Cancellation of multiple harmonic noise series in geophysical records

Abstract

We describe a procedure for the simultaneous estimation of multiple stationary sinusoidal contaminants in a time series and demonstrate its application to the cancellation of powerline noise in seismic and seismoelectric records. An estimate of the noise in each record is obtained by seeking a linear combination of sinusoids that are harmonics of one or more fundamental frequencies; this combination must fit the data in a least‐squares sense. The algorithm accommodates estimation windows of arbitrary length, including windows shorter than one fundamental period, without cross‐contamination between harmonic estimates.Provision is made for refining the fundamental frequencies, for which small errors (e.g., 0.01 Hz in 60 Hz) can result in significant residual noise near the ends of the record (beating). Our strategy is novel in that it uses all specified harmonics and iteratively searches frequency space for a best fit using numerical derivatives. This determination is very robust for at least two fundamentals (the limit of our investigation) and often converges rapidly to three or four decimal places.Cancellation of harmonic noise has been essential in our research to uncover seismoelectric signals that are often completely masked by powerline noise. We expect this procedure will be useful in other geophysical methods—especially exploration seismology, for which powerline contamination is a recognized problem.