Abstract：Surface micro-seismic data is characterized by lower signal-to-noise ratio. This affects severely the accuracy of first break picking and the reliability of inversion. We proposed in this paper a micro-seismic data denoising method based on sparse representations over learned dictionaries in the wavelet domain. The method calculates the noise variance through Curvelet transform and then it is applied to suppress random noise in real data. In order to improve denoising effects on low signal-to-noise ratio data, the sparse representation denoising method in the wavelet domain is put forward. Quantitative analysis is also carried out in the new and common sparse representation method. Tests results on theoretical and real data show that the number of iterations and the size of dictionary atoms have great influence on the final denoising result. The signal-to-noise ratio of denoised data is improved with both a big number of iterations and a large size of dictionary atoms, but it also leads to decrease computational efficiency. A medium size of dictionary atoms and a reasonable number of iterations for larger data should be needed, so a higher signal-to-noise ratio and a faster calculation can be achieved at the same time. In addition, this method can remove the background patch introduced in convenditional sparse representation, so it will greatly improve the signal-to-noise ratio of denoised data. Therefore, the proposed method has obvious advantages compared to conventional method.
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