Visualizing Time/Frequency Cyclicity with Circular Spectrograms

Abstract Visualizing the time/frequency evolution of a signal is a common task in geophysics. This is often done using a “spectrogram,” an image in which time increases monotonically on one axis, frequency on the other axis, and the signal property of interest (often spectral power) is shown via color. Although this is effective for identifying nonrepeating signals, capturing cyclic time/frequency patterns is difficult to do succinctly. Here, we present the “circular spectrogram,” a permutation that represents time/frequency pixels in polar coordinates. This highlights activity patterns inherent to the cycle of interest across both time and frequency. We describe how to construct the circular spectrogram and some of the data processing methods we found most effective. Then, we provide four examples of circular spectrogram utility: assessing patterns in diurnal winds and human activity on an infrasound microbarometer, determining the impact of trees at a geophone array, examining environmental noise reduction on a borehole seismometer, and exploring daily cycles at the Interior explorations using Seismic Investigations, Geodesy, and Heat Transport landing site on Mars.