地震数据高维统计滤波方法

地震数据的信噪比是地震波反演成像算法收敛性和结果精度的重要制约因素。基于线性信号模型的最佳预测滤波方法和基于随机信号概率分布特征的统计滤波方法是两种典型的滤波方法。重点讨论了地震数据统计滤波方法,基于实测数据的统计特征(或概率分布),在局部信号缓变的假设下,设计了各种高斯加权滤波器和中值类滤波器。高维空间中的地震信号具有显著的结构特征,为满足信号缓变的假设,需要发展沿着信号结构方向的高维统计滤波器。分析了邻域滤波器、双边滤波器、非局部均值滤波器三类各向异性高斯(加权)滤波器的设计思想。在非局部均值滤波算法的基础上设计了自适应搜索窗的非局部均值滤波方法,该方法采用局部数据窗的相关算法检测出滤波点附近的信号结构特征,依据地震数据变化自适应地改变非局部均值滤波器中的搜索窗。理论模型的数据测试表明,相比于固定搜索窗的非局部均值滤波算法,自适应搜索窗的非局部均值滤波方法能够在压制随机噪声的同时更好地保护有效地震信号。

The signal-to-noise ratio (SNR) of seismic data can affect the seismic inversion imaging in terms of convergence and accuracy.To overcome this issue,two filtering methods are typically utilized,namely the optimal prediction and the statistical filtering methods,which are based,respectively,on the linear signal model and on the random signal theory.This paper focused on the statistical filtering method.Under the assumption that,locally,the signal changes gradually,various Gaussian weighted filters and median filters are designed,which are based on the statistical characteristics of the measured data (i.e.,their probability density functions).Seismic signals in a high-dimensional space are characterized by specific structural features.Therefore,a high-dimensional statistical filter has to be employed along the structural direction of the seismic signal in order to meet the hypothesis of gradual local signal change.Three anisotropic Gaussian weighted filters are explored,namely the neighborhood filter,the bilateral filter,and the non-local mean filter.A non-local mean filter method which utilize an adaptive search window is proposed.This method employs a correlation algorithm in local data windows to examine the structural characteristics near the filtering points.Furthermore,based on the variation of the seismic data,it changes the search window adaptively in a non-local mean filter.A test on a theoretical model showed that the proposed method has a better performance than a non-local mean filter with a fixed search window in terms of signal preservation while suppressing random noise.

国家自然科学基金(41774126)和国家科技重大专项(2016ZX05024-001,2016ZX05006-002)共同资助。