A novel wavelet seismic denoising method using type II fuzzy

• We have found that wavelet coefficients of seismic signal contain vagueness.
• Hence for the first time, we have proposed using fuzzy concept in wavelet denoising.
• We have found that fuzzy schemes are insufficient to handle the vagueness.
• Hence type II fuzzy thresholder is being proposed as a new thresholder.
• The results show promising improvements, when compared to other landmark methods.

Wavelet based denoising of the observed non stationary time series earthquake loading has become an important process in seismic analysis. The process of denoising ensures a noise free seismic data, which is essential to extract features accurately (max acceleration, max velocity, max displacement, etc.). However, the efficiency of wavelet denoising is decided by the identification of a crucial factor called threshold. But, identification of optimal threshold is not a straight forward process as the signal involved is non-stationary. i.e. The information which separates the wavelet coefficients that correspond to the region of interest from the noisy wavelet coefficients is vague and fuzzy. Existing works discount this fact. In this article, we have presented an effective denoising procedure that uses fuzzy tool. The proposal uses type II fuzzy concept in setting the threshold. The need for type II fuzzy instead of fuzzy is discussed in this article. The proposed algorithm is compared with four current popular wavelet based procedures adopted in seismic denoising (normal shrink, Shannon entropy shrink, Tsallis entropy shrink and visu shrink).It was first applied on the synthetic accelerogram signal (gaussian waves with noise) to determine the efficiency in denoising. For a gaussian noise of sigma = 0.075, the proposed type II fuzzy based denoising algorithm generated 0.0537 root mean square error (RMSE) and 16.465 signal to noise ratio (SNR), visu shrink and normal shrink could be able to give 0.0682 RMSE with 14.38 SNR and 0.068 RMSE with 14.2 SNR, respectively. Also, Shannon and Tsallis generated 0.0602 RMSE with 15.47 SNR and 0.0610 RMSE with 15.35 SNR, respectively. The proposed method is then applied to real recorded time series accelerograms. It is found that the proposal has shown remarkable improvement in smoothening the highly noisy accelerograms. This aided in detecting the occurrence of ‘P’ and ‘S’ waves with lot more accuracy. Interestingly, we have opened a new research field by hybriding fuzzy with wavelet in seismic denoising.

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