A Primer on Fourier Analysis for the Geosciences

An intuitive introduction to basic Fourier theory, with an emphasis on geoscience applications. Numerous worked examples from R are used to illustrate the theory, making this an ideal practical guide for graduate students and researchers who are using time-series analysis to quantify periodic features in geoscience data.

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. The book 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.