Regarding choices for seismometer construction:

My 2cents worth is to strongly suggest making a vertical sensor;
it produces much more interesting data in general, and is much
less sensitive to site noise (floor tilting) by the square of the
operating period. A vertical has the complication of a spring to
counter gravity, but I think the construction effort is worth it.

THe question of a suitable dimensions for a horizontal sensor relates
directly to the expected operating period and sensitivity. For interesting
data, a period of 15 seconds is needed. THis can be achieved both
by making the boom longer and by tilting the boom closer to the
horizontal. (WHen the boom IS horizontal, the period is infinite, 
which is to say the sensor is unstable).

SO ... Lets consider some formulae of interest for the horizontal pendulum:
(assuming that the restoring force by the hinges and/or pivot are minimal):

The natural period: Tn = 2*pi*sqrt(L/(g*sine i))
 
where L is the boom length in cm, g=980cm/sec^2, i is the angle
that the boom makes wrt the horizontal, (if i is measured in radians,
(360 degrees = 2*pi radian, or 1 radian = 57.3 degrees), and i is small,
sine i = i). For example, a 40 cm boom hanging vertically (mass at the bottom)
as a simple tick-tock pendulum ( an angle of 90 degrees) has a period of 
1.3 seconds. (a one second clock pendulum is 24.8 cm). But the pendulum
supports or hinges can be arranged in a "garden gate" configuration. When 
tilted horizontally to about 4 degrees, the period is 5 seconds. At
about a 1 degree ((2*pi/360) radian) angle, it is 10 seconds, and at 
about 0.23 deg. it is 20 seconds. However, if we increase the boom length 
by times 4 to 160cm, (an impractical 60 inches), we also get a period of 
20 seconds.  So the period is changing with the square root of the boom
length as well as the inverse of the square root of the angle the boom
makes with the horizontal. In general, a practical boom length is 10"
to 15", with a baseplate of 15" to 24" long and about half as wide at
the leveling end (for a horizontal; leveling for a vertical, as shown
above, is nowhere as critical, and 4" to 8" widths are workable).

It is important to note that the size of the mass determines nothing
of the period or sensitivity to tilting. Any reasonable size will work;
larger is better for overcomming any torque of the hinges or flexures,
to the point where the mass/boom structure begins to distort any part
of the suspension.  (THe size of the mass IS a factor in a VBB fedback 
system). The total mass of the boom should be less than 10% of the main
mass, which includes the sensor coils.

The tilt sensitivity of a seismometer is therefore a function of the
square of the operating period Tn.

For a HORIZONTAL:
		(where z is the displacement, and phi is the tilt)
		z = (g * Tn^2 / 4 * pi^2) * phi 
For a VERTICAL:
		z = (g * Tn^2 / 8 * pi^2) * phi^2) (vertical)

Note the vertical sensor responds to the SQUARE of the tilt. BUT .. Since 
the angle is always small and less than 1, the square of a small angle
(measured in radians) is smaller than the original number. So conversely
the horizontal is MORE sensitive to tilt of the base by the square of
the angle.

SO what does this mean in comparing the tilt noise of a vertical
compared with a horizontal of the same period. Suppose the seis is
in a corner of the garage or basement. Then suppose that when you
walk up to the site you deflect the floor by 1 micron (10^-6 meter)
when you are 1 meter away (Or your neighbor parks his Humvee 100
meters away and deflects the neighborhood by 0.1 millimeter.) In both
cases the tilt is delta(L)/L or 10^-6 radian.  So if your horizontal
seis has a period of 10 seconds, the mass will offset 24.8 microns.
This is a large number; the 6-second microseisms run about 2 to 4 microns.
HOWever: if you have a vertical seis, the displacement from a 10^-6 tilt
is 10^-6th of the horizontal. Conversely, it takes a floor deflection
if 1mm at 1 meter distance to get the same 24.8 microns movement on a
vertical.

So when you push the operating period from 10 to 20 seconds, the tilt
sensitivity increases by 4. Even a modest period increase demands a good
site for the instrument. The WWNSS (worldwide network of standard 
seismographs) originally tried to operate the long period sensors at
30 seconds, but so many were always at the stops that they backed
off to 15 seconds as the standard.

You can test the tilt sensitivity using your leveling screw, which
I guess is something like 40 threads/inch. In the above formula, "phi"
is the angle in radians, so if you turn the screw one turn and if the base
support width is 10 inches, the tilt is 1/40" divided by 10", or 0.0025
radians. Using the formula above for a horizontal sensor:
The displacement then is 0.062cm times the square of the period. If Tn
is 10 seconds, it is 6.2cm; if Tn is 100 seconds, one turn of th 40 tpi
screw will try to move the boom 620 cm. Even if 1/100 turn can be used,
the displacement is still quite large. THis is why VBB instruments have
a feature that allows a shorter period to be switched in for setup at
installation, and a motor-driven lever of 100:1 to level the sensor in
operation. A typical tilt noise level for the 360-second STS-1 is 
equivalent to about 6 nanoradians. For practical operation of a home-made 
VBB, an operating period of 20 to 40 seconds would be preferred.


For construction materials, I would avoid wood, plastics, fiberglass,
etc: these have significant coefficients of temperature and humidity.
Since it is so easy to work with, and available in many shapes,
aluminum is generally preferred, although non-magnetic stainless 
steel is also used for the base and frame. I would also suggest that
aluminum channel at least 3/4" x 3/4" x 1/8" thick should also be used
for the boom; it is readily available and you can drill holes anywhere.
I cut open one end to make a fork that fits both sides of a 1/2" thick
x 2 3/4" dia 1 1/4 lb lead disk (McMaster 90385K22 $ 7.83) at the end of
the boom for either the vertical or horizontal. (I have a new horizontal
design that fits on a 1/2" x 4" x 15" baseplate with a 10" Tee piece at 
one end for leveling and uses folded shim stock box flexures that I have 
only partially documented; it works as either an velocity sensor
or, with a VRDT, a VBB instrument).

All the hardware should also be brass, aluminum, or stainless steel; 
the common 18-8 stainless alloy is slightly magnetic (a few percent of 
the effect on iron), and should not be used near magnets; the 316 stainless
alloy is pricier and NOT magnetic.  I have used molded fiberglass bolts 
for coil supports.

My experience with baseplates has been mostly in the realm of
tiltmeters, which are horizontal seismometers by another name.
In this regard, thicker is better, with even the smallest designs
using 1/2" aluminum plate.

For the vertical VBB sensor here, a base/frame made with aluminum
channel and angle material 1/8" thick is adequate. This is because
everything is moving in a vertical plane, not torqueing the base.
When I use the same structure for a horizontal, it is not rigid 
enough, since the movement is across the plane of the base, 
including the centering adjustment which is applied to one corner.
Even the slightest rotation or twisting of the base will 
affect the alignment of the transducers.  So I use 1/2" aluminum 
plate (from McMaster Supply) and drill and tap holes for mounting,
leveling feet, etc. An aluminum plate 1/2" thick x 4" wide x 72" costs
$57 from McMaster-Carr. THey have aluminum plate up to 8" wide.

I can also suggest that if the trip to the metal scrap yard yields
a piece of aluminum baseplate that needs to be cut or squared up,
I have been using a fine-toothed CARBIDE tipped table saw blade 
and a similar miter saw blade (60 teeth/10") to cut aluminum.
THey make clean (shiney) cuts; please use all precautions, though.
The "piranna" curve of the teeth can make them prone to gouge 
into aluminum and throw it at you; always clamp the pieces.

As I have said before, resistive damping is the best way to control
the movement in a consistent and predictable way.

Regards,
Sean-Thomas


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