Spectral Analysis for Geophysical Data

Summary The Fourier methods which underlie the statistical analysis of four types of data are presented. These are (a) stationary time series, (b) homogeneous planar processes, (c) homogeneous processes on a sphere and (d) a combination of (a) with (b) or (c). The data to be analysed will be modified by the effects, (i) of filtering of the continuous phenomenon (e.g. by the recording device), (ii) discrete sampling of the continuous phenomenon, (iii) further filtering of the discrete record. The effects of these are analysed and described, in the case of (i) and (iii) by a description of the response function of the filter and in case (ii) by describing the‘aliasing’involved (i.e. degree of indistinguishability of spectral components). Procedures for estimating the spectrum of the discrete record are described. Signal measurement in noise problems (and to some extent their analogues in cases (b), (c), (d)) are discussed as a principal example of the final use of these spectral methods.