Apparently, amateur seismometers are calibrated empirically, that is, recordings of known quakes are used to relate the max. reading to magnitude. I live in New Jersey, not a location of wild and wonderful seismic activity, so I expect that doing a reasonably accurate calibration using known quakes might take a long time. This has the virtue of including how well the seismometer is coupled to the crust, etc.. However, in many kinds of measurement it is useful to know instrumental sensitivity in terms of well -defined quantities. I may have reinvented the wheel but if not, I offer the following scheme. My Lehman is now hooked up to Larry Cochrane's A/D board and is working nicely. It got a good recording of the Easter Is. event of 9/5. I was surprised that there were no nasty surprises in getting the Lehman adjusted and running. A box made of 2" Styrofoam greatly reduced the noise due to air currents and I solved the problem with transmissions from my amateur radio 2 meter rig getting into the electronics.
Operation of the Lehman raised the question of what is its sensitivity and what is the seismic noise level on my basement floor (which is surprisingly flexible). I devised this calibration scheme to get at these questions. The heart of the calibrator is a common 1ma (or practically any other current range) D'Arsonval meter movement. These are available in unlimited numbers at ham flea markets for $3 or less. I measured the force vs meter current constant by mounting the meter (after removing its case ) on edge so that the needle was horizontal with 0.5ma. A measured length of #30 copper wire (about 0.2") was hung on the end of the needle and the additional current required to bring the needle back to horizontal was measured. This was 0.44 ma. The weight of the piece of wire was calculated (from the wire tables) to be 2.64mg. This process gave the force calibration of the meter which is 6 milligrams/milliamp or 6 dynes/ma. This whole calibration took about 1 hr. The greatest uncertainly is measuring the length of the wire. Be careful not to suddenly apply more that about 5ma to the meter (without the extension) or you'll bend the needle. A strip of 0.003" shim stock about 0.08 X 1.25" was fastened (using wax and a little heat from a soldering iron) to the needle so that the end of the strip extended beyond the edge of the meter movement. (Be careful not to let bits of magnetic material such as iron filings get into the area around the moving coil of the meter. )
The meter was then mounted on a sheet metal bracket attached to a heavy base. The meter was mounted with its needle (and shim stock extension) hanging down vertically and at a height such that the tip end of the extension could push horizontally on the side of the boom of the Lehman. The base was positioned so that with zero current, the extension tip was about 1/16" from the boom.
A 555 timer circuit giving a pulse of 0.83 secs. was used with a variable resistance between its output and the meter. This time was chosen to be short compared to the period of the Lehman (18 secs.) A manual push-button triggered the pulse. Since the output voltage from the 555 is constant (with reasonable loads), the current of the pulse and hence the force-time product on the boom is easily calculated.
The calibrator pushed on the boom 11" from the pivot and the mass is 27.5" from the pivot so the equivalent force at the mass is 0.4 times the force given by the current. Also, the tip of the calibrator is twice as far from the meter pivot as was the calibration weight so the force-current factor is 3 mg/ma times 0.4 or 1.2 mg/ma. The force in dynes is 0.98 times this or 1.2 dynes/ma.
The velocity of the mass is (force[in dynes] * time) / mass[in grams]. The mass is 3,500 grams. The table shows the values from the A/D of the initial deflection and the calculated velocity of the boom in nanometers/sec due to the current pulse in ma. for 0.83 secs.
ma nm/sec A/D value 1.15 590 75 1.7 860 120 3.2 1650 230 4.5 2310 300 6.5 3340 450
You can plot velocity vs. value and see that it is nicely linear and goes thru zero. A least-squares fit gives nm/sec = p-p value * 7.46 - 2.5. This measurement also gives the sense, e.g., positive value corresponds to a compression arriving from the west. At 3340 nm/sec., the deflection was calculated to be about 8 microns.
My seismic noise level seems to be somewhat less than half the 590 mn/sec velocity so I conclude that my seismic noise level is about 300 nm/sec. ( With no input to the amp, the noise is < 1/20 of this.) The only hard number I have to compare this with is the PEPP noise specification for their seismometers of 100 mn/sec.
Another use for this thing is to make occasional checks of the performance of the whole system. Since the calibrator can be left in place (it does not touch the boom), a check is just a matter of powering up the 555 and pushing the button.
It should be possible to do a frequency response curve of the whole Lehman-amp system by driving the meter movement with variable VLF sin wave oscillator. I plan to try that.
Comments on this scheme are welcome.
Bob Barns