Hi there,

       A Lehman type tiltmeter and a twin 30 m arm water manometer type 
tiltmeter, both capable of good performance in measuring earth tides, are 
fully described by M Kato in 'Observations of Crustal Movements by 
Newly-Designed Horizontal Pendulum and Water-Tube Tiltmeters with 
Electromagnetic Transducers', Bull. Disas. Prev. Res. Inst., Kyoto Univ, V 
27, part 4, No. 252, 1977, pp 155 to 171. I was able to get a reprint of this 
paper through my local library services. 
      He also compares the outputs of the two meters over a month. One 
problem with earth tide measurements is that there are two frequency 
components which give a beat type response, so the net component is not a 
simple sinusoid. And it changes from day to day. Another problem is that 
relatively small sensors like Lehmans are very sensitive to purely local 
ground tilts, which may be produced by solar radiation / temperature changes, 
frost, ground movement due to rain, changes in ground loading, where you park 
your car, etc. The earth tides give tilts of just 50 to 100 nano radians.
      The Lehman described uses a 225 mm pendulum extended to about 6.4 sec - 
gain ~45 - 1.27 deg. It could be an advantage to use a longer period to 
increase the tilt sensitivity. This would increase responses to the Ocean 
background signal and to seismic signals, which you don't really want to 
know. I presume that this period was chosen to minimise the response to Love 
and Rayleigh earthquake waves. You might wish to use electromagnetic rather 
than oil damping. The tilt sensitivity is proportional to the inverse of the 
angle that the suspension axis makes with the vertical, expressed in radians. 
If the sensor deflection is d, the period is T, for a tilt r radians, d = 248 
x T^2 x r mm. For the above example, d is about a micron. If you could 
increase the period to 20 sec, you would get about 10 microns. 
     One important point to remember is that your sensors have to be 
sensitive to DC components and must have excellent long term drift stability. 
The simple coil / magnet sensors usually used on Lehmans will not sense these 
very slow signals. You could modify a LX1358 LVDT Kit from 
http://www.nuovaelettronica.it/ (basic circuit gives ~0.3 mV / micron which 
can be amplified by 100) or by modifying a NE5521 LVDT circuit to use 
capacitative sensor plates. Or by using a 7.4 sq mm differential photodiode 
setup with a small tungsten filament bulb. Resonant circuit capacitative 
detectors like those described with the SG seismometers and in the recent 
'tiltometer' postings, are unlikely to have adequate long term temperature 
stability to give reliable results. You also need very good quality hinges 
for the arm and fine adjustment for your base setup screws.  
      You don't measure the ground displacement as you do for an earthquake, 
you measure the change in the tilt angle of the sensor and low pass filter 
reject any other disturbances. A suitable filter can be made with three 4.7 
muF polyester capacitors and four 10 M Ohm resistors, but you need an opamp 
with a very low bias current, like a LMC6001 or LPC661. It is tedious waiting 
for a filter of this sort to stabilise. A rapid zero setup method could 
involve providing bypass setup resistors of 100 K Ohm in series with reed 
relays across the 20 M Ohm filter resistors. You also need very low leakage 
currents on your PC boards and electrometer type ring shielding of the pins. 
The circuit is a Sallen and Key type with unity gain. The input is 20 M Ohm 
resistor connected to two 4.7 muF capacitors to the output and a connection 
to the second 20 M Ohm resistor. This is connected to the +ve opamp input and 
a 4.7 muF capacitor to earth.
       In comparison, the 30 m water manometer gives about 3 microns change 
for a tilt of 100 nano radians. Very good temperature stability is required. 
These are very small signals.

       Regards,

       Chris Chapman
Hi there,



       A Lehman type tiltmeter and a twin=20=
30 m arm water manometer type tiltmeter, both capable of good performance in=
 measuring earth tides, are fully described by M Kato in 'Observations of Cr=
ustal Movements by Newly-Designed Horizontal Pendulum and Water-Tube Tiltmet=
ers with Electromagnetic Transducers', Bull. Disas. Prev. Res. Inst., Kyoto=20=
Univ, V 27, part 4, No. 252, 1977, pp 155 to 171. I was able to get a reprin=
t of this paper through my local library services.=20

      He also compares the outputs of the two m=
eters over a month. One problem with earth tide measurements is that there a=
re two frequency components which give a beat type response, so the net comp=
onent is not a simple sinusoid. And it changes from day to day. Another prob=
lem is that relatively small sensors like Lehmans are very sensitive to pure=
ly local ground tilts, which may be produced by solar radiation / temperatur=
e changes, frost, ground movement due to rain, changes in ground loading, wh=
ere you park your car, etc. The earth tides give tilts of just 50 to 100 nan=
o radians.

      The Lehman described uses a 225 mm pendul=
um extended to about 6.4 sec - gain ~45 - 1.27 deg. It could be an advantage=
 to use a longer period to increase the tilt sensitivity. This would increas=
e responses to the Ocean background signal and to seismic signals, which you=
 don't really want to know. I presume that this period was chosen to minimis=
e the response to Love and Rayleigh earthquake waves. You might wish to use=20=
electromagnetic rather than oil damping. The tilt sensitivity is proportiona=
l to the inverse of the angle that the suspension axis makes with the vertic=
al, expressed in radians. If the sensor deflection is d, the period is T, fo=
r a tilt r radians, d =3D 248 x T^2 x r mm. For the above example, d is abou=
t a micron. If you could increase the period to 20 sec, you would get about=20=
10 microns.=20

     One important point to remember is that your se=
nsors have to be sensitive to DC components and must have excellent long ter=
m drift stability. The simple coil / magnet sensors usually used on Lehmans=20=
will not sense these very slow signals. You could modify a LX1358 LVDT Kit f=
rom http://www.nuovaelettronica.it/ (basic circuit gives ~0.3 mV / micron wh=
ich can be amplified by 100) or by modifying a NE5521 LVDT circuit to use ca=
pacitative sensor plates. Or by using a 7.4 sq mm differential photodiode se=
tup with a small tungsten filament bulb. Resonant circuit capacitative detec=
tors like those described with the SG seismometers and in the recent 'tiltom=
eter' postings, are unlikely to have adequate long term temperature stabilit=
y to give reliable results. You also need very good quality hinges for the a=
rm and fine adjustment for your base setup screws.  

      You don't measure the ground displacement=
 as you do for an earthquake, you measure the change in the tilt angle of th=
e sensor and low pass filter reject any other disturbances. A suitable filte=
r can be made with three 4.7 muF polyester capacitors and four 10 M Ohm resi=
stors, but you need an opamp with a very low bias current, like a LMC6001 or=
 LPC661. It is tedious waiting for a filter of this sort to stabilise. A rap=
id zero setup method could involve providing bypass setup resistors of 100 K=
 Ohm in series with reed relays across the 20 M Ohm filter resistors. You al=
so need very low leakage currents on your PC boards and electrometer type ri=
ng shielding of the pins. The circuit is a Sallen and Key type with unity ga=
in. The input is 20 M Ohm resistor connected to two 4.7 muF capacitors to th=
e output and a connection to the second 20 M Ohm resistor. This is connected=
 to the +ve opamp input and a 4.7 muF capacitor to earth.

       In comparison, the 30 m water manom=
eter gives about 3 microns change for a tilt of 100 nano radians. Very good=20=
temperature stability is required. These are very small signals.



       Regards,



       Chris Chapman