Study and application of translation invariant wavelet de-noising for blasting seismic signals

The traditional wavelet transform threshold de-noising method might produce the artifacts on discontinuities of blasting seismic signals because the wavelet is short of translation invariance. Firstly, the translation invariant wavelet transform de-noising method performs the cycle translation for blasting seismic signals to be analyzed. Secondly the soft or hard threshold is used to shrink the wavelet coefficient of the signals and reconstruct the signals. Lastly, using the inverse cycle translation, performing more translating-denoising-translating and averaging the obtained results, consequently the translation dependence of wavelet basis is eliminated. The method can not only effectively suppress Psuedo-Gibbs phenomenon in blasting seismic signals, but also diminish Mean Square Error(MSE) between the original blasting seismic signals and the estimated blasting seismic signals. It proves theoretically and practically that it is more effective to de-noise for blasting seismic signals.