PSN-L Email List Message

Subject: time/phase delay
From: S-T Morrissey sean@...........
Date: Mon, 10 Jan 2000 22:22:33 -0600 (CST)

Regarding a concern for the time delay of a seismic system:

This has generally been a "don't care" for seismology.

THe primary reason is that the measurable phase delays are
usually small when compared with the needed accuracy of determining
the arrival time of a seismic wave. The "pick" of the arrival
time of an impulsive wave is where the trace first diverges from
the background trace, so is at the most impulsive or high frequency
portion of the waveform. (emergent phases are another story).
The high frequency delay is usually determined by the low-pass
filters in the data, which include the pre-amplifier, the telemetry
or digitizer input, and the discriminator  or digital-to-analog output.

The phase response of the seismometer mass itself ranges from 0 to pi,
as the driving force ranges from very long periods to high frequencies,
where the phase lag is equal to pi/2 at the period of the seismometer. 
If the seis natural period Tn is 1 second, a phase lag of pi/2 is 90
degrees or 0.25 seconds. A lag of 0 means that the mass follows the
ground motion, which is also the case as would be expected if nothing is moving.
And if the damping is set to 0.7 of critical, the phase response is linear
about Tn, resulting in no phase distortion in the output. By saying that
the phase of the motion of the mass lags the ground motion at frequencies
higher than Tn (the seis period),  it means that the mass essentially 
stays put as the ground moves, which in an moving coil seis, means that
the voltage output has minimum delay (and maximum level) at high frequencies. 

The natural dispersion of seismic waves (the farther they travel, the
longer their period becomes), means that generally the arrival times
for many stations are being read from data from similar instruments 
that all would have a similar phase delay. Electronic filters would
add additional delays, but these would usually be low-pass filters at
for example, 25hz, which would have a delay of up to 10 milliseconds.
But again, even a closely spaced network would be using nearly identical
equipment, so the delays would all be the same, and not affect the 
hypocenter determination. In using data from both close (20km spacing) 
stations and near field (100 to 300km) stations, the data from the more 
distant stations would have significant propagation variables that generally
are much greater than instrumental errors.

Even electronic broadband stations have phase delays, which can be
significant. For example, a 120 second VBB sensor will have a 90 degree
lag at periods of 120 seconds, which is 30 seconds. But for purposes
of timing, ie determining the relative arrival times between stations,
any station registering a 120 second wave will have a similar delay
IF the phase delay is linear which is only true IF the damping is
set to (0.707) of critical. (Which is why we use this damping value).

So this is why phase delays are not a concern in timing of seismic
waveforms. Modern digital systems have their own problems with long
FIR and IIR digital filters, but usually correct for the delays of the 
filters in the output timing. High frequency multi-channel systems
have identical delays for every channel (which can be fine tuned),
so there is no net relative time difference between the outputs.
Even variations of 10% in natural frequency between geophones are
not a major problem.

The phase delay (and other parameters) of a seismometer can be easily
determined using the calibration coil or the signal coil in a bridge
circuit (unless you have access to a shake table: we have a pair 
(vertical and horizontal) at St. Louis Univ. that I can help anyone 
use; it runs from DC to 50hz, 1 to 100 microns at 0.5%, supporting 
seismometers up to 100 kgm). I have previously described how to use
a calibration bridge, which we permanently install in the circuit of
many short period stations; I can repeat it if necessary.



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Larry Cochrane <cochrane@..............>