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Simultaneous denoising of multicomponent microseismic data by joint sparse representation with dictionary learning

Microseismic data usually have a low signal-to-noise ratio, necessitating the application of an effective denoising method. Most conventional denoising methods treat each component of multicomponent data separately, e.g., denoising methods with sparse representation. However, microseismic data are often acquired with a 3C receiver, especially in borehole monitoring cases. Independent denoising ignores the relative amplitudes and vector relationships between different components. We have developed a new simultaneous denoising method for 3C microseismic data based on joint sparse representation. The three components are represented by different dictionary atoms; the dictionary can be fixed or adaptive depending on the dictionary learning method that is used. Our method adds an extra time consistency constraint with simultaneous transformation of 3C data. The joint sparse optimization problem is solved using the extended orthogonal matching pursuit. Synthetic microseismic data with a double-couple source mechanism and two field downhole microseismic data were used for testing. Independent denoising of 1C data with the fixed dictionary method and simultaneous denoising of 3C data with the fixed dictionary and dictionary learning (3C-DL) methods were compared. The results indicate that among the three methods, the 3C-DL method is the most effective in suppressing random noise, preserving weak signals, and restoring polarization information; this is achieved by combining the time consistency constraint and dictionary learning.