Random noise reduction using SVD in the frequency domain
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ORIGINAL PAPER--EXPLORATION GEOPHYSICS
Random noise reduction using SVD in the frequency domain Baotong Liu1 · Qiyuan Liu2 Received: 12 February 2020 / Accepted: 15 June 2020 © The Author(s) 2020
Abstract 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. Keywords Fourier transform · Eigenimage filtering · Random noise · Signal-to-noise ratio · Seismic data
Introduction Reflected seismic signals describing the underlying geological structure are usually contaminated by random noise. Irregular interference noise could be brought into the recorded data during the field data collection. In addition, some processing procedures, such as velocity analysis, deconvolution and migration, also lead to erratic noise (Yilmaz 1987). Noise interference may yield unrealistic artifacts in inversion or imaging results, hindering the extraction of geological information. Therefore, denoising is an important processing step. However, it is challenging to effectively remove noise from noisy seismic data. Various denoising methods have been developed and applied to eliminate seismic random noise, such as median filtering (Bednar 1983), predictive filtering (Canales 1984; * Baotong Liu [email protected] 1
School of Electronic Information and Electrical Engineering, Tianshui Normal University, Tianshui 741001, China
School of Sciences, Northeastern University, Shenyang 110819, China
2
Gulunay 1986; Spitz and Deschizeaux 1994; Abma and Claerbout 1995; Guo et al. 1995; Kang et al. 2003), K-L transform (Hemon and Mace 1978; Jones and Levy 1987; Al-Yahya 1991; Liu 1999; Kasina 2010), SVD (Freire and Ulrych 1988; Bekara and van der Baan 2007), wavelet transform (Zhang and Ulrych 2003; Fantine et al. 2019), shearlet transform (Zh
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