Introductory time-series analysis: how to apply and interpret the Fast Fourier Transform

Many natural hazards and other phenomena have cyclic/periodic behaviour, e.g. radon and soil gases, earthquakes (under some circumstances), annual/seasonal droughts and floods, whereas others are anomalous, recurring apparently randomly with regard to time, e.g. earthquakes and volcanic eruptions (under most circumstances). For the cyclic cases, an analysis of past time-series can yield an expectation and perhaps some degree of forecasting, even if only at the level of 'more probable' and 'less probable' times of occurrence. The aim of this two-part short-course is to provide an introduction to and overview of key techniques of time-series analysis to identify and quantify – and potentially predict – natural hazards and other phenomena. It will take the key question “Are we looking for cyclic, recurrent or anomalous phenomena?” as its starting point. In the first part, the aim will be to provide an introduction to and overview of what is arguably the key technique of time-series analysis in this context: the Fast (Discrete) Fourier Transform. The focus will be on the application of the Fast Fourier Transform, as implemented in many software packages, and interpretation of the output. In the second part, the aim will be to consider techniques which are based on and/or allied to the Fast (Discrete) Fourier Transform, such as Short-Time Fourier-Transforms and spectrograms and auto- and cross- correlation techniques. Anticipating that most of those who attend will be 'technique users' rather than 'technique developers', coverage of the underlying mathematics will be kept to a necessary minimum to facilitate informed interpretation of the techniques considered.