Re: Expected seismograph output:

For the benefit of estimating what amplitude a PSN seismograph
should expect to detect from an earthquake at a given distance,
we use the generic magnitude formula:

	Ms = log(A/T) + 1.66*log(distance) - 0.18

	where A is the peak-to-peak ground amplitude at the seismograph 
	in nanometers (10^-9 meters),
	T is the period in seconds, the distance is in degrees ( 1 deg =
	111 km, and the constant -0.18 is an attenuation adjustment.

which is solved for the amplitude:

	A = T * 10^[Ms -1.66*log(dist) + 0.18]

Then selected combinations of Magnitude and distance are used to determine
the seismograph amplitude in nanometers (m * 10^9), which are converted
to peak velocity by multiplying by w (omega) = 2*pi*f, where f = 1/T.

The possibilities are fortunately limited by the effect of dispersion
of the seismic wave, namely that the wave period increases with distance, so
a close quake will have periods of less than 1 second, while a distant
event will arrive with periods in excess of 20 seconds. While the possibilities
are endless, typical distance-period combinations are selected.

Other limitations are presented by the expectations of the seismograph
or seismometer-digitizer. Since these are velocity-recording systems,
we will assume a constant VBB output of 1000 volts/meter/second (v*sec/m) for
all periods/frequencies. THis then presents dynamic limits of a maximum
voltage of 10 volts and a background noise level of 1 millivolt. Of
course  for a reasonable signal-to-noise ratio of 100 to 1,.  the system 
noise floor must be 10 microvolts or less. 

Your particular seismograph parameters may be different, but the generalities
here can be scaled appropriately. Also, the generic magnitude formula
is not exactly applicable for nearby ( 100 to 200 km) quakes; special
formulas will expect up to twice the amplitude since the attenuation is
a fractional power of the distance. 

In the table below, the velocity in microns/second has the same
value as the seismometer output in millivolts if the sensitivity 
is 1000 volts/meter/second. A "*" indicates a clipped output over 10 V.

Magnitude     Amplitude    Velocity/output       acceleration 
Ms            microns      u/sec = millivolts    percent of g

Distance: 0.1 degree (11 km), period: 0.25 seconds (4 hz).
3             17           435                   0.11
4             173          4347 (ie 4.3volts)    1.11
5            1729          43469*                11.14


Distance: 1.0 degree (110 km), period: 0.50 seconds (2 hz).
3             0.76          9.5                  0.0012
4             7.6           95                   0.012
5             76            951                   0.12
6             760           9510                  1.12

Distance: 3 degrees (330km), period: 0.7 second (1.43hz).
3             0.17          1.5                  0.0001
4             1.7           15                   0.0014
5             17            154                  0.014
6             171           1535                 0.1406

Distance: 9 degrees (999 km), period 1.0 second (1.0hz).
3             0.039         0.247
4             0.39          2.478
5             3.9           24.78                 0.0016
6             39.4          247.8                 0.016
7             394.4         2478                  0.1589

Distance: 30 degrees (3330km), period 15 seconds
4             0.8           0.336
5             8.0           3.36
6             80            33.6
7             802           335.9                0.00143

Distance: 45 degrees (4995 km), period 15 seconds
4             0.4           0.17
5             4.1           1.71
6             40.9          17.1
7             409           171.3                0.00073

Distance: 90 degrees (9990km), period 25 seconds
5             2.16          0.542
6             21.6          5.42
7             215.7         54.22
8             2157          542.17               0.00139

Distance: 135 degrees (14985 km), period 25 seconds
5             1.1           0.27
6             11.0          2.76
7             110.0         27.65
8             1100.5        276.58

For example, if the quakes in Turkey are about 90 degrees from
St. Louis, I would estimate that a Ms 7.0 would have a peak-peak
amplitude at 25 seconds of about 54 microns/second. Since the
recording sensitivity here is 5290 Volts/meter/second (5.29mv/micron/sec),
the digitizer should see 285 millivolts (peak voltage), which
means that it clips on the 200mv scale, which it did for the 7.2
yesterday 12 Nov.

Regards,
Sean-Thomas


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