常规二次多项式拟合地震数据

Normal quadratic polynomial fitting seismic data

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.