Adaptive Damped Rank-Reduction Method for Random Noise Attenuation of Three-Dimensional Seismic Data

Rank-reduction methods are effective for separating random noise from the useful seismic signal based on the truncated singular value decomposition (TSVD). However, the results that the TSVD operator provides are still a mixture of noise and signal subspaces. This problem can be solved using the damped rank-reduction method by damping the singular values of noise-contaminated signals. When the seismic data include highly linear or curved events, the rank should be large enough to preserve the details of the useful signal. However, the damped rank-reduction operator becomes less powerful when using a large rank parameter. Hence, the denoised data contain significant remaining noise. More recently, the optimally damped rank-reduction method has been proposed to solve the extra noise problem as the rank value increases. The optimally damped rank-reduction operator works well for a moderately large rank, but becomes ineffective for a very large rank. We introduce an adaptive damped rank-reduction algorithm to attenuate the residual noise for a very large rank parameter. To elaborate on the proposed algorithm, we first construct a gain matrix by only using the input rank parameter, which we introduce directly into the adaptive singular-value weighting formula to make it more stable as the rank parameter becomes too large. Then, we derive a damping operator based on the improved optimal weighting operator to attenuate the residual noise. The proposed method, which can be regarded as an improved version of the optimally damped rank-reduction method, is insensitive to the input parameter. Examples of synthetic and real three-dimensional seismic data show the denoising improvement using the proposed method.