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

The Cadzow rank-reduction method can be effectively utilized in simultaneously denoising and reconstructing 5-D seismic data that depend on four spatial dimensions. The classic version of Cadzow rank-reduction method arranges the 4-D 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 are 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 tend 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 have extremely low signal-to-noise ratio. The feasibility of the improved 5-D seismic data reconstruction method was validated via both 5-D 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.