常规二次多项式拟合地震数据
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摘要
在传统的地震数据拟合技术中大都采用正交多项式拟合方法,这种拟合方法的拟合结果存在拟合不够准确的缺点,导致处理后地震数据的主频降低、断点变形。对产生这些现象的原因进行了分析,指出拟合过程中拟合中心点随正交多项式系数的改变是导致拟合不够准确的主要原因,提出采用常规二次多项式取代正交多项式进行数据拟合,以克服正交多项式拟合方法的缺陷。针对常规二次多项式系数扫描时由于系数彼此影响使计算量增大的问题,采用先线性拟合再微调的办法予以解决;针对扫描过程中拟合系数不能直接采用最优化算法的问题,采取了先大步长等间距扫描确定最佳拟合函数的单极值区间,然后再用二分法进行最佳拟合系数扫描的措施,节省了计算时间;针对拟合过程中出现断点模糊这一问题,采用中值约束下的矢量分解技术来解决。最后,利用理论模型和实际资料对常规二次多项式拟合方法进行了验证,结果表明,在处理后的地震数据中,随机干扰得到了很好的压制,同相轴的连续性得到了增强,断点准确。
Most of the conventional data fitting methods use orthogonal polynomials, which have shortcomings such as lowering the dominant frequency, distorting the breakpoint and the enormous error, etc. Through analysis, we find that the fitting center is changing with coefficient of the polynomial, which causes the error. Because the seismic data is linear in local, a fitting method using quadratic polynomials to replace orthogonal polynomials is presented. This method can avoid the above shortcomings. We overcome the computing cost from the coefficient scanning by primary linear fitting and following fine adjustment. That is, firstly identifying the single extreme value interval of the optimal fitting function using uniform large step scanning, then determining the optimal fitting coefficient using dichotomy. As for the breakpoint issue, the mean value constrained vector resolution is used. The method is tested by both synthetic data and real data. The results show good effect on suppressing random noise, enhancing the event and distinguishing the breakpoint.
Most of the conventional data fitting methods use orthogonal polynomials, which have shortcomings such as lowering the dominant frequency, distorting the breakpoint and the enormous error, etc. Through analysis, we find that the fitting center is changing with coefficient of the polynomial, which causes the error. Because the seismic data is linear in local, a fitting method using quadratic polynomials to replace orthogonal polynomials is presented. This method can avoid the above shortcomings. We overcome the computing cost from the coefficient scanning by primary linear fitting and following fine adjustment. That is, firstly identifying the single extreme value interval of the optimal fitting function using uniform large step scanning, then determining the optimal fitting coefficient using dichotomy. As for the breakpoint issue, the mean value constrained vector resolution is used. The method is tested by both synthetic data and real data. The results show good effect on suppressing random noise, enhancing the event and distinguishing the breakpoint.
引文
1俞寿朋．高分辨率地震勘探[M]．北京:石油工业出版社,1993．142-145
2崔若飞,王华忠,曹景忠．多项式拟合技术在煤田地震勘探中的应用[J]．地球物理学报,2000,15(2):47-53
3陆文凯,张学工,李衍达等．时频域零炮检距地震道拟合[J]．石油地球物理勘探,2001,36(1):56-59
4刘贵忠,宗涛,章珂等．利用纵向小波包变换和横向多项式拟合提高地震信号的信噪比和分辨率[J]．石油地球物理勘探,1995,30(5):585-592
5万海涛,苏永昌,俞寿朋．3D叠后地震资料多项式拟合提高信噪比和道内插[J]．石油地球物理勘探,1994,29 (2):208-212
6杨云飞,王华忠,曹景忠．正交多项式逼近去白噪[J]．石油地球物理勘探,2001,36(6):704-706
7熊翥．地震数据数字处理应用技术[M]．北京:石油工业出版社,1993．213-216
8夏洪瑞,周开明．地震资料处理技术中相干干扰消除方法分析[J]．石油物探,2003,42(4):526-528
9夏洪瑞,郭庭超,周开明等．均值加权消除相干干扰[J]．石油物探,2000,39(2):77-82
10南京大学数学系计算数学专业．最优化方法[M]．北京:科学出版社,1978．47-73
11夏洪瑞,陈德刚,周开明等．中值约束下的矢量分解消除随机干扰[J]．石油物探,2001,40(3):29-33
2崔若飞,王华忠,曹景忠．多项式拟合技术在煤田地震勘探中的应用[J]．地球物理学报,2000,15(2):47-53
3陆文凯,张学工,李衍达等．时频域零炮检距地震道拟合[J]．石油地球物理勘探,2001,36(1):56-59
4刘贵忠,宗涛,章珂等．利用纵向小波包变换和横向多项式拟合提高地震信号的信噪比和分辨率[J]．石油地球物理勘探,1995,30(5):585-592
5万海涛,苏永昌,俞寿朋．3D叠后地震资料多项式拟合提高信噪比和道内插[J]．石油地球物理勘探,1994,29 (2):208-212
6杨云飞,王华忠,曹景忠．正交多项式逼近去白噪[J]．石油地球物理勘探,2001,36(6):704-706
7熊翥．地震数据数字处理应用技术[M]．北京:石油工业出版社,1993．213-216
8夏洪瑞,周开明．地震资料处理技术中相干干扰消除方法分析[J]．石油物探,2003,42(4):526-528
9夏洪瑞,郭庭超,周开明等．均值加权消除相干干扰[J]．石油物探,2000,39(2):77-82
10南京大学数学系计算数学专业．最优化方法[M]．北京:科学出版社,1978．47-73
11夏洪瑞,陈德刚,周开明等．中值约束下的矢量分解消除随机干扰[J]．石油物探,2001,40(3):29-33
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