A Fast Rank Reduction Method for f-x-y Noise Attenuation

The Multichannel Singular Spectrum (MSSA) method is an effective technique to attenuate random noise in seismic data and has been recently attracting attention. The key stage of the MSSA method is the rank reduction of the Toeplitz matrix of the spatial seismic data which is commonly accomplished through applying Singular Value Decomposition (SVD). However, the computational cost of the traditional SVD is expensive. We present a fast rank reduction algorithm via Lanczos bidiagonalization and fast block Toeplitz matrix-vector multiplication to replace the SVD method. Our algorithm fully exploits the special structure of the block Toeplitz matrix and implements the block Toeplitz matrix-vector multiplication via multi-dimensional Fast Fourier Transforms (FFTs). The proposed algorithm greatly decreases the computational cost of the rank reduction stage required for denoising through MSSA in comparison to the SVD algorithm. Tests with 3D synthetic data and 3D poststack field data demonstrate the effectiveness of the fast rank reduction method for MSSA in the attenuation of random noise.