Improved Wavelet Packet Noise Reduction for Microseismic Data via Fuzzy Partition

It is crucial to retain as many signal components as possible, while noise is eliminated for wavelet packet noise reduction algorithms. Conventional thresholding functions take coefficients smaller than a given threshold as the noise component and get them removed in many ways. In this letter, considering the potential probability of being the signal-related component of coefficients whose value is smaller than the given threshold and the nonnegligible fact that microseismic (MS) event is sparse compared with the noise, we proposed a new wavelet packet-based denoising method via fuzzy partition. First, instead of a hard partition from a given threshold, wavelet packet coefficients get reduced by a fuzzy partition to retain more potential signal elements and suppress the noise. Second, we employ fuzzy c-means (FCM) clustering to identify the interval period of the MS event further to remove the residual noise and additional resonance in processed time series. We tested our method on synthetic datasets and real-field data from an MS monitoring experiment in a coal mine in Sichuan Basin, China. We utilize Pearson correlation coefficient and root-mean-square error between ideal signal and denoised data as performance indicators in synthetic tests, while sample entropy and kurtosis of denoised data are involved in the real field dataset. Test results from synthetic datasets and the real field dataset demonstrate that the proposed noise reduction method is superior to traditional hard-, soft-, and garrote-thresholding and is more applicable and effective in MS data processing.