How Processing Methodologies Can Distort and Bias Power Spectral Density Estimates of Seismic Background Noise

Abstract

Abstract Power spectral density (PSD) estimates are widely used in seismological studies to characterize background noise conditions, assess instrument performance, and study quasi-stationary signals that are difficult to observe in the time domain. However, these studies often utilize different processing techniques, each of which can inherently bias the resulting PSD estimates. The level of smoothing, the size of the data window, and the method used for actually estimating the spectral content can all have strong influences on PSD estimates and background noise statistics. We show that although smoothing reduces the variance of the PSD estimate, the corresponding decrease in frequency resolution can eliminate or distort features of interest. For instance, popular software packages such as Incorporated Research Institutions for Seismology Modular Utility for STAatistical kNowledge Gathering (MUSTANG) and earlier versions of Portable Array Seismic Studies of the Continental Lithosphere Quick Look eXtended (PQLX), which were designed for data quality control and are effective in that regard, are less suitable for scientific studies that require accurate resolution of spectral peaks, even for peaks as broad as the primary (∼14  s period) and secondary (∼7  s period) microseisms. We also demonstrate how the 1 and 3 hr data windows used in MUSTANG and PQLX can be strongly influenced by energy generated from moderate-size (M>∼4.8) teleseismic earthquakes. The ubiquity of these events is likely skewing median ambient-noise estimates by as much as 5 dB upward, for periods of 10–50 s at high-quality broadband stations. Finally, we illustrate that many of the discrepancies between global low-noise models are attributable to processing methodologies rather than fundamental differences in the underlying seismic data.