Calibrating your Volksmeter

The Volksmeter (VM) is an unusual seismic instrument, having at its heart a simple short pendulum.  The general principle of operation is straight forward, being a sensitive detector which measures the displacement of the pendulum, and which will therefore indicate either a tilt or horizontal acceleration of the whole instrument.  When considering a modern automobile engine, the theory of operation can get rather complex upon close inspection, and similarly with 'simple' pendulums and how they behave.  The inventor of the Volksmeter is a particular authority on the motion of pendulums and has written extensively on the subject.  In an appendix to the comprehensive Volksmeter User Manual, there is a detailed theory of operation covering seismometer detectors in general, and pendulums in particular.

One of the useful features of acceleration sensors is the ability to calibrate them by tilting them with respect to the Earth's gravitational field, and so it is with the Volksmeter.  Because of its extreme sensitivity, particularly when operated in 24-bit mode, the Volksmeter can take quite some taming, and some practice with setup is required.  The technique for leveling the VM is covered quite well in the on-line user manual in Chapter 2b.

Assuming that the reader has completed their Volksmeter's installation at a permanent site, and is operating it via WinSDR, there remains the question of what sensitivity figures should be entered into WinSDR's 'Sensor information' page, for both the acceleration channels (Channels 1 & 2) and the velocity channels (Channels, 3 & 4).  For Channels 1 & 2 this sensitivity figure represents the amount of horizontal acceleration required to register a change of 1-bit by the VM's detector.  WinSDR may be configured with various sensitivities by setting the digitisation range anywhere between 16-bit to 24-bit operation.  When operated in 24-bit mode the VM is very sensitive indeed and can be tricky to work with, due to flexure of just about everything within and external to the instrument.  At these levels of sensitivity, 'hard' substances such as reinforced concrete floor support, can effectively become a big slab of marshmallow.

The calibration process is relatively straight forward, and utilises the VM's leveling screws.  These screws are arranged in a triangle, with a single screw located on the left hand side (LHS) of the instrument, and two screws on the right hand side (RHS).  Consider turning just the LHS leveling screw, which will cause the whole instrument to tilt about an axis running between the tips of the two RHS leveling screws.  Since we know that the thread pitch of the leveling screws is 32 turns-per-inch, and the horizontal distance between the LHS leveling screw tip and axis of rotation is 9.70 inches (246mm), then a single turn of the LHS screw will cause the whole instrument to tilt by arctan(1/32"
÷9.7") = 0.185º = 0.00322 radians.

When operated in 24-bit mode, the VM's digitiser output ranges between ±8,388,608 'counts'.  In practice, and considering just Channel 2, it takes a little less than two complete turns of the LHS screw to cause the digitiser output to range between the maximum -ve counts
and maximum +ve counts.  I have found that 1½ turns of the LHS screw can be comfortably accommodated within the 24-bit digitisation span.  Firstly it is helpful to calculate the VM's counts/tilt ratio, normally expressed in units of counts/radian.  By adjusting the LHS screw to a point near maximum -ve counts, and then rotating it 1½ turns toward +ve counts, one can compute this ratio.  For example, I adjusted the LHS screw to a point where I read a figure of -7,129,000 counts, and after rotating the screw 1½ turns anticlockwise, this figure became +7,670,000 counts.  Taking the difference between these two and dividing by 1½, yields a figure of around 9,866,000 counts/turn.  But one screw turn changes the tilt by 0.00322 radians, so the counts/radian figure for my particular VM is 2.0×109 counts/radian.  Note that this figure is for 24-bit digitisation, and it will be reduced for lower-resolution digitisation.  For example, for 20-bit digitisation it would be reduced by a factor of 16.

allan keyAs a point of technique for accurately rotating a leveling screw by
1½ turns (or any other amount), I recommend placing a tiny dot of white paint (e.g. typewriter correction fluid) on the top of the screw to indicate its general rotation position (it's easy to lose track of rotation otherwise).  One may then use a 3/32" Allan key to rotate the screw.  As may be seen in the right-hand image, the Allan key shaft also acts as an analog pointer, and one can fairly accurately eyeball when the Allan key is pointing directly away from the instrument or when it is aligned parallel with the edge of the VM base plate.  Another handy tip, which may also be seen in this image, is to label the effect that screw rotation has on WinSDR's screen trace.  In this case, a clockwise rotation will cause the WinSDR screen trace to move downwards (i.e. towards -ve digitiser counts).  This knowledge can save a lot of mucking around when leveling the instrument.

The standard textbook constant for 'g', the vertical acceleration due to Earth's gravity, is
9.80665m/s/s (SI units) = 980.665cm/s/s (cgs units, used by WinSDR).  A single rotation of the LHS leveling screw will introduce a horizontal component of acceleration of 1/32"÷9.7"x980.665 = 3.159cm/s/s.  So in terms of acceleration/counts, for one turn of the screw and 24-bit digitisation, the figure for my particular VM is 3.159/9,866,000 3.2x10-7cm/s/s/count, which is the required figure to enter into WinSDR's sensor sensitivity field (specifically enter "3.2e-007" into this field).  On the same setup page the 'Output Type' field needs to be set to 'Acceleration'.  The 'Output Voltage', 'Amp Gain' and 'A/D Input' fields don't apply to the VM and may be set to 0.0.  Working on the assumption that VM channels 1 & 2 have similar performance, I have set both my Channel 1 & 2 sensitivity fields to "3.2e-007".

This is well and good for the VM acceleration channels 1 & 2, but what about the VM velocity channels 3 and 4?  What figure should be entered for the sensor sensitivity here?  This was a small puzzle for me for quite some time, and I firstly tried the hit-and-miss adjustment technique, by observing actual teleseismic quakes and by comparing my measured peak ground velocities with those modeled by the USGS arrival time calculator.  This produced pleasingly consistent results, but still not exactly a calibrated value.

This puzzle was solved one day by the realisation that WinQuake has a digital integration function, and it should therefore be possible to digitally integrate one of the VM's acceleration channels, and to compare it with a VM channel which produces velocity output directly (e.g. integrated data from VM Channel 1 should be very similar to that from Channel 3).  Exactly how WinSDR produces its real-time velocity channels (3 & 4), by performing a real-time integration of acceleration, is an algorithmic 'black box', but it seems to work well enough.  If one takes a hour's worth of VM acceleration data (say Channel 1, preferably containing something interesting such as a teleseismic quake), and then integrates it via WinQuake, and then prints out the resultant trace, this visually compares quite well with the trace of Channel 3 data acquired over the same period.  On close inspection the two traces won't be exactly the same, but usually pretty close, as may be seen with this example showing integrated acceleration (upper trace) and velocity (lower trace).

One thing to note when integrating data from VM Channels 1 & 2, is that small consistent accelerations (i.e. tiny slow near-DC changes in tilt occurring within the data period) can lead to some very peculiar looking (e.g. banana shaped) velocity traces.  After integrating VM acceleration data, it is advisable to then apply a high-pass filter of say 0.01Hz, to remove the near-DC components left over from integration.

WinQuake's 'Calculate RMS' function may then be used to calculate the velocity sensitivity figure.  Firstly, enter a 'first guess' sensitivity figure for WinSDR channels 3 & 4 by entering "3.00e-007" into the sensitivity fields.  Then take a hour's worth of VM Channel 1 data, integrate it, filter it, and calculate the RMS velocity.  Then take the channel 3 data for the same period and calculate its RMS velocity.  These two RMS numbers will not match, but will likely be similar.  For example, if the integrated acceleration [Channel 1] RMS figure was 40um/s and the velocity [Channel 3] RMS was 30um/s, then Channel 3 velocity needs to be scaled up by a factor of 40/30.  This would require multiplying the 'first guess' sensitivity by 4/3, that is 3.0x10-7 x 4/3 = 4.00e-007 in this case.  With my particular VM instrument, I have determined my Channel 3 & 4 sensitivity figure to be "3.89e-007".

Each individual Volksmeter will need its own calibration, but as an intermediate step to get a new VM owner up-and-running, I suggest entering the following sensitivity constants into WinSDR's sensor sensitivity fields.:

VM Channel no.
Sensor sensitivity
1
3.20e-007
2
3.20e-007
3
3.89e-007
4
3.89e-007

I would be interested to know what calibration figures other VM owners have found, so please feel welcome to email me and I will post the results on this page.

2010-02-14