Assessing the Quality and Limitations of Geophysical Time Series

In geosciences, we often wish to compare two time series and quantify their common signal. A reliable method of comparison, from traditional time series analysis, is the coherence spectra - a measure of correlation between two time series as a function of frequency. Increasingly large data sets and advances in numerical modelling allow us to easily generate a great many coherence spectra in an attempt to understand observations. But this approach may still hinder our ability to make concise inferences from a large data set. In this paper, we introduce two quantities that characterize the coherence in a precise way and show how they can be used to display the spectral qualities of a large collection of time series in a visually elegant way. These ideas are developed in the context of paleomagnetism, which serves as motivation and provides two practical applications. We perform an assessment of four relative paleointensity time series spanning the last ¡«120 kyr and explore the effects of errors and processing on a pair of simulated relative paleointensity time series.