Random noise attenuation using $f$-$x$ regularized nonstationary autoregression

Published as Geophysics, 77, no. 2, V61-V69, (2012)

Random noise attenuation using $f$-$x$ regularized nonstationary autoregression

Guochang Liu, Xiaohong Chen, Jing Du, Kailong Wu

China University of Petroleum (Beijing),
National Engineering Laboratory for Offshore Oil Exploration,
Beijing, China. E-mail: guochang.liu@yahoo.com; chenxh@cup.edu.cn;
wuyanping220@163.com China Petroleum & Chemical Corporation,
Shengli Geophysical Research Institute, China.
E-mail: dujing_421@yahoo.com

Abstract:

We propose a novel method for random noise attenuation in seismic data by applying regularized nonstationary autoregression (RNA) in frequency-space ($f$-$x$) domain. The method adaptively predicts the signal with spatial changes in dip or amplitude using $f$-$x$ RNA. The key idea is to overcome the assumption of linearity and stationarity of the signal in conventional $f$-$x$ domain prediction technique. The conventional $f$-$x$ domain prediction technique uses short temporal and spatial analysis windows to cope with the nonstationary of the seismic data. The proposed method does not require windowing strategies in spatial direction. We implement the algorithm by iterated scheme using conjugate gradient method. We constrain the coefficients of nonstationary autoregression (NA) to be smooth along space and frequency in $f$-$x$ domain. The shaping regularization in least square inversion controls the smoothness of the coefficients of $f$-$x$ RNA. There are two key parameters in the proposed method: filter length and radius of shaping operator. Synthetic and field data examples demonstrate that, compared with $f$-$x$ domain and time-space ($t$-$x$) domain prediction methods, $f$-$x$ RNA can be more effective in suppressing random noise and preserving the signals, especially for complex geological structure.

Random noise attenuation using $f$-$x$ regularized nonstationary autoregression