差分偏移,其结果表明该方法对陡倾角构造及纵横向速度急剧变化的地区具有更高的成像精度。显然基于多元最小二乘法优化系数傅里叶有限差分偏移法比常规优化系数的傅里叶有限差分法更适合在陡倾角地区的精确成像。
Complex structural reservoirs are the focus of exploration at present, but are the bottlenecks of high resolution seismic exploration. In order to obtain accurate images of complex structures, the Fourier finite-difference approach, which is featured by high angle, small frequency dispersion and strong ability of adapting to vertical and lateral velocity variations, is generally used to perform prestack depth migration. However, significant errors exist when it is used to image structures with high dip angles. To solve this problem, the global optimization method of multivariable nonlinear least-square approach is proposed to optimize the coefficients of Fourier finite-difference operators. The imaging accuracy of structures with high dip angles is improved and the scope of imaging an gles is enlarged, meanwhile the original computation efficiency is maintained. The Fourier finite difference migration with optimal coefficients is performed on the SEG/EAGE models, and the results show that this method can enhance the imaging accuracy of structures with high dip angles and in areas where vertical and lateral velocity variations are significant. For a high image accuracy of structures with steep dip angles, the Fourier finite difference prestack depth migration based on multivariable least-square optimal co efficients is more suitable for use than the conventional methods.
Complex structural reservoirs are the focus of exploration at present, but are the bottlenecks of high resolution seismic exploration. In order to obtain accurate images of complex structures, the Fourier finite-difference approach, which is featured by high angle, small frequency dispersion and strong ability of adapting to vertical and lateral velocity variations, is generally used to perform prestack depth migration. However, significant errors exist when it is used to image structures with high dip angles. To solve this problem, the global optimization method of multivariable nonlinear least-square approach is proposed to optimize the coefficients of Fourier finite-difference operators. The imaging accuracy of structures with high dip angles is improved and the scope of imaging an gles is enlarged, meanwhile the original computation efficiency is maintained. The Fourier finite difference migration with optimal coefficients is performed on the SEG/EAGE models, and the results show that this method can enhance the imaging accuracy of structures with high dip angles and in areas where vertical and lateral velocity variations are significant. For a high image accuracy of structures with steep dip angles, the Fourier finite difference prestack depth migration based on multivariable least-square optimal co efficients is more suitable for use than the conventional methods.
引文
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[2]张文生.波动方程成像方法及其计算[M].北京:科学出版社,2009:75-79.
[3]曹文俊,李振春,韩文功.波动方程叠前深度偏移对速度模型的敏感性分析[J].天然气工业,2007,27(增刊1):120-122.
[4]王开燕.优化参数分裂步Fourier波动方程叠前深度偏移方法研究[D].大庆:大庆石油学院,2008:25.
[5]RISTOW D,RüHI T.Fourier finite-difference migration[J].Geophysics,1990,55(4):410-421.
[6]XIE Xiaobi,WU Rushan.Improve the wider-angle accuracyof screen method under large contrast[C]∥The 68th Socie-ty of Exploration Geophysicists Annual International Meet-ing,USA.Tulsa:SEG.1998:1811-1814.
[7]杨卫峰,曾芳玲.基于区间全局优化的非线性最小二乘估计[J].通信技术,2010,43(6):232-234.
[8]马在田.高阶方程偏移的分裂算法[J].地球物理学报,1983,26:377-389.
[9]李灿,沈金蓉,曹香莲.一种修正的共轭梯度法及其全局收敛性[J].长沙大学学报,2010,24(2):7-9.
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