PSD Noise Analysis of Two Side-By-Side Seismometers with Similar Transfer Functions, Using Sigview (1), (2)
The Power Spectral Density (PSD) of a time series is defined as the power of the signal distributed over a range of frequencies. It is the primary method by which all seismometers are specified in terms of noise. The Acceleration Spectral Density (ASD) is used in most literature. It has the units of:
More accurately the PSD of a time series is the average of the Fourier transform squared over a time interval and is also equal to the Fourier transform of the autocorrelation of the time series.
These calculations were performed in Sigview, a general purpose signal analysis package which provides signal manipulation capabilities in both the frequency domain and time domain. See this description of the Sigview procedure. This is a direct adaptation of a procedure by Brett Nordgren and Dave Nelson using an HP/Agilent 35665A Dynamic Signal Analyzer.
The following plots show the PSDs, Self-Noise and Coherence for each seismometer. The upper and lower black traces are the New High Noise Model (NHNM) and New Low Noise Model (NLNM) from Peterson, 1993(3). This band represents the high and low background noise levels of over 70 seismic stations worldwide.
Plots for a 12 hour period on 02/14/14. There were no major seismic events on this day, however microseism activity was substantial, most likely due to a winter storm in the area.
Plots for a 24 hour period on 02/14/14.
Plots for a 12 hour period on 03/03/14. This was a quiet day.
Plots for a 24 hour period on 03/03/14.
Plots for a 48 hour period starting 02/15/14. These were quiet days with moderate microseisms but no major events. I was interested in seeing the effects of long periods on ground noise.
Plots for a 48 hour period starting 04/01/14, ***with Period Extension***. This was a turbulent period which includes the M8.2 Chilean event. Notice the extension of high coherence down to 0.01 Hz.
(1) Rogers, P. W., "Frequency Limits for Seismometers as Determined from Signal-to-Noise Ratios. Part 2. The Feedback Seismometer", BSSA, Vol.82, No. 2, April 1992.
(2) SigView V2.6.1, SignalLab, Goran Obradovic, 1995, FFTW-GNU open source FFT libraries.
(3) Peterson, J., "Observations and Modeling of Seismic Background Noise", USGS, Open-File Report 93-322, 1993.
(4) Sdrmanip V1.16, 1/2014, Karl Cunningham with input from Larry Cochrane.