Non-linear filter, using the wavelet transform, applied to seismological records

Abstract

As any process in Nature, seismic recordsare affected by noise that the analystwould want to eliminate. One of the mostcommon techniques used to minimise thisnoise effect is the application of linearfilters, which reduce the bandwidth of thesignal. This method is based on the FourierTransform, and therefore any perturbationon the coefficients affects the entirerecord.We have developed a non-linear filter basedon the multiresolution analysis of theDiscrete Time Wavelet Transform (DTWT). Themain idea is to use the time-frequencylocalisation properties of the waveletdecomposition. Each coefficient isassociated to a window on thetime-frequency plane, so any perturbationwould only affect the time and frequencyrange of the correspondent window.The procedure we propose has three stages:periodic noise elimination, spikesreduction and, finally, the non-linearfiltering. The non-linear filter acts bythresholding the wavelet coefficients. Thethresholding estimator will depend on thesignal-noise ratio (SNR) in each of thefrequency bands associated to the waveletdecomposition.We have compared the proposed method to thecoherent structures method (Mallat, 1998)and to two 4th order linear filterbanks (Butterworth and Elliptic filters),applying all of them to a syntheticdatabase, and a real earthquake databaserecorded by the Short Period ROA Network.The proposed method improves the SNR in the87% of the tested events, being therelative rms error less than three, and themaximum amplitude relative error less than10% in the 90% of the synthetic database.