Seismic noise suppression using weighted nuclear norm minimization method

The weighted nuclear norm minimization method as an extension of nuclear-norm minimization was applied to image denoising originally. It is a kind of low rank matrix approximation method that can estimate the noiseless matrix from its noise version. The effective structures of image have a certain degree of repeatability and the weighted nuclear norm minimization method just utilizes this property to construct an approximate low rank matrix. Taking into account the spatial characteristics of seismic data and the redundancies of valid information, we propose to adopt the weighted nuclear norm minimization method to suppress seismic random noise. In this method the block matching algorithm is helpful for the recovery of seismic events because the texture blocks sharing the same reflection events are the most similar. Even when the signal to noise ratio is − 10 dB, this novel method still be able to clearly recover signals. Experiments on both synthetic and real seismic data show that the weighted nuclear norm minimization method can not only suppress the random noise but also better preserves the valid information of seismic signal when compared to the common seismic denoising methods such as the Wavelet and Time Frequency Peak Filter.