Assessing Accuracy and Tradeoffs from Several Power Spectral Density Estimate Algorithms

Power Spectral Density (PSD) estimates are widely used in a variety of seismological studies to characterize background noise conditions, assess instrument performance, and study signals that would be otherwise be difficult to identify in the time domain. To accomplish this task, many researchers employ pre-packaged spectral analysis tools such as the IRIS MUSTANG or Noise Tool Kit (NTK), PQLX, or ObsPy routines. When generating PSDs these algorithms make tradeoffs between the resolution, variance, and uncertainty of the estimate. Additionally, when applying tapers and ensemble averaging to reduce the variance and spectral leakage in PSD estimates, the power levels of the time series are systematically changed and must be properly accounted for. It is also important to identify how varying smoothing algorithms can change the local structure of the PSD estimate. Finally, when converting recorded seismic data from digital counts to ground motion, care must be taken to properly deconvolve the instrument response and handle the digitizer's FIR filters. We examine how these factors influence power estimates in a variety of commonly employed spectral analysis software packages. We find that different processing algorithms can have substantial impacts on estimated power levels, particularly at long-periods and near the Nyquist frequency. Seismologists thus need to take care to account for these factors when comparing the PSDs output by these software packages to PSDs and noise models generated by other algorithms.