The Hi-Q Gravimeter/Seismometer

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This is an amateur scientist-friendly design for an inexpensive vertical seismometer and gravimeter, based on a high-Q magnetic spring combined with force feedback, using optical displacement detection, and all mounted within a magnetically shielded isothermal enclosure.

 

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This instrument, which I call the "Hi-Q", will work as either a teleseismic vertical seismograph or as a gravimeter. Its virtues are that it is relatively small, inexpensive, and easy to build. My design utilizes a very high-Q magnetic spring suspension in combination with active magnetic feedback in an isothermal enclosure to give a frequency response that extends to DC, making it also suitable for use as a gravimeter, able to see the daily background fluctuations in earth tide.

The only real problem with a gravimeter being used as a seismometer is that seismometers are designed to be so sensitive to vertical acceleration that slow drift and earth tides are likely to throw the readings off scale. A seismometer usually looks for the smallest possible acceleration changes, Since gravity is physically the same as acceleration, gravimeters are merely versions of seismometers with an infinitely long period response. My instrument is capable of recording acceleration or gravitational data at a fixed location for long periods of time with minor adjustment. My instrument works to detect teleseismic events that match known events recorded by official seismic stations.

The principle that  I use employs the repulsion and attraction between magnets as a spring force to balance the force of gravity. I prefer this approach to the metal springs more commonly used in vertical seismographs. Such high-Q systems, even with fairly short periods, are an excellent match for force feedback, because the low mechanical losses associated with high-Q systems imply that they can efficiently capture kinetic energy over periods of time much longer than their own natural frequency. These are the basic virtues needed to sense slow teleseismic events with a physically small instrument.

My Hi-Q is fine-tuned to remain within its proper range, i.e. to keep the sensor output from going off-scale, by shifting the position of a ceramic magnet placed on top of the instrument. This is possible because the nickel alloy shield together with a large iron pipe which surrounds the both the instrument and the isothermal enclosure does not shield it completely from external magnetic influence. However, this double shield seems to be sufficient to prevent most practical problems arising from ambient magnetic field changes.

The Hi-Q is designed to operate from a small three amp, 12 VDC power supply. Most of the power actually goes to supply the resistance heater needed to maintain a constant temperature set just above ambient or room temperature inside the Styrofoam insulation enclosure. The entire seismograph feedback circuit by itself requires very little power. Since ceramic magnets such as those I use for the magnetic suspension are decidedly sensitive to temperature, my design must remain at a carefully controlled constant temperature. This can be easily done with good thermal insulation and a simple feedback thermistor/ temperature regulation circuit.

Since both temperature control and magnetic shielding are necessary, my experimental designs have evolved in the direction of using a short stubby beam pivoting on a horizontal knife edge that can both be contained within a vertical nickel alloy magnetic shield tube 2.5 inches in diameter and 8 inches tall surrounded by the Styrofoam insulation enclosure.

 I anticipate the basic materials, exclusive of the magnetic shield and external electronics (mostly off the shelf from Radio Shack), to cost no more than about $25. Since everything is relatively small, it could also be sealed against barometric changes by hermetically sealing it inside a glass container at near atmospheric pressure.

I have also made progress in building a more miniaturized version of the instrument only about an inch in diameter, which appears to be nearer in its response characteristics to a geophone, but which remains sensitive to static displacements. The latter instrument is similar to the Hi-Q but smaller, and can be made to fit in a 6 inch tall section of iron pipe, 1.5 inch ID. Such a configuration is very compact and, with suitable adjustments, can be used at any angle from the vertical. My thinking is that the latter design is small enough so that these could be tilted at about a 45 degree angle and mounted in a common isothermal enclosure for full three axis recording with one instrument. For example, four of these could be aligned along the edges of a four-sided pyramid, and the outputs from opposite pairs of outputs added in such a way as to be able to calculate quake shocks as three-dimensional vectors of acceleration force. With computing power being relatively cheap, this should be practical.

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RELEVANT SEISMOGRAPH DESIGN THEORY

The Lehman seismograph, commonly used by amateur seismologists, is a horizontally balanced instrument, designed to be nearly blind to the influence of gravity but very sensitive to long-period horizontal acceleration forces. In some ways this is a great virtue, since this type of instrument is rather easy to build, but much of the data of seismographic interest is actually received in the form of vertical components of teleseismic signals. This makes it of value to design and build vertical seismographs too. I undertook the Hi-Q design as an interesting challenge and learning experience.

A vertical seismograph requires that we measure a few parts per million change in the earth’s gravity combined, in a well-concealed way, with some amount of a more rapidly changing acceleration force due to the seismic signal. The only practical way to measure this combined force is by exactly balancing it against some other equal and opposite force like a spring or a constant magnetic force, while assuming that any rapid imbalance must be due to seismic signals, since the earth’s gravity only changes very slowly in sinusoidal shifts over a period of hours, whereas teleseismic signals are more rapid; generally acceleration changes observable over a period of less than a minute.

My instrument tends to be a little bit seismometer/gravimeter, a little bit magnetometer, a little bit thermometer, and a little bit barograph, but the main design problems are due to unwanted magnetic and thermal influences. When one uses a magnetic force rather than a spring to cancel out the force of gravity, the goal is to balance a constant magnetic force against gravity in order to measure the gravity combined with other acceleration forces with the necessary accuracy. Natural magnetic storms can interfere with this data. These interferences are just plain bad, insofar as weak external magnetic fluctuations come in all frequencies and interact with the rather strong magnetic field used to balance the force of gravity inside the instrument. Temperature control is important in any case, since sensitive instruments are practically always also thermometers to some degree.

For vertical seismographs, it has been a common design practice to use a fairly sophisticated suspension system, commonly the La Coste zero length spring, to extend the natural period of a suspended mass and spring combination. Nevertheless, much simpler suspensions seem to be adequate when the travel of the inertial mass is restricted to practically zero net motion by force feedback balancing. For example, masses extending from horizontal torsion filaments seem to work well for this, as do various simple leaf spring arrangements (1, 7). If a very sensitive displacement detector such as a capacitance micrometer or LDVT is used, then a fairly ordinary metal leaf spring can be used.

One of the most valuable insights that I have gotten from a review of the literature is that the main reason fairly large masses have traditionally used for seismometers is that if the energy imparted by a slow seismic disturbance is very small, a large mass can store up more kinetic energy for detection. The use of force feedback and the elimination of air resistance could in theory at least, largely eliminate this requirement. However, the use of a small mass implies that the spring and mass combination must have a high Q to be able to detect the same seismic disturbance. This means the system must be able to maintain oscillations at its natural frequency for a long time, despite damping due to air resistance and other losses.

If the mass is very small, the damping losses must remain very slight, meaning that the Q remains very high (3; p 506). The realization that the thermal noise of a seismometer depended on its damping losses (rather than on its mass) suggested that a much lower mass and smaller seismometer could be devised, provided that amplifiers could compensate for reduced seismometer mass displacement output. Briefly stated, the thermal noise (force) of a periodic system, electrical or mechanical resides in its lossy elements. The system oscillations indicate the presence of some force, including thermal noise, but the amplitude of mass (or spring) oscillation is only a measure of energy, not the energy source itself (3; p 509).

Another way to put this is that if the natural period of the spring and mass combination is short compared to the period of the seismic disturbance to be detected, it is possible to do so provided that the energy being added to the resonant system is not dissipated during this long period of energy accumulation by by damping due to air resistance and the like.

The state of the art has increased considerably since the 1940’s and now nearly some relatively small instruments seem to approach certain theoretical performance limits -- except for cost and convenience of construction. Melton provided a list of eight useful principles for practical seismometer design in his excellent review article (4; p 113-114). Some of the biggest questions regarding optimum amateur design principles seem to me to be the choice of a suspension and the optimum size of the pendulum mass of a small teleseismic instrument.

A small vertical seismometer whose inertial mass is supported by a leaf spring has been developed as a replacement for conventional long-period (LP) seismometers. The mechanical sensor has a virtually infinite natural period and is operated in a force-balance feedback configuration with an overall response identical to that of a 20-sec LP seismometer. Main considerations in the design were economic production and efficient shielding against environmental disturbances. The sensor is thermally coupled to the ground and protected from atmospheric pressure variations by a bell jar. This allows increasing the useful gain at very long periods by two orders of magnitude compared to a standard LP seismograph. The instruments resolve ground noise at least from a 0.3 to 300-sec period (typically from 0.1 to 3000 sec) and have a dynamic range of 140 dB (7; p 2349).

It has been stated by Melton, a leading seismometer designer, that masses on the order of 100 grams or more are needed for good practical sensitivity. However, Block seems to have been the first to use a mass as small as 10 grams cantilevered on a quartz fiber with good results for detecting teleseisms (1). A large part of the justification for the 100 gram specification seems to be that air resistance tends to damp the spring and mass combination too much with smaller masses.
So why not enclose the instrument in a vacuum where there is little air damping and masses mounted on quartz suspensions could have a very high Q? Melton argues, interestingly, that a sufficiently good vacuum cannot be maintained within a seismometer due to vacuum contamination from outgassing from organic matter like insulation on the wire.

In any seismometer having a mass of less than 100 g, air damping at atmospheric pressure becomes somewhat significant, and any long period seismic energy dissipated in this way cannot then be detected. If the seismometer case is evacuated to reduce this loss, the vacuum obtained must be good enough to make the mean free path of the remaining gas or vapor molecules large with respect to the average cross section dimensions of elements moving with respect to one another. This is not a well defined value, but experience shows that such vacuums are not easily maintained in the presence of organic materials (4; p 113).

It is sometimes pointed out that Brownian motion of the seismometer mass sets a fundamental limit on the sensitivity of the seismometer, and that this limit is frequency dependent (7; p 2357). A similar theory was first worked out by Hardy and others to explain the theoretical resolution limits of small galvanometer mirrors on torsion fiber suspensions. While it is true that there are such sources of quantum noise that limit the ultimate sensitivity of all scientific instruments, it seems that this theoretical limit to the inertial mass is not nearly so likely to be limiting in practice for the frequencies of seismic disturbances compared to the reduced Q of the system due to air resistance. One should note that the Worden gravimeter achieves a very high long period sensitivity, making it a very sensitive tidal gravimeter for example, but yet the total mass of the quartz suspension and sensing mass together is less than one gram.

Clearly, however, a long-range trend of seismometer instrumentation since the 1940’s has been to reduce the size of the spring and mass combinations that comprise the physical basis for seismometry: Conventional seismometers often employ masses of several kilograms suspended with natural periods of several seconds, but in accord with the discussion above, it is now known to be possible to achieve the same detection capability with much smaller masses suspended at shorter periods. Such instruments are valuable for borehole applications or where many instruments must be rapidly set up. A force feedback system maintains the mass stationary with respect to the instrument frame and the instruments have a response defined by feedback from DC to 10 Hz. A single miniature instrument can thus provide data over the whole of the seismic range (6, p 605).

Small seismometers with uncommonly small masses, and which might be relatively cheap to build, and possibly still smaller instruments with a vacuum enclosure, thus appear to be a fertile ground for amateur experimentation. Small instruments can have other advantages such as easier temperature control and shielding. The issue of how far the trend toward small detection masses can continue until it becomes more trouble than it is worth or reduces practical sensitivity remains an open question. However there is clearly no need to increase instrumental sensitivity beyond the point that microseismic background noise, from ocean waves and local man-made disturbances, dominates the data.

Another issue is what sensitivities are desirable at low frequencies longer than about ten seconds. Low frequencies are associated with the important major earthquake tremors that refract from deep layers and travel through the center of the earth, and even lower frequencies associated with bell type surface wave oscillations of the earth.

One of the best easiest ways to calibrate the steady state sensitivity of an instrument is by tilting it very slightly so that the vertical vector of gravity changes slightly. The most favored locations for seismometers are on concrete piers or inside mines or in concrete enclosures, or best of all in deep bore holes (5; p 724-5). Interestingly , one sophisticated consideration is that deep bore hole sites are not so subject to local atmospheric pressure cells, which are actually reported by Sorrels to distort the surface of the earth enough to cause slight seismograph inaccuracies due to tilt (4; p 95).

References:

(1) Block B. and Moore R.D. (1970). Tidal to seismic frequency investigations with a quartz accelerometer of new geometry, J. Geophys. Res., 75, p 1493-1505.
(2) Jones R.V. and Richards J.C.S.,(1973), Design and applications of sensitive capacitance micrometers, J.Phys. E., 6, p 589-600.
(3) Melton B., (1981). Earthquake seismograph development: A modern history—Part 1, EOS, 62, p 505-510.
(4) Melton B., (1976). The sensitivity and dynamic range of inertial seismographs, Rev. Geophys. and Space Physics, 14, p 93-116.
(5) Melton B. and Kirkpatrick B. M., (1970) The symmetrical triaxial seismometer—its design for application to long period seismometry, Bull. Seism. Soc. Am., 60, p 717-739.
(6) Usher M.J., Guralp C., and Burch R.F. (1978). The design of miniature wideband seismometers, Geophys. J.,55, p 605-613.
(7) Wielandt E. and Streckeisen G. (1982). The leaf-spring seismometer design and performance, Bull. Seism. Soc. Am., 72, p 2340-2367.

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CONSTRUCTION DETAILS

Note: One unusual feature of the construction of practically my entire instrument is the use of silicone rubber as an adhesive, frequently in combination with glass. Many kinds of instrumental prototypes can be constructed with nothing more than glass carefully cut with a carbide wheel cutter, and perhaps ground with a diamond wheel to give a precision fit, and finally bonded with silicone rubber to to give a permanent and slightly flexible bond. Most of the metal parts can be cut with a jeweler's saw and soldered as needed.

Whereas some be tempted to think that prototypes made in this way would be floppy instead of rigid, this is not so. The thing to keep in mind is that glass is cheap, very easy to cut, easy to grind to fit, and very stiff and permanent, and that thixotropic silicone rubber makes setup easy while giving a nearly perfect bond. If there are rules to be kept in mind when doing such work, they are probably the need to use enough pressure always keep the rubber bonds very thin, and to make use of right angle pieces of glass to brace the various components of the instrument. If this is all kept in mind it will be found possible to rapidly build prototypes that are just as rigid and more permanent, in many cases, than similar structures made of metal, and also rapidly and with very few tools being required. It is possible to force a razor blade into the bond and disassemble and then reassemble the various components in a slightly different position if necessary.

Temperature control

I favor a small instrument that can be surrounded by insulated metal enclosures maintained a few degrees above the maximum anticipated ambient temperature variation using a temperature-sensing feedback control.

There are several principles to keep in mind when building isothermal enclosures. One is that the best isothermal temperature control results when the enclosure is made up of concentric layers or shells of a good thermal conductor like a metal alternated with a good insulation like Styrofoam. In this way lateral conduction along the layers of the enclosure gives an even temperature throughout and hot spots are discouraged. Some other principles are to apply the heat as evenly as possible with a distributed heating element and to have the thermal sensor mounted as close as possible to, or directly on, the heat source.

In my case, I used a nickel alloy magnetic shield tube as the good thermal conductor immediately outside of the seismograph components.  I used silicone rubber to glue a total of 20  carbon film resistors, 50 ohm, half watt, to the outer surface of the tube. These are spaced evenly and connected in several groups to give a final output resistance of 10 ohms. This resistance heater is controlled in analog fashion by putting it in series with an NPN power transistor. The transistor is controlled through a 1 K resistor connected to the output of a 324 op amp. When the heater is supplied with 12 V DC and surrounded by thermal insulation, the alloy tube heats up gradually and evenly to perhaps ten degrees Celsius above room temperature.

A standard Radio Shack thermistor, about 10 K at room temperature,  was glued directly to one of the heating resistors in a central location on the outside of the alloy tube. This thermistor is placed in series with a 10 K resistance to give a variable voltage at their midpoint. This midpoint voltage, which will be somewhere on the order of six volts when set up as described and near room temperature, is compared with an adjustable potentiometer voltage. The difference between the thermistor voltage and the potentiometer voltage amplified by a voltage factor of 100 with a 324 op amp in a instrumentation amp configuration to give an output voltage.  This voltage smoothly turns the transistor and its output into the heater circuit from full on to full off and smoothly through all points between. This feedback arrangement keeps the inner part of the seismograph controlled to within a few hundredths of a degree, while set a few degrees above average room temperature.

It is helpful to lead a part of this op amp output into a light emitting diode and resistor combination connected to ground so that the dim glow will indicate at a glance that the temperature control circuit is slightly turned on and thus working properly. The temperature drift effect on the seismograph may be easily seen by the fact that instrument drift practically disappears within an hour or so as the instrument warms up. Then any remaining drift will be mostly related to earth tides.

The thermal insulation enclosure is made in three pieces.

First there is a double thickness of 5/8" Styrofoam base on a pine board to make up the base. An aluminum flashing disc is bonded to the center of this and the vertical alloy tube with the heating resistors glued on the outside is bonded upright to this disc. Then there is a tall square open ended box made of double thicknesses of 3/8inch Styrofoam 8 inch tall 6 inch square and open at both ends that can be set down over the tube. The Styrofoam pieces are sanded square and smeared at the edges with silicone rubber to hold it together and make it pretty airtight when assembled.  Finally there is the double thickness Styrofoam top section that I  use as a cover with a lead weight to hold it down. Everything can be disassembled by lifting the components apart whenever necessary.

The thermistor and heater wires are led off to one side of the base where there are brass sheet terminals glued to the side of the Styrofoam base for making alligator clip connections to the electronic components; the heater circuit and the seismometer circuit.

All of this is surrounded by a large section of thick iron pipe from a scrap yard. This pipe is about 7.75 inches tall, 8.5 inches in outside diameter, open at the top and bottom with walls 3/8 inch thick.The corners of the vertical Styrofoam part of the enclosure had to be cut off to fit down inside this pipe.


 

The guts of the seismometer mechanism itself are build on a vertical glass strip mounting as described below. This main element is braced against the side of the alloy tube with a bent strip of springy brass, which can be seen above, and this brace is inserted last, just before the top is put on. There are five attached wires, one for the common ground and one each for the LED and the phtodiode output, and another two for the feedback coil. The seismo mechanism is lowered down inside the vertical alloy tube, and these slack magnet wire leads extend over the top of the alloy tube and down to the base and then over to the solder connections on the  terminals glued on the edge of the Styrofoam base. The heavy iron pipe rests on two bricks to the edge of the Styroroam base and surrounds the whole Styrofoam enclosure like a collar supported by the two bricks.

Magnetic shielding

The heavy section of iron pipe helps to shield the Hi-Q both thermally and magnetically. The bricks and everything else is set on top of a pine board which rests on my concrete slab house foundation.

Ideally, a better arrangement magnetic shielding arrangement would be to put a small iron tube shield around the seismic assembly and the much more magnetically efficient alloy shield on the outside of that. If I were building it over again from scratch, I would accordingly build it inside a section of common iron water pipe 2 1/2  inches in inside diameter. This would act as a shield to reduce the field generated by the magnetic suspension to the point that the more efficient nickel alloy can take over and shield the weakened field surrounding the magnetic suspension.

Accordingly, I would wrap the iron pipe with two or three layers of comercially available mu-metal or permalloy foil alternated with a spacer like paper or cardboard. The best way to magnetically shield low strength fields to wind a thin tube out of several layers of a thin sheet or foil of a very high permeability ferromagnetic metal such as permalloy or mu-metal.

If the ends of the tube extend beyond the instrument and the several layers of magnetic alloy are separated with a non-magnetic spacer before being wound into a tube, then an instrument placed inside the tube can be shielded by a factor of thousands. Iron or steel is a cheaper, but far less effective shield, except to reduce fields of thousands of Oersteds down to the point that permalloy can take over. (See W.G. Wadey; Review of Scientific Instruments, Nov. ,1956. p 910).

However, I had an ancient oscilloscope available, and this had a tubular mu-metal or permalloy high nickel alloy cylinder 2.5 inch in inside diameter and eight inches long, seam welded and lead gray in color. It was taken out of an ancient (circa 1950?) oscilloscope. i built the seismometer assembly to fit snugly inside this tube. Since the nickel alloy is a reasonably good thermal conductor, this shield  helped with the thermal design by helping to evenly distribute temperature inside the Styrofoam enclosure.

Magnetic spring suspension

I use the repulsion between two magnets as a spring force to balance the force of gravity rather than the metal spring more commonly used in vertical seismographs. The effective Q of magnetic spring systems can be very high, meaning that they are very efficient at capturing vertical acceleration energy with very little loss, partly since ceramic magnets are electrical non-conductors and thus generate no magnetically induced damping currents within themselves. Magnetic springs are also very easy to build. One simply takes two ceramic magnets and causes one to be repelled so that it tends to float above the second magnet, while restricting its tendency to move sideways with a knife edge pivot to one side, the latter contact also being maintained by a separate magnetic force.

My experimental designs evolved in the direction of being small and to use the repulsion between two magnets as a spring force to balance the force of gravity. Pretty quickly I discovered that an oiled steel razor blade edge attracted to another magnet mounted behind a thin brass strip makes an excellent pivot mechanism for such a design, at the same time being rigid enough to only allow only one accurately defined axis of rotation around a line running along the knife edge. There is very little off-axis wobble or vibration if the blade is stiff.

My latest design uses a total of seven ceramic  ring-shaped magnets from Radio Shack. They are about an inch and a quarter in diameter and have a hole in the center. They cost a little under two dollars for a pack of five. There is a stack of three toward the bottom, and a simiar stack of three toward the top. The knife-edged beam has one such magnet plus a one-ounce lead weight for added mass.

The main part of the seismograph is built around a vertical strip of window glass about 7.5 inches tall and 1.75 inches wide. This has a stack of three Radio Shack disc magnets mounted to the head of a stout brass screw near the bottom so that the vertical level of the magnets can be adjusted. Above this is a little horizontal glass shelf with the feedback coil mounted to that.  A thin brass strip backed with two small rare earth magnets is siliconed to the glass base to make a pivot for the beam to one side, and a support for the optical displacement detector is mounted on the same glass shelf that supports the coil. A motion-limiting aluminum strut is glued so it extends out just above the beam. Finally another three magnet stack is adjustably mounted on a second vertical brass screw toward the top.

The lower stack of three ceramic ring magnets may be raised or lowered by turning the screw with its magnetic axis remaining accurately vertical. The screw mount is made from two nuts soldered to a little brass plate siliconed to a stack of five pieces of window glass bonded to the vertical glass strip with silicone rubber. An identical mount holds a similar stack of three magnets at the top, and this stack may also be raised and lowered by turning its own screw. This second stack of magnets is oriented so as to try pull the beam upwards, limited by the strip of aluminum attached to the glass backing and extending out over the beam.

If the beam is attracted from above at the same time as it is repelled from below, the position of the beam will change quite a lot in response to a weak vertical force, which is the effect that we seek. In this way, the natural frequency of the magnetically suspended beam can be set at anywhere from several oscillations per second to one second or more by some mutually interactive adjustment of  the two magnet support screws.

As with a Lehman, some delicate combination of the magnetic and repulsion forces will be found to very nearly balance the force of gravity, and if this balance of forces changes little with beam position, the effect will be to lengthen the natural oscillation period of the beam, and to increase the sensitivity of the instrument. Even if the period is still a second or a half second, which may not seem very good by Lehman standards, the beam will be seen to move quite a lot in a response to a very small amount of force, which is what we are after (and which is also what the virtue of a zero length spring is all about).

As the natural frequency of oscillation is lengthened, the Q of such a system remains high, meaning that the magnetic spring suspension is efficient at capturing and retaining kinetic energy from seismic shocks with low losses.

When slightly disturbed, such a system can take three or four minutes to stop oscillating at several oscillations per second. Such high Q systems, even with short natural periods, are an excellent match for force feedback, because these low losses mean that it can efficiently integrate slow additions of mechanical energy of energy due to teleseismic events over periods of time much longer than the natural frequency. This is the quality needed to sense teleseismic events with physically small instruments.

The seismograph beam is little more than a ceramic disc magnet and a one ounce lead weight siliconed to the opposite faces of a common stiff single-edged carbon steel razor blade. The magnetic beam’s knife edge is placed so that it rests against the brass strip, its steel being attracted to the brass by the rare earth magnets siliconed between the glass backing and the brass strip. The outer end of this stubby little magnetic beam has a little vertical aluminum strip flag cut from an aluminum drink can glued onto it so that it extends straight outward a quarter of an inch or so.

The vertical motion of this little flag chops the light beam of the optical displacement detector. The latter is made by mounting the LED and phototransistor on struts supported by the glass shelf that will support the force feedback coil. These latter elements face each other with a close gap of several millimeters  between them.

The end result is that we have a little beam comprised of a weighted magnet pivoting up and down on a horizontal knife edge  just to one side. Below we have the stack of three circular magnets that can be raised or lowered by turning a screw, and which repels it. To its top we have the similar three magnet stack on a second screw that can also be raised or lowered to attract the beam. All seven of these magnets are thus horizontal and coaxial.

Force Feedback

At this point we have a very high-Q vertically sensitive spring and mass and sensor combination. The last step is to add the magnetic force feedback coil This coil is mounted on the horizontal glass platform just below the beam that supports the displacement sensor (another reason for a glass shelf is to prevent possible damping from metal). This ring-shaped horizontal feedback coil is thus mounted in a fixed position and sandwiched between adjustable magnets to its bottom and the beam magnet above it. This coil acts as a motion stop to the bottom of the beam. In this way, the coil has maximum interaction with the magnetic repulsion force that supports the beam which is free to bob up and down in response to any seismic disturbance.

When the force feedback circuit is turned on, the magnetic feedback force is such that the beam immediately stops oscillating at its natural period and is able to closely follow higher frequencies up to perhaps ten cycles per second with little ringing, unless the disturbance is fairly intense.

This coil is made by winding a wafer of several hundred turns of fine magnet wire wet with epoxy so that it is about the size and shape of one of the ring magnets (roughly ¼ inch thick and an inch and a quarter across).

The way I made my coil is to take something like a pencil and wind it up with masking tape until two ring magnets will just barely fit over the increased diameter. I cover the facing sides of two such magnets with masking tape before jamming them on the masking tape covering the pencil and separated by a distance of approximately one magnet width. This makes a sort of bobbin on a stick, and you wind the coil between the two masking tape-faced magnets under a few ounces of tension. One  needs to secure the wire first by winding a few turns on the pencil and taping it over the rim of one of the magnets. The wire I use is the finest of the three spools of magnet wire you get for a few dollars at Radio Shack, measuring .010 inches by my micrometer. In addition, I wind my coils wet with epoxy (but don’t use the quick setting kind!). When they are wound up to the diameter of the magnets, and the epoxy has set, the whole can be warmed up to melt the adhesive on the masking tape and the epoxy-potted coil is removed. Made in this way, a coil will have a DC resistance of around ten ohms.

Displacement Detection

Optical interferometry can sense displacements down to about .1 nanometer, as can linear variable differential transformers or LVDTs. For much more sensitivity, way down to one hundred thousandth of a nanometer, capacitance micrometers are probably the best way to go. The best overall review article I found was ‘Microdisplacement Transducers’ by P.H. Sydenham, Journal of Physics E, Scientific Instruments, Vol 5, p721-33, 1972. This has the disadvantage of being an old article, but has good insights.

Meanwhile, a good analytical comparison of capacitative and inductive displacement sensors is found in an article by A.L. Hugill in the Journal of Physics E, Scientific Instruments, vol. 15, 596-607, 1982. The conclusion: ‘It is concluded that capacitative transducers are most suitable in applications requiring high levels of accuracy, stability, and discrimination and low power dissipative and excitation forces. In situations where these requirements are not so stringent, both inductive and capacitative are suitable’.

The best general reference for capacitative transducers, including an illustration of the accidental detection of an earthquake by such a capacitative sensor, is given in the article ‘The design and some applications of sensitive capacitance micrometers’ by R.V. Jones, Journal of Physics, cited above.

After some initial trials using the kind of laser pointer used for lectures, I found that either an efficient red LED or infrared LED is quite adequate as a displacement detector, while being much smaller and and cheaper and more convenient to use than the laser. The proof is in the result; a phototransistor facing such a light source and interrupted by a flag mounted on a short magnetically supported beam is small, inexpensive and sensitive enough to register a full range of gravity and seismographic signals down to the ambient seismic noise levels.

In this case, microdisplacement sensing is done by what really amounts to photon counting. The displacement sensitivity seems to be primarily limited by photon noise between emitter and detector, meaning that one should mount these two as close together as possible and to drive the LED hard, with a maximum of current, short of tending to heat up or burn out the LED.

The achievable sensitivity of such optical displacement sensors is due to the fact that there is a flood of easily detectable photons totaling up to 16 milliwatts of infrared energy, emitted by the LED from an area of less than one square millimeter. This powerful beam of light crosses a gap of a few millimeters. This beam is restricted and defined at the bottom edge by pieces of blackened aluminum foil glued to both the light sensor and emmiter. The light beam is then chopped by the horizontal knife edge of the beam flag mounted on the beam.  This bobs up and down through the beam like a guillotine blade which can choke the beam down to nothing if it drops down far enough.

The detection area of the sensor is a phototransistor with a sensitive area less than 1 mm square; essentially comprised of a photodiode with a transistor amplifier stage built into the device. In such a way it is possible to use a combination of easily available photodetector and LEDs to achieve nanometer sensitivity, (i.e.—only about four dollars together for the LED and PT from Radio Shack). The end result is that this is a good sensor for small, cheap, easy-to-build tele-seismographs, where you want to detect a static displacement rather than acceleration.

For sensing acceleration, the conventional design wisdom among seisomograph designers is to use a coil. However, coil/magnet combinations tend to lose sensitivity where very slow teleseismic changes are involved, since not very many magnetic lines of force are intercepted per unit of time.  There is only so far we can go in reducing the noise of the amplifier to compensate for this. Physics thus tends to favor static displacement detectors for sensing very low frequency seismic motion. This limitation does not apply to differential transformers used as detectors, since these remain sensitive to slow static displacements.

If everything is set up properly and scattered light is mostly eliminated, the phototransistor signal, as the light is increasingly blocked off by the movement of the flag, should be a series of diffraction maxima and minima diffracting around the beam’s edge with a spacing determined by the wavelength of light. However, this does not mean that we cannot detect a displacement far smaller than one wavelength of light if enough total photons are involved to give a strong, low-noise signal in the phototransistor.

What it means, bottom line, is that the detected light level will change as a roughly linear sloping function of PT resistance versus beam displacement. The important issue is how the photon noise level in the optical sensor changes with a given displacement of the of the position of the seismic beam. If the change in phototransistor signal is smooth and quiet, then the displacement measurement will sensitive and accurate. This is the limiting factor in terms of displacement detection.

Most junction LEDs are fairly quiet compared to lasers, and photodiodes are very sensitive in the red and near infrared light. The limiting sensitivity in this case appears to be the accuracy of photon counting at the light level where the photoresistance of the phototransistor exactly equals that of the 10 k resistor in series with the phototransistor, corresponding to a point where the light beam is very nearly cut off by the motion of the magnetically suspended beam.

On the side of the beam away from the brass knife edge rest, I mounted a little aluminum flag that interrupts the strong light beam passing between the LED and the phototransistor. The latter devices have most of their integral plastic lens cut away so the emitting and sensing elements can be mounted very close together surrounding the beam flag (which swings out an arc with beam movement; this may be considered a pure vertical motion for very small displacements) for best movement detection sensitivity.

After cutting away most of the plastic cases to nearly uncover the sensitive areas of the chips inside, I recommend gluing small pieces of blackened aluminum foil so it covers the bottom half of the sensitive areas of both the LED and phototransistor. These horizontal  foil edges should line up square and define and block off the lower 50% of the light beam that passes between them.
Work spent getting these three edges accurately lined up parallel to each other will be rewarded as a maximum displacement sensitivity as the motion of the horizontal flag edge chokes off the light beam. See ‘A simple optical transducer for the measurement of small vibration amplitudes’; Measurement Science and Technology, p 947, 1985.

Electronics


 
(Important note: there are several minor changes to the above circuit which I have not yet incorporated into the schematic above. Jack Herron pointed out that the ground terminal of the 7812 needs  to actually connect to ground --duh! Also the 100 K feedback resistor shown in the schematic below and to the left of the feedback coil is better replaced with a 50 K resistor to slightly lower gain at the front end. One of the unused op amp amp outputs on the 324 to the bottom right of the schematic can then be used to multiply the final output voltage by a factor of ten after the filters, making up for this loss of two in gain, and giving a net output gain of five due to these two changes. The chart at the bottom of this page was made with this slightly modified circuit)

The circuitry is all fairly simple and straightforward and mostly built from off-the-shelf RadioShack parts. I use only 1% metal film resistors when possible, except for the heaters and 10 megs. The power all comes from a 3 amp, plus and minus 6.3 volt, center tapped Radio Shack transformer. The twelve volt leads are passed into a bridge rectifier and this ripple output is filtered with a 4700 Mfd, 35 volt electrolytic capacitor. Then the output from this is regulated with a common series pass twelve volt regulator on a heat sink, with two .1 mfd capacitors, according to standard series voltage regulator practice.

The temperature feedback circuit uses most of the total power; this being perhaps on the order of ten watts of power. I found that it was important not to try to use a switching circuit to try to save heater power, because abrupt on-off switching interferes with the voltage sensitive circuitry that supplies the rest of the seismograph circuit. On the other hand, if the heating circuit is constantly turned on at a low level with a analog feedback circuit, then the power consumption is nearly constant and does not interefere with the rest of the very sensitive seismograph circuit. Another option is to use a separate battery supply for the seismometer electronics, since batteries are inherently low noise power sources and since this part of the circuit uses little power. A car battery would be a good choice for remote siting.

The LED light source can be either red "superbright" or infrared, although I am currently using an infrared light since both its emission and detection are very efficient. Since the light emitter and detector are both inside an isothermal enclosure, there is little problem with thermal drift, which would especially affect the LED output.

The phototransistor is in series with a 10K 1% metal film resistor, followed by a voltage follower made from a 324 op amp (my circuits  use two 324 quad op amps and one 353 dual fet op amp, both common parts). If the beam is raised and lowered slightly, at some point it will let through just enough light that the resistance of the phototransistor equals 10 K and the voltage output will be at the 6 volt midpoint voltage; this is the one position where the 10 k resistor exactly equals the phototransistor resistance when the light beam is partially interrupted by the movement of the flag.
This will be the at-rest-position voltage generated at the midpoint of the resistor and phototransistor in series by the instrument as its output, when the magnetic suspension force balances gravity and with no electrical energy going  into the feedback coil.

This proper rest position adjustment is achieved with the screw and magnet. Then when the feedback circuit is turned on, the at-rest voltage output should be about six volts also except that any initial beam oscillations will be damped very quickly instead of going on for minutes. But this damped output signal with the feedback coil energized will still be full of seismic noise and will slowly drift in voltage in response to earth tides and the like.

We thus extract all gravimeter and seismic data from this initial DC voltage signal coming from the initial op amp voltage follower on the front end , and this initial voltage output is always held at pretty nearly six volts so the DC coupled circuits will operate near the center of their dynamic range. However a change of only one volt on this sensor signal might be generated by a movement measured in a few microns of the beam, and even a one volt change can be pretty easily amplified by a factor of nearly a thousand with op amps, and still more with the analog to digital converter, so this arrangement can chart with a displacement resolution down in the low nanometer range, good enough to see a constrant stream of microseisms with a duration of 3-4 seconds.
 
This sensor voltage output is led both to the feedback coil and also into the detection citcuit where it is amplified by a factor of five, which in this case was found to be the maximum permissible while still keeping it from drifting out of range due to earth tides.  I put an LED monitor light on this amplified DC output. This visual monitor is very helpful for making slight mechanical adjustments since one can easily see the DC signal output resulting from microscopic changes in beam position. This amplified signal is also full of all sorts of local seismic noise and should thus be run through a combination of  low pass and highpass filters to give a bandpass output in the teleseismic region of greatest interest. Finally, this low frequency signal is amplified a second time until its noise begins to to match the resolution of the A/D converter.  The converter signal is then led into the computer for final data aquisition.

The output from just one little 324 op amp can supply about 20 milliamps at twelve volts.  The second terminal of the force feedback coil is connected to a virtual ground pinned at +6 VDC with a voltage divider and second op amp voltage follower.This is sufficient feedback coil energy, in practice, to stabilize the beam position, even though the resistance of the feedback coil is fairly low.

Clearly the energy from one op amp output is not sufficient to push the beam around in order to faithfully follow and balance the motions from strong or rapid acceleration forces.
But there is no reason why this should disqualify such a low power arrangement from faithfully recording most teleseismic events, which are characteristically very slow motions with very little energy involved.

Currently for feedback stabilization I use a very simple stabilizing network comprised of a 10 MFD non-polarized tantalum and a 1000 ohm helipot in parallel. This combination is connected in series with the coil. This is not a very sophisticated force feedback stabilization arrangement, and does not give stability at high seismic shock levels, but it does effectively tame feedback oscillations and achieve good practical results when modest seismic forces are involved. Of course there is a right way and a wrong way to connect up the coil, but this issue is easily resolved by experiment. My instrument still rings a little at its natural frequency, but only in response to large disturbances.

If you reduce the sensitivity enough to have the daily earth tides move the instrument full scale, then you automatically reduce the sensitivity too much for it to be a very sensitive seismometer. The gain of the force feedback stage needs to be low enough so that the daily fluctuations in earth tides do not throw the feedback coil amplitude off-scale. In other words, we need to center the daily variations detected by the instrument using the magnet screw for coarse adjustment and the magnet on top for finer adjustments until the DC voltage from the phototransistor and the one stage of  DC amplification that follows it never hits the plus or minus voltage limits of the filter's electronics. After, and only after, this is accomplished, can we lead this well-managed signal into the amplifier and filters that give the teleseismic signal output. We can reduce the gain of the DC amplifier if needed by using a lower value of feedback resistor.

If I want to use my instrument as a gravimeter, I could directly tap the voltage output from the light sensor's voltage follower, or tap the first stage of DC amplification that goes into the monitoring LED and filters, or best of all, this latter signal after it has gone through the low pass filter but not the high pass filter, assuming that this voltage never never goes off scale.

For seismic purposes, you will usually need some way to constantly re-center the output signal, even if the instrument is perfect. this is so unless the constantly wandering DC output due to earth tides could be seen with very high resolution. Accordingly I use a combination of two Sallen and Key filters; both a low pass and a high pass filter to give a band pass output response centered roughly between a half second and a minute. Then I add a last stage of DC amplification, say X10, after the filters to get the output up to a level compatable with the the bit noise level of the A/D converter. No sense to waste hard-won  instrumental sensitivity.

Adjustment and Mounting

In practice, everything is set up and and turned on, and the heater allowed to warm up. Rough adjustments are made by removing the top piece of Styrofoam to expose the top of the instrument to expose the upper screw that raises or lowers the upper magnet. This adjustment is made while watching the monitoring LED (connected to the amplified DC sensor voltage) to find the point where it just barely turns the LED on and off. This shows that the beam flag is intercepting the light beam and affecting the phototransistor in the desired way. If one of the feedback coils terminals is disconnected, the LED should flash on and off for a long time, whereas with the circuit reconnected and the 1 k helipot leading to the coil properly adjusted, this motion should be damped nearly immediately.

A slight movement of the upper brass adjustment screw will turn the LED completely on or off. Then the top cover is then replaced, with the lead weight set back on top. Finally a strong ceramic magnet is placed on top of the instrument and shifted around until the monitor LED just dims. At this point, the instrument may work for weeks with little further adjustment other than shifting the position of the magnet slightly.

My instrument is as yet uncalibrated, but I can determine that it is working properly by watching the continuously fluctuating stream of microseisms (which are seen as a somewhat regular stream of small waves with periods of 3-5 seconds), by standing nearby and slowly shifting my weight from foot to foot  on my concrete slab floor while watching the chart, stomping on the floor from the other side of the room, or best of all by studying the static influence of a small magnet shifted at a distance of a few feet.

The latter test is the most useful since it replicates the character of a teleseismic event, insofar as it is a good way to generate a weak but highly predictable and low frequency force on the beam inside the instrument. The magnet is thus a very useful and easy means of checking as to whether everything is working properly. Specifically the Hi-Q can be periodically checked for sensitivity change by flipping a nearby ceramic ring magnet, stationed permanently a few feet away, upside down at intervals, and seeing if this shifts the chart output in a normal and predictable way. This  should generate an exponentially decreasing triangle wave output of predictable magnitude and polarity (this shape being due to the output filters) on the computer chart.

I use a two channel WinDaq A/D for chart recording. I usually set the chart sensitivity so that it charts at half a volt full vertical scale and ten seconds per horizontal devision with sampling at 12 samples per second. This A/D device costs about $100 from Radio Shack and is connected to the serial port of my computer, which runs Windows 95. The software is fairly easy to use and intuitive. Unfortunately, this device stores its recorded charts in a format that is difficult to transfer, so I use a screen capture program to transfer the seismic graphs.

I currently have my instrument set as nearly as possible directly on the concrete slab of a bedroom of my house. From what I understand, one of the optimum mountings for such an instrument would be to lower it into the bottom of a vertical iron pipe plugged with concrete at the bottom, resting underground. This would tend to be a good seismic platform, while largely buffering temperature changes, which are the general arch-enemy of instrumental accuracy.
 *********************************************************************

Ground Truth Examples from Oct. 9, 1998, about 12:00 GMT

Below from USGS Hockley Texas station (HKT), Oct. 9,1998:


 Below from USGS Albuquerque (ANMO), Oct. 9, 1998:

The chart below is the corresponding chart of my seismograph of the same event which started at about 12:00 GMT. Note that the lower amplitude and greater noise on my chart which may be due to my wider bandwidth, which would give greater noise. I assume that the USGS instruments may be narrow bandwidth carefully tuned for maximum signal to noise on teleseismic events. One minute per division horizontal scale

The chart below shows the approximately triangle wave results of a single ring magnet on a table about two feet from the beam of my seismograph being flipped end over end  at intervals of about one minute after the trace settles (also one minute per division on the horizontal scale, but four times reduced vertical scale from that above).

Roger Baker, Oct. 9, 1998

 How to build Small, Cheap, Easy-to-Build,  Supersensitive Magnetometers

--Roger Baker, Dec. 17, 1998

Such a deal!  Actually, this is about how to build a family of torsion magnetometers, and the stripped
down essentials could start at as little as $10-15, or even less assuming you have a well-stocked
scientific junk stockpile. Red laser pointers the size of lipsticks cost as little as $8 now and may be
easily rewired to work with flashlight batteries. The end result is that you can watch a red spot dance
around on the wall (much of the time at least; some days the universe seems awfully quiet) in response to variable magnetic micropulsations. You can also watch or even chart more dramatic magnetic storm events caused by solar flares on the sun.

******************************************************************

There is no better, more well-written, and generally useful source of information on the topic of
geomagnetism than "Introduction to Geomagnetism" by W.D. Parkinson (reader at the university of
Tasmania), 1983, Elsevier. Especially see section 4.6; p 299+ on Pulsations and Solar Flare Effects.

Geomagnetic micropulsations usually occur in long trains, each with their own titles and causes,  in
many often simultaneously ocurring frequency bands, (extending up into the audio too) as follows:

Pc1 = .2-5 seconds
Pc2 = 5-10 seconds
Pc3 = 10-45 seconds
Pc4 = 45-150 seconds
Pc5 = 150-600 seconds
Pc6 = >600 seconds

and the more irregular types of waves

Pi1 = 1-40 seconds
Pi2 = 40-150 seconds
Pi3 = >150 seconds

******************************************************************

Anyhow, one ends up with a small  instrument in several parts (a magnetometer, a balancing magnet,
a laser pointer, and a screen which could actually be just a light colored wall) that can be transported
anywhere, but is normally meant to demonstrate hour-long slow fluctuations all the way up in
frequency to perhaps ten cycles per second from some fixed instrument position.

A magnetometer built as described should be able to see cars pass at 50 feet, and should allow you
to see the fairly constant short term magnetic fluctuations, which sometimes resemble heartbeats and
are called magnetic micropulsations, as well as magnetic storm events and the like.
 
Construction Details:

Consider the topic of torsion fiber instrumentation a moment. Perhaps you have seen a bit of debris
caught on a strand of spider silk spin around slowly in response to faint air currents. This same
mechanism of acute physical sensitivity to a minute force is the principle used by a large group of
torsion fiber instruments. In fact it would probably not be an exaggeration to say that various kinds of
torsion fiber physics instruments like galvanometers were at the foundation of modern physics until at
least the turn of the century, and progress still continues, as witness here.  Even in the early 1950’s, a
British instrumentationist named Blackett was able to build a torsion magnetometer which was the
most sensitive instrument of its type until the invention of squids in the mid-1960’s. Torsion was used
to confirm experimental gravitation in the lab centuries ago.

This principle is still the most sensitive way to measure weak forces at room temperature when the
force can somehow be arranged to rotate a sensor mass supported on a vertical fiber. Magnetic
fields happen to excel at generating attracting and repelling forces, making this property a nearly
perfect match from the point of view of coupling it to torsion fiber instruments. So one of the best
ways to detect minute magnetic fields boils down to arranging to detect a sufficiently small amount of
such attraction or repulsion force, exerted as a twisting force on a fiber bearing a small strong
magnet, which has lots of magnetic field force concentrated into each unit of mass.

Here the detection sensitivity is near the theoretical limit for objects at room temperature. In fact
since the early nineteen thirties, galvanometers designers have known that attempts to measure small
displacements by  the use of small coils suspended in magnetic fields or by the use of  small magnets
suspended in coils is ultimately limited in accuracy by the Brownian motion of the mass suspended
from the fiber, which limit has nearly been reached in some carefully built instruments. Above a
fraction of a gram or so this theoretical consideration fades compared to such practical
considerations as the force of minor air convection currents on the exposed area of the instrument.
Quite small instruments are often excellent in practice.

There are various other ways to detect magnetic fields known to physicists, including solid state Hall
effect devices, which are tiny but not very sensitive, and flux gate magnetometers  (an amateur
scientist, Erich Kern, in California, distributes some nice ones made by Speake in England, for about
$50 the last I heard). However in general magnetometers get expensive fast and involve exotic
physics  like particle physics phenomena, atomic light emission spectra,  superconductivity, etc. ,
when they get any more sensitive than my simple torsion instrument.

There are many possible experimental variations of my instrument.  You can save the cost of a laser
pointer by using a light beam from an infrared LED, or a bright red LED, or you might try using a
snip of aluminized space blanket as an ultra light mirror along with electronic feedback and so on.
There are many reflective surfaces and sources of light, but no amateur friendly combination beats a
little chip of cheap glass mirror in combination with a red laser pointer for the best optical sensitivity.

The combination is so easy to arrange and sensitive that its just plain fun to hang a tiny bit of mirror
and a magnet from a tiny fiber and bounce a laser beam off the mirror. Let us get started. The first
step in building one is to go down to the hardware store and buy some glossy, silky nylon twine.
Then unravel about a one foot section into lesser strands, and learn to tease single fibers roughly a
thousandth of an inch in diameter out of these strands with a tweezers and a little stroking. One single
short piece of twine contains enough nylon fibers to last for years, probably. Nylon is nice because
although it drifts, it is strong and easy to get and safe to work with, and forgiving to the bumbling
experimenter, fine wire is good, and then glass is probably better and quartz is the best fiber of all for
torsion instruments.  But the temperature and humidity drift with Nylon can be slow, whereas the
magnetic shifts you probably want to observe most often happen over not more than a minute in
duration, so Nylon is still very good and stretchy enough to be quite durable and somewhat forgiving
of clumsy fingers.

I start off by mounting a stretched nylon fiber within a kind of little glass case, which is really half of
the job. I start with a square foot of plain window glass which I cut into strips 2 in wide. I two of
these 6 in long. Then silicone glue two stacks of glass each three pieces high, made of  glass strips
1/2 by 2 in  to each end.

(You can make many kinds of instrument prototypes out of pieces of window glass and silicone
rubber faster than any other way.  Try to get a tungsten carbide wheel cutter to cut the glass).

This will give raised plateaus about 1/4 in high on the top side on the outer ends of each 6 in piece.
After the rubber is set, we face the plateaus with stretchy black vinyl electrical tape to keep the
edges of the glass from cutting into the fiber. Then we stretch our nylon fiber between two of these
plateaus and tape it in place to the glass with black tape, and some epoxy to help inhibit slow creep.
Actually we proceed by securing the fiber to top half , letting the fiber hang vertically, and then
hanging a stack of four nickels to the lower end of the fiber. This stretches the fiber with 20 grams
before we tape it to the bottom end, locking in this 20 grams of pre-tension when we secure the
other end.

We now have a microscopic tensioned fiber spanning about a five inch wide gap. The next step is to
use silicone rubber to glue two tiny rare earth magnets, (which I think are made of an
iron/boron/neodymium alloy and which are sold in pairs by Radio Shack), to the middle of the fiber.
Actually they will leap to cling to each other, so smear one magnet with silicone and position it it in
the middle of the fiber, supported somehow from below with a stack of coins placed on the glass or
something similar until the rubber sets up. Then let the other magnet jump onto to this side and finally
nudge the pair onto perfect symmetry, sandwiching the fiber in the center of the two tightly clinging
disc magnets.

Now for the mirror. I merely cut small square pieces from an inexpensive Chinese import glass vanity
mirror about 1 mm thick. I dissolve the lacquer off by rubbing the mirror with with ME ketone, or
other strong solvent, with a cotton Q-tip to expose the bare silver coating. You can also use the bits
of mirror without removing the protective coating, and this will work nearly as well, but the glass will
regrade the optical performance slightly and also absorb some light.

I now glue two such identical mirror chips with silicone, silvered side out but flat glass sides facing
inwards, to one edge of the magnet pair.  These are pushed inward to contact and trap the filament,
similar to the way the magnets trap the fiber, but just to one side of the magnets so they are all glued
into contact. The whole should retain good rotational balance, like the well-balanced wheel of a car.
If it were not for the restraining influence of the earth’s magnetic field, the mass would now spin
freely around the filament whenever disturbed. In other words, we now have a sort of tiny reflective
compass needle glued to a nylon filament.

Finally, in a curious twist of instrument design, we silicone a copper (pre-1980 or so) penny to the
glass just  beneath the magnet, but spaced far enough from the filament so that the  free rotation of
the magnet-mirror combination is not impeded.  This copper helps greatly by damping the magnet
oscillations, which induce eddy currents in the copper, which are then converted into heat by the
electrical resistance of the copper and so damp the oscillations. Of course any flat piece of copper
or even aluminum will also do, but something of the sort is important to damp out rotary oscillations
of the suspended magnet and mirror combination.

All the essentials are now in place. Now put the second strip of glass on top to enclose the fiber,
magnet, and mirror in a sort of shell in which the stacks of glass spacers hold the six inch strips strips
of glass about 1/2 in apart at their ends. If everything is properly arranged, we can use black vinyl
tape to hermetically seal the chamber  from air currents along the two open edges. You have easy
optical access to the side of the glass which isn’t covered up by the penny. You now need to figure
out a way to support this gadget in various orientations without having anything magnetic nearby. The
instrument is now a compass. If you walk around the room holding the gadget, the magnet should
obediently shift direction on the vertical fiber, in a manner that puts the performance of most
magnetic compasses to shame with regard to its stability and immediate response.

The last critical step is to null or balance the earth’s magnetic field as nearly as possible with an earth
field nulling magnet. This is easier to do when the fiber is vertical, since the field balancing magnet can
be mounted on a pedestal and moved around or rotated to any position off to  one side, and at the
same height as the axis of rotation of the suspended magnet. This field balancing magnet is made by
cementing four 1.25  inch ring magnets from Radio Shack flat and pushed together despite their
repulsion, to a stiff backing such as glass using silicone using clothes pins to hold them until the
rubber has set. This makes a kind of magnetic paddle. Using even more magnets might make it work
better. It is mounted at the same height as the magnets on the filament.

One should approach the magnetometer from exactly the direction that the magnet pair is facing on
the fiber, from somewhere in line with the magnet’s axis of rotation, and with this magnetic paddle
squarely facing the face of the suspended magnet. From one direction, it will pull the pair into even
stronger alignment, but from the other, it will tend to flip the pair. Which way the pair flips is strongly
dependant on the exact position of the paddle. As you slowly approach the magnet pair from this
direction, stright on at a distance of about one foot in my experience, the pair will begin to wobble
and flip around at some point where the opposing field from the paddle exactly balances the earth’s
field. The slightest paddle movement can now cause the magnet pair to flip and spin around

The magnetometer will be at its most sensitive at some balance point determined by  the intersecting
magnetic fields. There is a critical point in space such that the total effect of gravity, the torsion of the
fiber and the external influence of the surrounding magnetic field is balanced, on some invisible knife
edge of critical stability, where we get the maximum rotation of the suspended magnets with the least
external force. This approaching condition can be seen by a lengthening of the oscillation period of
the magnet, until it may oscillate with a period of a second or longer. When you find a sensitive
adjustment of the field magnet, the sensitivity will be a little different each time but reasonably stable.

This magnetometer can either be used with the suspension fiber in either a vertical or horizontal
position to detect different vectors of magnetic force by just tilting the axis of rotation in the
appropriate direction. The vertical fiber position usually gives better sensitivity than a horizontal
position. If we want to determine magnetic fields in three dimensional space, we would need three
(or more) such magnetometers, with their fibers aligned along the X,Y and Z axes.

The earth's magnetic field may be thought of as a tilted arrow pointed through space, with its length
representing the strength of the field. Even if we bring the magnetometer into a whole room full of
magnets, all the fields will add together so that at any one point, the resulting field is still conceptually
like a single arrow pointing through space, and magnetic fluctuations can be thought of a wobbling or
tilting or contraction of the arrow.

We should  keep in mind that the torque is at a maximum when a magnet's axis is at a 45 degree
orientation from the axis of the magnetic field. In other words magnets made to squarely face each
other will not try to twist a fiber, but will only attract or repel until one or the other magnet is
somewhat tilted. Thus we might want to have two similar devices with their magnetic axes tilted at
ninety degrees to each other, with their signals added to get the vector of magnetic force along a
single plane.

Geomagnetic forces caused by things, like magnetic storms and so on, disturb the strong earth field
by causing the imaginary arrow representing the earth field to vibrate in different directions or axes
that tell us something about the geophysical nature of the fluctuations. For this reason, we might want
to have two or more magnetometers for comparison to determine the direction of the fluctuation in
three dimensional space. A corresponding problem, which we can solve in various ways, is how to
adjust and hold the field balancing magnet at just the right position in just the right position in space to
retain the best sensitivity when the axis of the fiber is not vertical.

In other words, the magnetometer can demonstrate similar fluctuations along any axis in space, but
the vertical fiber position is the easiest to set up, because finicky magnetic adjustments of the paddle
and laser pointer are easy to make on a flat tabletop. I often put a clothespin on the laser pointer to
push its switch button on and then  prop it up six inches away from the magnetometer on a few
books to hold it so that the beam shines directly onto the mirror through the little vertical glass
magnetometer case.

We should now have a very sensitive instrument indeed, perhaps sensitive to a gamma or nanoTesla
(which are the same thing, and equal about one 50,000 of the earth’s magnetic field). You can now
play around with this instrument by watching the reflected laser pointer beam shift around on the wall
due to the pretty constant micropulsations, or as cars drive by, screen your visitors for handguns like
they do at the airport, etc.

But good scientists like to gather data. So we can rig up a circuit that will detect a shift in the beam
and feed back an equal and opposite magnetic field to keep the position of the beam steady. If a
torsion magnetometer is to be used as a serious instrument, you will probably want to use a
feedback field to keep the light beam centered on a phototransistor (the so-called infrared ones sold
by Radio Shack work very well for red light) or other similar detector.  A simple 324 op amp circuit
will suffice.

Otherwise slow drift factors like temperature changes, and likely the effect of humidity on the nylon
fiber mean that a laser beam reflection will probably drift out of the range of any fixed
photodetector.  I bought a $100 dataq 12 bit, two channel A/D converter  from Radio Shack that
makes nice charts on my PC in combination with such instruments as this magnetometer operated
with a 6 VDC battery circuit.

In this way very small amounts of force in the form of torque on the fiber, involving far far less than
one degree of our mirror rotation, can easily be made to cause a full scale deflection of an electronic
circuit. The best and most linear results of this type should use a counter magnetic force to hold the
position of the mirror constant--this is a feedback principle called force feedback.

For force feedback, we can build a Helmholtz coil to create a weak but precise magnetic field and
mount the photo-detector behind a half covered ground glass screen; this gives the direction of
imbalance so the photo-signal can tell the circuit which way to go to rebalance the force with a
feedback coil. The best way to do this is with a pair of Helmholtz coils, which are coaxial pairs of
large short wire coils separated by their own radius so as to provide a nearly constant field in a
largish volume of the central region between the coils. I wound a pair of such coils on a cylindrical
oatmeal container with about a hundred turns for each. Even with such large coils, a milliamp or so of
current is enough to provide feedback to reposition the beam and keep it centered on the detector.

Since the field of Helmholtz coils can be easily calculated from the size, turns, and current, based on
standard formulas, they are also the best way to calibrate magnetometers like this one, where the
sensitivity may be different each time the instrument is set up. Of course one can get a  rough idea of
the sensitivity by watching micropulsations, which tend to be a few gamma in magnitude. At any time,
we can check the relative sensitivity of the instrument by flipping a small ceramic magnet about six
feet away.

**************************************************************
It has not escaped my attention that one could also use this basic magnetometer setup to build a two
axis scanner to reflect a laser beam to any chosen point in front of the apparatus. One purpose
would be a low frequency oscilloscope -- which would make a super-duper amateur science
project.

Another use for small light scanners of this kind would be to scan statues or other three-dimensional
shapes in combination from several fixed positions in combination with a video camera  to build up
images line by line. Clearly this sort of data could be processed in various ways to generate
computer models of the surfaces in three dimensions.

For the latter purposes, one would need to construct small Helmholtz coils to surround and control
each of the two reflecting mirrors needinded for full scanning, each of these being supported by two
filaments mounted at 90 degrees to each other to generate the X and Y axes. --RB

If you have comments or suggestions, email me at rcbaker@eden.com
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