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

Random noise in seismic data affects the signal-to-noise ratio, obscures details, and complicates identification of useful information. We present a new method for reducing random, spike-like noise in seismic data. The method is based on a 1-D stationary median filter (MF) – the 1-D time-varying median filter (TVMF). We design a threshold value that controls the filter window according to characteristics of signal and random, spike-like noise. In view of the relationship between seismic data and the threshold value, we chose median filters with different time-varying filter windows to eliminate random, spike-like noise. When comparing our method with other common methods, e.g., the band-pass filter and stationary MF, we found that the TVMF strikes a balance between eliminating random noise and protecting useful information. To demonstrate the feasibility of our method in reducing seismic random, spike-like noise, we present results for one synthetic dataset. Results of applying the method to seismic land data from Texas demonstrate that the TVMF method is effective in practice. INTRODUCTION 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 complextrace analysis to seismic data for random-noise suppression, recommending it for lowfold 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