Complex Demodulation of Geomagnetic Data and the Estimation of Transfer Functions

Abstract

Complex demodulation is a technique that allows the examination of the variation with time of the amplitude and phase of selected frequency components of a time series. Complex demodulates can form the basis for estimates of the power spectrum of the time series. They are computed most efficiently by the use of the Fast Fourier Transform. Two examples of the application of complex demodulation to the analysis of geomagnetic time series are given. In the first example, the technique is used to demonstrate the modulation of a periodic phenomenon, the daily variation, by mechanisms with apparent periods of 6 months and 27 days. The second example, discussed in greater detail, is an application to the calculation of Geomagnetic Deep Sounding transfer functions. The spectra of simultaneous records of variations in the three components (H, D and Z) of the magnetic field recorded at a single station are divided into bands, and each band demodulated in turn. The polarization azimuth of the horizontal field at each instant of time can be computed, and, for the example considered, the azimuth tends to be constrained to the north‐south direction. The detailed response of the local conductive structure to different source field polarizations can be demonstrated. Everett & Hyndman's Unit Vector Method is used to investigate the effect of the observed bias in the azimuth of the source field on estimates of GDS transfer functions made by conventional methods. The demodulates can be used to devise criteria for selecting events according to their signal/noise ratio. The selection procedure is most useful when applied to records containing only sporadic activity in the frequency band of interest. Copyright © 1975, Wiley Blackwell. All rights reserved