Spectral analysis of tremor: Understanding the results

Abstract

Spectral analysis of a tremor record can sometimes produce a spectrum with multiple components of significant amplitude. The problem is to determine whether the presence of several peaks represents the coexistence of separate tremor mechanisms or be a consequence of fluctuations in the frequency or amplitude of a single tremor. The spectrum of a tremor whose frequency or amplitude vary and are independent has the recognisable pattern of a central carrier frequency with sidebands of equal amplitudes distributed symmetrically around the carrier. However, if tremor amplitude and frequency fluctuate and are not independent, (frequency proportional to amplitude or frequency inversely proportional to amplitude), the spectrum has a pattern of sidebands which are asymmetrical in amplitudes and may resemble the spectrum of the combined signal from different independent oscillators. The investigation of sidebands in spectra has been neglected in tremor studies and multiple irregular peaks on a tremor spectrum have sometimes been used wrongly as evidence for the coexistence of multiple tremor mechanisms or frequency components assumed to be concurrent.