Published as Geophysical Journal International, 206, 1695-1717, (2016)

Simultaneous denoising and reconstruction of 5D seismic data via damped rank-reduction method

Yangkang Chen% latex2html id marker 4149
\setcounter{footnote}{1}\fnsymbol{footnote}, Dong Zhang% latex2html id marker 4150
\setcounter{footnote}{2}\fnsymbol{footnote}, Zhaoyu Jin% latex2html id marker 4151
\setcounter{footnote}{3}\fnsymbol{footnote}, Xiaohong Chen% latex2html id marker 4152
\setcounter{footnote}{2}\fnsymbol{footnote}, Shaohuan Zu% latex2html id marker 4153
\setcounter{footnote}{2}\fnsymbol{footnote}% latex2html id marker 4153
ootnote}{2}<SPAN CLASS=% latex2html id marker 4154
\setcounter{{}{0}\fnsymbol{{}, Weilin Huang% latex2html id marker 4155
\setcounter{footnote}{2}\fnsymbol{footnote}% latex2html id marker 4155
ootnote}{2}<SPAN CLASS=% latex2html id marker 4156
\setcounter{{}{0}\fnsymbol{{}, and Shuwei Gan% latex2html id marker 4157
\setcounter{footnote}{2}\fnsymbol{footnote}% latex2html id marker 4157
ootnote}{2}<SPAN CLASS=
% latex2html id marker 4159
\setcounter{footnote}{1}\fnsymbol{footnote}% latex2html id marker 4159
ootnote}{1}<SPAN CLASS=Bureau of Economic Geology
John A. and Katherine G. Jackson School of Geosciences
The University of Texas at Austin
University Station, Box X
Austin, TX 78713-8924
State Key Laboratory of Petroleum Resources and Prospecting
China University of Petroleum
Fuxue Road 18th
Beijing, China, 102200 & &
School of Geosciences
University of Edinburgh
Edinburgh,UK, EH9 3JW


The Cadzow rank-reduction method can be effectively utilized in simultaneously denoising and reconstructing 5D seismic data that depends on four spatial dimensions. The classic version of Cadzow rank-reduction method arranges the 4D spatial data into a level-four block Hankel/Toeplitz matrix and then applies truncated singular value decomposition (TSVD) for rank-reduction. When the observed data is extremely noisy, which is often the feature of real seismic data, traditional TSVD cannot be adequate for attenuating the noise and reconstructing the signals. The reconstructed data tends to contain a significant amount of residual noise using the traditional TSVD method, which can be explained by the fact that the reconstructed data space is a mixture of both signal subspace and noise subspace. In order to better decompose the block Hankel matrix into signal and noise components, we introduced a damping operator into the traditional TSVD formula, which we call the damped rank-reduction method. The damped rank-reduction method can obtain a perfect reconstruction performance even when the observed data has extremely low signal-to-noise ratio (SNR). The feasibility of the improved 5D seismic data reconstruction method was validated via both 5D synthetic and field data examples. We presented comprehensive analysis of the data examples and obtained valuable experience and guidelines in better utilizing the proposed method in practice. Since the proposed method is convenient to implement and can achieve immediate improvement, we suggest its wide application in the industry.