Published as Geophysical Prospecting, 68, 2783-2807, (2020)

Seismic signal enhancement based on the lowrank methods

Min Bai% latex2html id marker 5909
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\setcounter{footnote}{2}\fnsymbol{footnote}, Guangtan Huang% latex2html id marker 5911
\setcounter{footnote}{1}\fnsymbol{footnote}, Hang Wang% latex2html id marker 5912
\setcounter{footnote}{1}\fnsymbol{footnote}, and Yangkang Chen% latex2html id marker 5913
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\setcounter{footnote}{1}\fnsymbol{footnote}School of Earth Sciences
Zhejiang University
Hangzhou, Zhejiang Province, China, 310027
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\setcounter{footnote}{2}\fnsymbol{footnote}Key Laboratory of Exploration Technology for Oil and Gas Resources of Ministry of Education
Yangtze University
Wuhan, Hubei Province, China, 430100


Based on the fact that the Hankel matrix constructed by noise-free seismic data is lowrank (LR), LR approximation (or rank-reduction) methods have been widely used for removing noise from seismic data. Due to the linear-event assumption of the traditional LR approximation method, it is difficult to define a rank that optimally separates the data subspace into signal and noise subspaces. For preserving the most useful signal energy, a relatively large rank threshold is often chosen, which inevitably leaves residual noise. To reduce the energy of residual noise, we propose an optimally damped rank-reduction method. The optimal damping is applied via two steps. In the first step, a set of optimal damping weights is derived. In the second step, we derive an optimal singular-value damping operator. We review several traditional lowrank methods and compare their performance with the new one. We also compare these lowrank methods with two sparsity-promoting transform methods. Examples demonstrate that the proposed optimally damped rank-reduction method could get significantly cleaner denoised images compared with the state-of-the-art methods.