Random noise reduction using SVD in the frequency domain

The frequency spectrum of irregular interference noise has broad bandwidth and poor coherence. But in the same prospecting area, the dominant frequency and bandwidth of effective signals are nearly the same (especially for post-stack section); that is to say, the frequency spectra of effective signals in seismic traces show a high degree of trace-to-trace correlation. Based on this conclusion, we present a novel denoising technique, which works by SVD filtering in the frequency domain. First, the input seismic data are transformed to the frequency domain via the Fourier transform. Then, the frequency spectra are decomposed into eigenimages by means of SVD. We perform the eigenimage filtering of the frequency spectra by selecting singular values to be used in the reconstruction, suppressing the random noise. Compared with the traditional band-pass filtering, the presented method is capable of attenuating the interference noise components within the range of frequency pass band and protects effective signals in high frequency. Tests on both synthetic and field seismic data show that our method can remove random noise and does no damage to effective signal. By comparison with the median filtering and the curvelet domain filtering, we concluded that the presented denoising method performs better in removing background noise and protecting reflection events.