Dictionary Learning for Single-Channel Passive Seismic Denoising

Passive seismic denoising is mostly performed using a simple band-pass filter, which can be problematic when signal and noise share the same frequency band. More advanced passive seismic denoising methods take advantage of fixed-basis transforms, for example, the wavelet, to remove noise. Here, we present an open-source package for datadriven denoising based on adaptively learning sparse transform. Contrary to the fixedbasis transforms, the proposed method belongs to the adaptive-basis transforms. We learn the 1D features embedded in the passive seismic data from all the available waveform data sets without requiring spatial coherency in a data-driven way. Thus, the new method is flexible to apply in any passive seismic monitoring project because of its datadriven and single-channel nature when implemented. Considering the computationally expensive K-singular-value-decomposition (KSVD) in the traditional dictionary learning framework, we suggest applying a fast SVD-free dictionary learning method that can be readily applicable to process massive seismic data during passive seismic monitoring. The proposed method is applied to two synthetic data examples and three real passive seismic data sets to demonstrate its effectiveness in improving the signal-to-noise ratio, and its potential in applications like arrival picking. The open-source reproducible package can be found in the Data and Resources section.