Efficient Estimation of Empirical Green’s Function by Removing Transients From Sensor Data Using Time–Frequency Normalization Technique

Abstract

Clean ambient noise data is the preliminary requirement to perform ambient noise tomography of the earth. Conventional 1-bit time-domain normalization (TDN) is the most popular method to remove the effect of earthquakes and other transient signals obscured by the continuous recording of ambient noise at the sensors. The presence of monochromatic noise sources is also reduced by performing spectral whitening. In this manner, recorded ambient noise data is first normalized in the time domain and then in the frequency domain. It is observed that these normalization procedures do not make the amplitude “even” within the small segments of the complete normalized ambient noise time series and hence, ambient noise remains nondiffusive within these segments. Therefore, in this article, a time–frequency normalization technique is proposed to efficiently remove the temporal and spectral components of the unwanted signals. In this article, continuous wavelet transform (CWT) is used to transform raw ambient noise time series to time–frequency domain to exploit its time–frequency localization property. Complex Morlet wavelet best captures the oscillations present in the raw ambient noise data and then upon normalizing CWT coefficients, a nearly diffusive ambient noise data is retrieved which is suitable to estimate empirical Green’s function (EGF). The performance of the proposed method is tested using synthetic data and the EGFs are estimated using real ambient noise data of a subset of STS-2 USArray sensors. The EGFs are evaluated quantitatively by calculating the signal-to-noise ratio (SNR) and comparing them with those estimated using the conventional method.