基于小波变换的曲率属性提取和重构方法
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摘要
曲率属性研究提供了深入观测目标层面的手段,然而求取曲率值是借助一种基于二阶导数的数学方法,对地震数据中的任何噪声都很敏感。因此,有必要采用空间滤波等手段,对输入数据进行预处理。在小波域分频成像的基础上,引入微分几何的有关曲率概念,推导了基于小波分频的曲率属性提取、重构和三维曲率数据体生成方法。其实现过程为:①对地震资料进行小波变换、分频重构,获得高质量的地震资料;②采用最小二乘法一次逼近,对局部二次曲面进行拟合,求取二次曲面拟合系数,并利用这些系数对网格化成图层面计算平均曲率和高斯曲率,再从两个曲率的不同线性组合,获取其他曲率;③将层面曲率推广,计算和重构曲率数据体。实际资料应用表明,该方法能够有效检测微小裂隙、划定特殊地质体边界等。该方法可以在储层预测研究中发挥重要作用,是DFT频谱分解技术的补充和拓展。
The curvature attribute research provides a tool to observe the target horizons further, however, a mathematic method based on second order derivative is used in calculation of the curvature value, which is very sensitive to any interference in the seismic data. Therefore, such tools as spatial filtering etc. are essential to perform preprocessing of the input data. On the basis of the frequency decomposition imaging in wavelet domain, the paper introduced the responding curvature concepts related to the differential geometry, and derived the method for curvature attribute extraction, reconstruction and 3D volume generation based on the wavelet frequency decomposition. Its implementation processes include: ①to perform wavelet transform and frequency decomposition and reconstruction to gain the seismic data with high quality; ②to adopt least square method to approach and fit the local secondary curved face, and compute the fit coefficients of the secondary curved face, then use these coefficients to gridding mapping bed plane to compute the average curvature and Gauss curvature, then, obtain other curvatures through the various linear combinations of the two curvatures above; ③to generalize the curvature of the bed layer to compute and reconstruct the curvature volume. The real data application indicates that this method can effectively detect micro fracture, delineate the boundary of the special geologic bodies and so on. This method will play an important role in reservoir prediction research and is a supplement and extension of DFT spectrum decomposition technique.
The curvature attribute research provides a tool to observe the target horizons further, however, a mathematic method based on second order derivative is used in calculation of the curvature value, which is very sensitive to any interference in the seismic data. Therefore, such tools as spatial filtering etc. are essential to perform preprocessing of the input data. On the basis of the frequency decomposition imaging in wavelet domain, the paper introduced the responding curvature concepts related to the differential geometry, and derived the method for curvature attribute extraction, reconstruction and 3D volume generation based on the wavelet frequency decomposition. Its implementation processes include: ①to perform wavelet transform and frequency decomposition and reconstruction to gain the seismic data with high quality; ②to adopt least square method to approach and fit the local secondary curved face, and compute the fit coefficients of the secondary curved face, then use these coefficients to gridding mapping bed plane to compute the average curvature and Gauss curvature, then, obtain other curvatures through the various linear combinations of the two curvatures above; ③to generalize the curvature of the bed layer to compute and reconstruct the curvature volume. The real data application indicates that this method can effectively detect micro fracture, delineate the boundary of the special geologic bodies and so on. This method will play an important role in reservoir prediction research and is a supplement and extension of DFT spectrum decomposition technique.
引文
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[3]李世雄.小波变换及其应用[M].北京:高等教育出版社,1997.
[4]梅向明.微分几何[M].北京:高等教育出版社,2002.
[5]王西文,等.地震资料在小波域的分频处理与重构[J].石油地球物理勘探,2001,36(1):78-85.
[6]王西文,杨孔庆,杨午阳,等.基于小波变换拟瞬时属性吸收系数的计算方法及应用[J].石油地球物理勘探,2002(增刊):205-209.
[7]王西文,杨孔庆,刘全新,等.基于小波变换的地震相干体算法的应用[J].石油地球物理勘探,2002,(37)4:328-331.
[8]杨午阳,王西文,雷安贵,等.综合储层预测技术在包1—庙4井区中的应用[J].石油物探,2004(6).
[9]杨午阳.粘弹性波动方程保持振幅偏移技术研究[D].中国地质科学院博士学位论文,2004.
[10]杨午阳,邓央,等.地震综合反演及油气检测系统[J].天然气工业,2005,25(增刊B):116-120.
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