PSD algorithm

We have been characterizing the vertical and horizontal seismic background noise levels observed in Northern and Central California via Power Spectral Density (PSD) analysis of the seismic background signals recorded by the BDSN broadband seismic stations (BK network) and by the USArray broadband seismic stations (TA network). Two frequency bands, the 1-5 Hz short-period (SP) band and the 30-60 second long-period (LP) band, are analyzed to characterize the background noise in the seismic bands of interest particularly for the study of the seismic signals from local and regional seismic events.

The PSD algorithm uses a statistical approach to robustly estimate the background noise PSD. The PSD estimates are reported in dB relative to 1 (m/s2)2/Hz. The input time series is parsed into eight (possibly overlapping) time series and each of the resulting time series are appropriately windowed prior to calculating their PSD estimates. For short time series, less than 1.5 hours in length, the time series are detrended and sine tapered while for longer time series the dominant semi-diurnal gravitational tide signal is also removed to avoid biasing the long-period PSD estimates. The PSD estimates are smoothed and reported at twenty logarithmically spaced intervals per decade in period.

Owing to the statistical nature of the PSD algorithm, it is required that the time series to be processed contain at least 65,635 (216) contiguous samples. Shorter time series are not processed and a warning is issued. The PSD algorithm can process data with a wide variety of sampling rates (from $<0.01$ sps to $>500$ sps). A typical usage with broadband data is for the time series to contain one day of continuous LH (1 sps) data (86,400 samples), say. Since the sensor transfer function representation in the SEED data volume for a typical inertial seismometer does not include the static component of the response, the background noise PSD estimates for periods longer than approximately an hour will be biased high; and hence, they will be unreliable.

The PSD code distribution along with examples of its usage are available via the Web at http://seismo.berkeley.edu/algorithms/.

Berkeley Seismological Laboratory
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