Conclusion

Traditional rank-reduction method cannot obtain acceptable result for 5D seismic data denoising and reconstruction when the signal-to-noise ratio (SNR) is extremely low. The traditional truncated singular value decomposition (TSVD) formula will cause residual noise in the seismic data after iterative reconstruction since the denoised data space is a mixture of the signal subspace and noise subspace. In order to better decompose the noisy data into signal and noise components, we introduce a damping operator into the traditional TSVD formula to dampen the singular values that contain significant information of residual noise. The improvement via the damped rank-reduction method is shown to be very appealing from both 5D synthetic and field data examples and can be achieved conveniently following the introduced damped TSVD formula. As shown from the comprehensive analysis of different 5D seismic data examples, we get some extra insightful conclusions in addition to the reconstruction result itself. First, the block Hankel matrix after damped rank-reduction is smoother than that of traditional rank-reduction, which is caused by damping the singular values and matches with the overall superior performance of the proposed approach well when the block Hankel matrix is transformed back to time-space domain. Second, the advantage of the proposed rank-reduction method over the traditional method becomes more dominant as the noise level in the observed data increases, which makes the proposed approach very attractive in processing 5D land seismic data. We suggest to replace the current 5D seismic data interpolation framework with our proposed framework for better dealing with the highly noisy incomplete dataset.