改善经验模态分解端点问题的方法

Methods to improve the EMD endpoint problems

由于采集到的地震资料包含各种各样的噪声,导致地震资料信噪比较低,给之后的解释工作带来较大困难。为了更准确地了解地下地质信息,需要提高地震资料的信噪比。针对地震资料中的随机噪声,采用镜像对称延拓法、边界局部特征尺度延拓法以及多项式拟合法3种方法,在60 Hz的正弦信号与白噪声的合成信号中找到极值点,再计算均值,得到本征模态函数后并重构地震信号,有效压制了地震噪声。研究结果表明,使用镜像对称延拓法、边界局部特征尺度延拓法以及多项式拟合法均可以消除地震信号的端点效应并有效压制混叠现象,使用多项式拟合法分解得到的相似系数最大,而边界局部特征尺度延拓法得到的相似系数最小,平均相对误差最小;边界局部特征尺度延拓法运算速度最快,多项式拟合法则耗时较长。镜像对称延拓法和边界局部特征尺度延拓法,不仅有效地抑制了传统经验模态分解中存在的端点效应,而且增加了经验模态分解得到的本征模态函数的正交性,提高了经验模态分解精度。

The collected seismic data contains various noises,which leads to the low signal-to-noise ratio of seismic data,which brings great difficulties to the subsequent interpretation work.In order to understand underground geological information more accurately,it is necessary to improve the signal-to-noise ratio.In response to the random noise in seismic data,three methods were used:mirror symmetric extension,boundary local feature scale extension,and polynomial fitting.The extreme points were found in the composite signal of 60 Hz sine signal and white noise,and the mean was calculated to obtain the intrinsic mode function.After reconstructing the seismic signal,the seismic noise was effectively suppressed.The results show that the end effect of seismic signals can be eliminated and aliasing can be suppressed effectively by using the three methods.The similarity coefficient obtained by the polynomial fitting is the largest,while by the boundary local feature scale extension is the smallest,and the average relative error is the smallest.The boundary local feature scale extension is the fastest,while the polynomial fitting takes longer time.The mirror symmetric extension and the boundary local feature scale extension methods not only effectively suppress the endpoint effect in traditional EMD decomposition,but also increase the orthogonality of the IMF obtained from EMD decomposition,improving the accuracy of EMD decomposition.