SPECTRAL ANALYSIS OF GEOMORPHIC TIME SERIES: AUTO-SPECTRUM

• Published in: Earth surface processes and landforms Vol. 21; no. 11; pp. 1021 - 1040
• Main Authors: HEGGE, BRUCE J., MASSELINK, GERHARD
• Format: Journal Article
• Language: English
• Published: Sussex John Wiley & Sons, Ltd 01.11.1996; Wiley
• Subjects: auto-spectrum; Earth sciences; Earth, ocean, space; Exact sciences and technology; Geomorphology, landform evolution; spectral analysis; Surficial geology; time series; time series analysis; spectral analysis
• ISSN: 0197-9337; 1096-9837
• DOI: 10.1002/(SICI)1096-9837(199611)21:11<1021::AID-ESP703>3.0.CO;2-D

The collection of time series data is an essential component in the investigation of earth surface processes. Spectral analysis of these time series can provide an invaluable insight into the behaviour of geophysical processes. Spectral analysis of a single time series produces an auto‐spectrum which provides a representation of the amount variance of the time series as a function of frequency. Prior to spectral analysis, the time series should be plotted to identify the presence of any trends in the mean or the variance of the series, and to identify anomalies in the data which should be corrected. To satisfy the assumption of stationarity, any trend (in either the mean or variance) should be removed from the time series. Consequently, the probability density function of the time series should be plotted and compared with the Gaussian distribution. The final stage in preparing the time series for spectral analysis is to apply a taper to reduce spectral leakage and distortion of the auto‐spectrum. Following the calculation of the periodogram, spectral estimates should be combined to reduce the variability associated with the estimates and thereby ensure that the autospectrum is more representative. Finally, confidence limits should be constructed around the spectral density function so that statistically significant spectral peaks (or troughs) can be identified.