Considerations for effective rank based noise attenuation

Incoherent noise attenuation remains a challenging problem in seismic data processing. While many tools are successful at removing noise, this often comes at the expense of some signal. We seek the ideal noise attenuator– one that is effective, practical, and above all safe. Multichannel Singular Spectrum Analysis (MSSA) is a step in this direction. MSSA exploits the spatial redundancy of data by expressing a frequency slice as a structured matrix. This matrix is then projected onto its low rank subspace, thereby removing incoherent energy. The maximum rank of a frequency slice increases as a product of the spatial dimension half-lengths, making the rank constraint more powerful in higher dimensions; although this power comes at a significant increase in computational cost. In this article we address several considerations that make MSSA an effective noise attenuation algorithm. We first introduce the algorithm and outline an efficient matrix-free implementation of MSSA that exploits the redundancy of multi-level Hankel structures. Finally, we discuss the unique ability of MSSA to automatically estimate the signal to noise ratio (SNR) as a function of time, space and frequency and illustrate this ability on a dataset from northeast BC.