A 1-D time-varying median filter for seismic random, spike-like noise elimination |

Random noise in prestack seismic data can come from various sources, such as wind motion, poorly planted geophones, or electrical noise, and some of this seismic random noise invariably exhibits spike-like characteristics. Although stacking can at least partly suppress random noise in prestack data, residual random noise after stacking will decrease the accuracy of final data interpretation. In recent years, several authors have developed effective methods of eliminating random noise. For example, Gülünay (2000) used the noncausal prediction filter for random-noise attenuation, Ristau and Moon (2001) compared several adaptive filters, which they applied in an attempt to reduce random noise in geophysical data. Karsli et al. (2006) applied complex-trace analysis to seismic data for random-noise suppression, recommending it for low-fold seismic data, and some transform methods were also used to eliminate seismic random noise, e.g., seislet transform (Fomel, 2006; Fomel and Liu, 2008), discrete cosine transform (Lu and Liu, 2007), and curvelet transform (Neelamani et al., 2008).

On the other hand, the median filter, a well-known method that can effectively suppress spike-like noise, refers to nonlinear signal processing. Bednar (1983) and Duncan and Beresford (1995) found the method to be both simple and effective for seismic prospecting. More recently, new median filters have been proposed. Mi and Margrave (2000) incorporated median-filter noise reduction into standard Kirchhoff time migration. Zhang and Ulrych (2003) used a hyperbolic median filter to suppress multiples. Liu et al. (2006) advocated random-noise attenuation using the 2-D multistage median filter (MLM).

Because the median filter is a nonlinear filter, filter-window length needs to be adjusted before its characteristics can be changed. The stationary filter, on the other hand, maintains a fixed window length, retaining useful information and random noise at the same scale. An unsuitable filter-window choice would therefore end up in useful information being destroyed or noise remaining. Here we propose a time-varying median filter that adjusts to different filter-window lengths by threshold, making value judgments on useful information versus noise throughout the process. We show that the time-varying window is more powerful than the stationary window.

In this paper, a new nonlinear filter called the *time-varying median filter* (TVMF)
is presented, which we designed by defining a threshold value. After adjustment
of the filter window in the time domain, this filter eliminates
random noise in seismic data. We compare TVMF with other common methods.
We use numerical examples, along with synthetic and field data, to demonstrate
the validity of the proposed method in practice.

A 1-D time-varying median filter for seismic random, spike-like noise elimination |

2013-07-26