A Primer on Fourier Analysis for the Geosciences

Time-series analysis is used to identify and quantify periodic features in datasets and
has many applications across the geosciences, from analysing weather data, to
solid-Earth geophysical modelling. This intuitive introduction provides a practical
‘how-to’ guide to basic Fourier theory, with a particular focus on Earth system
applications. The book starts with a discussion of statistical correlation, before
introducing Fourier series and building to the Fast Fourier Transform (FFT) and
related periodogram techniques. The theory is illustrated with numerous worked
examples using R datasets, from Milankovitch orbital-forcing cycles to tidal
harmonics and exoplanet orbital periods. These examples highlight the key concepts
and encourage readers to investigate more advanced time-series techniques. It
concludes with a consideration of statistical effect-size and significance. This useful
book is ideal for graduate students and researchers in the Earth system sciences who
are looking for an accessible introduction to time-series analysis.
dr robin crockett is Reader in Data Analysis in the Faculty of Arts, Science
and Technology at the University of Northampton, UK. He is a member of the IMA
and the IOP and holds Chartered Scientist Status. He specialises in investigating
periodic, recurrent and anomalous features in data, and has led a highly successful
short course on Fourier analysis at the European Geosciences Union General
Assembly for many years.