Separating signal from noise and from other signal using nonlinear thresholding and scale-time windowing of continuous wavelet transforms


A procedure for removing noise or signal from seismic time series using the continuous wavelet transform (CWT) is developed through the common assumption of noise stationarity for pre‐event or postevent estimates of the noise. Noise and signal are efficiently separated using nonlinear thresholding of the CWT avoiding computationally intensive block thresholding algorithms on the wavelet scale‐time plane. Efficiency is gained by estimating the characteristic statistics of pre‐event noise using empirical cumulative distribution functions and then using these characteristics to threshold the entire time series using hard or soft nonlinear thresholding. In addition, scale‐time windowing of the CWT scalogram and inverse transforming into the time domain allows unprecedented control in partitioning a seismogram into component wave types that can subsequently be used to infer characteristics of Earth structure and source excitation. Noise can be separated from signal and signals decomposed into discrete wave groups. CWT techniques offer unique and intuitive alternatives to traditional Fourier methods for analyzing noise and signal useful for structure and source studies, event detection, and ambient‐noise interferometry.

Publication Title

Bulletin of the Seismological Society of America