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

Abstract

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.

Long‐range lightning geolocation using a VLF radio atmospheric waveform bank

“…Natural noise sources, which are incoherent and broadband, include sferics from very distant (>10,000 km) lightning discharges and, depending on the sensor location, chorus, which ranges from hundreds of hertz to 5 kHz [ Sazhin and Hayakawa , 1992]. A least‐squares method for powerline noise mitigation in geophysical records is described by Nyman and Gaiser [1983], Butler and Russell [2003], and Saucier et al [2006], and a technique to isolate narrowband transmitter signals in VLF data is considered by Shafer [1994, chapter 3]. These techniques for reducing coherent interference sources have been applied to the data used in this paper in order to improve the SNR of sferic measurements.…”

Mitigation of 50-60 Hz power line interference in geophysical data

“…A second possible method of estimating the hum comes from least squares estimation, described by Saucier et al [2006] and reviewed here. The hum interference signal p ( t ), can be written in terms of a sum of individual harmonic components as follows: where A k and B k are real coefficients, which indicate the sine and cosine components of the hum at the k th harmonic, assuming the hum has K harmonics that need to be subtracted.…”

“…For instance, in the presence of natural noise which obscures the hum components below ∼1 kHz, the values of k can be chosen to include only higher‐order harmonics of 50/60 Hz, those above 1 kHz. Saucier et al [2006] present a technique to analytically solve the least squares inversion to reduce the computation time.…”

Doubling the spectrum of time-domain induced polarization by harmonic de-noising, drift correction, spike removal, tapered gating and data uncertainty estimation

“…Deo & Cull (2015) suggested the use of a wavelet technique for de-noising TDIP data, but without retrieving IP response information at early times or high frequencies. This paper employs another method for handling the noise, which allows for use of these early times: for the first time in TDIP, a well-known method used in other geophysical disciplines for cancelling harmonic noise (Butler & Russell 1993, 2003Saucier et al 2006;Larsen et al 2013) is successfully applied on full waveform data. This method models and subtracts the harmonic noise from raw full-waveform potential data.…”