Tutorials: Waveforms and their Power Spectral Density Expressions

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Contributed by Mary Templeton
Affiliation IRIS DMC

This article is a small compendium of waveform features:

and their expression in power spectral density (PSD) plots. It’s intended to serve as a growing reference for interpreting PSDs. The figures shown here (from the pqlx software developed by Richard Boaz) include:

  • a one-hour (usually) trace window and
  • its corresponding PSD.

The Peterson new high and low noise model curves are displayed on the PSD plots for reference (grey lines).

At the end of the article is a Self Quiz showing each PSD so you can try naming the waveform that generated it. Clicking on the PSD displays the answer.

Background Noise

ISCO is an example of a quiet site in a cave with minimal background noise:

The PSD for this quiet site shows low power, even at long periods on horizontal channels:

Background Noise PSD View
Example of normal background noise in PSD view.

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Digitizer Noise

For a few days, the sensor at RLMT went out and the station recorded digitizer noise:

Digitizer Noise Trace View
Example of digitizer noise in trace view.

The PSD reflects that the amplitudes are only a few counts and vary from sample to sample:

Digitizer Noise PSD View
Example of digitizer noise in PSD view.

The response is similar to a channel mass resting against the stops.

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Diurnal Thermal Noise

SRU resides in a near-surface vault and shows long period diurnal thermal noise during daylight hours (~14:00-02:00 UTC). The PSD below shows the SRU during its quieter times:

Diurnal Noise Quiet PSD View
Example of diurnal noise when quiet in PSD view.

The bars below show time of day corresponding to the PSD. All curves represent local night time:

The trace shows night time background noise levels of ~300 counts:

Diurnal Noise Quiet Trace View
Example of diurnal noise when quiet in trace view.

The next PSD below shows the SRU during its noisier times:

Diurnal Noise PSD View
Example of diurnal noise in PSD view.

All curves for this PSD represent local day time:

Diurnal Noise Noisy Time Periods
Example of noisy time periods associated with diurnal noise.

The trace shows the large (~7000 count) long-period noise levels during the warm hours:

Diurnal Noise Noisy Trace View
Example of diurnal noise when noisy in trace view.

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Local Earthquake

This local event:

Local Earthquake Trace View
Example of a local earthquake in trace view.

is rich in short-period body waves:

Local Earthquake PSD View
Example of a local earthquake in PSD view.

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Teleseism

PSD for these teleseismic surface waves:

Teleseismic Earthquake Trace View
Example of a teleseismic earthquake in trace view.

is rich in long-period energy:

Teleseismic Earthquake PSD View
Example of a teleseismic earthquake in PSD view.

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Gaps

A data gap maps as a line in a PSD plot with a slope of about 20 dB per decade. The line’s intercept depends on the amplitude difference across the gap. Gaps with larger amplitude offsets:

Large Amplitude Gaps Trace View
Example of a gap with a large amplitude difference in trace view.

have larger intercepts (lie farther above the noise model curves):

Large Amplitude Gaps PSD View
Example of a gap with a large amplitude difference in PSD view.

than do gaps with smaller amplitude offsets:

Small Amplitude Gaps Trace View
Example of a gap with a small amplitude difference in trace view.

Small Amplitude Gaps PSD View
Example of a gap with a small amplitude difference in PSD view.

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Harmonic Ringing

The STS-2 at PASC is ringing at 80 seconds for some unknown reason. The trace below, which has been low-pass filtered below 1 second, illustrates this:

Harmonic Ringing Trace View
Example of harmonic ringing in trace view.

The corresponding PSD shows that energy near 80 seconds never falls below a certain level, even when the rest of the pass band is quiet:

Harmonic Ringing PSD View
Example of harmonic ringing in PSD view.

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Mass Against Stops

The trace below shows the pegging of a Guralp CMG-3T borehole mass recorded on a Q330:

Pegging of Mass Trace View
Example of a CMG-3T mass drifting against its stop in trace view.

This horizontal component began showing long period noise and drift followed by an episode of bouncing between both stops. This behavior may have coincided with a mass recenter attempt, but it’s unconfirmed. Large amplitude acausal spikes are recorded on this channel while the mass is against its stops:

Bouncing Mass Spikes Trace View
Example of a mass drifting between stops in trace view.

The PSD for these spikes is high power and fairly white:

Bouncing Mass Spikes PSD View
Example of a mass drifting between stops in PSD view.

When the spikes abate and the mass finally rests against a single stop, the channel records little or no seismic energy:

Mass Resting Against Stop Trace View
Example of a CMG-3T mass at rest against its stop in trace view.

and the resulting PSD is low power and fairly white:

Mass Resting Against Stop PSD View
Example of a CMG-3T mass at rest against its stop in PSD view.

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Mass Recenter

A mass recenter on an STS-2::

Mass Recenter Trace View
Mass re-centering in the trace view.

has this PSD signature:

Mass Recenter PSD View
Mass re-centering in the PSD view.

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Reservoir Pump

Station US.PKME lies in a state park near a water tank that supplies water for visitors. As the tank empties to a certain point, more water is pumped into the tank. The long period tilt on the horizontal channels of the seismic trace:

Water Pump Trace View
Influence of a nearby water pump in trace view.

is probably a combination of the pump and loading at the tank. Its signature is evident at the long-period end of the PSD:

Water Pump PSD View
Influence of a nearby water pump in trace view.

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Step Calibration

Two step calibrations (boxcar function) on a Guralp CMG-3T:

Step Calibration Trace View
Example of a step calibration pulse on a CMG-3T in trace view.

have the following PSD signature:

Step Calibration PSD View
Example of a step calibration on a CMG-3T in PSD view.

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Storm

Sunday June 3, 2007, a storm with heavy rains delayed flights along the US east coast and nearly rained out the baseball game between the New York Yankees and the Boston Red Sox. Storm-related noise swelled throughout the Julian day on the seismic trace below:

Storm Noise Trace View
Example of microseism noise due to a storm in trace view.

Data from the time window between the black vertical lines shows a large microseismic peak on its PSD:

Storm Noise PSD View
Example of microseism noise due to a storm in PSD view.

relative to other PSDs from that week:

Storm Noise 1 Week PSD View
Example of a week surrounding microseism noise due to a storm in PSD view.

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Self Quiz

See if you can name the waveform from the article that gave rise to each of the following PSDs. Clicking on the PSD reveals the answer; use your browser’s Back button to continue with the quiz.

PSD 1

Quiz PSD 1
Click here to review answer.

PSD 2

Quiz PSD 2
Click here to review answer.

PSD 3

Quiz PSD 3
Click here to review answer.

PSD 4

Quiz PSD 4
Click here to review answer.

PSD 5

Quiz PSD 5
Click here to review answer.

PSD 6

Quiz PSD 6
Click here to review answer.

PSD 7

Quiz PSD 7
Click here to review answer.

PSD 8

Quiz PSD 8
Click here to review answer.

PSD 9

Quiz PSD 9
Click here to review answer.

PSD 10

Quiz PSD 10
Click here to review answer.

PSD 11

Quiz PSD 11
Click here to review answer.

PSD 12

Quiz PSD 12
Click here to review answer.

PSD 13

Quiz PSD 13
Click here to review answer.

PSD 14

Quiz PSD 14
Click here to review answer.

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Tutorial , Quality Assurance

Tags

signal processing