A fast and accurate frequency estimation method for canceling harmonic noise in geophysical records

The cancellation of harmonic noise from geophysical records can be achieved by subtracting an estimate of the harmonic noise. Estimating the harmonic noise consists of estimating the fundamental frequency and the amplitudes and phases of all harmonics. We propose a new frequency-estimation method that builds upon the estimator originally proposed by Nyman and Gaiser. This Nyman and Gaiser estimation (NGE) method exploits the fact that the noise fundamental frequency is known to be close to 60 Hz. The NGE method is based on solving a system of four equations that determine the amplitude, phase, and frequency of a given harmonic in the harmonic noise. Hence, NGE can produce frequency estimates for all harmonics. Our improved estimator uses a suitable linear combination of these NGE frequency estimates to produce a more accurate estimate of the fundamental frequency. Our method is more accurate than NGE, and its accuracy is comparable to least-squares estimation (LSE). The advantage of our method is that it is about two times faster than LSE. This speed gain can become valuable when processing large magnetotelluric (MT) data records. Applying our method to the restoration of MT data, we found that the harmonic noise amplitude in the periodogram is reduced by at least 60 dB to a level below that of MT data.