Open AccessMultiple‐taper spectral analysis of terrestrial free oscillations: part I
Author(s) -
Park Jeffrey,
Lindberg Craig R.,
Thomson David J.
Publication year - 1987
Publication title -
geophysical journal of the royal astronomical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.302
H-Index - 168
eISSN - 1365-246X
pISSN - 0016-8009
DOI - 10.1111/j.1365-246x.1987.tb01668.x
Subject(s) - white noise , series (stratigraphy) , mathematics , fourier series , noise (video) , spectral leakage , mathematical analysis , fast fourier transform , algorithm , statistics , computer science , paleontology , artificial intelligence , image (mathematics) , biology
We present a new method for estimating the frequencies of the Earth's free oscillations. This method is an extension of the techniques of Thomson (1982) for finding the harmonic components of a time series. Optimal tapers for reducing the spectral leakage of decaying sinusoids immersed in white noise are derived. Multiplying the data by the best K tapers creates K time series. A decaying sinusoid model is fit to the K time series by a least squares procedure. A statistical F ‐test is performed to test the fit of the decaying sinusoid model, and thus determine the probability that there are coherent oscillations in the data. The F ‐test is performed at a number of chosen frequencies, producing a measure of the certainty that there is a decaying sinusoid at each frequency. We compare this method with the conventional technique employing a discrete Fourier transform of a cosine‐tapered time‐series. The multiple‐taper method is found to be a more sensitive detector of decaying sinusoids in a time series contaminated by white noise.