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OPTICAL ANCHOR NOTE OA-11
Title: mV to nm geophone conversion numbers.
Author: Tim Slaton
Date: 15 April 1999
The voltage signal from a geophone is proportional to its velocity with respect to an
internal mass hanging from a spring. Actually, it is a little more complicated then this
(for details see the NLC ME NOTE No. 1-94), but for SHM above a few hertz a simple
relationship exist as shown in equation 1
S = GKA
equation 1
where S is the signal from the geophone system with units of (V), G is the gain of the
amplifier used for amplifying the geophone signal which is unitless, K is a constant
determined by the parameters of the geophone and amplifier for converting velocity to
voltage with units of (V/m/s) (see the NOTE mentioned above), A is the amplitude of the
motion with units of (m).
Equation 2 obtained from rearranging equation 1 gives the motion of the geophone
A = S/(GK).
equation 2
Converting from meters to nanometers and from volts to millivolts leads to equation 3
A = 1e6S/(GK).
equation 3
For the geophones and amplifiers being used, K = 178.85 (V/m/s) which gives equation 4
A = 890S/(Gf).
equation 4
Using equation 4, a look up table, table 1, can be generated to convert the signal in mV
from the geophone to nm of geophone motion.
Table 1. Look up table to convert from mV to nm.
Freq(Hz)
1
10
20
30
40
50
60
70
80
90
100
30
29.6626
2.9663
1.4831
0.9888
0.7416
0.5933
0.4944
0.4238
0.3708
0.3296
0.2966
Amplifier Gain
232
522
3.8357
1.7047
0.3836
0.1705
0.1918
0.0852
0.1279
0.0568
0.0959
0.0426
0.0767
0.0341
0.0639
0.0284
0.0548
0.0244
0.0479
0.0213
0.0426
0.0189
0.0384
0.0170
1
920
0.9673
0.0967
0.0484
0.0322
0.0242
0.0193
0.0161
0.0138
0.0121
0.0107
0.0097
One must be careful in these measurements because there are several factors of 2 or so
involved. Peak to peak or just peak value, a factor of 2. There is a factor of 2 difference
in what the geophones are measuring as the motion and what the motion is suppose to be
from the voltage being supplied to the piezo-electric drivers, the drivers are high. There
is a factor of 2 / 2 if the motion is being analyzed by power, which gives the rms
motion, or if the rms of the signal is used, this is only valid for SHM.
2