Robust singular value decomposition filtering for low signal-to-noise ratio seismic data

ABSTRACT Reduced-rank filtering is a common method for attenuating noise in seismic data. Because conventional reduced-rank filtering distinguishes signals from noises only according to singular values, it performs poorly when the signal-to-noise ratio (S/N) is very low or when data contain high levels of isolate or coherent noise. Therefore, we have developed a novel and robust reduced-rank filtering method based on singular value decomposition in the time-space domain. In this method, noise is recognized and attenuated according to the characteristics of the singular values and the singular vectors. The left and right singular vectors corresponding to large singular values are selected first. Then, the right singular vectors are classified into different categories according to their curve characteristics, such as jump, pulse, and smooth. Each kind of right singular vector is related to a type of noise or seismic event, and it is corrected by using a different filtering technology, such as mean filtering, edge-preserving smoothing, or edge-preserving median filtering. The left singular vectors are also corrected by using the filtering methods based on frequency attributes such as main frequency and frequency bandwidth. To process seismic data containing a variety of events, local data are extracted along the local dip of the event. The optimal local dip is identified according to the singular values and singular vectors of the data matrices that are extracted along different trial directions. This new filtering method has been applied to synthetic and field seismic data, and its performance is compared with that of several conventional filtering methods. The results indicate that the new method is more robust for data with a low S/N, strong isolated noise, or coherent noise. The new method also overcomes the difficulties associated with selecting an optimal rank.